• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Foreword
 Preface
 Table of Contents
 List of Figures
 List of Tables
 Introduction
 Part I. Physical and economic aspects...
 Part II. An examination of liquid...
 Part III. Methodological procedures...
 Part IV. Farm planning procedures...
 Part V. Agricultural policy implications...
 Index














Title: Economic and technical analysis of fertilizer innovations and resource use
CITATION THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00089532/00001
 Material Information
Title: Economic and technical analysis of fertilizer innovations and resource use
Alternate Title: Fertilizer innovations and resource use
Physical Description: 393 p. : illus. ; 24 cm.
Language: English
Creator: Baum, E. L. ( Editor )
Heady, Earl O. ( Editor )
Pesek, John T. ( Editor )
Hildreth, Clifford G. ( Editor )
Publisher: The Iowa State College Press
Place of Publication: Ames, Iowa
Publication Date: 1957
Copyright Date: 1957
 Subjects
Subject: Fertilizers   ( lcsh )
Fertilizer industry -- United States   ( lcsh )
Agriculture -- Economic aspects -- United States   ( lcsh )
Genre: non-fiction   ( marcgt )
 Notes
Statement of Responsibility: edited by E.L. Baum ... et al..
 Record Information
Bibliographic ID: UF00089532
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 01578527
lccn - 57007851

Table of Contents
    Front Cover
        Page i
        Page ii
    Title Page
        Page iii
        Page iv
    Foreword
        Page v
        Page vi
    Preface
        Page vii
        Page viii
    Table of Contents
        Page ix
        Page x
        Page xi
        Page xii
    List of Figures
        Page xiii
        Page xiv
        Page xv
    List of Tables
        Page xvi
        Page xvii
        Page xviii
        Page xix
        Page xx
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
    Part I. Physical and economic aspects of water solubility in fertilizers
        Page 5
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    Part II. An examination of liquid fertilizers and related marketing problems
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    Part III. Methodological procedures in the study of agronomic and economic efficiency in rate of application, nutrient ratios, and farm use of fertilizer
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    Part IV. Farm planning procedures for optimum resource use
        Page 241
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    Part V. Agricultural policy implications of technological change
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    Index
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Full Text












Economic and Technical Analysis of
Fertilizer Innovations and
Resource Use

























In This Same Series:
Methodological Procedures in the
Economic Analysis of Fertilizer Use Data
E. L. Baum, Earl O. Heady, and
John Blackmore, Editors (1956)











Economic and Technical Analysis of


Fertilizer Innovations and

Resource Use





E. L. BAUM
Chief, Agricultural Economics Branch,
Tennessee Valley Authority
EARL O. HEADY
Professor of Economics,
Iowa State College
Economic Consultant,
Tennessee Valley Authority
Edited by
JOHN T. PESEK
Associate Professor of Agronomy,
Iowa State College
CLIFFORD G. HILDRETH
Professor of Agricultural Economics,
Michigan State University
Economic and Statistical Consultant,
Tennessee Valley Authority








LLs i THE IOWA STATE COLLEGE PRESS Ames, Iowa, U.S.A.
































1957 by The Iowa State College Press.

All rights reserved.








Library of Congress Catalog Card Number: 57-7851


















Foreword


RESEARCH oriented toward problems in the field of the economics
of fertilizer use is expanding rapidly. Coupled with this expan-
sion is a conscious effort to improve and develop more efficient
experimental designs and analytical tools. Fertilizer economics re-
search is also being broadened to include fertilizer production, mixing
and plant location economics, pricing and distribution, and the role of
fertilizer in over-all farm planning.
In line with TVA's national responsibility to encourage the produc-
tion, distribution, and use of high analysis-low cost fertilizers, a se-
ries of economic studies is being supported in representative areas of
the United States. Research results, new theories, and techniques are
presented in a seminar held annually for the cooperators in TVA's
agricultural economics research program. This book contains many of
the reports and papers presented at the latest of these seminars, which
was held in Knoxville, Tennessee, March 27-30, 1956.
The scope of the 1956 seminar was quite broad, emphasizing recent
thoughts on the numerous economic aspects of fertilizer, the fertilizer
industry, and fertilizer relative to the over-all economy. These chap-
ters appraise fertilizer problems which range from the minute con-
siderations of microanalytical technique to the broader policy impli-
cations of increased fertilizer use.
The development and the significant increased use of improved
chemical fertilizers represent a major innovation in American agri-
culture since World War II. The contributions in this book represent
the most recent thinking and the latest research findings relative to
many aspects of fertilizer in the American economy. The book pre-
sents new methodological techniques, which provide for more efficient
handling of many fertilizer research problems than have been possible
previously.


LELAND G. ALLBAUGH, Director
Division of Agricultural Relations
Tennessee Valley Authority
Knoxville, Tennessee
October, 1956






















Preface


N the interest of stimulating further study and the promotion of
greater integration of research and related educational efforts in
fertilizer development, distribution, use, and the economic implica-
tions of technological innovations in agriculture, such as newly de-
veloped high analysis fertilizers, TVA conducted a seminar on these
matters in Knoxville, Tennessee, March 27-30, 1956. The seminar
sessions were conducted under five closely related subject matter
categories. They were: (a) research in agronomic and economic ef-
ficiency in rate of application, nutrient ratios, and farm use of ferti-
lizers, (b) physical and economic aspects of water solubility of ferti-
lizers, (c) an examination of liquid fertilizers, and some related
marketing problems, (d) farm planning research and its practical ap-
plication, and (e) agricultural policy implications of technological inno-
vations in agriculture.
The seminar sessions were an outgrowth of a symposium sponsored
previously by TVA in June, 1955. The earlier symposium dealt mainly
with methodological procedures in the economic analysis of fertilizer
use data. It resulted from several meetings on the economics of ferti-
lizer use. The initial conference conducted by TVA in June, 1953, de-
veloped from a suggestion made by Dr. Joseph Ackerman, Managing
Director of the Farm Foundation. Since that time Dr. Ackerman has
aided the development of research in the economic interpretation of
fertilizer response data through the sponsorship of regional farm
management research projects sponsored by the Farm Foundation.
The 1956 seminar sessions were designed to integrate the thinking
of agronomists, economists, and statisticians on agricultural problems,
but on a much broader basis than for previous conferences. The
papers presented at the 1956 seminar sessions form the basis of this
book. The objectives of the seminars and the book are to examine the
most recent thought and research findings on the many aspects of ferti-
lizers in the American economy; and to present new methodological
techniques that will enable the more efficient handling of difficult re-
search problems related to fertilizers, and at the same time secure
more meaningful answers for practical application.
TVA is concerned with agronomic and chemical development prob-
lems which have a direct bearing upon the economic evaluation of







PREFACE


fertilizers (Parts II and II). Statisticians discuss some modifications
of existing statistical methodologies, as well as new ideas about
handling such difficult methodological problems as the economic analy-
sis of fertilizer use in crop rotations (Part III). Included in this book
are some chapters on timely problems related to fertilizer marketing
(Part II). There are many problems involved in determining the most
efficient marketing system for fertilizer. Some of the problems that
might lead to greater efficiency in the marketing of fertilizer are
considered.
"Programming a Fertilizer Mixing Operation" is the only chapter
contained in this book that was not formally presented at the seminar.
Due to other commitments, Earl R. Swanson was not able to attend the
meetings.
A debt of gratitude is owed particularly to those in the Tennessee
Valley Authority's management who made possible this seminar and its
reporting in this book, and to the Iowa State College Press, through
which publication was effected. Appreciation is extended to Lois R.
Carr, Agricultural Economics Branch, Division of Agricultural Re-
lations, Tennessee Valley Authority, for her fine cooperation in pre-
paring the manuscript for publication.
The editors believe that the information presented in this book will
contribute materially to the improvement and expansion of economic
research in the interpretation of agronomic data, fertilizer production
and distribution, and the use of fertilizer in whole-farm planning.


E. L. BAUM
Tennessee Valley Authority
Knoxville, Tennessee

EARL O. HEADY
Iowa State College
Ames, Iowa

JOHN T. PESEK
Iowa State College
Ames, Iowa

CLIFFORD G. HILDRETH
Michigan State University
East Lansing, Michigan


October, 1956


















Table of Contents


1. Introduction ........................ 1
Leland G. Allbaugh, Tennessee Valley Authority


PART I: PHYSICAL AND ECONOMIC ASPECTS OF WATER
SOLUBILITY IN FERTILIZERS

2. General Considerations Regarding Water Solubility of
Fertilizers and Availability to Crops . . . . 7
George Stanford, Tennessee Valley Authority

3. Economic Interpretation of the Importance of Water
Solubility in Phosphorus Fertilizers When Used as
Hill Fertilizer for Corn. . . . . . . ... 15
John T. Pesek and John R. Webb, Iowa State College

4. Technical and Economic Factors Involved in Production
of Fertilizers of High Water-Soluble P20s Content by
Conventional Processes . . . . . . .... 29
T. P. Hignett, Tennessee Valley Authority

5. Crop Response to Commercial Fertilizers in Relation to
Granulation and Water Solubility of the Phosphorus .37
G. L. Terman, Tennessee Valley Authority


PART II: AN EXAMINATION OF LIQUID FERTILIZERS
AND RELATED MARKETING PROBLEMS

6. Factors Affecting the Evaluation of Liquid Fertilizers .57
L. S. Robertson, J. F. Davis, and C. M. Hansen
Michigan Agricultural Experiment Station

7. Economics of Manufacture of Liquid Mixed Fertilizers 61
Z. A. Stanfield, Tennessee Valley Authority






CONTENTS


8. Programming a Fertilizer Mixing Operation. . . ... 72
Earl R. Swanson, University of Illinois

9. The Potential Market for Liquid Fertilizer ...... 77
Harold G. Walkup and John N. Mahan
Tennessee Valley Authority

10. Economic Comparison of Farm Application of Dry
and Liquid Types of Nitrogen in Iowa . . . .... 89
Earl O. Heady, Iowa State College
E. L. Baum, Tennessee Valley Authority

11. Methods of Studying Attitudes Relevant to the Economics
of Fertilizer Marketing . . . . . . ... 115
Norman Nybroten, West Virginia University


PART III: METHODOLOGICAL PROCEDURES IN THE STUDY
OF AGRONOMIC AND ECONOMIC EFFICIENCY IN
RATE OF APPLICATION, NUTRIENT RATIOS, AND
FARM USE OF FERTILIZER

12. Over-All Economic Considerations in Fertilizer Use .125
E. L. Baum, Tennessee Valley Authority
Earl O. Heady, Iowa State College

13. An Agronomic Procedure Involving the Use of a Central
Composite Design for Determining Fertilizer Response
Surfaces ................... ...... 135
Bruce L. Baird and J. W. Fitts,
North Carolina State College

14. Some Methodological Considerations in the Iowa-TVA
Research Project on Economics of Fertilizer Use. . 144
Earl O. Heady and John T. Pesek
Iowa State College

15. A Suggested Procedure for Agronomic-Economic
Fertilizer Experiments ................ 168
Thomas E. Tramel, Mississippi State College

16. Possible Models for Agronomic-Economic Research .176
Clifford Hildreth, Michigan State University

17. Some Statistical Problems in the Analysis of Fertilizer
Response Data... ................... 187
R. L. Anderson, North Carolina State College







CONTENTS


18. Some Statistical Aspects of the TVA-North Carolina
Cooperative Project on Determination of Yield
Response Surfaces for Corn. . . . . . .. 207
David C. Hurst and David D. Mason
North Carolina State College

19. Planning Agronomic-Economic Research in View
of Results to Date ..................... 217
Glenn L. Johnson, Michigan State University

20. Problems Involved in the Integration of Agronomic and
Economic Methodologies in Economic Optima
Experiments ................... . 226
L. S. Robertson, G. L. Johnson, and J. F. Davis
Michigan Agricultural Experiment Station


PART IV: FARM PLANNING PROCEDURES
FOR OPTIMUM RESOURCE USE

21. Some Problems and Possibilities of Farm
Programming ................... ... 243
Clifford Hildreth, Michigan State University

22. The Role of Management in Planning Farms
for Optimum Fertilizer Use. .............. 261
Glenn L. Johnson, Michigan State University

23. Methodological Problems in Programming Farms. . 271
Earl 0. Heady, Iowa State College
E. L. Baum, Tennessee Valley Authority

24. Programming Part-Time Farms in Georgia . . ... 283
Fred B. Saunders, University of Georgia

25. An Application of Linear Programming Techniques to the
Planning of Commercial Farms in North Georgia . 299
Roger Woodworth, University of Georgia

26. Relations of Farm Resource Use to Farm Family Incomes
and Hydrology in the Parker Branch Watershed . . 316
A. J. Coutu and C. E. Bishop
North Carolina State College







CONTENTS


PART V: AGRICULTURAL POLICY IMPLICATIONS
OF TECHNOLOGICAL CHANGE

27. Reflections on Agricultural Production,
Output, and Supply. ................
Theodore W. Schultz, University of Chicago


... 335


28. Need for Production Economics Research
in Solving Policy Problems . . . . . .... 348
Earl O. Heady, Iowa State College

29. Some Contributions of Microanalysis
to Agricultural Policy. . . . . . . . ... 362
Glenn L. Johnson, Michigan State University

30. The Economist and National Policy in Relation to
Low-Income Farm Families . . . . . ... 375
Charles E. Bishop, North Carolina State College


INDEX ................... ............. 387
















List of Figures


Figure
Number Title

4.1.--Effect of degree of ammoniation on water solubility
of P205 in ordinary superphosphate. . . . . ... 30

4.2.--Effect of degree of ammoniation on water solubility
of P20 in concentrated superphosphate . . . ... 31

5.1.--Effect of granule size and percent water-soluble P on mean
relative yields of two greenhouse crops of Sudan-grass and
oats. (Mean yield of each crop from all phosphate
fertilizers on 2 Tennessee and 3 Virginia soils = 100.) .46

5.2.--Effect of granule size and percent water-soluble P on mean
relative yields of wheat forage in Mississippi. (Mean yield
from all phosphate fertilizers in 4 field experiments
= 100.) . . . . . . . . . . . . . . 47

5.3.--Effect of granule size and percent water-soluble P on mean
relative yields of corn grain and seed cotton in Georgia,
Kentucky, and Tennessee. (Mean yield from all phosphate
fertilizers in 6 corn and 1 cotton experiments = 100.). . 49

5.4.--Effect of granule size and percent water-soluble P on mean
relative yields of vegetable crops in Washington. (Mean
yield from all phosphate fertilizers in 5 experiments
= 100.) . . . . . . . . . . . . . 50

7.1.--Effect of sales volume and seasonal operation on selling
price in South Atlantic region . . . . . ... 64

7.2.--Effect of sales volume and seasonal operation on selling
price in Pacific region ................... 65

10.1.--Fixed costs per acre for selected sizes and combinations
of equipment in applying high-pressure nitrogen
fertilizer .. ... .... .... ..... .. .. .. .. 102


I







xiv LIST OF FIGURES

10.2.--Fixed costs per acre for selected sizes and combinations
of equipment in applying dry-type and non- and low-pressure
nitrogen fertilizer ..................... 103

10.3.--Comparison of total costs (fixed plus variable) with labor
included as cost for dry-type and high-pressure nitrogen
fertilizer--50 pounds of N per acre . . . . .... 104

10.4.--Comparison of total costs (fixed plus variable) with labor
included as cost for dry-type and non- and low-pressure
nitrogen fertilizer--50 pounds of N per acre ...... ..105

10.5.--Comparison of total costs (fixed plus variable) with labor
included as cost for dry-type and high-pressure nitrogen
fertilizer--100 pounds of N per acre. . . . .... 106

10.6.--Comparison of total costs (fixed plus variable) with labor
included as cost for dry-type and non- and low-pressure
nitrogen fertilizer--100 pounds of N per acre ...... 107

10.7.--Less costly machines: fixed costs per acre for selected
sizes and combinations of equipment in applying dry-type
and high-pressure nitrogen fertilizer . . . . ... 108

10.8.--Less costly machines: fixed costs per acre for selected
sizes and combinations of equipment in applying dry-type
and non- and low-pressure nitrogen fertilizer. . . . 109

14.1.--Predicted yield surface for corn on Carrington soil. . 149

14.2.--Ninety-five percent confidence limits for corn response
to K20 at 104 pounds of N (dashed vertical line is limit
of KIO in experiment) ................... 150

14.3.--Isoquants and isoclines. Dashed lines are ridge lines
O. N OK
denoting and values of zero. Ratios attached
OK 9N
to isoclines are price ratios denoting expansion paths.
Yield figures are attached to isoquants . . . ... 151

14.4.--Production surface for corn on Moody soil predicted
from equation 14.9 ................... .. 153

14.5.--Yield isoquants and isoclines for Moody soils. Dotted
OP ON
lines are and zero, the ridge lines of the
predicted surface ........... ......... 154






LIST OF FIGURES xv

14.6.--Predicted P-K yield surface with no N application. .... 157

14.7.--Predicted P-K yield surface at 40 pounds of N . . .. 158

14.8.--Predicted P-K yield surface at 80 pounds of N . . .. 159

14.9.--Yield isoquants and isoclines with dashed ridge lines at
zero level KO. Equalities on isoclines indicate price
for N as a ratio of the price for KIO. Derived from
equation 14.12 ........................ 160

14.10.--Yield isoquants and isoclines with dashed ridge lines at
zero level of N. Derived from equation 14.14. . . ... 161

14.11.--Nonlinear isoclines for a soil completely deficient in
two nutrients ........................ 162

14.12.--Alternative nonlinear isoclines for soil completely
deficient in two nutrients. . . . . . . . ... 163

14.13.--Linear isoclines with available quantities of both
nutrients originally in the soil . . . . . .... 165

16.1.--Distribution of observations . . . . . . ... 184

17.1.--Increasing-decreasing returns response curve . . .. 192

18.1.--Graphical representation of treatment combinations of the
composite design (table 18.1 for actual rates corresponding
to code) .. ........ ......... ....... 210

23.1.--Alternative outcomes under budgeting and linear
programming ................... ..... 276

24.1.--Conceptual definition of part-time farming. . . . ... 284

24.2.--Illustration of enterprise relationships between farm
and nonfarm activities ................... 286

24.3.--Illustration of the application of choice criteria for
assumed relationship between farm and nonfarm
activities .......................... 288











List of Tables


Table
Number Title

3.1. Sources and Water Solubilities of Phosphates Used in the
Hill Fertilization Experiments From 1952 to 1955. .... 17

3.2. Equations Expressing the Estimated Yield, Y, as a
Function of Rate of P205 in the Hill, P, and the
Percent Water Solubility, S. . . . . . . ... 18

3.3. Multiple Correlation Coefficients and t Values for
Regression Equations Presented in Table 3.2. . . ... 19

3.4. The Maximum Predicted Yield Increases in Bushels Per
Acre and Rate of P205 at Maximum As Computed From
Equation 3.1 for 1953, 1954, and 1955, and the Maximum
Predicted Yield by the Spillman Equation 3.7 ...... . 21

3.5. Optimum Rates of P205 and Estimated Increases in Yield
of Corn for Specified Price Ratios of P205 to Corn (Pp/Pc)
for Phosphorus Materials of Different Water Solubility. 23

3.6. The Optimum Rates of P205 at Selected Pp/Pc Ratios
and the Expected Increases in Yield at Certain Levels
of Water Solubility of the Phosphorus. Calculations
Are Based on Equations 1953, 3.2;. 1954, 3.2; and
1955, 3.2 . . . .. . . .. .. .. .. ... 24

3.7. Percent of Water-Soluble P20s at Which Maximum
Yields Are Reached in 1953, 1954, and 1955 as Estimated
by Two Forms of the Regressions Used . . . ... 25

4.1. Formulations and Costs for 3-12-12. . . . . .... 32

4.2. Formulations and Costs for 5-20-20. . . . . .... 33

4.3. Formulations and Costs for 10-10-10 . . . . ... 34

4.4. Formulations and Costs for 12-12-12 . . . . ... 35

5.1 Crop Response to TVA Diammonium Phosphate
Fertilizers, 1950-55 . . . . . . . .. .. 43

xvi






LIST OF TABLES xvii

5.2. Fertilizers Used in the Granule Size and Water
Solubility Experiments ................... 44

6.1. The Effect of Liquid and Solid Fertilizers on
Corn Yields in 1955 ..................... 59

6.2. The Effect of Liquid and Solid Fertilizers on Yields
of Onions, Table Beets, and Carrots Grown on
Houghton Muck in 1955 ................... 60

7.1. Effect of Plant Size on Operating Costs in Liquid
and Solid Mixed Fertilizer Plants . . . . . .. 65

7.2. Formulation Costs for Several Grades of Liquid
and Solid Mixed Fertilizer . . . . . . . .. 66

7.3. Effect of Increasing Concentration of Solids. . . .. 67

7.4. Estimates of Selling Price of 10-10-10 Liquid and Solid
Fertilizer (Sales Volume: 40,000 Tons Per Year; Plants
Operated 6 Months Per Year To Produce 40,000 Tons) .68

7.5. Estimated Costs of Distribution of Solid and Liquid
Fertilizers (Sales Volume: 5,000 Tons; Cost Delivered
to Farm) .......................... 69

7.6. Estimated "Delivered to Farm" Selling Prices for
40,000-Ton Annual Sales Volume (One Manufacturer
and Eight Distributors). .................. 70

8.1. Composition of Fertilizer Material. . . . . . .. 73

8.2. Price Situations Used To Compute Materials Needed
To Minimize Cost of a Ton of Neutral 4-12-4 ...... . 73

8.3. Quantities of Materials Needed To Minimize Cost
of a Ton of Neutral 4-12-4 ................. 74

9.1. Plant Nutrient Consumption Per Acre of Crops and
Pasture Land ................... ..... 79

9.2. Consumption of Liquid Fertilizers in the United States
and Territories (Short Tons of Material as Applied) . 82

9.3. Consumption of Liquid Fertilizers in California. . . 83

10.1. Fixed Costs for Different Methods of Nitrogen Application
and Different Sizes of Equipment. Costs Figured on a
Basis of 1955 Prices .................... 92






LIST OF TABLES


10.2. Total Investment in Equipment and Storage Tanks for
Selected Dry- and Liquid-Form Distribution Systems. . 93

10.3. Total Fixed Cost Per Acre for Alternative Methods
of Fertilizer Application . . . . . . . ... 94

10.4. Total Cost Per Acre of Applying Fertilizer (Fixed Plus
Variable With Cost of Nutrients Excluded) for Alternative
Methods of Fertilizer Application (Labor Included in
Costs). ............ .... ........... 95

10.5. Total Cost Per Acre of Applying 50 Pounds of Nitrogen
Per Acre for Alternative Methods of Fertilization
Application (Labor Included as a Cost). . . . . ... 96

11.1. Farmers' Opinions on Bases for Discounts on Fertilizer
Prices Other Than Paying Cash . . . . . .... 118

11.2. Farmers' Valuations of Delivery Service for Fertilizer
and Whether Fertilizer Was Hauled by the Dealer or the
Farmer for Three Relationships of the Valuations and
the Dealer's Charge or Discount for Hauling ...... 120

13.1. Fertilizer Treatments of Fertility Trials With Corn
in North Carolina in 1955. . . . . . . . ... 137

13.2. The Average Yield of Shelled Corn at 15.5 Percent
Moisture for Selected Locations of Fertility Trials
in 1955 ................... ....... 139

13.3. The Average Results of Chemical Analysis of Soil
Samples Collected From the Surface Soil in 1955 ..... .140

13.4. Rainfall for the Months of June and July at Locations
of Selected Trials in 1955 . . . . . . ... 141

14.1. Analysis of Variance of Corn Yields on Carrington
Soil, Randomized Block Design. . . . . . . .. 146

14.2. Values of t for Coefficients of Individual Block
Regressions and Test of Difference Between
Corresponding Coefficients of the Two Blocks. . . ... 147

14.3. Analysis of Variance for Regression of Corn Yield . .. 148

14.4. Analysis of Variance of Corn Yields on Moody Soil,
Randomized Block Design . . . . . . ... 152


xviii






LIST OF TABLES xix

14.5. Analysis of Variance of Corn Yields on Haynie Soil,
Randomized Block Design . . . . .... .... 155

14.6. Values of t for Individual Regression Coefficients
of Equation 14.10 ................... ... 156

15.1. Design Matrix, Squares, and Cross Products for Box's
Second-Order Composite Design With Treatment Combi-
nations on Each Major Axis Taken To Be Two Increments
of Each Variable ................... .. .. 171

15.2. Design Matrix, Squares, and Cross Products for Modified
("Triple Cube") Second-Order Design of Same "Size" as
Box's Design in Table 15.1 . . . . . . ... 172

15.3. Form of Matrix of Sums of Squares and Cross Products
for Box's Second-Order Composite Design and "Triple
Cube" Design ......... ............... 173

15.4. Elements of Matrices of Sums of Squares and Sums
of Cross Products for Both Original Box Design and
"Triple Cube" Design .................... 173

15.5. Form of Inverse Matrix for Both Original Box Design
and "Triple Cube" Design . . . . . . ... 173

15.6. Elements of Inverse Matrix for Both Original Box
Design and "Triple Cube" Design . . . . ... 173

15.7. Correlation Between Coefficients for Both Original
Box Design and "Triple Cube" Design . . . .... 174

15.8. NCii of Original Box Design and of "Triple Cube"
Design ............................ .. 175

17.1. Equations for Iowa Data . . . . . . . ... 188

17.2. Mean Estimated Corn Yields (Bu. Per Acre) as Derived
by Use of Various Production Functions for Iowa Data . 189

17.3. Estimated Optimal Nitrogen Applications (in Pounds) for
Various Input-Output Price Ratios As Derived by Various
Production Functions for Iowa Data . ..... .... 191

17.4. Observed and Estimated Yields, 25V1, and 95 Percent
Confidence Limits for Each of Eight Points . . ... 203

17.5. Estimated Optimal Yields for Five Values of r and
for Each Estimating Equation . . . . . ... 205






xx LIST OF TABLES

18.1. Rates in Pounds Per Acre and Coded Levels of N,
P205, and KaO Used in Forming Treatment Combinations
for the Composite Design (Figure 18.1) . . . ... 210

18.2. Parameter Estimates and Their Variances as Estimated
on 6 Norfolk-Like Soils. . . . . . . . . .. 213

23.1. Use of Negative Coefficients in Simplex Calculations . 280

24.1. Description of Part-Time Farming Situations Included
in Analysis Under Approach 1 (Determining Farm
Situation To Combine With a Given Nonfarm Job) . . 293

24.2. Comparison of Returns for All Part-Time Farming
Situations With the Basic Farm Situations ........ 295

24.3. Comparison of Farm Organization for All Part-Time
Farming Situations With the Basic Farm Situations
(Only for Situations Under Approach 1) . . . ... 297

25.1. Resource Requirements and Income for 26 Alternative
Activities Used in Programming. . . . . . ... 302

25.2. Farm Plan 1, Maximum Income Farm Plan for Situation
A (Investment Plus Operating Capital Limited to
$3000) ................... ........ 309

25.3. Marginal Value Productivities of Resources for
Highest Income Farm Organization for Situation A
(Operating and Investment Capital Limited to $3000) . 310

25.4. Opportunity Costs, Net Income Per Unit and Marginal
Revenues for Highest Income Plan, Situation A .... .. 311

25.5. Comparison of Maximum Farm Organizations for Four
Situations--Case-Study Farm . . . . . ... 313

25.6. Comparison of Marginal Value Productivities for
Resources for Four Situations, Case-Study Farm ..... 314

27.1. Recent Changes in Output and Input in Agriculture
in the United States ........................ 339

27.2. Recent Changes in Output and Input in Agriculture
in Brazil, Mexico, and Argentina. . . . . . ... 341

27.3. Recent Changes in Output and Input in Agriculture
in the U.S.S.R. ........... ............ 343







LELAND G. ALLBAUGH
Tennessee Valley Authority



Chapter 1



Introduction




INTEREST in economic problems of fertilizer use has been stimu-
lated among economists, agronomists, and statisticians during the
past several years. In exploring methodological research problems,
professional workers from these three fields have developed a mutual
respect for each other's abilities and viewpoints. At the same time,
they have become more keenly aware of the possible contributions each
could make to the solution of common problems.
Agricultural economists depend upon research in the many pro-
duction sciences for basic data. Accordingly, they perhaps recognize
the need for the integration of scientific skills more than other groups
of professional workers. However, agricultural production scientists
also are beginning to recognize the need for a better understanding of
the economic problems which their research is expected to solve.
Hence, a coordinated approach to research on fertilizers and basic re-
source development is becoming widely accepted.
Interest in the economics of fertilizer use subsided after the im-
portant contributions made by Mitscherlich, Liebig, and Spillman. It is
difficult to explain why so little research was conducted in the eco-
nomics of fertilizer use from 1925 to 1953. Since 1953, this field of
research has expanded rapidly. The Farm Foundation, through its
sponsorship of regional farm management research committees, along
with economists and agronomists in the land-grant colleges, the USDA,
and TVA have had a part in this resurgence of research interest in
agronomic and economic efficiency in the rate of application, nutrient
ratios, and farm use of fertilizers.
Section 5 of the TVA Act is the basis for TVA's interest and re-
sponsibility in the economic development and economic use of new and
improved fertilizers. Because of this national responsibility, TVA
recognizes the need for helping in the rapid development of improved
research methodologies, both agronomic and economic, and the use of
such information in educational programs. TVA's national fertilizer
and munitions laboratory at Wilson Dam, Alabama, is mainly concerned
with developing new and improved techniques of manufacturing chemi-
cals for fertilizers and defense purposes. The development of new and
improved fertilizers which lower the cost of plant nutrients to the
American farmer enables food and fiber to be produced more efficiently.







L. G. ALLBAUGH


Section 22 of the Act also delegates to TVA the regional responsi-
bility for the efficient development of resources in the Tennessee
Valley. As a resource development agency, TVA is vitally concerned
with the economic well-being of the people living in the Valley. In the
public interest, TVA conducts studies and related educational activities
designed to increase efficiency in the farming and rural life of the
Valley area. In addition, it is a TVA policy to conduct most of its agri-
cultural research activities through the land-grant colleges.
TVA considers the role of fertilizer to be important in its resource
development programs. TVA emphasizes the use of fertilizers for
proper land cover in its tributary watershed programs, and in planning
farming systems for maximum profits. In the Tennessee Valley states,
fertilizers and water are as essential as sunshine and soil to agri-
cultural production.
Upon the suggestion of Dr. Joseph Ackerman, Managing Director of
the Farm Foundation, TVA arranged a conference in June, 1953, with
interested professional workers to discuss the possibilities of under-
taking research in the economics of fertilizer use. Representatives of
the Southern Farm Management Research Committee, the USDA, the
Farm Foundation, and the TVA staff and its consultants attended this
meeting in Knoxville. No agronomists were present at this initial
meeting.
A follow-up meeting was held at Muscle Shoals in January, 1954. In
addition to the group attending the 1953 meeting, several agronomists
and statisticians participated in the discussions, and a new field of re-
search emphasis was initiated. Consideration was given to needed
methodological procedures for handling developments in fertilizer eco-
nomics. From these meetings, it became evident that research in ferti-
lizer economics should be broader in scope. Fertilizer response re-
search should consider not only the three major applied plant nutrients;
it should include also such other considerations as soil type, fertilizer
placement, and the time and method of application. Experiments in-
cluding these variables ought to be conducted for multicrop rotations,
as well as for single crops.
The increased amount of research in the economics of fertilizer use
has been helped greatly by the interest of the various regional farm
management research committees sponsored by the Farm Foundation;
the continuing interest of the USDA; the interest of agronomists, econo-
mists, and statisticians at the land-grant colleges; and the increased
interest of the nation's fertilizer industry.
A third meeting, sponsored by TVA, was the June, 1955, symposium
held at Knoxville. The papers presented at the symposium pointed up
areas for new work in agronomic-economic research.' Methodologies
used in the past were examined; alternative methodologies were

'The symposium on Methodological Procedures in the Economic Analysis of Fertilizer
Use Data was held in Knoxville, June 14-16, 1955. These papers were published in Method-
ological Procedures in the Economic Analysis of Fertilizer Use Data, Iowa State College
Press, 1956.






INTRODUCTION


proposed to handle better the problems involved. Following these
several meetings, sufficient research progress had been made to war-
rant a conference sponsored by TVA in March, 1956. This volume in-
cludes the papers presented at the latter conference.
The purpose of this book is to present information on research con-
ducted in the land-grant college-TVA cooperative agricultural economic
research program, to describe new methodological techniques enabling
more efficient analysis of difficult research problems, to indicate prob-
lems in need of solution, and to provide meaningful answers to practical
farm problems.
Exchange of ideas among agronomists, economists, and statisticians
on research methodologies and agricultural policy problems not only
leads to better mutual understanding but also provides a basis for
more effective research. This need was stressed by a quote appearing
in the USDA Agricultural Research Service letter of March 9, 1956, by
Dr. Harry C. Trelogan, Director of the AMS Marketing Research Di-
vision. He stated: "One of the greatest needs of our present-day agri-
cultural research system is a common language, better understanding,
and closer working relationships among the various specialized
subject-matter fields."
One purpose of this book is to fulfil this need. Another is to stimu-
late more meaningful research, with the objective of bettering the eco-
nomic and social welfare of agriculture and the nation. Some chapters
are concerned with means of obtaining a better application of research
results. Discussion between extension and research personnel, in
carrying out the TVA program, suggests that some important funda-
mental research is lacking. These gaps sometimes occur because the
research worker does not look far enough ahead to determine how the
proposed results of his research might best be conveyed to the ex-
tension worker, and how the results might be applied in practical situ-
ations on farms and in agricultural industries.
Fundamental research ordinarily is several steps away from the ex-
tension application. However, if research is useful, its results must be
disseminated at some future time. Accordingly, the research worker
should give some thought to the possible use of his results in determin-
ing the framework for analyzing his problem. This problem of coordi-
nation is similar to the problem of establishing better understanding be-
tween the production scientist and the agricultural economist, who often
can make their research more meaningful with full cooperation. TVA
is interested in bringing about a closer coordination of research and
extension in the selection of research problems and the use of re-
search information in extension programs. This volume not only
emphasizes methodological needs and basic research results for a
more fundamental solution of fertilizer economic problems; it also
stresses the need for integration of research results and extension ap-
plication in solution of farm problems.
























PART I


Physical and Economic Aspects of

Water Solubility in Fertilizers

0 Solubility and Availability to Crops
0 Economics of Water Solubility
Relative Crop Response


i









GEORGE STANFORD
Tennessee Valley Authority

Chapter 2

General Considerations Regarding

Water Solubility of Fertilizers

and Availability to Crops


SOIL scientists have recognized that poor correlation exists between

the content of water-soluble soil nutrients and the capacity of soils
to supply nutrients to plants. Concentrations of various major es-
sential nutrients present in the soil solution, even in fertile soils, are
very low at any particular instant and would not supply plant require-
ments for any appreciable time. The nutrient-supplying capacity of a
soil, therefore, is dependent on rate of replenishment by dissolution of
the soil minerals and by ion exchange from colloidal surfaces, as well
as on concentration of nutrients in the soil solution. Water solubility of
nutrients in fertilizers applied to soils likewise bears no simple re-
lation to plant availability. The instant that a dissolved salt contacts
the soil, it essentially loses its identity through reaction with soil con-
stituents.
Consideration will be given in this chapter to the water-soluble
compounds of nitrogen, phosphorus, and potassium contained in ferti-
lizers and their behavior when applied to soils. Particular emphasis
will be placed on plant availability of applied nutrients in relation to
soil-fertilizer reactions.


NITROGEN

Nitrogen Fertilizers (9,11)'

The principal nitrogen fertilizers are liquid anhydrous ammonia (82
percent N), ammonium nitrate (33.5 percent N), ammonium sulfate (20
percent N), ammonium phosphates (11-21 percent N), and urea (46 per-
cent N). Other less extensively used materials are sodium nitrate (16
percent N) and calcium cyanamide (20-21 percent N). All of these car-
riers are water soluble. Those designated above as principal carriers
are used for soil application both in solid form and in solution, except
for anhydrous ammonia which occurs as liquid under pressure. Nitro-
gen solutions being used for direct application are anhydrous ammonia,

'Numbers in parentheses which appear in sentences refer to reference citations listed at
the end of each chapter.






GEORGE STANFORD


aqua ammonia, urea, urea-ammonium nitrate, solutions of ammonia-
ammonium nitrate, ammonia-urea, or ammonia-ammonium nitrate-
urea. The solutions containing ammonia plus nitrogen salts, however,
are primarily used in production of mixed solid fertilizers (see
Chapter 4).
The water-insoluble nitrogen fertilizers, principally natural organic
proteinaceous materials, comprise less than 5 percent of the nitrogen
sold in fertilizers. Recently, synthetic urea-formaldehyde, a slowly
soluble nitrogen source, has come into limited commercial production
(9).


Behavior of Nitrogen Fertilizers in Soils

Ammonia (NH3), ammonium ion (NHI), nitrate ion (NO-), and urea
[(NH)2 CO] are the chemical forms comprising practically all the
nitrogen marketed in fertilizers. When ammonia is injected in soil, it
is converted to the ammonium form either through reaction with car-
bonic acid of the soil solution (equation 2.1), or direct attachment to
negatively charged soil colloids through neutralization of hydrogen (H+)
ion (equation 2.2).

(2.1) 2NH, + H2CO3 -- (NH4)2CO,

(2.2) NH3 + Hn-colloid Hn-INH4-colloid

Ammonium salts such as (NH4)2SO4 when dissolved in the soil water
ionize rather completely to give NH4+ and SO4= ions. Some of the NHI+
ions become adsorbed through replacement of cations already held on
soil colloid surfaces (equation 2.3), while some remain in the soil
solution.

(2.3) 3NH4+ + HCa-colloid -- (NH4)3-colloid + H+ + Ca++

Urea hydrolyzes to form (NH4)2COs as in equation 2.4. The am-
monium ions thus produced, as well as those represented in equation
2.1, may react with soil colloids as depicted in equation 2.3.

(2.4) (NH2)2CO + 2 HOH -* (NH4)2CO3

The negatively charged nitrate ion does not react with soil colloids
of like charge nor does it enter directly into formation of insoluble in-
organic compounds in soils. Thus, extraction with water readily re-
moves nitrates from soils.
Fixation of ammonium ions by particular types of clay minerals is
known to occur in certain soils. Further study is needed, however, to
determine the significance of NH4-mineral formation in relation to ef-
ficiency of nitrogen fertilizer use (2, 3, 6, 7).






WATER SOLUBILITY OF FERTILIZERS


Biological Transformations of Nitrogen

Both ammonium and nitrate forms of nitrogen are utilized by soil
microorganisms during active decomposition of crop residues. The
accompanying disappearance of soluble inorganic nitrogen forms,
termed immobilization, often results in temporary deficiencies of
nitrogen to growing crops in soils possessing low reserves of easily
mineralizable nitrogen (16).
As readily available energy sources such as crop residues become
depleted, ammonium nitrogen is again released by decomposition of
high-nitrogen microbial tissue. Ammonium ions resulting from or-
ganic matter decomposition and those introduced directly through ferti-
lizer application are converted to nitrate ions through the action of
nitrifying organisms. Under favorable environmental conditions, this
conversion occurs readily (16). In well aerated, fertile soils, and with
favorable temperature and moisture conditions prevailing, only 2 to 3
weeks may be required to bring about nearly complete nitrification of
ammonium applied in fertilizer.


Availability of Fertilizer Nitrogen to Plants

Plant roots absorb ammonium and nitrate ions. Whether or not
there is preferential absorption of either of these forms is a question
which must be examined in relation to kind of plant, stage of growth,
characteristics of the root environment such as pH, oxygen supply,
concentration of other ions capable of influencing ammonium or nitrate
uptake, and other factors (10). It is sufficient to point out that certain
crops (potatoes, corn, rice, and buckwheat, for example) prefer am-
monium nitrogen while others (beets and wheat) thrive better on nitrate
nitrogen (10). Numerous plants feed equally well on both forms. Nor-
mally, however, nitrate is the dominant form presented to the roots
during much of the growing season, regardless of the form applied. It
is not surprising, therefore, that comparisons of nitrogen sources in
field experiments frequently reveal no differences in crop response.


Mobility of Fertilizer Nitrogen in Soils

As would be anticipated from equation 2.2, adsorbed ammonium ions
are relatively immobile in soils. That is, percolating waters move
little of this form of nitrogen below the application zone in medium to
heavy-textured soils. Under Midwestern conditions, late fall appli-
cation of ammonia or ammonium salts is deemed an acceptable prac-
tice, since prevailing low temperatures reduce the rate of nitrification,
and losses of nitrogen over winter and early spring likely are of minor
consequence (17).
Nitrate nitrogen, on the other hand, is readily leached, especially in






GEORGE STANFORD


coarse-textured soils. Moreover, nitrate ions move upward in the
capillary stream of water as the soil surface dries. During prolonged
dry periods, a high concentration of nitrate may accumulate in a few
inches of surface soil and become effectively unavailable to growing
plants (13). A redistribution takes place, of course, with further rain-
fall. Thus, in relatively dry seasons, deep placement may prove su-
perior to shallow broadcast application of nitrogen, since the plant
roots utilize more nitrogen from the deeper moist zone than from the
extremely dry surface layer.
The ready mobility of nitrate nitrogen accounts for the high re-
covery (60 percent or more) of applied nitrogen by plants (8). Such a
high recovery is evidence of the rapidity with which nitrate diffuses
from one point to another in the soil solution and to plant root surfaces.


POTASSIUM

Potassium Fertilizers

The principal potassium fertilizer, potassium chloride (50-60 per-
cent K20), accounts for about 90 percent of the consumption of potash
fertilizer in the United States (19). Sulfates of potassium account for
most of the remainder. Both the chloride and sulfates are water solu-
ble. Another potassium fertilizer of potential importance is potassium
metaphosphate, KPO3, containing approximately 34 percent K20 which
has been produced experimentally by the Division of Chemical Develop-
ment, Tennessee Valley Authority.


Reactions of Potassium Salts in Soil

Potassium ions react with colloidal surfaces in the same manner as
depicted for ammonium ions in equation 2.3. Thus, the mobility of this
nutrient ion is relatively restricted once adsorption occurs. That is,
mass movement of soil water brings about little leaching where suf-
ficient clay and organic matter are present. Other cations, however,
may readily replace the adsorbed potassium.
Some of the potassium ions penetrate between lattice sheets of
certain clay minerals and resist replacement by other cations (20). It
is generally believed that the dissolved, adsorbed, and difficultly re-
placeable potassium tends to equilibrate in soils according to equation
2.5 (4, 20).

Adsorbed.*- Fixed
(2.5) K+ in solution K K K






WATER SOLUBILITY OF FERTILIZERS


Availability of Potassium to Plants

Plant roots readily absorb potassium ions (K+) from solution.
From equation 2.5, it is evident that there will be a tendency toward
replenishment of soil solution potassium as plant absorption lowers the
concentration in solution or is adsorbed. Soils differ, however, in the
rate at which this readily available form of potassium is replenished.
There is evidence that plant roots, in intimate contact with colloidal
clay and organic matter, obtain potassium ions by "contact exchange"
(12). This is illustrated in equation 2.6, in which a hydrogen ion ad-
sorbed on the root surface is pictured as exchanging with a potassium
ion on the colloid surface.

(2.6) H-Root + K-colloid K-Root + H-colloid

Except in soils which fix appreciable amounts of potassium in slowly
replaceable form or those which possess little clay and organic matter
and, therefore, permit extensive leaching losses, recovery of applied
soluble potassium fertilizer is relatively high often 50 percent or
greater (16).


Slowly Soluble Potassium Fertilizers

With very large application of soluble potassium fertilizer, it fre-
quently has been observed that certain plants absorb larger quantities
of potassium than are required for maximum yield (16). Brief con-
sideration has been given to the importance of leaching losses in sandy,
low-colloid soils subjected to high rainfall. In some soils, the fixation
of potassium (equation 2.5) becomes important enough to affect greatly
recovery and efficient use of applied potassium (1, 22). These obser-
vations suggest the need for a slowly soluble potassium fertilizer for
most efficient use under certain conditions. Such a fertilizer ideally
should dissolve slowly enough to prevent "luxury consumption" by
plants, reduce the proportion lost by leaching, and minimize fixation
where these factors are problems.
Phosphorus-potassium fertilizer containing chiefly a slowly soluble
potassium-calcium pyrophosphate and potassium metaphosphate has
been prepared on an experimental scale in the Division of Chemical De-
velopment, TVA. Products of this nature varying widely in water solu-
bility are currently being compared with completely water-soluble
sources such as vitreous potassium metaphosphate, potassium chloride,
and potassium sulfate in greenhouse pot tests at Wilson Dam.







GEORGE STANFORD


PHOSPHORUS

Water-Soluble Phosphorus Fertilizers

The chief water-soluble phosphorus carriers are ordinary super-
phosphate (18-20 percent P20,), concentrated superphosphate (45-50
percent PO2), fertilizer-grade monoammonium phosphate (48 percent
P20), diammonium phosphate (53 percent P2zO), and phosphoric acid
(62 percent P20O). The superphosphates, when used in manufacture of
mixed fertilizers, usually are ammoniated in the process of formu-
lation. The water-soluble phosphorus present following ammoniation is
predominantly ammonium phosphate (see Chapter 5). Liquid fertilizers
containing phosphorus are prepared by ammoniating phosphoric acid.
Usually, about equal proportions of the monoammonium and diam-
monium phosphates are present (21).
Upon ammoniation of superphosphates in formulation of mixed ferti-
lizers, the water solubility of phosphorus decreases (see Chapter 4).
The relative availability to plants of water-soluble and water-insoluble
phosphorus compounds under different soil conditions is discussed in
Chapter 5. The scope of this chapter is largely restricted to a con-
sideration of water-soluble fertilizer constituents.


Reactions and Mobility in Soils

When water-soluble phosphorus compounds are applied to soils, re-
action with soil constituents occurs rapidly upon dissolution of the
fertilizer particles. A variety of compounds might be formed, depend-
ing particularly on the pH of the soil. Basic calcium phosphates, par-
ticularly dicalcium phosphate, form readily in neutral to calcareous
soils (14, 18). Even in acid soils, appreciable amounts of dicalcium
phosphate are formed upon application of soluble phosphates (15). For-
mation of complex iron and aluminum phosphates likewise occurs to an
unknown extent in acid soils (14). This tendency increases as the pH
decreases, with its accompanying increase in soluble or active iron and
aluminum and decrease in percent saturation of the exchange complex
with calcium.
The rapid reactions of applied soluble phosphates with soils make
for an extreme lack of mobility. Consequently, in soils there is rela-
tively little movement of phosphorus to plant roots. This contrasts
sharply with nitrate, which moves readily. The extent of root develop-
ment determines the amount of phosphorus uptake by the plant to a
much greater extent, therefore, than is the case with nitrate nitrogen.
The effective root feeding zone for phosphorus is the thin layer of soil
immediately adjacent to active root surfaces (perhaps only a few milli-
meters in thickness), whereas the entire root-soil zone may be re-
garded as being involved in supplying nitrogen, and, to a lesser extent,
potassium to the plant (8). The limited mobility as well as the slow







WATER SOLUBILITY OF FERTILIZERS


solubility of the compounds formed on reaction between soils and
phosphorus fertilizers are responsible for the very low recovery of ap-
plied phosphorus (10-20 percent) during the year of application.


Factors Affecting Plant Availability
of Water-Soluble Phosphorus Fertilizers

Effectiveness of water-soluble phosphorus fertilizers applied to
soils may be influenced particularly by granule size and method of
placement as is discussed elsewhere in this book. For example, on
acid soils, larger granules may be more effective than smaller gran-
ules; and band placement usually is superior to mixing with the soil.
On the other hand, in neutral to calcareous (alkaline) soils, the smaller
granules often provide more phosphorus to plants and mixed placement
frequently proves superior to banding. Possibly the determining
factors are: (a) volume of soil influenced by the fertilizer, and
(b) amount of plant-available phosphorus remaining per unit of soil in
the soil-fertilizer reaction zone (5). The relative significance of these
factors evidently varies markedly among soils, as indicated above, in
comparing acid and calcareous soils. Scattered evidence suggests that
the second factor, concentration of available phosphorus per unit of
soil, is of particular importance in determining the ability of plants to
absorb phosphorus from acid soils. In calcareous soils, the first
factor apparently is of relatively greater significance.
There is need for more research to determine the specific manner
in which soluble phosphorus compounds react with soils of varying
characteristics. Gradual increase in use of phosphates in solution is
another area requiring investigation (21). It is not known whether dis-
solved phosphates and solid water-soluble phosphates behave similarly
under varying soil conditions. Moreover, little evidence is available
concerning placement methods and concentrations which result in most
effective use of phosphate solutions.


REFERENCES CITED

1. ALLAWAY, H., and PIERRE, W. H., 1939. Availability, fixation and liberation
of potassium in high-lime soils. J. Amer. Soc. Agron. 31:940-53.
2. ALLISON, F. E., KEFAUVER, M., and ROLLER, E. M., 1953. Ammonium
fixation in soils. Soil Sci. Soc. Amer. Proc. 17:107-10.
3. ROLLER, E. M., and DOETSCH, J. H., 1953. Ammonium fixation and
availability in vermiculite. Soil Sci. 75:173-80.
4. ATTOE, O. J., and TRUOG, E., 1945. Exchangeable and acid-soluble potassium
as regards availability and reciprocal relationships. Soil Sci. Soc. Amer.
Proc. 10:81-86.
5. BOULDIN, D. R., 1956. Particle size effects of soluble phosphate fertilizers.
Ph.D. Thesis, Iowa State College Library, Ames, Iowa.







GEORGE STANFORD


6. BOWER, C. A., 1950. Fixation of ammonium in difficultly exchangeable form
under moist conditions by some soils of semiarid regions. Soil Sci. 70:375-83.
7. 1951. Availability of ammonium fixed in difficultly exchangeable
form by soils of semiarid regions. Soil Sci. Soc. Amer. Proc. 15:119-22.
8. BRAY, R. H., 1954. A mobility concept of soil-plant relationships. Soil Sci.
78:9-22.
9. CRITTENDEN, E. D., 1953. Fertilizer Technology and Resources in the
United States, Chapter IV. (Edited by K. D. Jacob.) Academic Press, Inc.,
New York.
10. GORING, C. A. I., 1956. The nitrogen nutrition of plants. Down to Earth. 2:7-9.
11. GRIBBINS, M. F., 1953. Fertilizer Technology and Resources in the United
States, Chapter III. (Edited by K. D. Jacob.) Academic Press, Inc., New York.
12. JENNY, H., and OVERSTREET, R., 1939. Cation exchange between roots and
soil colloids. Soil Sci. 47:257-72.
13. KRANTZ, B. A., OHLROGGE, A. J., and SCARSETH, G. D., 1943. Movement
of nitrogen in soils. Soil Sci. Soc. Amer. Proc. 8:189-95.
14. KURTZ, L. T., 1953. Soil and Fertilizer Phosphorus in Crop Nutrition, Chapter
III. (Edited by W. H. Pierre and A. G. Norman.) Academic Press, Inc., New
York.
15. LEHR, J. R., BROWN, W. E., and BROWN, E. H. Chemical behavior of mono-
calcium phosphate monohydrate in soils. Submitted to Soil Sci. Soc. Amer.
Proc. for publication in 1957.
16. LYON, T. L., BUCKMAN, H. 0., and BRADY, N. C., 1952. The Nature and
Properties of Soils. The Macmillan Co., New York.
17. NELSON, L. B., and UHLAND, R. E., 1955. Factors that influence loss of
fall applied fertilizers and their probable importance in different sections of
the United States. Soil Sci. Soc. Amer. Proc. 19:492-96.
18. OLSEN, S. R., 1953. Soil and Fertilizer Phosphorus in Crop Nutrition, Chapter
IV. (Edited by W. H. Pierre and A. G. Norman.) Academic Press, Inc., New
York.
19. REED, J. F., 1953. Fertilizer Technology and Resources in the United States,
Chapter VIII. (Edited by K. D. Jacob.) Academic Press, Inc., New York.
20. REITEMEIER, R. F., 1951. Soil potassium. Advances in Agronomy (Edited
by A. G. Norman) Vol. 3, pp. 113-64. Academic Press, Inc., New York.
21. SLACK, A. V., 1955. Production and use of liquid fertilizers. Agri. and Food
Chem. 3:568-74.
22. VAN DER MAREL, H. W., 1954. Potassium fixation in Dutch soils. Mineral-
ogical analyses. Soil Sci. 78:163-79.






JOHN T. PESEK and JOHN R. WEBB
Iowa State College

Chapter 3

Economic Interpretation of the Importance of

Water Solubility in Phosphorus Fertilizers

When Used as Hill Fertilizer for Corn'


HE phosphorus content of commercial fertilizers in the United
States is guaranteed according to the procedure for determining
available P20s of the Association of Official Agricultural Chemists
(1). The tacit assumption is made that if the phosphorus in a fertilizer
is "available," according to the procedure, then the fertilizer is of
equal value as a source of phosphorus to another source of the same
composition determined in like manner. Manufacture and merchandis-
ing of fertilizer has been based on the above assumption, and conse-
quently different fertilizers of the same legal grade actually may con-
tain most of their phosphorus in widely differing chemical forms. To
remain within the legal limits, the chemical form of the phosphorus
may vary from compounds of very low water solubility such as tri-
calcium phosphate and dicalcium phosphate to the highly water-soluble
monocalcium phosphates, ammonium phosphates, and others.
Much agronomic work has been supported by the Tennessee Valley
Authority in connection with its development of various phosphorus
fertilizer materials. The materials, which were tested, varied widely
and were applied to many different crops and over a wide range of soil
types, climatic conditions, and cultural practices. The results of these
tests have been summarized from time to time by TVA agronomists.
Seatz et al. (5) have pointed out the advantages and disadvantages of the
fused tricalcium phosphate as a fertilizer and indicated its general
range of use, while Tisdale and Winters (9) evaluated calcium meta-
phosphate in the same manner. Both of these materials are essentially
water-insoluble and they were usually compared with concentrated
superphosphate as the standard. The available P20, in the latter is ap-
proximately 90 to 95 percent water-soluble.2
First, Rogers (4) and later Thorne et al. (8) presented summaries
of agronomic results with nitric phosphates (formerly and temporarily
designated as "nitrophosphates") from all of the cooperating experiment

'The work reported in this chapter has been supported in part by two grants-in-aid from
the Tennessee Valley Authority.
2The water solubility or percent water-soluble refers to the percent of the neutral am-
monium citrate soluble phosphorus in water-soluble form, both determined by the A.O.A.C.
Method (1), and, in this chapter, will refer only to phosphorus unless specifically stated
otherwise.






J. T. PESEK AND J. R. WEBB


stations. Nitric phosphates are interesting materials for research be-
cause the different grades produced by various processes vary from 1
to over 40 percent water-soluble phosphorus (table 3.1). The con-
clusions in general were that the phosphorus in these materials was
about equal in plant availability to that in concentrated superphosphate,
particularly in the southeastern United States. According to Rogers (4)
there was some evidence that higher water solubility appeared desir-
able in limited tests in Iowa and Nebraska. Conclusions of Thorne et al.
(8) were about the same but they noted that commercial fertilizers with
low water-soluble phosphorus levels produced by other processes were
just as inferior for some purposes as were the nitric phosphates of
similar water solubility. More recently, Webb (10) has measured and
reported highly significant advantages of fertilizers with a high percent
of water-soluble phosphorus when used as hill fertilizers for corn. The
evaluation was made on the basis of different vegetative response and
yield increases caused by materials of varying water solubility of
phosphorus.
Archer and Thomas (2) have reported that the water solubility of the
phosphorus in commercial grades produced by selected plants varies
widely from one grade and plant to another, and also some within
grades. They also cited some of the factors which seemed to contribute
to lowering of water solubility of the phosphorus and those which tended
to maintain it at higher levels. Rogers (4) reported how nitric phos-
phates vary in water-soluble phosphorus percent and Hignett (3) pre-
sented data to show how the water solubility of phosphorus decreases
upon ammoniation of both ordinary and concentrated superphosphate.
Hignett (3) also indicated that it costs somewhat more to produce the
same grade of fertilizer at higher levels of water-soluble phosphorus
by current commercial processes.
Since the water solubility of phosphorus in hill fertilizers for corn
plays an important part in their value and since there is a tendency for
materials of higher water solubility to cost more, it seems appropriate
to evaluate these factors within an economic framework. It is therefore
the purpose of this chapter to investigate the functional relationships
between percent water-soluble phosphorus and phosphorus rates in hill
fertilizers for corn and how fertilizer recommendations may be influ-
enced by possible price differentials due to water solubility of phos-
phorus.


SOURCE OF DATA AND PROCEDURE

The data utilized in this study were selected from a series of ex-
periments designed to compare the effectiveness of phosphorus ferti-
lizers in which the water solubility of the phosphorus varied. The ex-
periments were conducted each year from 1952 to 1955 and the different
sources of phosphorus used are presented in table 3.1. These experi-
ments are described in detail elsewhere (10). Briefly, rates of 10 and






ECONOMICS OF SOLUBILITY


Table 3.1. Sources and Water Solubilities of Phosphates Used in the
Hill Fertilization Experiments From 1952 to 1955


Fertilizer
Source of Phosphorus Grade of Percent Water-Soluble P205 in
P205 Source 1952 1953 1954 1955

Nitric phosphate (COZ)a 12-12-12 2
Aluminum nitric phosphate 15-15-15 4
Aluminum nitric phosphate 11-14-16 5
Nitric phosphate (IV)b 12-12-12 10
Nitric phosphate (I)b 17-22-0 14 14 14
Nitric phosphate (III) b 12-12-12 16
Aluminum nitric phosphate 15-15-15 28
Aluminum nitric phosphate 13-16-15 33
Commercial type 10-10-10 34
Nitric phosphate (II)b 11-14-0 36
Nitric phosphate (I)b 12-33-0 43 43 43
Concentrated superphosphate 0-49-0 90
Concentrated superphosphate 0-46-0 92 93
Ammo-phosphatec 11-48-0 100d
Diammonium phosphate 18-18-18 100
Diammonium phosphate 20-54-0 100

aA commercial trial process.
bTVA process designation.
CA commercial material.
d Estimated.

20 or 15 and 30 pounds of P20s per acre with uniform levels of nitrogen
and potassium were applied in the hill for corn at or shortly after
planting. Uniformly high levels of nitrogen and potassium were also
applied where needed to insure good yields.
Yield estimates were made and population counts at maturity were
recorded. The experiments were analyzed by the method of covariance
(6) and mean yields adjusted to uniform plant density within each ex-
periment. The mean treatment yields from all experiments showing a
significant response to phosphorus were considered and used in this
study.
The data from each year were pooled together because all experi-
ments had the same fertilizer rates and sources, and were comparable
in the number of replications. The data for each year were fitted with
multiple regression equations of the general forms:


(3.1)

and

(3.2)

where


Y = bo + biP + b2P2 + b3S + b4S2 + b5PS


Y = be + biP + b2P2 + b3S + b4S2


Y is the estimated yield, be the intercept, b, through b5 the regression






J. T. PESEK AND J. R. WEBB


coefficients, P the rate of available P205 per acre applied, and S the
percent water solubility of the phosphorus in the fertilizer.
The equations were selected because they represent the simplest
types which would express curvilinear effects in both variables and, in
case of equation 3.1, the interaction effects as well. It is well known
that response to fertilizer rates usually follows the law of diminishing
returns, and it was assumed that response to water solubility would do
likewise because an increase in water solubility is basically an in-
crease in rate of water-soluble PzO, applied at a fixed rate of available
P205. A rough plot of the data also showed that a curvilinear relation-
ship between yield response and water solubility was likely.


RESULTS AND DISCUSSION

The equations which were fitted to the pooled data are presented by
years in table 3.2. An examination of these equations indicates that the
equations for 1952 differ from the rest in that the second derivative of
Y with respect to P is positive. This means that for that year there
was an increasing return rather than a diminishing return from ferti-
lizer use within the range of the experimental treatments. The reason
for this is of agronomic interest and will not be considered in this
chapter. Equations for the last three years all showed a diminishing
return to scale with respect to both rates and water solubility of phos-
phorus.
Table 3.3 presents the multiple correlation coefficients, t values
and probabilities associated with the eight equations in table 3.2. The

Table 3.2. Equations Expressing the Estimated Yield, Y, As a Function of Rate of
P205 in the Hill, P, and the Percent Water Solubility, S


Form of
Year Equation Algebraic Expression

1952 (3.1) Y = 85.3 .0336 P + .00701P2 + .135S .000909S2 + .000418PS
(3.2) Y = 85.3 .0384 P + .00756P2 + .143S .000908S2
1953 (3.1) Y = 52.6 + .373 P .077812 + .122S .00105S2 + .00193PS
(3.2) Y = 52.6 + .285 P .00427P2 + .165S .00105S2
1954 (3.1) Y = 66.9 + .251 P .00127P2 + .228S .00137S2 + .000112PS
(3.2) Y = 66.8 + .244 P .000983P2 + .231S .00137S2
1955 (3.1) Y = 57.6 + .959 P .0278P2 + .141S .000630Sa + .00136PS
(3.2) Y = 57.6 + .877 P .0228P2 + .161S .00063058
1952 Aa (3.1) Y = 77.6 + 1.12 P .0264P2 .333S + .0017882 + .00803PS
(3.2) Y = 77.6 + .658 P .00807P2 .153S + .0017882
1952 Bb (3.1) Y = 100.7 .198 P + .0145P2 + .0968S .0000284S2 .00307PS
(3.2) Y =100.7 .0219 P + .00747P2 + .0277S .0000280S2

aExperiments with decreasing return to scale with respect to rates.
bExperiments with increasing return to scale with respect to rates.






ECONOMICS OF SOLUBILITY


Table 3.3. Multiple Correlation Coefficients and t Values for
Regression Equations Presented in Table 3.2


Year and t Values for the Coefficients Number of
Equation R bi b2 b3 b4 b5 Experiments

1952 (3.1) .336 0.04 0.27 0.42 0.37 0.06 6
1952 (3.2) .334 0.04 0.25 0.45 0.36 6
1953 (3.1) .883** 2.77** 2.01a 2.54* 2.78** 1.56b 4
1953 (3.2) .873** 2.28* 1.33b 4.14** 2.73** 4
1954 (3.1) .894** 1.05c 0.18 3.03** 2.28* 0.07 3
1954 (3.2) .894** 1.17c 0.18 3.63** 2.32* 3
1955 (3.1) .941"* 3.46** 2.42* 2.40* 1.35b 0.79d 2
1955 (3.2) .940** 3.44** 2.39* 3.08** 1.35b 2
1952 (3.1)A .406 1.05c 0.86d 0.87d 0.61 0.91d 4
1952 (3.2)A .373 0.70 0.35 0.47 0.61 4
1952 (3.1)B .273 0.11 0.27 0.14 0.01 0.20 2
1952 (3.2)B .267 0.01 0.19 0.05 0.01 2

Probabilities: ** =.01; = .05; a= .1 to .05; b = .2 to .; c = .3 to .2; d=.5 to .4.

information shows that the type of equation used gives a very poor fit
for the data in 1952, but that the equations for the other years represent
fits which would be considered good for this type of work. In all of the
last three years the coefficient of determination is at least as high as
0.76 and indicates that the selected regressions accounted for a large
part of the differences among treatments which were observed. For
1952, the coefficient of determination was only 0.11 which is very low
and unsatisfactory. In order to ascertain the reason for such poor fits,
the data for 1952 were reexamined. This revealed that four experi-
ments indicated a decreasing return and two an increasing return from
increasing rates of fertilizer applied. The latter experiments were the
greater responders, and their effect offset the smaller response and
decreasing return to scale of the other four experiments. This is why
the original equations for 1952 in table 3.2 indicate an increasing return
to scale. In an effort to overcome this, regressions were computed
separately for the two groups of experiments with different response
characteristics and these equations also appear in table 3.2 with the
pertinent R and t values in table 3.3. An examination of the results
indicates that little was gained and that those regressions showing de-
creasing returns to scale for rates of P205 show increasing returns to
scale for water solubility and vice versa.
It is evident that the simple second order regressions with two inde-
pendent variables are inadequate and that possibly a cubic or even
higher order equation would be necessary. Since the exact fitting of the
data was originally outside of the scope of this study and the data from
the other years agree very closely, it was decided to develop this chap-
ter without the data for 1952. It is felt that the general conclusions will







J. T. PESEK AND J. R. WEBB


not be altered, however, a more thorough agronomic study of these data
is needed.
In view of the difficulty with the data of 1952, some question might
arise with regard to the fit obtained for the other years. The R and t
values in table 3.3 give some estimate of the precision with which the
regressions express the relationships observed, and the fact that the
equations selected are in agreement with the generally accepted con-
cept of response curves and surfaces provides further confidence in the
regressions in table 3.2. A further test would be to compare certain
predictions obtained by these equations with the equation of Spillman
(7).3 One of the comparisons is the maximum predicted response and
these comparisons are made in table 3.4. Spillman values were calcu-
lated using the response to the two rates of P2 O for each source of
phosphorus independently. Hence the standard error of these values
may be assumed to be considerably greater than that of the values ob-
tained from the multiple regression equation 3.1.
There is remarkably good agreement between the predicted yields
by the two equations especially in 1953 and 1955. Agreement is also
good for the materials of high water solubility in 1954, but agreement
is somewhat poorer with less soluble materials. The reason for this is
that while, with only one exception, maximum estimated yields in 1953
and 1955 occurred within the experimental rates of application, the
maximum predicted yields in 1954 were estimated to occur far beyond
the highest rate of 30 pounds of P205 per acre applied. It is not sur-
prising, then, that agreement was not as good in 1954. The explanation
of why this occurred is an agronomic problem, and for purposes of this
study it will be assumed that this behavior is real and does occur from
time to time. On the additional basis of good agreement with certain
parameters of a generally accepted equation (Spillman or Mitscherlich)
it is again concluded that the equations which were selected correctly
reflect the relationships which existed.
Once the relationship of yield to the water solubility and rate of
phosphorus has been established, it is possible to answer several ques-
tions about the economy of using these different fertilizers. It would be
interesting to know what the optimum rate of hill fertilizer would be
under the experimental conditions.
To calculate the optimum rate of P Os it will be assumed that either:
(a) the rate of nitrogen and potassium is a constant, as it was in these
experiments, and therefore represented a fixed cost similar to cost of
application or cultivation, or (b) no nitrogen or potassium was applied.
In the latter case the "fixed cost" of nitrogen and potassium would be
zero. Either assumption will lead to the same solution and will give the
number of pounds of P205 necessary to maximize profit (or minimize
loss in case fixed costs, i.e., cost of needed nitrogen and potassium,
and application costs, exceed profit from use of phosphorus). It is

3The Spillman and Mitscherlich equations trace the same curves when plotted; however,
since the Spillman form has some advantages in certain calculations, this form was used.











Table 3.4. The Maximum Predicted Yield Increases in Bushels Per Acre and Rate
of P205 at Maximum As Computed From Equation 3.1 for 1953, 1954,
and 1955, and the Maximum Predicted Yield by the Spillman Equation 3.7


Percent 1953 1954 1955
Water Max. Yield Incr. Lbs. P2Os for Max. Yield Incr. Lbs. P205 for Max. Yield Incr. Lbs. P20s for
Solubility Eq. 3.1 Spillman Max. Yielda Eq. 3.1 Spillman Max. Yielda Eq. 3.1 Spillman Max. Yielda

100b 19.5 19.5 103.5 18.3 19.6 19.3
100b 18.3 20.0 19.2
93 22.8 19.3 103.2 18.1 17.6 18.0
92 12.0 11.0 35.4
43 10.0 10.2 29.3 20.2 12.1 101.0
34 13.2 10.9 17.9
33 13.1 13.6 17.9
28 8.4 8.0 27.4
16 11.2 11.2 17.6
14 6.6 8.0 25.7 15.6 12.8 99.7
10 9.4 11.7 17.4
5 5.3 5.5 24.6
4 8.6 8.3 17.3
2 12.9 4.7 99.2

aCalculated by equation 3.1.
bSources were diammonium- and monoammonium-phosphate, respectively.






J. T. PESEK AND J. R. WEBB


further assumed that the response observed in the data is a true re-
sponse to phosphorus and does not represent an interaction effect with
other nutrients in the fertilizer. Agronomically, this may not be the
case because phosphorus often interacts with nitrogen. The data used
cannot be made to make the distinction, so only a phosphorus effect
must be assumed. The optimum rate of P Os is given by equating the
P2Os:corn price ratio to the partial derivative of yield with respect to
the rate of P20s. When the partial derivatives dY/dP, of equations 3.1
and 3.2 are taken the following equations result:

(3.3) dY/dP = bl + 2b2P + bsS
and
(3.4) dY/dP = b, + 2b2P,

respectively.
In equation 3.4 it is apparent that the solution will lead to a value
which is independent of the water solubility. That is, the optimum rate
of P20O and corn will be the same whether the water solubility is 0 or
100 percent. On the other hand, the solution involving equation 3.3 in-
volves water solubility of phosphorus and, therefore, the optimum rate
will vary with the solubility. If the sign of the coefficient of S in this
equation is positive, i.e., the sign of the coefficient of the PS term in
equation 3.1 is positive, the optimum rate of P205 will be higher for the
more soluble sources of phosphorus. When the sign is negative the re-
verse will be true.
In table 3.5 are presented selected solutions for optimum rates of
P205 at specified P20s:corn price ratios. The general relationship indi-
cates that the optimum rates of P2Q, decrease as the percent water
solubility decreases and this results from the positive sign of the coef-
ficient of PS in the equations listed in table 3.2. The larger the abso-
lute value of the coefficient of this term, the greater the effect water
solubility has on the optimum rate, hence the small relative effect from
59.6 pounds per acre to 64.0 pounds in 1954 and the greater effect rang-
ing from 17.5 to 29.9 pounds in 1953. The expected yield increase is
also greater with higher water solubility and the profit per acre also
greater. Take for example the 0 and 100 percent water solubility in
1953. With the price of P2Os at 10 cents per pound and corn at $1.00
per bushel (P,/Pc = .10) the profit is $11.60 2.99 = $8.61 at 100 per-
cent water solubility but only $4.20 1.75 = $2.45 at 0 water solubility.
Other comparisons are not as extreme but important to remember in
making decisions regarding fertilizer use.
In passing, it should be pointed out that as the relative price of corn
increases (i.e., the Pp/Pc decreases) it is profitable to apply more
P205 and this results in increased yields. Profit is also increased. It
was shown above that the profit at 100 percent water solubility in 1953
was $8.61 per acre with P205 at 10 cents per pound and corn at $1.00
per bushel. With the price of P20s decreasing to 5 cents per pound and















Table 3.5. Optimum Rates of P20s and Estimated Increases in Yield of Corn for
Specified Price Ratiosa of P2 O to Corn (Pp/Pc) for Phosphorus
Materials of Different Water Solubility


Percent Equation 1953, 3.1 Equation 1954, 3.1
Water Pp/Pc = .10 Pp/Pc = .05 Pp/Pc = .10 Pp/Pc = .05
Solubility Lbs. P205 Incr. Lbs. P20s Incr. Lbs. P2Os Incr. Lbs. P205 Incr.

S 100 29.9 11.6 33.2 11.9 64.0 20.7 83.7 22.2
80 27.5 11.5 30.7 11.9 63.1 20.8 82.8 22.3
60 25.0 10.9 28.2 11.1 62.2 19.9 82.0 21.4
40 22.5 9.4 25.7 9.6 61.3 17.8 81.1 19.3
20 20.0 7.1 23.2 7.4 60.5 14.7 80.2 16.2
0 17.5 4.2 20.8 4.4 59.6 10.4 79.3 11.9

aThe price ratio is taken as the price per pound of P2Os to the price of a bushel of corn.


Equation 1955, 3.1
Pp/Pc = .10 Pp/Pc = .05
Lbs. P205 Incr. Lbs. P2O, Incr.

17.8 18.5 18.7 18.6
17.4 17.4 18.3 17.5
16.9 15.7 17.8 15.9
16.4 13.7 17.3 13.8
15.9 11.2 16.8 11.3
15.4 8.2 16.3 8.3






J. T. PESEK AND J. R. WEBB


corn remaining the same (Pp/Pc = .05), the profit becomes $11.90
- $1.66 = $10.24 per acre.
If calculations are based on equation 3.2 form without a PS term, the
optimum rate of P20, will be the same for any Pp/Pc ratio regardless
of the water solubility. The optimum rates of P2 0 for certain Pp/Pc
ratios are presented in table 3.6 together with the expected yield re-
sponses for materials with different levels of water solubility. As was
the case in table 3.5 above the higher the water solubility, the higher
the expected response and profit and the lower the Pp/Pc ratio, the
higher the optimum rate of P2 05 and the higher the profit.
In general the optimum rates are within the range of optimum rates
calculated by the form of equation 3.1 with the possible exception of 1954
at low Pp/Pc ratios where estimates are somewhat higher. Predicted
responses also agree well with the exception of estimates at high water
solubility in 1955. It should be pointed out that perfect agreement can-
not be expected because the two forms of the equations are somewhat
different. There seems to be some basis for a logical choice of one
form of equation over the other, however, and the choice would be for
equation 3.1. The reason is that an interaction between water solubility
and rate should exist because as water solubility decreases, the availa-
ble phosphorus for plant growth does not decrease proportionately. If
the availability of water-insoluble phosphorus is expressed in terms of
the availability of the water-soluble part it becomes apparent that at a
given rate, more and more of the plant available phosphorus will come
from the water-insoluble part as water solubility decreases. Hence,
while a given rate of 100 percent water-soluble phosphorus provides,
for example, 100 units of available phosphorus, the same rate of 50

Table 3.6. The Optimum Rates of P20s at Selected Pp/Pc Ratios.and the Expected
Increases in Yield at Certain Levels of Water Solubility of the Phosphorus.
Calculations Are Based on Equations 1953, 3.2; 1954, 3.2; and 1955, 3.2


Equations
1953, 3.2 1954, 3.2 1955, 3.2
Pp/Pc Pp/Pc PP/Pc
.10 .05 .10 .05 .10 .05

Optimum rate
of PzOs 21.7 27.5 73.1 98.6 17.0 18.1

Percent water
solubility Estimated Increase in Bushels per Acre
100 10.2 10.6 21.9 23.8 24.4 24.5
80 10.6 11.1 22.2 24.2 21.2 21.3
60 10.3 10.7 21.5 23.4 18.0 18.1
40 9.1 9.5 19.6 21.5 14.8 14.9
20 7.1 7.5 16.6 18.5 11.5 11.6
0 4.2 4.6 12.6 14.5 8.3 8.4







ECONOMICS OF SOLUBILITY


Table 3.7. Percent of Water-Soluble POs at Which Maximum Yields
Are Reached in 1953, 1954, and 1955 As Estimated by
Two Forms of the Regressions Used


Rate of POs Equation 3.1 for Equation 3.2 for
in Lbs. per Acre 1953 1954 1955 1953a 1954a 1955a

10 67 83 123 78 84 128
20 76 84 133 78 84 128
30 85 85 144 78 84 128

aThe absence of P in the first derivative makes the water solubility percent for maxi-
mum yield independent of the rate of P20s.
percent water-soluble phosphorus will supply more than 50 units, and
that of 0 percent water solubility will provide some available phos-
phorus as well. This is apparent from tables 3.5 and 3.6 which predict
reasonable increases in yield even with materials with no water solu-
bility. It is felt that these figures are not artifacts of extrapolation be-
cause table 3.1 indicates that in each of the three years analyzed, ma-
terials close to 0 percent water solubility were included in the
experiments. It is realized that the statistical data present in table 3.3
do not bear out this point of view as strongly as would be desired in all
cases. But it must be remembered that the interaction effect is
measured with more difficulty than the other effects and that these ex-
periments were not designed specifically for evaluation of the inter-
action nor even to measure it with a relatively high level of efficiency.
One way to estimate the level of water solubility which should be in-
corporated into fertilizers used as hill fertilizer for corn is to de-
termine the percent water solubility at which the maximum yield in-
crease for a given rate is obtained. This is done by equating the first
partial derivative of yield with respect to water solubility (dY/dS) to
zero and solving for the maximum. The resulting equations based on
equations 3.1 and 3.2 are

(3.5) dY/dS = b, + 2bS + bP
and
(3.6) dY/dS = b, + 2b4S

respectively. The results are presented in table 3.7 and indicate that
high water solubility is definitely an advantage. As a matter of fact 100
percent water solubility is not high enough according to equations 3.1,
1955 and 3.2, 1955. In this year as well as in 1954, materials of 100
percent water solubility were included in the experiments and, there-
fore, there is a high degree of confidence in the prediction that at least
100 percent water-soluble phosphorus may be needed under certain con-
ditions for maximum yields when it is used in a manner similar to that
in the experiments. The highest level of water solubility in 1953 was






J. T. PESEK AND J. R. WEBB


92 percent and this may have been partly responsible for the lower
estimated level of water solubility needed to attain maximum yields at
a fixed rate of phosphorus. One interesting result of choosing an equa-
tion with an interaction (PS) term is the prediction that as lower rates
of P2 Os are applied, lower water solubility should also be used. This is
most pronounced in 1953, and it so happens that the coefficient of the
interaction term in that year had the highest level of probability ob-
served. An explanation of this relationship is reserved for an agro-
nomic study.
It is concluded above that at the same price for water-insoluble (but
citrate-soluble) and water-soluble P205 it is advantageous to have up to
100 percent water solubility when using the fertilizer in the hill for
corn. However, Hignett (3) has shown that it costs more to produce
mixed fertilizers of the same grade with higher degrees of water solu-
bility. The problem now becomes somewhat different since water solu-
bility has a cost and the higher the water solubility, the greater will be
the cost per unit of P20s. Consequently, the ratio Pp/Pc will vary de-
pending upon the water solubility of the phosphorus in the fertilizer
which is used and becomes necessary to obtain the relationship between
the price and water solubility.
To relate price to water solubility it is first necessary to estimate
cost of producing a particular material. Hignett (3) estimated cost of
producing 3-12-12 at $40.55 per ton with 23 percent water solubility and
$41.30 per ton with 65 percent water solubility. The cost of producing
5-20-20 is $62.74 at 50 percent water solubility and $64.50 per ton at
75 percent water solubility. Allowing an arbitrary 10 percent profit on
each to manufacturer and to dealer the prices for 3-12-12 to the farmer
would be $49.07 and $49.97 per ton respectively for 23 and 65 percent
water-soluble phosphorus material. Likewise the price of 5-20-20
would be $75.91 and $78.05 per ton for 50 and 75 percent soluble ma-
terial.
The cost, C, of the P205 with the associated nitrogen and potassium4
may be expressed in terms of water solubility by a simple linear
equation such as

(3.7) C = n + ms

where n and m are coefficients determined by the prices used. By
assuming that the function is continuous between the 23 and 65 percent
points the equation for the 3-12-12 is obtained by substituting the cost
per pound of POs (with the nitrogen and potassium) and the percent


4The price of fertilizer is used in this ratio instead of the price of phosphorus. This is
necessary because each unit of P20s is associated with .25 unit of nitrogen and one unit of
K20 which cannot be separated. When more phosphorus is applied more of the others are
applied as well. For the purpose studied, this ratio of elements is a good one on many Iowa
soils. This does not preclude the possibility that lower cost ratios may be found and that
different ratios might offset the level of water solubility desired or vice versa. This is an-
other study and cannot be made with the data on hand.





ECONOMICS OF SOLUBILITY


water solubility into equation 3.7 and solving simultaneously for n
and m. This leads to the cost of water solubility of

(3.8) C = .2025 + .0000881S

for the 3-12-12, and

(3.9) C = .1792 + .000212S

for the 5-20-20.
To find the optimum level of water solubility, it is necessary to
equate the first partial derivative of yield with respect to percent water
solubility (dY/dS) for any response function to the first derivative of the
cost with respect to solubility (dC/dS) and solve. Taking the first de-
rivative of equation 1955, 3.2 and equating it to the first derivative of
equation 3.8, equation 3.10 is derived.

(3.10) .161 .00126S = .0000881

Solving for S a figure of 121 percent solubility is secured, or for prac-
tical purposes 100 percent. Using equation 1953, 3.2 a figure of 78 per-
cent water solubility is secured, which is the same as the tabular value
for maximum solubility desired in table 3.7. This serves to emphasize
the relatively insignificant cost of increasing the water solubility on the
basis of the available information.
The solution is slightly different when the equation has an inter-
action term such as equation 1955, 3.1. Equating dY/dS of this equation
to dC/dS of equation 3.8, equation 3.11 is derived.

(3.11) .141 .00126S + .00136P = .000081

Solving for S in equation 3.12,

(3.12) S = 111 + 1.09 P

the rate of 30 pounds of P20O is obtained, the optimum solubility is 144
percent, or again at least 100 percent. Practically, dC/dS is vanishingly
small and does not affect the result. Even for the 5-20-20 dC/dS is only
.000212 and will not alter the results at the three significant figures
justified by the data. These results indicate that it would be economi-
cal for users to pay the difference in cost necessary to produce phos-
phorus fertilizers of high water solubility as estimated by Hignett (3).


ECONOMIC INTERPRETATIONS

It has been shown that it is possible to apply economic principles to
satisfactory data on the effect of water solubility of phosphorus on corn






J. T. PESEK AND J. R. WEBB


yields. In this study the multiple quadratic equation with two independ-
ent variables was fitted to summarized data for three separate years.
One form of the equation also contained a cross product term allowing
for the interaction of water solubility and rate of application.
The economically optimum rates of P205 were calculated for various
P205:corn price ratios and the expected yields at the optimum fertilizer
rate were estimated. The lower the Pp/Pc ratio the greater were the
optimum rates, expected responses, and estimated profits.
Water solubility of phosphorus is important in not only determining
the optimum rate of P20s but in affecting expected yields and profits.
By using materials of low water solubility, it is possible to lose by
(a) not getting the best response from the P205 used, or (b) by utilizing
less per acre than would be optimum at higher water solubility.
The small increase in cost of producing fertilizers with higher
water solubility is offset by the higher returns when used as hill ferti-
lizers for corn. It is possible that extra cost of high water solubility
could affect the optimum water solubility with higher increases in cost
than those used in this study.


REFERENCES CITED

1. Association of Official Agricultural Chemists, 1955. Methods of Analysis,
8th edition.
2. ARCHER, J. R., and THOMAS, R. P., 1956. Water-soluble phosphorus in
fertilizer. Agricultural and Food Chemistry 4:608-13.
3. HIGNETT, T. P., 1956. Technical and economic factors involved in produc-
tion of fertilizers of high water-soluble P2Os content by conventional processes.
Commercial Fertilizer 92: No. 5., 23-26, and 67.
4. ROGERS, H. T., 1951. Crop response to nitrophosphate fertilizers. Agron-
omy Journal 43:468-76.
5. SEATZ, L. F., TISDALE, S. L., and WINTERS, ERIC, 1954. Crop response
to fused tricalcium phosphate. Agronomy Journal 46:574-80.
6. SNEDECOR, G. W., 1946. Statistical Methods, Iowa State College Press.
7. SPILLMAN, W. J., 1933. Use of the exponential yield curve in fertilizer ex-
periments. USDA, Tech. Bul. 348.
8. THORNE, D. W., JOHNSON, P. E., and SEATZ, L. F., 1955. Crop response
to phosphorus in nitric phosphates. Agricultural and Food Chemistry 3:136-40.
9. TISDALE, S. L., and WINTERS, ERIC., 1953. Crop response to calcium meta-
phosphate on alkaline soils. Agronomy Journal 45:228-34.
10. WEBB, J. R., 1955. Significance of water solubility in phosphate fertilizers.
Ag. Chem. 10:(3) 44-46.




T. P. HIGNETT
Tennessee Valley Authority
Chapter 4


Technical and Economic Factors Involved in

Production of Fertilizers of High Water-Soluble

P 0, Content by Conventional Processes


HE effect of the water solubility of phosphorus in fertilizers has

been a subject of many agronomic experiments. These experi-
ments have shown that under certain conditions the crop yield was
increased by increasing the solubility of phosphorus in the fertilizer.
Under other conditions, crop yields were not affected by the water sol-
ubility of the phosphorus in the fertilizer.
It seems appropriate to examine the relative costs of producing
fertilizers of various degrees of water solubility and to compare these
costs with their relative value for crop production. In Chapter 3, Dr.
Pesek presents a study of the relationship between the phosphorus sol-
ubility and the value of fertilizers for certain specific uses. A com-
parison is shown of the cost of producing certain grades of fertilizer by
formulations that would provide different levels of water solubility
ranging from about 20 to 80 percent. The cost comparisons will be re-
stricted to fertilizers produced in a typical manufacturing plant from
conventional raw materials. The formulations used will be those that
have been shown by experience to be suitable for production of ferti-
lizers of satisfactory physical properties.
The term "water-soluble P205" as used in this chapter refers to the
amount of P205 dissolved in an A.O.A.C. (1) analytical procedure. In
this procedure a 1-gram sample is placed on a filter paper and washed
with successive small portions of water until 250 milliliters of filtrate
is collected. Vacuum filtration is used, if necessary, to complete the
washing in one hour. The term "water solubility" of the phosphorus
content of fertilizers refers to the percentage of the available P205
content that is water soluble, as determined by A.O.A.C. procedures.
The A.O.A.C. water-washing procedure originally was intended to
remove the readily soluble phosphorus compounds from superphosphate
in preparation for extraction with neutral ammonium citrate solution.
No determination of the amount of phosphorus dissolved by the water-
washing procedure is required in the course of determining available
P2O, and such determinations are seldom made in commercial prac-
tice. However, the method seems fairly satisfactory for separating the
readily soluble compounds, ammonium phosphates and monocalcium
phosphate, from the relatively insoluble phosphorus compounds in most
conventional fertilizers. The method should be re-examined if it is to be
used for evaluation of the quality of commercial fertilizers.





T. P. HIGNETT


At present, no guarantee of the water-soluble P205 content of ferti-
lizers is required, and usually none is made. Most manufacturers do
not determine the water-soluble P205 content of their products. In view
of the importance of water solubility for some fertilization practices, it
appears that some method of recognizing and reporting water solubility
is needed.


8I
_J
- 80




so

0






S2 4 6 8
DEGREE OF AMMONIATION,
S0 /


L" 0


Most commercial ferti-
-lizers derive their phosphor-
us content from ordinary or
triple superphosphate or
-mixtures of these materials.
Ammoniation of the super-
phosphates is an almost uni-
-versal step in producing
grades containing both nitro-
gen and phosphorus. Ammo-
niation is an economical
means of supplying nitrogen,
and it is a necessary step in
most granulation processes.
In many cases it would be
difficult to produce high-
analysis grades of satisfactory
10 physical properties from con-
ventional raw materials with-


z 5 out ammoniation.
Ammoniation of super-
Fig. 4.1 Effect of degree of ammoniation on phosphates results in a series
water solubility of P20s in ordinary superphos- of chemical reactions by
phate. which monocalcium phosphate
is converted to ammonium
phosphates which are water-soluble and dicalcium phosphate and other
more basic calcium phosphates which are water-insoluble. Figure 4.1
shows the effect of the degree of ammoniation on the water solubility of
P2Os in ordinary superphosphate. These data were obtained in a TVA
pilot-plant study of ammoniation of superphosphates as a step in the
production of mixed fertilizers. The maximum practical degree of
ammoniation in commercial processes is between 6 and 7 pounds of free
ammonia per unit of Pz20 in ordinary superphosphate. This degree of
ammoniation reduces the water solubility of the P20s from about 20 to
25 percent. Since ammonia or ammoniating solutions are the cheapest
forms of nitrogen available to fertilizer manufacturers, most manu-
facturers try to achieve a high degree of ammoniation when producing
high-nitrogen grades.
Figure 4.2 shows the effect of the degree of ammoniation on the
water solubility of P20O in triple superphosphate. The minimum water
solubility obtained was about 50 percent at 2.5 to 3.8 pounds of free
ammonia per unit of P20s. Higher degrees of ammoniation tended to






FACTORS IN PRODUCTION OF P2Os FERTILIZERS


increase the water solubility because some of the dicalcium phosphate
reacted with ammonia to produce tricalcium phosphate or hydroxyapatite
and diammonium phosphate.


0 1 2 3 4 5 6
DEGREE OF AMMONIATION, LB. FREE NH3/UNIT AVAIL. P205


Fig. 4.2 Effect of degree of amhmoniation on water
solubility of P205 in concentrated superphosphate.

The data of figure 4.2 are for ammoniation of straight triple super-
phosphate with anhydrous ammonia. Several tests were made in which
a 10-20-20 fertilizer was made by ammoniation of mixtures of triple
superphosphate, potassium chloride, and sulfuric acid with ammonia -
ammonium nitrate solutions. The degree of ammoniation varied from
3.5 to 4.3, and the water solubilities varied between 60 and 70 percent;
these solubilities are somewhat higher than the curve in figure 4.2.
The reason for this difference is not known.
The water solubility of P20s in mixed fertilizers may be decreased
by inclusion of basic materials other than ammonia. Limestone, dol-
omite, and calcium cyanamide are examples of basic materials that
may be added to mixed fertilizers which may decrease the water sol-
ubility. Fertilizers in which the water solubility of the P2Os content is
less than 20 percent may be made by heavy ammoniation of super-
phosphate plus the addition of limestone or other basic materials.
A survey of the water solubility of phosphorus in mixed fertilizers
in 1949-1950 was reported by K. G. Clark and W. M. Hoffman (2). The
water solubility of mixed fertilizers varied from 3 to 100 percent and
averaged about 50 percent.






T. P. HIGNETT


Table 4.1. Formulations and Costs for 3-12-12


23% of PO2 65% of P205
in a Water- in a Water-
Price Soluble Form Soluble Form
$ per Lb. per $ per Lb. per $ per
Raw Material Grade Ton Ton Ton Ton Ton

Ordinary superphosphate 20% P205 20.00 1224 12.24 1224 12.24
Ammonia 82% N 90.00 75 3.38
N solution X 40.8% N 57.00 150 4.28
Potassium chloride 60% K20 34.00 408 6.94 408 6.94
Filler 4.00 293 0.59 218 0.44
2000 23.15 2000 23.90
Operating cost and
overhead 7.70 7.70
Bags 3.00 3.00
33.85 34.60
Sales cost (10 cents
per unit) 2.70 2.70
36.55 37.30
Freight (100 mi.) 4.00 4.00
Delivered cost 40.55 41.30
Delivered cost per unit (1.50) (1.53)
Price to dealer 46.00 46.00
Profit 5.45 4.70

aBefore corporation income taxes.




Formulations and Costs for 1-4-4 Fertilizers

Formulations and costs for typical mixed fertilizers were calculated
using raw material costs that were believed to be typical of a midwest-
ern location. The most common 1-4-4 ratio grades are 3-12-12 and
5-20-20. Two formulations for 3-12-12 are shown in table 4.1. One
formulation uses anhydrous ammonia for ammoniation; the other uses a
typical ammoniating solution containing 21.7 percent free ammonia, 65
percent ammonium nitrate, and 13.3 percent water. When anhydrous
ammonia is used, the degree of ammoniation is about 6.2 pounds of free
ammonia per unit of 2 OQ and the resulting water solubility of the phos-
phorus content is about 23 percent (figure 4.1). When the ammoniating
solution containing 21.7 percent free ammonia is used, the degree of
ammoniation is 2.7 and the water solubility is 60 percent. The differ-
ence in cost between these two formulations is only 75 cents per ton
which is less than 2 percent of the price to dealers. However, this cost
difference is equivalent to 14 percent of the manufacturer's profit.






FACTORS IN PRODUCTION OF P205 FERTILIZERS


Table 4.2. Formulations and Costs for 5-20-20


50%of P20s 75% of P2Os
in a Water- in a Water-
Price Soluble Form Soluble Form
$ per Lb. per $ per Lb. per $ per
Raw Material Grade Ton Ton Ton Ton Ton

Ordinary superphosphate 20% P2Os 20.00 297 2.97 192 1.92
Triple superphosphate 46% P20s 58.00 758 21.98 803 23.29
Ammonia 82% N 90.00 125 5.63
N solution Y 40.8% N 57.00 250 7.13
Sulfuric acid 660 Be 20.00 140 1.40 140 1.40
Potassium chloride 60% K2O 34.00 680 11.56 680 11.56
2000 43.54 2065 45.30
Operating cost and
overhead 7.70 7.70
Bags 3.00 3.00
54.24 56.00
Sales cost (10 cents
per unit) 4.50 4.50
58.74 60.50
Freight (100 mi.) 4.00 4.00
Delivered cost 62.74 64.50
Delivered cost per unit (1.39) (1.43)
Price to dealer 71.00 71.00
Profit a 8.26 6.50

aBefore corporation income taxes.

If limestone were used as a filler, the water solubility might be
decreased below 20 percent. The effect on cost would depend on the
relative cost of limestone and other filler materials.
Formulations and costs for 5-20-20 are shown in table 4.2. This
grade is one that is usually produced in granular form. The formula-
tions shown are known to be satisfactory for granulation by commonly
used processes. The formulation that uses anhydrous ammonia is the
cheaper and the more satisfactory for granulation. The degree of
ammoniation is 3.9, and the water solubility of the P20O content is about
50 percent, as determined experimentally (3). In the formulation that
uses an ammoniating solution containing 26 percent free ammonia, the
degree of ammoniation is about 1.0 and the water solubility is about 75
percent. Use of an ammoniating solution containing only 21.7 percent
free ammonia in this formulation would decrease the degree of ammo-
niation to about 0.5 and would increase the water solubility to about 85
percent (figure 4.2); the cost would not be affected appreciably. The
difference in cost between the two formulations shown in table 4.2 is
$1.76 per ton, or about 2.5 percent of the price to dealers. However,
this difference is equivalent to 21 percent of the manufacturer's profit.






T. P. HIGNETT


Table 4.3. Formulations and Costs for 10-10-10


23%of P205 40%of P20s
in a Water- in a Water-
Price Soluble Form Soluble Form
$ per Lb. per $ per Lb. per $ per
Raw Material Grade Ton Ton Ton Ton Ton

Ordinary superphosphate 20% POs 20.00 1020 10.20 1020 10.20
N solution X 40.8% N 57.00 500 14.25 397 11.31
Ammonium sulfate 21%N 48.00 200 4.80
Sulfuric acid 20.00 120 1.20 120 1.20
Potassium chloride 60% KaO 34.00 340 5.78 340 5.78
Filler 4.00 100 0.20 -
2080 31.63 2077 33.29
Operating cost and
overhead 7.70 7.70
Bags 3.00 3.00
42.33 43.99
Sales cost (10 cents
per unit) 3.00 3.00
45.33 46.99
Freight (100 mi.) 4.00 4.00
Delivered cost 49.33 50.99
Delivered cost per unit (1.64) (1.70)
Price to dealer 60.30 60.30
Profit a 10.97 9.31

aBefore corporation income taxes.

Comparison of tables 4.1 and 4.2 shows that the most economical
way to increase the water solubility of a 1-4-4 ratio fertilizer is to in-
crease the grade. Comparison of the more economical formulations for
3-12-12 and 5-20-20 shows that the delivered cost for 5-20-20 is less
per unit of plant food ($1.39 versus $1.50/unit) and that the water sol-
ubility is higher (50 versus 23 percent).


Formulations and Cost for 1-1-1 Ratio Fertilizers

Two important grades of 1-1-1 ratios are 10-10-10 and 12-12-12.
These grades are often produced as granular fertilizers; the formula-
tions considered are suitable for granulation.
Two formulations for 10-10-10 are shown in table 4.3. Ordinary
superphosphate is the only source of P205 in both formulations. In the
first case, all of the nitrogen is supplied from ammoniating solution;
the degree of ammoniation is about as high as is practical (6.8 percent),
and the water solubility is about 23 percent (3). In the second formula-
tion, the degree of ammoniation is decreased to 4.8 by deriving some of
the nitrogen from ammonium sulfate and thereby decreasing the amount






FACTORS IN PRODUCTION OF P2Os FERTILIZERS


Table 4.4. Formulations and Costs for 12-12-12


50% of P2Os 75% of P2Os
in a Water- in a Water-
Price Soluble Form Soluble Form
$ per Lb. per $ per Lb. per $ per
Raw Material Grade Ton Ton Ton Ton Ton

Ordinary superphosphate 20% P2zO 20.00 513 5.13 147 1.47
Triple superphosphate 46% P205 58.00 311 9.02 467 13.54
N solution X 40.8% N 57.00 500 14.25 308 8.78
Ammonium sulfate 21%N 48.00 200 4.80 567 13.61
Sulfuric acid 660 Be 20.00 150 1.50 150 1.50
Potassium chloride 60% K20 34.00 406 6.90 406 6.90
2080 41.60 2045 45.80
Operating cost and
overhead 7.70 7.70
Bags 3.00 3.00
52.30 56.50
Sales cost (10 cents
per unit) 3.60 3.60
55.90 60.10
Freight (100 mi.) 4.00 4.00
Delivered cost 59.90 64.10
Delivered cost per unit (1.66) (1.78)
Price to dealer 73.70 73.70
Profit 13.80 9.60

aBefore corporation income taxes.


of ammoniating solution. The water solubility of the P205 content is
about 40 percent (figure 4.1). The product of lower solubility costs
$1.66 per ton less. Producing the material of higher solubility would
decrease the manufacturer's profit by 15 percent.
Two formulations for 12-12-12 are shown in table 4.4. Since
12-12-12 derives a large proportion of its P2O5 from triple superphos-
phate, the water solubility is higher than in 10-10-10 even when both are
ammoniated to the maximum practical degree. In the first formulation
the degree of ammoniation is about as high as is practical; the water
solubility is about 50 percent.
In the second formulation the degree of ammoniation has been de-
creased by deriving less nitrogen from ammoniating solution and more
from ammonium sulfate. In order to make room in the formulation for
the ammonium sulfate, it is necessary to derive a higher percentage of
the PzO5 from triple superphosphate. The water solubility of this for-
mulation is 75 percent; it costs about $4.20 per ton more to produce
than the 50 percent solubility product. The manufacturer's profit would
be about 30 percent less.






36 T. P. HIGNETT

Comparison of tables 4.3 and 4.4 shows that a 12-12-12 of 50 percent
water solubility costs about the same per unit of plant food as a 10-10-10
of 23 percent solubility.


REFERENCES CITED

1. A.O.A.C., 1955. Methods of Analysis, 8th edition, p. 10.
2. CLARK, K. G., and HOFFMAN, W. M., May, 1952. Farm Chemicals, pp. 17-23.
3. HEIN, L. B., HICKS, G. C., SILVERBERG, J., and SEATZ, L. F., 1956. Gran-
ulation of high-analysis fertilizers. Jour. Agric. Food Chem. 4:318-30.





G. L. TERMAN
Tennessee Valley Authority

Chapter 5

Crop Response to Commercial Fertilizers

in Relation to Granulation and

Water Solubility of the Phosphorus



DEMAND for granular fertilizers in the United States and other
countries has grown in recent years. The chief reasons are the
physical advantages of granular fertilizers in regard to better
storage properties and ease and uniformity of distribution for crops.
Recent technological advances in granulation techniques (15) have given
a marked stimulus to the production of granular fertilizers.
In addition to the physical advantages of granular fertilizers, recent
investigations (10,30,46) indicate that application of nitrogen and phos-
phorus fertilizers together in intimate contact usually increases the
availability of the phosphorus to crops, as compared to application sep-
arately. This tends to increase the efficiency of the phosphate fertilizer
applied. Granulating the various components of NPK fertilizers into
homogeneous granules insures very intimate contact in application for
crops.
The relationships between granulation of fertilizers and water solu-
bility of the phosphorus component will be discussed in this chapter,
pointing out possible combinations which tend to increase the efficiency
of fertilizer use. This, in turn, closely affects the economic return which
the farmer can obtain from expenditures for fertilizer. Data from a sum-
mary of greenhouse and field experiments conducted cooperatively be-
tween TVA and seven state experiments (49) will be used extensively.
For convenience and brevity, the following abbreviations will be used:
SP Ordinary superphosphate, 18-20 percent P205.
CSP Concentrated superphosphate, 40-49 percent P205.
MCP Monocalcium phosphate, 56 percent P205.
DCP Dicalcium phosphate, 49 percent P205.
TCP Tricalcium phosphate, 46 percent P205.
FTP Fused tricalcium phosphate, 28 percent P205.


SOLUBILITY OF VARIOUS PHOSPHORUS FERTILIZERS

Rock phosphate, which occurs largely as insoluble apatite, is the raw
material from which more soluble phosphatic fertilizers are manufac-
tured. It is also ground finely and used as a phosphorus fertilizer with-
out further treatment. Numerous investigations have shown that crop






G. L. TERMAN


response to rock phosphate is much poorer under most soil conditions
than to more soluble phosphate fertilizers. Crop response to rock phos-
phate will not be considered any further.
Ordinary superphosphate (SP), prepared by treating rock phosphate
with sulfuric acid, contains 18 to 20 percent available P2Os. This mate-
rial was practically the only soluble phosphorus fertilizer used for
nearly 75 years after it was first made in England in 1843. The prin-
cipal phosphorus compound in superphosphate is monocalcium phosphate
(MCP) which is water soluble. The other major component of SP is
gypsum, which supplies calcium and sulfur for plant growth.
Since about 1930, concentrated superphosphate (CSP), containing
40-49 percent available P2Q and prepared by treating rock phosphate
with phosphoric acid, has been increasing in supply. Its principal com-
ponent is also MCP. Gypsum is absent in the product prepared with
electric-furnace acid and present in only very small amounts in the
product prepared with wet-process phosphoric acid. Mixtures of SP and
CSP containing 30-40 percent available P2Os are also sold commercially.
In recent years increasing amounts of ammonium phosphate ferti-
lizers, in which the phosphorus is also water soluble, have been sold.
The principal components of these fertilizers are monoammonium and
diammonium phosphates. Water-soluble sodium and potassium phos-
phates are used in very small amounts as fertilizers. Liquid phos-
phoric acid is also used as a fertilizer, especially in irrigation water
and in preparation of liquid fertilizers.
Water-insoluble phosphates which have been used commercially as
fertilizers include considerable quantities of dicalcium (DCP) and
tricalcium (TCP) phosphates. TVA manufactured a fused. phosphate for
several years, in which the phosphorus was present largely as alpha
tricalcium phosphate. Rhenanian phosphate, prepared by sintering a
mixture of rock phosphate, soda, and silica, is another water-insoluble
phosphate material used in the areas adjacent to the western phosphate
deposits. DCP is considered to be a major phosphorus component in
nitric phosphate fertilizers and in ammoniated superphosphates.
Superphosphates are used as the base for preparing a large part of
the NP and NPK fertilizers used in the United States. In preparing these
fertilizers, the SP is usually ammoniated to varying degrees with ammo-
nia, ammonium nitrate, or urea solutions, or mixtures of these. Exten-
sive use of nitrogen solutions has been made since about 1928, because
nitrogen in such solutions costs less than that added in solid forms of
nitrogen. As a result of ammoniation, the water-soluble MCP is con-
verted into varying amounts of water-insoluble DCP and TCP, depend-
ing on the degree of ammoniation and perhaps on the nature of other
fertilizer constituents. Data of Keenen (20), White et al. (52), and others,
indicate practically complete reversion of MCP to DCP an addition of
about 2 percent N to SP and 6 percent N to CSP from ammoniating solu-
tions. With further ammoniation of SP up to 6 percent N, TCP is pre-
cipitated in increasing amounts to about 30 percent of the phosphorus
present. Fluorapatite may also be formed at very high degrees of






CROP RESPONSE


ammoniation. Ammoniation of CSP to about 12 percent N results in
about 10 percent of the phosphorus precipitating as TCP. Ross et al.
(37) found that including ground limestone in a fertilizer to render it
physiologically neutral increased the reversion of phosphorus in SP
ammoniated above 3 percent N. From the above effects of ammoniation,
it may be concluded that crop response to ammoniated superphosphates
may be dependent in large part upon the relative contents of MCP, DCP,
and TCP. These effects, from later information, are discussed by
Hignett (16). With extreme ammoniation, the more insoluble hydroxy-
apatite may be formed.


AVAILABILITY TO CROPS OF VARIOUS CHEMICAL
FORMS OF PHOSPHORUS FERTILIZERS

Calcium Phosphates on Acid to Neutral Soils

Rogers, Pearson, and Ensminger (36) have published a comprehen-
sive review of literature concerning calcium phosphates and other phos-
phate fertilizers. They conclude that DCP is as good a source of phos-
phorus as SP on acid to neutral soils. TCP is less effective than MCP
or DCP. Liming to near neutrality or above would be expected to de-
crease effectiveness of TCP.
Gilbert and Pember (12) found DCP in pot tests to be about 95 per-
cent as available as SP. Jacob and Ross (18) reported that DCP was
slightly more effective, while MCP was less effective than SP in pot
tests conducted by five state experiment stations and USDA. Karraker
et al. (19) in pot tests from 1934-39, found the following relative yields
from various phosphate sources: SP-100; CSP-94; DCP-101; TCP-77;
and FTP-100.
Odland and Cox (26) found in a six-year test in Rhode Island that DCP
produced slightly higher yields of hay and potatoes than SP. A later re-
port (27) indicated no significant differences in potato yields between SP,
CSP, and DCP. Houghland et al. (17) reported that DCP was nearly as
effective as CSP for potatoes grown on soils ranging from pH 5.2 to 5.6
in Maine, New Jersey, and Pennsylvania.
Roberts et al. (35) found no significant differences in yields of corn,
wheat, and hay, on unlimed land for SP, CSP, DCP, and TCP, although
TCP was slightly less effective for corn and wheat. On limed land TCP
was considerably less effective for corn and wheat than the other mate-
rials. These tests were conducted at 10 locations in Kentucky over the
1934-1940 period.
Bauer et al. (1) reported MCP, DCP, and TCP to be about equally
effective for wheat in Illinois. Rich and Lutz (34) summarized results of
phosphate comparisons in Virginia through 1947. They found relative
yield values for DCP as follows, as compared to 100 for CSP: wheat-94;
corn-99; alfalfa-100; and mixed hay and pasture-104. Similar values for
TCP were: wheat-90; corn-96; and alfalfa-98.






G. L. TERMAN


Stanford and Nelson (44) reported similar yields of oats grown on pH
6.0 Webster silty clay loam fertilized with DCP and SP, although the per-
centage of plant phosphorus derived from DCP was much lower than from
SP. Similar uptake of phosphorus was found on two other soils on which
there was no response to phosphorus fertilization. Blaser and McAuliffe
(2) reported similar forage yields from different phosphorus sources on
pH 5.3 Mardin silt loam, but more of the plant phosphorus was derived
from SP than from DCP or TCP. Likewise, similar yields of cotton
fertilized with SP, DCP, and FTP also were reported by Hall, et al., (13).
Again, much more phosphorus was taken up from SP than from DCP or
FTP.
Ensminger (8) reported results from an experiment at 358 locations
in Alabama over the 1934-1938 period. Relative yield increase values
were: SP-100; CSP-92; DCP-99; and TCP-81. In other experiments,
the relative yield increases with CSP and TCP were 90 and 87 for cotton;
106 and 109 for corn, and 89 and 89 for legumes, respectively, as com-
pared to 100 with SP. Ensminger and Cope (9) found that yields of cot-
ton grown on pH 6.0 unlimed Norfolk fine sandy loam were lowest for
MCP, intermediate for DCP, and highest for TCP. These results indi-
cated a response to calcium in the phosphates, since there was no con-
sistent difference in yields on limed plots. Soils on plots fertilized with
TCP over a 16-year period contained more dilute acid soluble phosphorus
than on those fertilized with SP, MCP, or DCP.
Seatz, Tisdale, and Winters (40) summarized results of 425 field ex-
periments conducted from 1941 through 1953, comparing FTP and CSP.
FTP was usually a satisfactory source of phosphorus on acid soils for
forage crops and small grains but was less satisfactory for corn, cotton,
and vegetable crops. Effectiveness of FTP, as compared to CSP, was
slightly less on limed than on unlimed soils. The 10-mesh FTP was less
effective than that ground more finely.
Stewart (47) has summarized much of the work in Great Britain on
comparisons of various phosphate fertilizers. He concluded that DCP
and various other citric acid-soluble phosphates were similar to SP in
effectiveness for crops on acid soils. Cooke (5), however, reported that
DCP was more efficient than SP for potatoes on soils below pH 5.5, but
was inferior on less acid soils.
In summary, results cited above indicate that response to MCP in SP
and CSP is equal to or slightly better than to DCP or TCP on acid soils.
Liming to near-neutrality tends to decrease effectiveness of DCP and
TCP, especially of the latter. Early growth response is usually greater
to water-soluble than to water-insoluble phosphorus sources.


Calcium Phosphates on Alkaline Soils

Rogers, Pearson, and Ensminger (36) concluded from a review of the
literature that DCP and FTP were not satisfactory sources of phosphorus
on alkaline soils. Seatz, Tisdale, and Winters (40) also concluded that






CROP RESPONSE


FTP was not a satisfactory source of phosphorus on alkaline soils for
any crop tested. The relative yield increase in 20 tests was only 38 per-
cent for 40-mesh FTP, as compared to 100 for CSP.
Olsen et al. (28) found that absorption of phosphorus from DCP or FTP
by various crops grown on alkaline soils in Arizona, Colorado, and Idaho
was much less than from SP or phosphoric acid. Yield response to phos-
phorus was obtained in part of the various tests. Dion, et al., (7), also
reported that DCP was inferior to MCP on neutral to alkaline soils in
Canada. Speer et al. (43) similarly reported that DCP and TCP were
unsatisfactory for beans on pH 8.1 Houston black clay. Fuller (11) found
that phosphorus in FTP was the least available of any source tested on
alkaline soils in Arizona.
It may be concluded from the various reports cited above that DCP
is less efficient, and that FTP and TCP are much less efficient, than
MCP or other water-soluble sources for crops on alkaline soils.


Ammoniated Superphosphates

Parker (32) concluded from a review of the available information that
the phosphorus in ammoniated SP varied in availability to crops from 75
to 100 percent of that in SP. Williamson (53) summarized results from
185 experiments conducted in Alabama from 1931-34. The following rel-
ative yield increases were obtained: SP-100; SP ammoniated to 2 percent
N-100; and SP ammoniated to 4 percent N-85. Response to phosphorus
was reduced much more by mixing dolomite with the SP ammoniated to 4
percent than was the case with unammoniated SP.
Salter and Barnes (39) found that the effectiveness of superphosphates
ammoniated to 5 and 7 percent N decreased in pot tests with increase in
soil pH from 5.5 to 7.0. The decrease was greater at the higher ammo-
niation. SP ammoniated below 3 percent N was 72 to 100 percent as
effective as unammoniated SP over this pH range. These results agree
relatively with those obtained in tests of MCP, DCP, and TCP.
Ross et al. (38) concluded that long-season crops such as wheat and
Sudan grass (second cutting) can utilize phosphorus in highly ammoni-
ated fertilizers better than short-season crops, such as millet, sorghum,
and Sudan grass (first cutting).
Speer, et al., (43), reported that ammoniated SP was somewhat lower
in availability than SP for beans grown on calcareous Houston black clay.
The two fertilizers were equally available on pH 6.0 Susquehanna sandy
loam. Martin et al. (24) also found that no effect of ammoniation of SP
on availability of the phosphorus to lettuce grown on four acid soils. On
two calcareous soils, however, availability was reduced by ammoniation
to 4.5 percent N but not by ammoniation to 2 percent N. The unammoni-
ated SP and that ammoniated to 2 and 4.5 percent N and 95, 67, and 30
percent, respectively, of the phosphorus in a water-soluble form.
Terman et al. (48) found little effect of ammoniation of SP to 3 or 6
percent N on yield, phosphorus content, or percentage of the phosphorus






G. L. TERMAN


from the fertilizer for potatoes grown on unlimed and limed Caribou
loam. In similar experiments in North Carolina and Virginia (33), no
differences were found in yield of corn and tobacco or in the percentage
of the plants' phosphorus derived from the fertilizer. Results in Mis-
sissippi (33) indicated a tendency for lower yields of seed cotton on a
neutral soil with increasing degrees of ammoniation. Ammoniation to 6
percent N decreased the percentage of the plants' phosphorus derived
from the fertilizer. Ammoniation to 2, 3, or 4 percent N had no effect.
It may be concluded from the above research that ammoniated super-
phosphates are increasingly less efficient than the unammoniated mate-
rials on calcareous soils with increase in reversion of MCP to DCP and
TCP. On acid soils, this tendency is less, although liming to neutrality
or above often reduces efficiency of the phosphorus in ammoniated fer-
tilizers. Yields of short-season crops and early growth of long-season
crops are usually reduced by ammoniation, especially on soils in the
higher pH ranges.


Ammonium Phosphates

Monoammonium phosphates are usually produced commercially alone
as a 11-48-0 fertilizer or together with ammonium phosphate-sulfate as
16-20-0. Diammonium phosphate is produced by TVA and a few ferti-
lizer producers as a 21-53-0 material. The phosphorus in all of these
fertilizers is entirely water-soluble.
MacIntire et al. (23) found no difference in crop response on acid
soils to CSP and monoammonium or diammonium phosphates.
Olson et al. (29, 30) found higher crop response to CSP plus nitrogen
and ammonium phosphates than to most other phosphorus materials on
Nebraska soils. In these experiments placing the nitrogen and phosphorus
together increased availability of the phosphorus.
A summary of crop yields in 82 experiments as shown in table 5.1,
indicates that the phosphorus in diammonium phosphate and CSP is of
similar availability.


Phosphoric Acid

Thorne (50) found no differences in yields of potatoes, wheat, or sugar
beets fertilized with CSP and HRPO4. Fuller (11) obtained results show-
ing somewhat more of the plant phosphorus in alfalfa and cotton grown on
calcareous soils in Arizona was taken from H3PO4 than from SP. Yield
response to phosphorus was not obtained in most tests. Olsen, et al.,
(28), also found similar yields and percentages of the plant phosphorus
in alfalfa grown on calcareous soils in Colorado with SP and I PQI.
H3P04 supplied appreciably more of the plant phosphorus than CSP from
a late application for sugar beets. Hausenbuiller and Weaver (14) re-
ported that H3PO4 produced slightly higher yields of alfalfa on calcareous






CROP RESPONSE


Sagemoor fine sandy loam than CSP. Amounts of phosphorus taken up
by the crop were also higher. Converse (4), however, found that alfalfa
yielded considerably less with HPO4 than with SP or CSP. He concluded
that more leaching of phosphorus from HPO4 by irrigation water had
occurred on the calcareous, Superstition fine sand overlaying coarse
sands.

Table 5.1. Crop Response to TVA Diammonium Phosphate Fertilizers, 1950-55a


States Reporting Number Relative Response
Crop Field Test Results of Tests (CSP = 100)

Corn Ga., Iowa, Ky., Miss., Tenn. 27 99
Cotton Ala., Miss., Tenn. 6 98
Legume hay Tenn., Va., Wash. 7 94
Small grains Ala., Colo., Ga., Iowa, Ky.,
N.C., N.Y., Tenn., Va. 26 101
Vegetables Colo., Wash. 16 102
All crops All states 82 100

aData taken from annual reports to TVA of cooperative fertilizer evaluation experiments.

Less work with HsP04 has been done on acid soils. MacIntire et al.
(22) reported slightly lower contents and uptake of phosphorus by rye
grass grown in pot tests on pH 5.2 Fullerton silt loam from various di-
lutions of H3PO4 than from CSP. Similar results were obtained with red
clover grown on this soil limed to pH 7.2.
Results of research indicate in general that effectiveness of phosphor-
us in HIPO, for crop growth is similar to that in SP or CSP.


WATER SOLUBILITY AND GRANULE SIZE RELATIONSHIPS
WITH SUPERPHOSPHATES AND NPK FERTILIZERS

Effects of granulation on the efficiency of fertilizers are largely in
relation to the availability of the phosphorus component. Most nitrogen
and potassium compounds are readily water-soluble and move rapidly
into the soil from fertilizer, in either granular or powdered forms.
Mehring et al. (25), for example, found that a large part of the phosphorus
applied in granular fertilizers for cotton remained in the fertilizer zone,
while nitrogen and potassium had disappeared. Subsequent discussion will
be in regard to water solubility and granule size relationships with the
phosphorus component of fertilizers.
Lawton and Vomocil (21) found that at field moisture capacity, 50-80
percent of the water-soluble phosphorus moved out of granules of super-
phosphate in 24 hours. Twenty to 50 percent moved out in this period
from soils containing as low as 2-4 percent moisture. The movement of







G. L. TERMAN


water-soluble phosphorus out of NPK fertilizer granules into a sandy
loam soil was found by Owens et al. (31) to be essentially complete in
48 hours. The extent of movement from large granules and the concen-
tration of phosphorus in the soil around the granules were directly re-
lated to the percentage of water-soluble phosphorus in the fertilizer.
Skinner et al. (42) observed that about 50 percent of the available P205
remained in granules of 6-7.5-6 fertilizer applied for cotton.

Table 5.2. Fertilizers Used in the Granule Size and
Water Solubility Experiments (47)


Granule Available Water-Soluble
Fertilizer Grade Size-Meshes P205, % P20s, % of
and Abbreviationa per Inch of Total Available Formulationsa

7-14-14 -6+14 99 7 Mixture of
(DCP) -14+35 99 8 DCP, AS,
-35 99 5 and KCI
6-12-12 -6+14 96 27 Ammoniated
(AOSP) -14+35 96 25 OSP, AN,
-35 96 28 and KC1
10-20-20 -6+14 94 60 Ammoniated
(ACSP) -14+35 94 60 CSP, AN, AS,
-35 93 61 and KC1
11-22-22 -6+14 100 100 Mixture of
(DAP) -14+35 100 99 DAP, AS,
-35 100 100 and KCl

aDCP dicalcium phosphate; OSP 18 to 20 superphosphate; CSP concentrated
superphosphate; DAP diammonium phosphate; AN ammonium nitrate; AS am-
monium sulfate; and KC1 muriate of potash.

Results of studies of crop response to granular and pulverized ferti-
lizers have been inconclusive, as pointed out by Sherman and Hardesty
(41) and Starostka et al. (45). Most of the results indicated that for fer-
tilizers broadcast and mixed with the soil, differences in granule size
had no measurable effect on crop response, or else granules 10-mesh or
larger, or briquettes, produced the highest yields. Presumably, the large
granules or briquettes were most effective on soils of high phosphorus-
fixing capacity. In the case of localized hill or band placements of ferti-
lizers, occasional decreases in yield have been reported for granulated,
as compared to pulverized fertilizers. Terman et al. (48), for example,
found that granular superphosphate produced lower yields of potatoes
than pulverized material when both were applied in row side bands.
Starostka et al. (45) reported that 14-20 mesh granules of superphos-
phate and 28-35 and -35 mesh granules of dicalcium phosphate resulted
in best response by wheat grown in greenhouse pots. Bouldin (3) com-
pared 8-10, 12-14, 16-20, and 28-32 mesh granules of a water-soluble
phosphate for oats on six Iowa soils. He found that the phosphorus in the






CROP RESPONSE


larger granules was most available in five acid to neutral soils but that
the reverse was true for the calcareous Ida silt loam. Owens et al. (31)
found that absorption of phosphorus from fertilizer by wheat increased
markedly with increase in soluble phosphorus in 4-6 mesh granules, but
was affected very little in the case of pulverized fertilizer. Webb (51)
found that the effectiveness of fertilizers applied with or near the seed
for corn and oats increased with increase in water solubility of the phos-
phorus. This relationship was more pronounced on alkaline than acid
Iowa soils, and much less for broadcast than for localized applications.
Terman et al. (49) reported crop responses in 21-field and 2-green-
house pot experiments to NPK fertilizers having percentages of water-
soluble phosphorus of 7, 27, 60, and 100. Each fertilizer was granulated
into three mesh sizes: 6-14, 14-35, and -35. The fertilizers were pre-
pared in 1-2-2 ratio from DCP, ammoniated SP, CSP, and diammonium
phosphate, respectively. Characteristics of these fertilizers are sum-
marized in table 5.2.


Crop Response in Greenhouse Experiments

There was a marked interaction between granule size and level of
water-soluble phosphorus in the fertilizers compared in greenhouse ex-
periments (47), especially for the first crop. These relationships are
shown in figure 5.1. Yields increased markedly with decrease in granule
size of the low water-soluble 7-14-14 DCP mixture and to a lesser ex-
tent for the 27 percent water-soluble 6-12-12 ammoniated SP. A marked
reverse relationship was found for the 100 percent water-soluble 11-22-22
diammonium phosphate mixture and to a lesser extent for the 60 percent
water-soluble 10-20-20 ammoniated CSP. Very similar relationships
were found for uptake of phosphorus by the crops. This interaction of
water solubility and granule size was highly significant for 4 of the 5 soils
on which the comparisons were made. Crop response to the 35-mesh
DCP and to the 6-14 mesh diammonium phosphate fertilizers was of sim-
ilar magnitude. A lower mean response to ammoniated SP than to DCP
was obtained for the first crop, although the former has the higher water
solubility of phosphorus. Reasons for this are not evident. Lower avail-
ability of the water-insoluble phosphorus fraction of the ammoniated SP
than DCP might be a cause, although petrographic observations do not
support this explanation. It was observed that the granules of the ammo-
niated SP were much harder than those of DCP and slaked much more
slowly in water. The effects of such physical characteristics on availa-
bility of fertilizers to plants have not been adequately determined. The
presence of gypsum in the ammoniated SP may also result in reduced
solubility of DCP, as found by Starostka and Hill (46). They did not, how-
ever, find the application of gypsum with DCP to decrease the availabil-
ity of its phosphorus significantly to crop plants.
In the second crop the yield of dry matter and uptake of phosphorus
again increased with decrease in granule size of the 7 and 27 percent






G. L. TERMAN


water-soluble materials, but to a lesser extent than for the first crop.
For the 60 and 100 percent water-soluble fertilizers there was no ap-
preciable effect of granule size on second crop response or uptake of
phosphorus.

-RELATIVE YIELD


Fig. 5.1 Effect of granule size and percent water-soluble P on mean relative
yields of two greenhouse crops of Sudangrass and oats. (Mean yield of each
crop from all phosphate fertilizers in 2 Tennessee and 3 Virginia soils = 100.)

Presumably, the marked influence of granule size on phosphorus
availability in the lower water-soluble fertilizers is largely an effect on
rate of solubility. The opposite influence of granule size in the case of
the more highly water-soluble fertilizers is apparently related to greater
fixation of phosphorus into difficultly available forms when smaller gran-
ules are applied. As evidenced by first crop response, it appears that in
the range of water solubility of phosphorus between 27 and 60 percent, the
tendencies for dissolution of phosphorus in the granules and fixation by the
soil tended to balance each other in the soils used in these experiments.
At some level in this range, granule size evidently would have little effect
on availability of the phosphorus for crop growth. This level would be
expected to vary among soils differing in phosphorus-fixing capacity and
other characteristics influencing soil-phosphorus reactions. This obser-
vation may account for some of the inconclusive results with granulated
and nongranulated superphosphates, as reviewed by Sherman and Hardesty
(41), and others.






CROP RESPONSE


f RELATIVE YIELD
120
118 119


112

110 -
108


102 102

100 98
96


90 89
87
84 84


80 6-14
6-14 14-35-35 6-14 14-35 -35 6-14 14-35 -35 6-14 14-35-35
7% 27% 60% 100%
(7-14-14) (6-12-12) (10-20-20) (11-22-22)

Fig. 5.2 Effect of granule size and percent water-soluble P on mean rela-
tive yields of wheat forage in Mississippi. (Mean yield from all phosphate
fertilizers in 4 field experiments = 100.)


It would appear that by the time of growth of the second crop,- much ol
the phosphorus in all granule sizes had undergone dissolution and fixa-
tion, so that original granule size had much less effect on second crop
response.


Crop Response in Field Experiments


Wheat for Forage--Results of winter wheat forage experiments in
Mississippi (47), summarized in figure 5.2, show about the same rela-
tionships between granule size and water solubility of the phosphorus as
do the data from the first crop in the greenhouse experiments shown in
figure 5.1. The interaction between granule size and water solubility
was also significant at the 5 percent level in one of the four experiments
This agreement might be expected, since the crops in both sets of exper-
iments were harvested at a comparable stage of growth prior to heading.
The relative yield differences among granule sizes were less in the field
than in the greenhouse, especially with 6-12-12 ammoniated SP. One fac
tor may be that more soil phosphorus was utilized in the field than in the
greenhouse, so that the applied fertilizer had relatively less effect. In






G. L. TERMAN


the field, all granule sizes of diammonium phosphate (11-22-22) resulted
in greater yields than the other fertilizers of lower water solubility.
These results obtained in the field are essentially in agreement with
those reported on wheat grown in the greenhouse by Starostka et al. (43).
Wheat for Grain--There was much less difference in yield of wheat
grain for the various fertilizers than for wheat forage shown in figure
5.2. No differences in yield of grain were statistically significant in a
winter wheat experiment in Georgia on Fannin loam and in the North
Carolina and Tennessee experiments, in which early growth yields were
not taken. In a Georgia experiment on Altavista loam, the 14-35 mesh
granules yielded significantly more wheat (5 percent level) than the
other granule sizes. Apparently, with the longer growth period necessary
for harvest of grain from winter wheat, a high content of water-soluble
phosphorus in the fertilizer is of much less importance than for early
growth. Similar observations were made by DeMent and Seatz (6) and
Olson et al. (29).
In a Washington experiment with spring wheat forage, both in field
and greenhouse, response to the 6-12-12 fertilizer was significantly
poorer (1 percent level) than to the other fertilizers. The interaction
between water solubility and granule size was also significant (5 percent
level) for wheat forage in the greenhouse and one field experiment. Sim-
ilar differences were found in yield and phosphorus content for wheat
forage harvested both in early joint stage of growth and in final grain
yields. The interaction between water solubility and granule size was
significant for both the early forage yields and phosphorus content.
Corn and Cotton--Only in the case of the low water-soluble 7-14-14
fertilizer, as shown in figure 5.3, was there an appreciable difference
in mean yield response of corn and cotton resulting from difference in
granule size. Mean yields for the seven experiments conducted also
showed practically no difference among the fertilizers of different water
solubility. There were no significant differences in any experiment for
granule size, water solubility, or interaction, except for a Georgia ex-
periment on Altavista loam, in which the 14-35 mesh granule size
yielded significantly higher (5 percent level) than the other mesh sizes.
Early growth response was closely related to water solubility of the
phosphorus in all of the experiments. In one Kentucky experiment in
1955, there was a highly significant increase in height of corn four weeks
after planting with increase in water solubility. Early growth differences,
however, did not carry through the relatively long growing season on
these southern soils or have an appreciable effect on yield of corn grain
or seed cotton. Similar effects on corn were observed by DeMent and
Seatz (6). Content of phosphorus in the leaves when the corn was two to
four feet and the cotton was eight inches high, on Sequoia and Mountview
soils in Tennessee, was likewise not significantly affected by differences
in the fertilizer. Owens et al. (31), on the other hand, found that phos-
phorus content of sugar beet plants fertilized with a highly water-soluble
phosphate was significantly higher than for plants fertilized with one of
lower water solubility. No differences, however, were found in final
yields of beets.






CROP RESPONSE


f RELATIVE YIELD


I 6-14 14-35-35 I 6-14 14-35-35 I 6-14 14-35-35 I 6-14 14-35-35 I
7% 27% 60% 100%
(7-14-14) (6-12-12) (10-20-20) (11-22-22)

Fig. 5.3 Effect of granule size and percent water-soluble P on mean rela-
tive yields of corn grain and seed cotton in Georgia, Kentucky, and Tennessee.
(Mean yield from all phosphate fertilizers in 6 corn and 1 cotton experi-
ments = 100.)

Vegetable Crops--As shown in figure 5.4, there was a pronounced
increase in yield of vegetable crops in Washington with decrease in
granule size of the 7-14-14 and 6-12-12 fertilizers. Differences for
the fertilizers higher in water solubility were not appreciable. Mean
response to DCP was significantly poorer (5 or 1 percent levels) than to
the other fertilizers in all experiments except with potatoes. The in-
teraction between granule size and water solubility was significant in the
experiment with potatoes and one with sweet corn. Phosphorus content
of potato leaves sampled 45 days after planting was significantly higher
with diammonium phosphate than with fertilizers of lower solubility.
This effect did not, however, influence final potato yields appreciably.


CONCLUSIONS

Water-insoluble sources of phosphorus such as DCP and TCP are
less available to crops on alkaline soils than water-soluble sources and
generally should not be recommended for use on these soils. DCP has
been found to give satisfactory yields on some alkaline soils, however, if
applied as a finely divided material and mixed well with the soil. On acid






G. L. TERMAN


to neutral soils availability of the phosphorus in water-insoluble mate-
rials tends to be a function of solubility and increases with decrease in
particle size. Granulation of water-insoluble materials in granules
larger than about 35 mesh usually lowers availability of the phosphorus
to crops.

c RELATIVE YIELD


Fig. 5.4 Effect of granule size and percent water-soluble P on mean rela-
tive yields of vegetable crops in Washington. (Mean yield from all phosphate
fertilizers in 5 experiments = 100.)

For highly water-soluble phosphorus fertilizers, the forces of solu-
tion and movement of phosphorus from the fertilizer granule or band
tend to interact with the tendency for fixation by the soil in determining
the availability of phosphorus to plants. The results of several investi-
gators indicate that the movement of water-soluble phosphorus from
fertilizer granules or bands is essentially complete in a few days after
application to the soil. This phosphorus moves out into a relatively
small sphere surrounding the granule or point of application of pulver-
ized fertilizer, leaving behind a residue which, in the case of superphos-
phate, may contain as much as 50 percent of the total phosphorus con-
tent. Once the initial movement of phosphorus is completed, it is made
relatively immobile by fixation in the soil, in contrast to nitrogen which
moves about freely in the soil with movement of water.
Phosphorus applied for a crop at time of planting is thus largely







CROP RESPONSE


immobilized by the time of emergence of the plants and remains so
throughout the growth period. Concentration of phosphorus near the
emerging plant is quite important and tends to govern the early growth
response to phosphorus.
Because of the variable tendencies for movement and fixation, the
best combination of percentage water solubility and granule size may
differ markedly for different soils. In general, the greater the phos-
phorus-fixing capacity of a soil, the larger should be the granule size
of a highly water-soluble fertilizer. Banding of pulverized water-soluble
materials near the seed appears to be a satisfactory substitute for gran-
ulation in many soils. In alkaline soils, where fixation of phosphorus
into difficulty soluble forms is less important than in acid soils, appli-
cation of pulverized fertilizers mixed with the soil may be more satis-
factory than application of granular fertilizers mixed with the soil, or
of pulverized fertilizers in bands.
Considerable research must be done to determine more exactly the
relationships among water solubility, granule size, placement and var-
ious soil characteristics in relation to plant availability of phosphorus.
The nature of the fertilizer salts with which the phosphorus is associ-
ated is also of considerable importance in determining its availability
to plants.


REFERENCES CITED

1. BAUER, F. C., LANG, A. L., BADGER, C. J., MILLER, L. B., FARNHAM, C.
H., JOHNSON, P. E., MARRIOTT, L. F., and NELSON, M. H., 1945. Effects
of soil treatment on soil productivity. Ill. Agr. Exp. Sta. Bul. 516.
2. BLASER, R. E., and McAULIFFE, C., 1949. Utilization of phosphorus from
various fertilizer materials: I. Orchard grass and ladino clover in New York.
Soil Sci. 68:145-50.
3. BOULDIN, D. R., 1956. Particle size effects of soluble phosphate fertilizers.
Ph.D. Thesis, Iowa State College.
4. CONVERSE, C. D., 1948. Phosphorus fertility and movement studies on newly
reclaimed sandy soils. Proc. Soil Sci. Soc. Amer. 13:423-27.
5. COOKE, G. W., 1956. Alternatives to superphosphates. Jour. Ministry of
Agr. 62:27-30.
6. DEMENT, J. D., and SAETZ, L. F., 1956. Crop response to high-alumina
nitric phosphate fertilizers. Jour. Agr. Food Chem. 4:432-35.
7. DION, H. G., DEHM, J. E., and SPINKS, J. W., 1949. Study of fertilizer up-
take using radioactive phosphorus. Sci. Agr. 29:512-26.
8. ENSMINGER, L. E., 1950. Response of crops to various phosphate fertilizers.
Ala. Agr. Exp. Sta. Bul. 270:1-39.
9. and COPE, J. T., Jr., 1947. Effect of soil reaction on the efficiency
of various phosphates for cotton and loss of phosphorus by erosion. Jour.
Amer. Soc. Agron. 39:1-11.







G. L. TERMAN


10. FINE, L. O., 1955. The influence of nitrogen and potassium on the availability
of fertilizer phosphorus. S. D. Agr. Exp. Sta. Bul. 453:1-22.
11. FULLER, W. H., 1953. Effect of kind of phosphate fertilizer and method of
placement on phosphorus absorption by crops grown in Arizona calcareous
soil. Ariz. Agr. Exp. Sta. Tech. Bul. 128:231-55.
12. GILBERT, B. E., and PEMBER, F. R., 1936. A study of the availability of
ammoniated superphosphate and various unusual phosphate carriers by means
of vegetative pot tests. R. I. Agr. Exp. Sta. Bul. 256.
13. HALL, N. S., NELSON, W. L., KRANTZ, B. A., WELCH, C. D., and DEAN, L.
A., 1949. Utilization of phosphorus from various fertilizer materials: II. Cot-
ton and corn in North Carolina. Soil Sci. 68:151-56.
14. HAUSENBUILLER, R. L., and WEAVER, W. H., 1954. A comparison of phos-
phate fertilizers for alfalfa on irrigated Central Washington soils. Wash. Agr.
Exp. Sta. Cir. 257.
15. HEIN, L. B., HICKS, G. C., SILVERBERG, J., and SEATZ, L. F., 1956. Granu-
lation of high-analysis fertilizers. Jour. Agr. Food Chem. 4:318-30.
16. HIGNETT, T. P., 1956. Technical and economic factors involved in produc-
tion of fertilizers of high water soluble P205 content by conventional processes.
Com. Fert. 92:(5)23-24, 26, 67.
17. HOUGHLAND, G. V., CLARK, K. G., HAWKINS, A., and CAMPBELL, J. C.,
1942. Nutrient value of some new phosphatic materials used on potatoes.
Amer. Fert. 97(7):5-8,24,26.
18. JACOB, K. D., and ROSS, W. H., 1940. Nutrient value of the phosphorus in
defluorinated phosphate, calcium metaphosphate, and other phosphatic mate-
rials as determined by growth of plants in pot experiments. Jour. Agr. Res.
61:539-60.
19. KARRAKER, P. E., MILLER, H. F., BORTNER, C. E., and TODD, J. R., 1941.
Greenhouse tests of the availability of phosphorus in certain phosphate ferti-
lizers. Ky. Agr. Exp. Sta. Bul. 413:57-86.
20. KEENEN, F. G., 1930. Reactions occurring during the ammoniation of super-
phosphate. Ind. Eng. Chem. 22:1378-87.
21. LAWTON, K;, and VOMOCIL, J. A., 1954. Dissolution and migration of phos-
phorus from granular superphosphate in some Michigan soils. Proc. Soil Sci.
Soc. Amer. 18:26-32.
22. MACINTIRE, W. H., WINTERBERG, S. H., CLEMENTS, L. B., and JOHNSON,
H. W., Jr., 1947. The effectiveness of liquid orthophosphoric acid. Jour.
Amer. Soc. Agron. 39:971-80.
23. and STERGES, A. J., 1950. Fertilizer evaluation of monoammonium
and diammonium phosphates by means of pot cultures. Agron. Jour. 42:442-46.
24. MARTIN, W. E., VLAMIS, J., and QUICK, J., 1953. Effect of ammoniation on
availability of phosphorus in superphosphate as indicated by plant response.
Soil Sci. 75:41-49.
25. MEHRING, A. L., WHITE, L. M., ROSS, W. H., and ADAMS, J. E., 1935. Ef-
fects of particle size on the properties and efficiency of fertilizers. USDA,
Tech. Bul. 485.
26. ODLAND, T. E., and COX, T. R., 1942. Field experiments with phosphate
fertilizer. R. I. Agr. Exp. Sta. Bul. 281.







CROP RESPONSE


27. BELL, R. S., and SCHALLOCK, D. A., 1951. Potato growing in Rhode
Island. R. I. Agr. Exp. Sta. Bul. 310.
28. OLSEN, S. R., SCHMEHL, W. R., WATANABE, F. S., SCOTT, C. O., FULLER,
W. H., JORDAN, J. V., and KUNKEL, R., 1950. Utilization of phosphorus by
various crops as affected by source of material and placement. Colo. Agr.
Exp. Sta. Tech. Bul. 42:1-43.
29. OLSON, R. A., DREIER, A. F., LOWREY, G. W., and FLOWERDAY, A. D.,
1956. Availability of phosphate carriers to small grains and subsequent clover
in relation to: I. Nature of soil and method of placement. Agron. Jour. 48:106-
11.
30. --- and 1956. Availability of phosphate carriers
to small grains and subsequent clover in relation to: II. Concurrent soil
amendments. Agron. Jour. 48:111-16.
31. OWENS, L., LAWTON, K., ROBERTSON, L. S., and APOSTOLAKIS, C., 1955.
Laboratory, greenhouse, and field studies with mixed fertilizers varying in
water soluble phosphorus content and particle size. Proc. Soil Sci. Soc. Amer.
19:315-19.
32. PARKER, F. W., 1931. The availability of phosphoric acid in precipitated
phosphates. Com. Fert. 42:(5)28-44.
33. PEARSON, R. W., 1951. Summary of cooperative radiophosphorus field ex-
periments, 1950. Div. Soil Management and Irrigation, USDA.
34. RICH, C. I., and LUTZ, J. A., Jr., 1950. Crop response to phosphate fertiliz-
ers in Virginia. Va. Agr. Exp. Sta. Tech. Bul. 115:1-14.
35. ROBERTS, G., FREEMAN, J. F., and MILLER, J., 1942. Field tests of the
relative effectiveness of different phosphate fertilizers. Ky. Agr. Exp. Sta.
Bul. 420:1-31.
36. ROGERS, H. T., PEARSON, R. W., and ENSMINGER, L. E., 1953. Compara-
tive efficiency of various phosphate fertilizers. Agronomy 4:189-242. Aca-
demic Press, Inc., New York.
37. ROSS, W. H., RADER, L. F., Jr., and BEESON, K. C., 1938. Citrate-insoluble
phosphoric acid in ammoniated mixtures containing dolomite, Jour. Assoc.
Offic. Agr. Chem. 21:258-68.
38. ADAMS, J. R., HARDESTY, J. O., and WHITTAKER, C., 1947. Fac-
tors affecting the availability of ammoniated superphosphates as indicated by
pot tests in the greenhouse. Jour. Offic. Agr. Chem. 30:624-40.
39. SALTER, R. M., and BARNES, E. E., 1935. The efficiency of soil and ferti-
lizer phosphorus as affected by soil reaction. Ohio Agr. Exp. Sta. Bul. 553:1-
49.
40. SEATZ, L. F., TISDALE, S. L., and WINTERS, E., 1954. Crop response to
fused tricalcium phosphate. Agron. Jour. 46:574-80.
41. SHERMAN, M. S., and HARDESTY, J. O., 1950. Plant Food Memo. Report
No. 20. Div. Fert. and Agr. Lime, USDA.
42. SKINNER, J. J., MCKAIS, N., Jr., HARDESTY, J. O., COLLINS, E. R.,
KILLINGER, G. B., and STACY, S. V., 1941. Effectiveness on cotton soils of
granulated mixed fertilizers of different particle size. Jour. Amer. Soc.
Agron. 33:314-24.
43. SPEER, R. J., ALLEN, S. E., MALONEY, M., and ROBERTS, A., 1951. Phos-
phate fertilizers for the Texas blacklands. Soil Sci. 72:459-64.







G. L. TERMAN


44. STANFORD, G., and NELSON, L. B., 1949. Utilization of phosphorus from
various fertilizer materials: III. Oats and alfalfa in Iowa. Soil Sci. 68:157-61.
45. STAROSTKA, R. W., CARO, J. H., and HILL, W. L., 1954. Availability of
phosphorus in granulated fertilizers. Proc. Soil Sci. Soc. Amer. 18:67-71.
46. and HILL, W. L., 1955. Influence of soluble salts on the solubility and
plant response to dicalcium phosphate. Proc. Soil Sci. Soc. Amer. 19:193-98.
47. STEWART, A. B., 1953. Factors influencing phosphate usage in Great Britain.
Agronomy 4:427-48. Academic Press, Inc., New York.
48. TERMAN, G. L., HAWKINS, A., CUNNINGHAM, C. E., and CARPENTER, P.
N., 1952. Rate, placement and source of phosphorus fertilizers for potatoes
in Maine. Me. Agr. Exp. Sta. Bul. 506:1-24.
49. --- ANTHONY, J. L., MORTENSEN, W. P., and LUTZ, J. A., Jr., 1956.
Crop response to NPK fertilizers varying in granule size and water solubility
of the phosphorus. Proc. Soil Sci. Soc. Amer. 20:551-56.
50. THORNE, D. W., 1944. The use of acidifying materials on calcareous soils.
Jour. Amer. Soc. Agron. 36:815-28.
51. WEBB, J. R., 1955. Significance of water solubility in phosphate fertilizers.
Ag. Chem. 10:(3)44-46.
52. WHITE, L. M., HARDESTY, J. O., and ROSS, W. H., 1935. Ammoniation of
double superphosphate. Ind. Eng. Chem. 27:562-67.
53. WILLIAMSON, J. T., 1935. Efficiency of ammoniated superphosphate for
cotton. Jour. Amer. Soc. Agron. 27:724-28.





















PART II

An Examination of Liquid Fertilizers and

Related Marketing Problems

> Economics of Manufacture
SEconomics of Farm Use
> Potential Markets
SResponse Effects




r






L. S. ROBERTSON, J. F. DAVIS, and C. M. HANSEN
Michigan Agricultural Experiment Station

Chapter 6



Factors Affecting the Evaluation

of Liquid Fertilizers


A LIQUID fertilizer is defined as any liquid containing one or more

available plant nutrients. Such materials containing a single
plant food or a mixture of two or more plant foods are on the
market in many states. At the present time there is considerable inter-
est in this new form of fertilizer because an intensive advertising cam-
paign is in effect and because liquid fertilizers offer certain advantages
over the solid forms. Since the widespread use of liquid fertilizer is
relatively new, it is natural that its advantages are stressed by produc-
ers and distributors. However, certain disadvantages in utilization do
exist and should be included in an evaluation of liquid fertilizers.
The interest of the research personnel of the Michigan Agricultural
Experiment Station was greatly stimulated when the price of the liquid
fertilizer became competitive with the conventional dry forms. In 1955,
research was initiated to determine the value of liquid as compared to
dry fertilizers. The advantages and disadvantages of liquid fertilizers
over conventional dry fertilizers as determined by experience with
these new materials are listed below. With increased use and interest
in liquid fertilizers, some of the problems now present, undoubtedly,
will be solved in the future. The remarks with regard to liquid ferti-
lizers will refer only to those without free ammonia pressure.


ADVANTAGES OF LIQUID OVER CONVENTIONAL
DRY FERTILIZERS

1. Liquid fertilizers can be handled with small pumps with a saving
of labor.
2. Uniform broadcast application is easily obtained by spraying.
3. Materials are completely soluble in water so they can be used in
irrigation water and as starter solutions.
4. Uniform mixtures of plant nutrients result from their use.
5. Pesticides are compatible with many liquid fertilizers. Simulta-
neous application saves time and insures uniform application.
6. The use of liquids simplifies custom mixing of fertilizer grades.
7. Liquids may be used as foliar sprays.
8. The availability of nitrogen and potassium is not decreased when
applied to the soil in liquid form.






L. S. ROBERTSON, J. F. DAVIS, C. M. HANSEN


DISADVANTAGES OF LIQUID OVER CONVENTIONAL
DRY FERTILIZERS

1. Special equipment is required.
2. Special storage containers are necessary.
3. Complete fertilizers in liquid form can be made only in relatively
low grades and they contain very small quantities of secondary or
minor elements.
4. Application equipment for placing fertilizer in recommended posi-
tion with respect to the seed in the soil is generally unavailable.
5. Phosphorus fixation (a decrease in solubility or availability) in the
soil may be increased.
6. Calcium and magnesium contents of liquid fertilizers have to be
kept low to prevent precipitation of other plant nutrients.
7. Rates of actual nutrients applied may be limited because of the
large volume of water needed.
8. Liquid fertilizers corrode certain metals.
9. Liquid fertilizers may be more difficult to merchandise.
10. Completely soluble carriers are required for the manufacture of
solutions; setting a limitation on carriers which may be used.
11. Grades high in potassium, suitable for several crops growing on
light sandy or organic soils, are difficult to formulate unless low
grade fertilizers are accepted.


EFFECT ON CROP YIELDS

In summarizing the 1955 results, it is realized that data obtained in
one year are not sufficient to completely evaluate the new form of ferti-
lizer. A summary of results is included because in several instances
a significant difference in yield caused by liquid and solid forms was
obtained. Also, the summary is included because only a limited amount
of such information is available.
In one trial on wheat, the two forms of complete fertilizer had equal
effects on yield. In three trials on oats, similar results were obtained.
Corn grown in four trials showed phosphorus deficiency symptoms
to various degrees of intensity in the early part of the season. The
yields from these trials are shown in table 6.1. At one location, the
liquid fertilizer plots yielded 20 bushels less corn per acre than did
the dry fertilizer plots. At another location, in a fertilizer rate and
placement experiment, corn yields were 17 bushels lower where N,
P205 and KO, each at 50 pounds per acre, were sprayed on the surface
of the soil than where they were injected in liquid form into the soil
near the row before the first cultivation. Higher rates of the same fer-
tilizer (100 pounds of N, P205 and K20 per acre) sprayed on the surface
of the soil were as effective as solid fertilizer and as effective as the
lower rate of liquid fertilizer injected into the soil.
In trials on organic soils, liquid fertilizer resulted in lower yields







EVALUATION OF LIQUID FERTILIZERS

Table 6.1. The Effect of Liquid and Solid Fertilizers on
Corn Yields in 1955


Pounds per Acre Yield Bushel per
Soil Type N + POs5 + KO2 Liquid Acre Solid

Kalamazoo sandy loam 20+40+20 48.1b 39.4c
40+80+40 49.0b 44.6c
80+160+80 49.0b 49.9c
160+320+160 49.0b 49.0c
320+640+320 46.4b 44.7c
Conover silt loam 10+40+40 63.0a 62.7d
Conover loam 10+40+40 74.0b 94.0d
Kalamazoo sandy loam 50+50+50 injected 72.9
50+50+50 sprayed 56.0
100+100+100 injected 73.7
100+100+100 sprayed 73.6
100+100+100 75.7e

aTopdressed after the crop was planted.
blnjected into the soil near the row before the first cultivation.
CBroadcast and plowed down before planting.
dFertilizer applied at planting time in bands below and to the side of the seed.
eBroadcast at same time as liquid was sprayed on surface.
of onions, carrots, and table beets than were obtained with solid ferti-
lizers (table 6.2). In each of these experiments, the fertilizer was ap-
plied with a specially designed applicator in a band 2 inches below the
seed thus eliminating any effect from differential placement. Where
800 pounds of 5-10-10 was applied, the onions with liquid fertilizer
yielded 151, 50-pound bags per acre less than did those grown with
solid fertilizer. Based on harvest time prices, this difference
amounted to $300 an acre.


SPECIAL USES FOR LIQUID FERTILIZER

Inquiries are sometimes made in regard to treating seed with liquid
fertilizer. Tests made in several states have shown that there is little
or no value obtained in early growth characteristics or yield from treat-
ing seed with liquid fertilizer.
Liquid fertilizers are of value as starter solutions for transplanted
vegetable crops, especially if the transplants are large in size.
Liquids containing the major plant food elements nitrogen, phos-
phorus, and potassium are sometimes used for leaf feeding. Under
some conditions this has proven to be a desirable practice. For field
crops, this practice usually is not recommended because only a small
amount can be applied without injury to foliage. Foliar applications of
secondary and minor elements such as manganese, magnesium, copper,
zinc, or boron are more satisfactory because small quantities are







L. S. ROBERTSON, J. F. DAVIS, C. M. HANSEN


required. In Michigan, 1.2 pounds of manganese sprayed on leaves of
sugar beets and beans have given as good results as 24.0 pounds broad-
cast on the surface of the soil.

Table 6.2. The Effect of Liquid and Solid Fertilizers on Yields of Onions,
Table Beets, and Carrots Grown on Houghton Muck in 1955


Treatment Onionsb
Lbs. 5-10-10 50 Lb. Bags Tons per Acre
per Acre per Acre Table Beetsc Carrotsd

Expt. No. la 800 dry 925 20.6 39.4
800 liquid 774 18.3 38.7
400 dry 712 18.4 38.5
400 liquid 691 17.4 38.9
No fertilizer 254 11.8 36.6
Expt. No. 2a 800 dry 861 25.2 31.2
400 dry 837 26.8 32.0
2400 liquid 769 27.5
1200 liquid 838 27.0 30.9
No fertilizer 505 14.9 29.6


aExperiment No. 1 planted 5/6/55;
mental Farm.
bDownings Y.G. Onions.
CDetroit Dark Red Beets.
dChantenay Carrots.


Experiment No. 2 planted 5/5/55 Muck Experi-






Z. A. STANFIELD
Tennessee Valley Authority

Chapter 7



Economics of Manufacture of

Liquid Mixed Fertilizers'


HE manufacture and use of liquid fertilizers containing two or

more of the major plant nutrients have received considerable at-
tention during the past few years. Several papers have been pub-
lished on this subject (2, 3, 4). Most of the activity in this business has
occurred in California and some has occurred in the Midwest and
Southwest.
Although significant,. the estimated quantity of liquid mixed fertiliz-
ers used in the United States has been very small in comparison with
the total estimated quantity of mixed fertilizers. For example, one
estimate (4) showed that the quantity of liquid mixed fertilizers used
during 1953-54 was 27,548 tons, or less than 0.2 percent of the total
amount of mixed fertilizers used.
The present growth of the business began with the introduction on
the market of "phosphatic fertilizer solution" at a price low enough to
compete in some areas on the fertilizer materials market. In addition
to use in making liquid mixed fertilizers, this phosphoric acid solution
is used in making solid nitric phosphate and solid diammonium phos-
phate fertilizers. The material usually is sold as 75 percent H3PO4
It is made by burning elemental phosphorus.
Previously, the price of phosphoric acid from phosphorus was too
high for it to be considered as a fertilizer material. Most of the phos-
phorus is used to make chemicals that are marketed at a higher price
than fertilizers.
The liquid mixed fertilizer industry currently appears to be in a
period of market development and early growth. Many plants are oper-
ated only during the sales season and some plants are additions to ex-
isting solid fertilizer businesses. Different types of processing and
marketing techniques are being carried on and tested.
The present study points out some of the economic factors in evalu-
ating liquid mixed fertilizers and suggests methods of taking them into
account. The cost and price data developed for this purpose are only
illustrative and cost and price data developed for most commercial
situations are expected to be different from those in this chapter.

'Acknowledgment is made to P. W. Roden of the Development Branch for assistance in
making the estimates.






Z. A. STANFIELD


The method used for the purpose of the present study was to com-
pare the relative economics of the manufacture of liquid and solid
mixed fertilizers. Estimates were made of the investment and produc-
tion costs for hypothetical new complete plants and of the hypothetical
selling prices for various grades of fertilizers made in these plants.
Information on process technology was obtained from the literature for
the liquid products and from TVA pilot-plant work for the solid prod-
ucts. The study was based on (a) purchase of raw materials at current
market prices, (b) conversion of these materials to finished products,
(c) storage of the finished products at the manufacturing plant in forms
suitable for sale to distributors, and (d) distribution of products to the
consumer.


Assumptions for Estimates

The estimates were made for five different sales volumes: 2,500,
5,000, 10,000, 20,000, and 40,000 tons of product per year. For each
sales volume, three types of operation were assumed. In the first case,
the plant was designed for seasonal operation with provision for only 2
days of product storage. In the second case, the plant was designed for
operation 6 months per year with provision for storage of 20 percent of
the sales volume. In the third case, the plant was designed for opera-
tion 12 months per year with provision for storage of 40 percent of the
sales volume. These variations were selected in order to determine
the economic effects of scale and method of operation.
The acid-neutralization method was selected for the manufacture
of liquid mixed fertilizers. By this method, phosphatic fertilizer solu-
tion is neutralized with ammonia. Other nitrogenous materials, such
as urea and ammonium nitrate, are added to increase the ratio of nitro-
gen to P205 in the product. Potassium chloride is added to provide K20.
Sufficient water is added to dissolve the salts that are formed in the
reactions and to make the desired grade of product. It is desirable to
produce neutral solutions so that low cost steel tanks can be used to
store and transport the products. Product grades assumed for the
study were 10-10-10, 5-10-10, and 8-24-0. Grades with concentrations
higher than those selected do not appear practical using existing known
technology.
The process selected for the manufacture of solid mixed fertilizers
was that in which the TVA-type continuous ammoniator is used (1). In
this process, superphosphates are ammoniated with nitrogen solutions
and other materials are added in the ammoniator to make the desired
grades. The ammoniator product goes to a granulator and then to a
rotary dryer. In making some grades, the dryer is not required. The
product is sized and the oversize and fines are recycled. Product of
the desired size is stored in the product-storage building and is shipped
either bulk or bagged. Product grades assumed for the study were
10-10-10, 15-15-15, 6-12-12, 10-20-20, and 8-24-0.






ECONOMICS OF MANUFACTURE


It was assumed that plants would be located in the South Atlantic and
Pacific regions. The former was selected because of its established
solid mixed fertilizer industry, high rate of fertilizer consumption, and
relatively low price of superphosphate. The latter region was selected
because of its rapidly expanding fertilizer industry, present low rate of
fertilizer consumption, and relatively high price of superphosphate.
Conditions in the South Atlantic and Pacific regions appeared to be typi-
cal of conditions that are least favorable and most favorable, respec-
tively, for liquid mixed fertilizers. Conditions in other regions proba-
bly are intermediate between the two regions selected.
Estimates of cost of construction of process plants and storage fa-
cilities were based on typical 1955 conditions. These estimates were
made for comparative purposes only, and it is probable that plant esti-
mates made for an actual set of particular conditions would be some-
what different from these estimates. The same method of estimating
was used for both processes. The estimates included provisions for
process equipment, raw material storage, product storage, buildings,
engineering, and construction supervision costs equal to 10 percent of
physical cost, and an item for contingencies equal to 20 percent of phys-
ical cost. Working capital was calculated as being equal to one month's
production cost.
Estimates of production cost were prepared for each assumed
method of operation and sales volume. Typical current market prices
for the raw materials in each region were used. The most economical
formulation was used for each grade of product. Operation labor sched-
ules were prepared for each set of conditions and average rates of pay
for each class of work were used. Seasonal use of labor was assumed
in appropriate cases. Estimated costs of utilities, supplies, chemical
analyses, and plant overhead were included. Estimates of costs for de-
preciation, property tax, and insurance were included in production cost.
Estimates of manufacturer's selling price were made for each case.
Selling price was assumed to be equal to the sum of production cost,
selling expense of $3.00 per ton of product in each case, and 30 percent
annual pretax return on total investment including working capital. The
basis for prices of liquids was f.o.b. works loaded in tank cars or tank
trucks for shipment. The basis for prices of solids was f.o.b. works,
bagged and bulk, loaded in cars or trucks for shipment.


RESULTS OF ESTIMATES

Effect of Sales Volume

Estimated selling prices of liquid and solid 10-10-10 fertilizers for
the South Atlantic and Pacific regions are shown in figures 7.1 and 7.2.
The estimates showed that sales volume had a considerable effect on
the selling prices for both the liquid and solid products. The estimated
selling prices at the annual sales volume of 2,500 tons were about 40






Z. A. STANFIELD


percent higher than those at the annual sales volume of 40,000 tons.
These results indicate that a small producer of either liquid or solid
mixed fertilizers would be at a competitive disadvantage in comparison
with large producers. The disadvantage of being a small producer is
somewhat less for liquids than for solids.
There was a significant decrease in estimated unit capital cost with
increase in sales volume for both types of plants. For example, using
the 10-10-10 grade and 6 month's operation for two shifts, 6 days per
week, as a basis, estimated process plant costs for the liquid plants
decreased from $25.00 per annual ton at the 2,500-ton sales volume to
$4.00 per annual ton at the 40,000-ton sales volume. Estimated process
plant costs for the solid plants decreased from $40.00 per annual ton at
the 2,500-ton sales volume to $10.00 per annual ton for the 40,000-ton
sales volume. The estimated costs of product storage facilities varied
from $16.00 to $5.00 per annual ton for the liquid fertilizer plants and
from $3.20 to $3.00 per annual ton for the solid fertilizer plants for the
smallest and largest sales volumes, respectively.
It is expected that investment cost estimates based upon designs for
specific conditions could be developed for both liquid and solid plants
that might be 25 to 50 percent lower than those used in this study. How-
ever, for the purpose of comparing the processes, the estimates of this
study appear to be adequate. Decrease or increase of the investment
costs used by 50 percent did not change the relative economic position
of the processes. The wide variation of unit capital cost with sales

SELLING PRICE, S/UNIT OF PLANT NUTRIENT,
SFO.B. MANUFACTURING PLANT


SALES VOLUME, TONS/YEAR


Fig. 7.1 Effect of


sales volume and seasonal operation on selling price in
South Atlantic region.







ECONOMICS OF MANUFACTURE


SELLING PRICE, 8/UNIT OF PLANT NUTRIENT,
FO.B. MANUFACTURING PLANT
2.80
PACIFIC REGION
2.60 10-10-10 FERTILIZER BAGS

2.40 G-- BULK
LIQUID SOLID
2.20 -- --

2.00 -

1.80 -

1.60 -

1.40 -

I.20 204
0 20 40 0 20 40 0 20 40 0 20 40 0 20 40
2,500 5,000 10,000 20,000 40,000
SALES VOLUME,TONS/YEAR


Fig. 7.2 Effect of sales volume and seasonal operation on selling price in
Pacific region.

volume for both types of plants suggests the importance of careful con-
sideration of initial capital cost.
The effect of size of plant on operating cost is shown in table 7.1.
For the liquid mixed fertilizers, the operating cost decreased from
$10.59 to $3.23 per ton for increase in sales volume from 2,500 to
40,000 tons per year. A greater decrease was shown for the solid
mixed fertilizers; the operating costs (excluding costs of bags and bag-
ging) were $17.20 and $4.63 per ton, respectively, for the 2,500-ton and
40,000-ton sales volumes. The estimates indicate that for 10-10-10 the
advantage for liquids is about 5 cents per unit at the 40,000-ton sales
volume and 22 cents per unit at the 2,500-ton sales volume.

Table 7.1. Effect of Plant Size on Operating Costs in Liquid and
Solid Mixed Fertilizer Plants


Operating Cost,
$ per Ton Product
Sales Volume, Solid
Tons per Year Liquid (Excluding Bags)

2,500 10.59 17.20
5,000 9.34 10.81
10,000 8.60 9.68
20,000 5.39 7.10
40,000 3.23 4.63







Z. A. STANFIELD


Effect of Product Storage

The effect of providing for storage of different percentages of a
given sales volume was different on prices of liquid mixed fertilizer
than it was on prices of solid mixed fertilizer. For liquids, the lowest
price was obtained for the 3-month operating period, in which case
there was no provision for seasonal storage of product. For solids,
the lowest price generally was obtained for the 6-month operating pe-
riod, in which case provision was made for storage of 20 percent of the
annual production.
Comparisons between liquids and solids were made on the basis of
providing seasonal storage of 20 percent of the annual sales volume
even though the lowest estimates of prices for liquids were obtained
when no seasonal storage was provided. Operation of liquid mixed fer-
tilizer plants with provision for some seasonal storage appeared to be
the most likely case. Seasonal operation merely pushes the storage
problem back onto the manufacturer of raw materials (phosphoric acid,
ammonia, etc.). A great increase in the storage requirement of these
materials probably would result in premium prices for in-season de-
livery.


Formulation Costs

The estimated costs of raw materials (formulation costs) for 10-10-10,
6-12-12, and 8-24-0 solidgrades and 10-10-10, 5-10-10, and 8-24-0
liquid grades for both regions are shown in table 7.2. For the South
Atlantic region, the formulation costs of solid grades were significantly
lower than the formulation costs of the liquid grades of comparable
plant nutrient ratio and were 28, 26, and 23 cents per unit lower for the
1:1:1, 1:2:2, and 1:3:0 ratios, respectively. For the Pacific region, the
formulation cost of 10-10-10 was 10 cents per unit lower for solids; for
the 1:2:2 ratio, liquid and solid formulation costs were about the same;
and for the 1:3:0 ratio, the formulation cost of liquid was 10 cents per
unit lower for the liquid. In this comparison the position of liquids
with respect to solids was improved with decrease of N:P2Os ratio.
The improvement was most pronounced for the Pacific region.

Table 7.2. Formulation Costs for Several Grades of Liquid
and Solid Mixed Fertilizer

Cost of Raw Materials, $ per Unit
South Atlantic Pacific
Solid Liquid Solid Liquid

10-10-10 1.08 1.36 1.33 1.43
5-10-10 1.19 1.21
6-12-12 0.93 1.19
8-24-0 1.25 1.48 1.58 1.48







ECONOMICS OF MANUFACTURE


The major factor causing the different results obtained for the two
geographic regions was the difference in prices of the superphosphate
for the two regions. The price used for superphosphate was $18.00 per
ton for the South Atlantic region and $30.00 per ton for the Pacific re-
gion. The effect of the $12.00 difference was to make the price of solid
10-10-10 $6.24 per ton (21 cents per unit) higher in the Pacific region.
These results indicate that a reduction in the market price of phos-
phatic fertilizer solution below that used in the estimates could place
liquid mixed fertilizer in a more competitive position in the South At-
lantic region. Calculations indicated that the price of solution would
have to be cut about 10 percent for the selling price of liquid 10-10-10
to be the same as that of bagged solid 10-10-10.


Effect of Concentration

The effect of increasing the concentration of solid grades in the
Pacific region is shown in table 7.3. The estimated selling price of
liquid 10-10-10 was 13 cents per unit lower than the price for bagged
solid 10-10-10. However, the estimated price of liquid 10-10-10 was
the same as the price of bagged solid 15-15-15 made using concen-
trated superphosphate. The price of liquid 5-10-10 was 15 cents per
unit lower than the price of bagged solid 6-12-12. However, the esti-
mated price of liquid 5-10-10 was 6 cents per unit higher than the price
of solid 10-20-20 made using concentrated superphosphate.


Effect of Geographic Area

The results plotted in figures 7.1 and 7.2 show that the estimated
selling price of liquid 10-10-10 was higher than either bulk or bagged
solid 10-10-10 in the South Atlantic region for sales volumes of 5,000
tons per year or more; it was about 4 percent higher than bagged and
about 11 percent higher than bulk solids. In the Pacific Coast region,

Table 7.3. Effect of Increasing Concentration of Solids

Manufacturer's Selling
Price, $ per Unit,
Pacific Region

Bagged solid 10-10-10 1.89
Bagged solid 15-15-15 1.76
Liquid 10-10-10 1.76
Bagged solid 6-12-12 1.75
Bagged solid 10-20-20 1.54
Liquid 5-10-10 1.60












Table 7.4. Estimates of Selling Price of 10-10-10 Liquid and Solid Fertilizer
(Sales Volume, 40,000 Tons per Year; Plants Operated 6 Months per
Year to Produce 40,000 Tons)


Item


Anhydrous ammonia
Nitrogen solution,
40.6% N
Ordinary super-
phosphate
Phosphoric acid,
75% H3PO4
Urea
Potassium chloride
Sulfuric acid
Water
Filler (sand)
Total raw materials
Operating labor
Maintenancea
Electricity
Supplies, 2% operating
labor
Analyses
Property tax, 1% plant
investment
Insurance, 1% plant
investment
Depreciation, 10%
process plant and 5%
storage investment
Plant overhead,
50% operating labor
Bags and bagging
Total operating cost
Total production cost
Selling expense
Return, 30% of total
investment
Selling price, f.o.b.
plant, $/ton product
Selling price, f.o.b.
plant, $/unit plant food


Process plant
Product storage
Working capital
Total investment for return


South Atlantic Region Pacific Region
$ per Ton Product $ per Ton Prod
$/Ton Solid Solid $/Ton Solid Solid
Material Bulk Bagged Liquid Material Bulk Bagged I


95.00 3.80

60.00 15.30 15.30

18.00 9.36 9.36

85.00 15.73
101.00 14.95
37.75 6.42 6.42 6.42
18.00 1.33 1.33
0.02 0.01
3.00 0.10 0.10
32.51 32.51 40.91
1.23 1.23 1.20
0.67 0.67 0.17
0.40 0.40 0.20

0.02 0.02 0.02
0.20 0.20 0.20

0.14 0.14 0.09

0.14 0.14 0.09


95.00

62.00

30.00

85.00
114.00
37.75
25.00
0.02
3.00


1.21 1.21 0.66

0.62 0.62 0.60
4.00
4.63 8.63 3.23
37.14 41.14 44.14
3.00 3.00 3.00

5.09 5.09 3.92

45.23 49.23 51.06

1.51 1.64 1.70

investment Cost, $/Annual Ton
Solid Liquid
10.60 4.12
3.00 5.00
3.35 3.92
16.95 13.04


15.81 15.81

15.60 15.60

-
-
6.42 6.42
1.85 1.85

0.10 0.10
39.78 39.78
1.23 1.23
0.67 0.67
0.40 0.40

0.02 0.02
0.20 0.20

0.14 0.14

0.14 0.14


1 01 1 01


uct

iquid

3.80





15.73
16.87
6.42

0.01

42.83
1.20
0.17
0.20

0.02
0.20

0.09

0.09


n C


0.62 0.62 0.60
4.00 -
4.63 8.63 3.23
44.41 48.41 46.06
3.00 3.00 3.00

5.27 5.27 3.97

52.68 56.68 53.03

1.76 1.89 1.76


aFor liquid plants: 3 percent process plant investment plus 1 percent storage investment.
For solid plants: 6 percent process plant investment plus 1 percent storage investment.







ECONOMICS OF MANUFACTURE


the price of liquid 10-10-10 was about 6 percent lower than bagged
solid 10-10-10 and about the same as for bulk solid. These small dif-
ferences indicate that specific locations probably could be found where
the manufacture of liquid and solid 10-10-10 would be closely competi-
tive, economically, in both regions especially at the larger sales vol-
umes.
Typical estimates of selling prices of 10-10-10 liquid and solid
mixed fertilizers are shown in table 7.4. The 40,000-ton-per-year
sales volume was selected for this comparison because the lowest unit
costs for both liquid and solid were obtained for this sales volume.
From this table it is observed, in the South Atlantic region, the advan-
tages of lower operating cost and lower investment cost for liquids
were not enough to overcome the disadvantage of higher formulation
cost. In the Pacific region, the disadvantage in formulation cost for
liquid 10-10-10 was not so great as in the South Atlantic region and
this disadvantage was overcome by lower operating and investment
costs.



Table 7.5. Estimated Costs of Distribution of Solid and Liquid Fertilizers
(Sales Volume: 5,000 Tons; Cost Delivered to Farm)


Bagged Solid Liquid
Item Description $/Ton Description $/Ton

Labor 4 drivers at $2.30/hr. 1.32 10 drivers, 25%of time, 0.83
at $2.30/hr.
Maintenance 5%/yr. of equipment cost 0.09 5%/yr. of equipment cost 0.24
Fuel Gasoline 0.30 Gasoline 0.19
Supplies 5%of labor cost 0.07 5% of labor cost 0.04
Property tax and
insurance 5% of investment 0.16 5% of investment 0.27
Office overhead 50%of labor 0.66 50%of labor 0.42
Depreciation 0.60 1.31
Operating cost 3.20 3.30
Administrative
expense 1.00 1.00
Return on investment 1.86 2.55
Total cost of distribution 6.06 6.85
Freight, manufacturer to distributor 4.00 4.00
Total cost delivered to farm 10.06 10.85

Investment
Amount Amount
Charged to Charged to
Fertilizer Fertilizer
Trucks Four 10-ton trucks Seven 2000-gal. trucks
at $6000 = $24,000 $ 6,000 at $10,000=$70,000 $17,500
Storage and office 1 week 20,000 3 days 20,000
Working capital 1 mo. operatingcost 5,000 1 mo. operating cost 5,000
Total investment for return $31,000 $42,500







Z. A. STANFIELD


Distribution Costs

In order to make a general comparison of the prices of the several
products delivered to the farm, rough estimates were made of the cost
of distribution of liquid and bagged solid fertilizers. A breakdown of
the estimated distribution costs is shown in table 7.5. In these esti-
mates it was assumed that the annual sales volume of 40,000 tons would
be distributed by eight distributors each handling 5,000 tons of product
per year. It was assumed that each distributor would be located 100
miles from the manufacturing plant and would deliver to farms located
(on the average) 20 miles from the distribution point. Investment and
operating costs for the distributor were prepared in which the distribu-
tor was allowed a profit equal to 30 percent per year of the estimated
investment.
The estimates indicate that the costs of delivering fertilizer from
the manufacturing plant to the farm would be $10.00 per ton for the
bagged solids and $11.00 per ton for liquids. For fertilizers of the
same concentration, the difference probably is not significant. However,
distribution costs per unit of plant nutrient would decrease with increase
in concentration of fertilizer. This fact could be important in the choice
of process since higher concentrations cannot be attained with liquid

Table 7.6. Estimated "Delivered to Farm" Selling Prices for 40,000-Ton
Annual Sales Volume (One Manufacturer and Eight Distributors)


Estimated Delivered Price to Farm $/Unit
South Atlantic Region Pacific Region
Grade of Bagged Bagged
Product Solid Liquid Solid Liquid

1:1:1 Ratio
10-10-10 1.97 2.05 2.22 2.12
(1.64) (1.70) (1.89) (1.76)
15-15-15 1.88 1.98
(1.66) (1.76)
1:2:2 Ratio
5-10-10 1.99 2.03
(1.58) (1.60)
6-12-12 1.82 2.08
(1.49) (1.75)
10-20-20 1.65 1.74
(1.45) (1.54)
1:3:0 Ratio
8-24-0 2.11 2.14 2.44 2.14
(1.79) (1.80) (2.12) (1.80)

Note: Figures in parentheses are prices f.o.b. manufacturing plant.
Other figures are prices delivered to farm.







ECONOMICS OF MANUFACTURE 71

mixes because of solubility limitations. Estimated delivered prices of
several grades of liquid and solid fertilizers are shown in table 7.6.


REFERENCES CITED

1. HEIN, L. B., HICKS, G. C., SILVERBERG, JULIUS, and SEATZ, L. F., 1956.
J. Agr. Food Chem. 4, No. 4, 318-30.
2. JACOB, K. D., and SCHOLL, WALTER, 1955. Commercial Fertilizer Year-
book, 94-107.
3. LANGGUTH, R. P., PAYNE, J. H., Jr., ARVAN, P. G., SISLER, C. C., and
BRAUTIGAM, G. F., Jr., 1955. J. Agr. Food Chem. 3, No. 8, 656-63.
4. SLACK, A. V., 1955. J. Agr. Food Chem. 3, No. 7, 568-74.







EARL R. SWANSON
University of Illinois

Chapter 8




Programming a Fertilizer

Mixing Operation


INEAR programming is being applied to an increasing number of

problems which involve quantitative aspects of management deci-
sions. This chapter illustrates the application of the technique to
the problem of mixing a fertilizer to meet a certain set of requirements
with a minimum expenditure for ingredients. Once the requirements
for the fertilizer and the composition and cost of the plant food carriers
have been specified, linear programming unfailingly provides the mini-
mum cost mix. The theoretical basis of linear programming, as well
as the computational methods, has been treated elsewhere (1, 3).
Consider the problem of mixing a formula containing N, P20O and
K20. If each carrier considered contained only N, P205 or K20 the
several sources of, say N, could be evaluated on the cost per pound of
N and the least expensive source chosen. A similar procedure could
be followed for choosing the carriers of P205 and K20. The resulting
mix would then be the least expensive one considering all of the car-
riers which contain only a single plant food. However, the mixer may
also wish to consider carriers which contain more than one plant food.
If the plant food ratios in the carriers considered as possible ingredi-
ents for the mix are not in the same proportions, the problem of eval-
uating the least expensive sources becomes difficult. Further, as re-
quirements regarding the physical properties of the mix are added, the
problem becomes even more complex. By casting the problem in a lin-
ear programming form for solution, one can be assured that the mini-
mum cost mix will be systematically selected and that the specified
requirements are met.


REQUIREMENTS

As an illustration of application of the linear programming tech-
nique, suppose that a mixer wishes to blend several carriers into a ton
of 4-12-4 mixed fertilizer. The fourteen available carriers are listed
in table 8.1. The mixer also desires that the product be neutral, that
is, neither acid nor basic. He also wishes to insure drillability of the
final product.
Letting the quantities of the materials be designated as xi







PROGRAMMING A FERTILIZER MIXING OPERATION


Table 8.1. Composition of Fertilizer Materiala


Water- Equivalent Acidity (A)
Available Soluble or Basicity (B) in
Fertilizer Material N P205 KzO Pounds of CaCOs
i ai bi di ki
(Percent) (per 100 Pounds Material)
1. Ammonium nitrate 32.5 60A
2. Ammonium sulfate 20.5 110A
3. Calcium cyanimid 22.0 -- 63B
4. Calcium limestone 90B
5. Castor pomace 6.0 1.5 0.5 6A
6. Cottonseed meal 6.6 2.5 1.5 10A
7. Dried blood 13.0 23A
8. Fish scrap (dried) 9.5 6.0 7A
9. Manure salts 25.0
10. Muriate of potash 60.0
11. Sand -
12. Sulfate of potash
magnesia 26.0
13. Superphosphate 20.0
14. Tankage 7.0 13B

aSauchelli, Vincent, 1946. Manual on fertilizer manufacture. The Davison Chemical
Corporation, Baltimore, Table 2, p. 19 and Table 39, p. 88.


(i = 1, 2, 3, ..., 14), the total quantity of mixed fertilizer that is to be
produced is specified. In this case one ton will be produced; hence:

14
(8.1) Z xi = 2,000 pounds
i=1

The formula of the mixed fertilizer to be produced must, of course,
be considered as a requirement. In this example, assume a production
of a 4-12-4 mixed fertilizer; thus there must be at least 80 pounds of
N, 240 pounds of P20s, and 80 pounds of K20 in the mixture. Letting ai
equal the percentage of N, bi equal the percentage of P20s and di equal
the percentage of K20 in each of the 14 ingredients, the formula require-
ment may be written as follows:

14
(8.2) a aixi > 80 pounds
i=1


14
(8.3) E bixi > 240 pounds
i=1







EARL R. SWANSON


14
(8.4) dixi > 80 pounds
1=1

Letting the equivalent acidity or basicity in pounds of CaCO3 (table
8.1) be designated as ki one may write the neutrality restriction as
follows:
14
(8.5) Z kixi =0
i=1

where opposite signs are attached to the acidity and basicity equivalents.
The drillability requirement may be met by specifying the maximum
and minimum quantities of certain nitrogen carriers. In this case it is
specified at least 13 pounds of N must come from organic sources:

(8.6) a3x3 + asxs + a4x6 + a7x7 + a8gX + a14x14 > 13 pounds

where the subscripts refer to the ingredient numbers in table 8.1. In
addition, the quantity of N that may be obtained from ammonium nitrate
is restricted to 35 pounds. Hence:

(8.7) aixi < 35 pounds


COST CONSIDERATIONS

The requirements stated above could be satisfied by a large number
of combinations of the 14 ingredients. The single combination which
minimizes ingredient cost is insured by the linear programming method.

Table 8.2. Price Situations Used to Compute Materials Needed to
Minimize Cost of a Ton of Neutral 4-12-4


Price Situations
Fertilizer Material I II III IV V VI VII
(Dollars per Ton Delivered to Mixing Plant)
Ammonium nitrate 70.00 80.00 60.00 80.00 70.00 50.00 60.00
Ammonium sulfate 60.00 70.00 50.00 70.00 80.00 40.00 60.00
Calcium cyanimid 70.00 60.00 80.00 150.00 150.00 120.00 130.00
Calcium limestone 3.50 4.00 3.00 5.00 3.50 2.00 4.00
Caster pomace 32.00 30.00 34.00 30.00 40.00 40.00 35.00
Cottonseed meal 80.00 60.00 100.00 60.00 60.00 35.00 40.00
Dried blood 140.00 120.00 160.00 120.00 90.00 70.00 75.00
Fish scrap (dried) 110.00 80.00 140.00 80.00 70.00 60.00 55.00
Manure salts 20.00 15.00 25.00 15.00 20.00 20.00 15.00
Muriate of potash 40.00 45.00 35.00 45.00 40.00 50.00 35.00
Sand 3.50 2.00 5.00 2.00 3.00 3.50 3.00
Sulfate of potash
magnesia 32.00 25.00 39.00 15.00 20.00 20.00 30.00
Superphosphate 30.00 35.00 25.00 30.00 50.00 40.00 30.00
Tankage 120.00 100.00 140.00 45.00 45.00 80.00 50.00







PROGRAMMING A FERTILIZER MIXING OPERATION


Letting pi indicate the price per pound of each ingredient (table 8.2) the
cost, C, may be written as follows:


(8.8)


14
C= T xiPi


The xi that will minimize the cost and yet furnish the desired product
is chosen by linear programming.


RESULTS

Computation of the solutions was performed by using the simplex
method (1). The results for seven different price situations are pre-
sented in table 8.3.
Several interesting observations may be made concerning the least-
cost combinations in table 8.3. For example, in moving from price sit-
uation I to II, it is obvious that the nitrogen from calcium cyanimid is
cheaper (14 cents a pound) than that from ammonium sulfate (17 cents
a pound). However, calcium cyanimid does not completely replace am-
monium sulfate due to the requirement of a neutral mixture. Price
situation III in table 8.2 results in the same quantities of materials as
situation I, even though there has been some change in the prices com-
pared with situation I.
In price situation IV, manure salts are a cheaper source of potash


Table 8.3. Quantities of Materials Needed to Minimize
Cost of a Ton of Neutral 4-12-4


Price Situations (See Table 8.2)
Fertilizer Material I II III IV V VI VII
(Pounds)
Ammonium nitrate 107.7 107.7 107.7 107.7 107.7 107.7 107.7
Ammonium sulfate 156.1 38.1 156.1 156.1 156.1 156.1 156.1
Calcium cyanimid 59.1 169.0 59.1 22.0 22.0 16.9 16.9
Calcium limestone 221.2 221.2 256.2 256.2 266.4 266.4
Castor pomace 136.0 136.0
Cottonseed meal 140.7 140.7
Dried blood -
Fish scrap (dried) -
Manure salts 320.0 -
Muriate of potash 133.3 133.3 132.2 132.2 129.8 129.8
Sand 122.6 165.2 122.6 -
Sulfate of potash
magnesia -
Superphosphate 1,200.0 1,200.0 1,200.0 1,189.8 1,189.8 1,182.4 1,182.4
Tankage -
Total 2,000.0 2,000.0 2,000.0 2,000.0 2,000.0 2,000.0 2,000.0
Material cost per ton $31.79 $34.28 $27.47 $34.92 $47.22 $36.45 $32.37







EARL R. SWANSON


than muriate of potash, but they are not used. These two sources of
potash have the same price relation in situation IV as in situation II,
but the manure salts were selected in situation II. When all require-
ments are considered, the cost per pound of any particular plant food
may be misleading. Note also that the least-cost combinations in situa-
tions IV and V are the same even though in situation V the nitrogen in
tankage is slightly cheaper (32 cents a pound) than the nitrogen in castor
pomace (33 cents a pound).
Finally, situations VI and VII result in the same combination of ma-
terials. The cost per pound of nitrogen from dried blood in situation
VII is 29 cents a pound compared with 30 cents a pound in cottonseed
meal. However, cottonseed meal is used because its contribution to
requirements other than nitrogen makes the over-all cost of the mix-
ture a minimum. Thus, all of the requirements must be considered in
calculating a minimum-cost mixture.
It is possible to determine from a linear programming solution the
amount by which the price of a carrier not selected for the mix must
fall in order for it to be an ingredient of the minimum cost mixture. In
the literature these values are frequently referred to as zj-cj(l). Take
as an example the result under price situation I. Note that castor pom-
ace does not appear in the mixture. Examining the zj-cj for castor
pomace it is evident that its price would have to drop $8.08 per ton
(other ingredient prices remaining the same) in order for it to appear
in the minimum-cost mix. Price decreases necessary for selection of
other ingredients not presently appearing in the mixture also can be
readily determined.

CONCLUDING REMARKS
It is hoped that the relatively simple illustration presented is sug-
gestive of further application of the technique to problems in fertilizer
mixing. A more complete analysis would need, of course, to consider
costs other than only the ingredients. Such factors as capacities of
blending apparatus, baggers, and other machinery may also be included
in a more comprehensive programming analysis. Further, in situations
where more than one analysis may be mixed it may be also desirable to
include choice of the amounts of each analysis to be prepared as a part
of the problem.

REFERENCES CITED
1. CHARNES, A., COOPER, W. W., and HENDERSON, A., 1953. An introduction
to linear programming, New York, John Wiley and Sons, Inc.
2. and MELLON, B., 1952. Blending aviation gasolines, Econo-
metrica 20:135-59.
3. KOOPMANS, T. C., 1951. Activity analysis of production and allocation,
Cowles Commission for Research in Economics, Mono. 13, N. Y., John Wiley
and Sons, Inc.
4. WAUGH, Frederick V., 1951. The minimum-cost dairy feed, Journal of Farm
Economics 33:299-310.







HAROLD G. WALKUP and JOHN N. MAHAN
Tennessee Valley Authority

Chapter 9




The Potential Market

for Liquid Fertilizer



INTRODUCTION
NUMEROUS considerations should be explored in an investigation
of market potential for a relatively new product such as liquid
fertilizer. First of all, however, it appears appropriate to define
what products the authors consider to be liquid fertilizers; second, it
seems desirable that market potential considerations be defined. Nei-
ther of these topics has become sufficiently staid that its specific uni-
versal interpretation is assured. Rather, it appears judicious to de-
velop definitions in line with the investigative aspects of this chapter.
Liquid fertilizers are defined as those fertilizers and fertilizer
materials which, when used by farmers, are completely in water solu-
tion or which are not in water solution but being liquid themselves are
thus applied either directly to the soil through an irrigation system or
other means of water conveyance and application. Hence, it can be
seen that liquid mixtures and complete liquid fertilizers, anhydrous
ammonia, aqueous ammonia, and phosphoric acid' all can be included.


MARKET POTENTIAL CONSIDERATIONS

Market potential for a product usually refers to the quantity which
will be purchased within the confines of an area during a specified pe-
riod at a specified price or series of prices.2 The estimation of mar-
ket potential for a new product is at best a speculative matter. How-
ever, there are certain fundamental considerations, particularly for a
commodity which is to be used for productive purposes, which are
helpful in appraising potential use. This is particularly true for a

'It is difficult to make an adequate and discriminating distinction between liquid and dry
type fertilizers. For the purposes of this chapter it appeared to be desirable to distinguish
between the liquid and dry types on the basis of their liquid or dry form at the time of appli-
cation through applicating machinery on the farm.
2This is an obvious oversimplification of the complexity of the economic aspects of market
potential. Additional considerations include such matters as: (a) price relationships between
the subject product and competitive, complementary, and supplementary goods; (b) a desig-
nated consistency, degree of change or trend in the techniques of production; (c) a continuity
of quality of competing products and numerous other considerations which one may call to mind.







H. G. WALKUP AND J. N. MAHAN


product like liquid fertilizer which is nearly a perfect substitute for the
older, dry type fertilizers.3 These fundamental considerations relate
to: (a) the costs of new products and their close substitutes; (b) the
productivity response of the product when used in enterprises which
are currently employed in the area or which may be employed as the
result of technical or economic changes within or outside the area
under consideration; (c) the continuity or alteration in income flow
either on a legal basis or due to social or family sanction. Market po-
tential studies have for the most part been directed toward these funda-
mental considerations.


Methods of Studying Market Potential

One method frequently used is the survey method whereby a scien-
tifically drawn sample of respondents from a given population are indi-
vidually questioned as to their willingness, desire, and ability to pay
for various quantities of the product at specified prices. If competitive
goods are available, a price reference between the product and competi-
tive goods is usually considered by respondents. Another method fre-
quently employed, particularly with a new product, involves the selec-
tion of areas in which the saleability of the product may be tried. Price
adjustments may be made within the areas to determine price effects
on demand, or similar areas may be charged different prices to esti-
mate price effects. In both methods detailed basic data on income and
other pertinent information are collected in the areas being studied for
market potential. Statistical studies are sometimes made to develop
predicting equations relating to demand. Important variables usually
included in these equations are prices of the product and closely com-
peting products as well as measures of income. The use of this method
depends to a considerable degree on the existence of an already estab-
lished market and is not well suited to the examination of a potential
where a product has not previously been marketed or only recently
introduced.
A closely allied consideration which often should be made in connec-
tion with a market potential study relates to the costs required to place
the product in the specified marketing areas. In the case of a new prod-
uct which is closely competitive with an already established product in
the selected area, it is usually helpful to compare the costs of placing
both products in the area, as a clue to the share of the market each shall
receive. Such estimations and interpretations require judicious and
comprehensive use of budgeting and farsighted interpretation. Of par-
ticular importance is the necessity for detecting those attributes of the
competing products which give them uniqueness in the various produc-
tion situations in the marketing area studied. In the case of

'The term "perfect substitute" is used in the sense that, when applied to the soil, equal
quantities of plant nutrients (N, P, or K) in either the dry or liquid form substitute for one
another at a constant ratio of 1 to 1.







POTENTIAL MARKET FOR LIQUID FERTILIZER


noncompeting but complementary product goods, considerations relating
to attributes contributing to production complementarity are of great
significance.


HISTORICAL ASPECTS OF FERTILIZER USE

A brief historical consideration of fertilizer use in the United States,
although not of primary importance to this study, may lend some per-
spective to the present technological stage of development in the ferti-
lizer industry.
The use of fertilizers to improve the production of forage and grain
crops (3) has a long and interesting history (table 9.1). Until recently,
many agricultural areas of the United States have used only animal
manures produced on or near the farm on which they were spread. In
the older agricultural areas of the United States and particularly in the
southeastern part of the country, commercial fertilizers have been used
for a long time. Interestingly enough, the first imported fertilizers were
of animal origin. The material was Peruvian guano (bird dung) which
was shipped into this country during the 1840's. Slightly more than 100
years ago the first mixed fertilizers were manufactured in the United
States and about 8,000 tons of plant nutrients were used annually. By
1900, farmers were using 394,000 tons of plant nutrients in commercial
fertilizers.
Organics, ammoniates, dissolved bone or bone black, kanit and

Table 9.1. Plant Nutrient Consumption per Acre of Crops and Pasture Land

Millions of Poundsb Pounds of Primary Average Primary
Millions of of Primary Plant Nutrients Applied Plant Nutrient
Year Acresa Nutrients per Acre Content (Percent)

1910 631 1,712 2.71 15.7
1920 730 2,290 3.14 16.G
1925 722 2,482 3.44 16.9
1930 792 3,048 3.85 18.5
1935 826 2,430 2.94 19.3
1940 860 3,432 3.99 20.8
1945 932 5,658 6.07 21.4
1950 894 8,828 9.87 24.5
1955 12,506c

aAcreage includes cropland and pasture land in farms. 1953 Agricultural Statistics,
USDA, Table 643, p. 550.
bAgricultural Statistics, 1952, USDA, Table 710, p. 705.
CMehring and Graham, 1955, USDA. Fertilizer situation for 1954-55, Commercial
Fertilizer and Plant Food Industry, 90:44 p. 44.






H. G. WALKUP AND J. N. MAHAN


hardwood ashes were used in the early mixtures. Even up to the first
World War the fertilizer industry was considered to be a scavenger in-
dustry, one that absorbed the waste from other industries such as dried
blood, fish scrap, hoof and bone meal, animal tankage, process tankage,
cottonseed meal, cottonseed hulls, castor pomace, and tobacco stems.
Although inorganic sources of plant nutrients were developed, the com-
mon belief that organic materials were superior sources of plant nutri-
ents had to be combated with mounting agronomic results and forceful
educational programs. World War I unveiled the commercial potash
potential in this country. Synthetic ammonia was first produced com-
mercially in 1921. In 1940, there were 9 plants in operation. The Gov-
ernment built 10 plants during World War II. At the present time there
are 43 synthetic ammonia plants in the United States. Due apparently
to location economics, these are widely scattered throughout the coun-
try. Immediately after World War II the fertilizer industry was faced
with a larger demand than it could supply at the prices then charged
for fertilizer. A program for governmental assistance to the fertilizer
industry was initiated in 1951 so that our food and fiber needs could be
met.4


Technological Improvements in Fertilizer and
Other Industries Related to Agriculture

There is one notable difference between the technological develop-
ment of the fertilizer industry as it affects farmers, as compared to
many other industries which are closely related to agriculture. Al-
though fertilizers now contain more nutrients per ton, the techniques
farmers may use to handle them have changed but little. Most fertilizer
is sold in bags and the bags must be handled manually several times
before the fertilizer gets on the land. Maintaining proper physical con-
dition in dry types of fertilizers further aggravates the problem. A
wider acceptance of bulk handling may facilitate convenient and efficient
handling of fertilizers on farms. However, it appears that liquefaction
of fertilizers and handling with pumps and valves offers much promise
to convenience and perhaps to economy in application.
Liquid metering devices are much more accurate than the gates
used to regulate rates of application for dry fertilizers. Also equip-
ment for applying liquid fertilizers may have accessories for applying
fumigants, insecticides, pesticides, and defoliants which help spread
the fixed cost of equipment. In addition, the rate of application is twice
as great as for solid fertilizer.

4The expansion of fertilizer production facilities was encouraged by the Defense Produc-
tion Act of 1950. Under this program certificates were granted for rapid depreciation of
assets for tax purposes. Goals were established during the period when certificates were
granted as follows: for nitrogen, 3,500,000 tons; for phosphate (P20s), 3,550,000 tons; for
potash (K20), 2,000,000 tons.




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