Tire friction coefficients and their relation to ground-run distance in landing

MISSING IMAGE

Material Information

Title:
Tire friction coefficients and their relation to ground-run distance in landing
Series Title:
NACA WR
Alternate Title:
NACA wartime reports
Physical Description:
12 p., 5 leaves : ill. ; 28 cm.
Language:
English
Creator:
Gustafson, F. B
Langley Aeronautical Laboratory
United States -- National Advisory Committee for Aeronautics
Publisher:
Langley Memorial Aeronautical Laboratory
Place of Publication:
Langley Field, VA
Publication Date:

Subjects

Subjects / Keywords:
Airplanes -- Tires -- Traction   ( lcsh )
Aerodynamics -- Research   ( lcsh )
Genre:
federal government publication   ( marcgt )
bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )

Notes

Summary:
Summary: A summary of published information on braking friction coefficients is presented. An analysis is included which indicates that the magnitude of the friction coefficient available will affect the technique required for obtaining the shortest ground run only under extreme conditions. In this connection, technique refers to the choice between utilizing air drag and ground friction through choice of attitude. The analysis further shows that the landing attitude is almost never the attitude for the shortest ground run. A chart is presented for rapid estimation of ground-run distance for any set of values of friction coefficient, airplane attitude, initial drag-weight ratio, and initial velocity. Sample studies are presented for high- and low-wing loadings.
Bibliography:
Includes bibliographic references (p. 12).
Statement of Responsibility:
by F.B. Gustafson.
General Note:
"Originally issued June 1942 as Advance Restricted Report."
General Note:
"NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were previously held under a security status but are now unclassified. Some of these reports were not technically edited. All have been reproduced without change in order to expedite general distribution."

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 003808568
oclc - 130028912
System ID:
AA00009455:00001


This item is only available as the following downloads:


Full Text

Or L-


21fs!


NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS






WARTIME REPORT
ORIGINALLY ISSUED
June 1942 as
Advance Restricted Report
-r

TIRE FRICTI0Q COE TICIETS AD THEIR RELATIC(
/ TO GROTED-RUN DISTMCE IN LANDING

'y By F. B. Gustafson
/


Langley Memorial Aeronautical Laboratory
Langley Field, Va.

UNIVERSITY OF FLORIDA
DOCUMENTS DEPARTMENT
120 MARSTON SCIENCE LIBRARY
PO. BOX 117011
GAINESVILLE, FL 32611-7011 USA


WASHINGTON


NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of
advance research results to an authorized group requiring them for the war effort. They were pre-
viously held under a security status but are now unclassified. Some of these reports were not tech-
nically edited. All have been reproduced without change in order to expedite general distribution.

L 245









































Digitized Iay ile Inlernel Arcnive
in 2011 Wilh funding Irom
University of Florida, George A. Smaihers Libraries wilh support Irom LYRASIS and Ihe Sloan Foundation


http://www.archive.org details Iwrelric ioncoelOOlang










NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS


ADVANCE RESTRICTED REPORT


TIRE FRICTION COEFFICIENTS AND THEIR RELATION

TO GROUNj-RUN DISTANCE II LANDING

By F. B. Gustafson


SUMMARY


A summary of published information on braking fric-
tion coefficients is presented. An analysis is included
which indicates that the magnitude of the friction coef-
ficient available will affect the technique required for
obtaining the shortest ground run only under extreme con-
ditions. In this connection, technique refers to the
choice between utili-ing air drag and ground friction
through choice of attitude. The analysis further shows
that the landing attitude is almost never the attitude
for the shortest ground run. A chart is presented for
rapid estimation of ground-run distance for any set of
values of friction coefficient, airplane attitude, initial
drag-weight ratio, and initial velocity. Sample studies
are presented for high- and low-wing loadings.


INTRODUCTION


At the suggestion of Dr. Edward Warner of the Civil
Aeronautics Board, the NACA has recently reviewed avail-
able information on tire friction coefficients, with par-
ticular reference to the effect of field condition on co-
efficients available for braking. A summary of the infor-
mation found on braking friction coefficients is included
in this report.

An analysis was made to indicate the extent to which
a variation in landing technique, from consideration of
choice between utilizing air drag or ground friction
through choice of attitude, becomes desirable as a result
of changes in field conditions. For this purpose it was
assumed that the choice was not influenced by nosing-over
tendencies. It was further assumed that the load carried













by unbraked wheels was negligible. This analysis indicated
that only under extreme conditions would the technique re-
quired for obtaining the shortest ground run be affected
by the value of the friction coefficient. The analysis
did show, howe-er, that the landing attitude is almost
never the attitude for shortest ground run. A chart has
been prepared for rapid estimation of ground-run distance
for any set of valued of friction coefficient, airplane
attitude, initial drag-weight ratio, and initial velocity.
Sample studies of ground-run distance are included for
both high- ani low-wing loadings.


BRAKI:G FRICTION COEFFICIENTS


Sufficient published information was found on the
effect of surface type and condition and of tire tread on
braking friction coefficients to este.blish the limits im-
posed far most of the coubinaticns normally anticipated.
Most of t.is information resulted from highway research,
and these results are directly applicable to airplanes
during ground runs. While all available dati of this
nature were re-iewed, references 1, 2, anc 3 cover the
subject well; other consulted sources largely served to
check rather than to adi to the information contained in
these papers.

On hnrd surfaces, such as concrete or asphalt, the
coefficient available wnen the surface is clean and dry
is likely to be 0.7 or higher, even for tires without
trend Although values'above 1.0 are seldom retorted for
speeds above 10 or 15 miles per hour, coefficients in the
neighborhood of 0.9 are common. The adverse conditions,
however, normally govern the permissible length of run.
Tne cost common adverse condition is wetness of the sur-
face. For smooth-tread tires skidding straight ahead at
speeds in the neighborhood of 30 to 40 miles per hour,
most highway surfaces, incluiine Portland cement concrete
in both smooth and rough condition, give coefficients be-
tween 0.3 and 0.4 when wet. Reference 1 gives fairly
complete data on coefficients for different surfaces.
The follo:.ing coefficients of sliding friction for smooth-
tread tires skidding straight ahead on a wet surface at
speeds of bout 30 or 40 riles per hour ire taken from
this source:












Surface Coefficient

Penetration macadam, soft seal coat
Fine aggregate asphalt plank All values of
Wooden plank coeffidient
Steel traffic plates below 0.3
liud on concrete

Ohio tar macedan
High-type asrhaltic pavements All values of
Iowa untreated gravel, loose coefficient
Cinders, loose above 0.4

Values for an incipient skid are usually higher than the
foregoing values for sliding friction. Tne effect of
tread is quite pronounced on most hard surfaces when wet,
the coefficient for a trealdd tire being of the order of
one-quarter greater than the coefficient for a smooth tire
on the same surface.

Ice, including snow with an icy surface, provides
the limiting condition for any field w'hEre such a condi-
tion is anticipated. Values of braking coefficient of
0.05 and 0.06 for tires on ice have been reliably reported
but are thought not to be the lowest values obtainable.
An approximate normal value is 0.10. Temperature has a
very important effect on the coefficient for clean ice,
the value dropping rapidly as the surface temperature
rises tow-ird the melting point.

The spreading of abrasives on ice is quite effective.
Some information on this point is given in reference 1,
and a fairly thorough treatment may' be found in references
2 and 3. It appears that the value with abrasives is quite
independent of temperat-re and that a coefficient of the
order of 0.20 can be quickly reached by thorougnly practi-
cable methods of spreading. Reference 1 states that a
value of 0.42 wis reached several days after the applica-
tion of cinders, as a result of their having become em-
bedded.

The importance of the good performance credited to
abrasives is enhanced by the fact that tire treai does
not offer even a potential solution to the problem of
stopping on ice and packed snow. Although tread provides
a marked advantage over smooth tires on nearly all bare,
wet roadway surfaces, as has been already noted, the ef-
fect on ice or snow is quite different. References 2 and









4


3 show that on ice at a temperature near freezing, tires
with tread have higher braking coefficients than smooth
tires but, at lower temperatures, smooth-tread tires give
higher values. On loose snow a lug tread shows advan-
tages, but on packed snow stopping distances are usually
shorter with smooth tires than with traded tires. Values
for an impending skid are likely to be somewhat better for
the traded tire than for the smooth tire on either ice
or packed snow, but with brakes locked the grooves fill
and the coefficients drop. In brief, the differences pro-
duced by tread on packed snow and smooth ice are small,
and '-nenever ice and snow are anticipated, the limiting
condition will not be appreciably altered by the use of
tread on tires.

In suite of the predominant use of hard-surfaced run-
ways, landings on turf must still be given consideration;
for Pxample, for temporary or emergency airports. Exper-
imental values for braking friction coefficients on grass
are rather scarce. From horizontal and vertical acael-
erations recorded at contact during a series of landing
tests conducted by the NACA on the turf surface at
Langley Field, Va., it is concluded that such a surface
when in typical condition has a friction coefficient of
about 0.5. The highest continuous deceleration recorded
during fully braked runs was 0.42, and it is felt that
this value represents very nearly the friction coefficient
available during that run.

For a turf field when wet, very little data are
available. The values found do not appear to be conclu-
sive and more information on this point is desired.

Information is also lacking on the effects of high
speed ani of tire size on braking coefficients. The
values given, with the exception of the data obtained
from NACA landing tests, are for Putomobile tires tested
at speeds not exceeding 45 miles per hour. The evidence
at hand, however, does not point to the likelihood of any
radical changes in the general conclusions when these
factors become ::nown. Likewise, although reference 1
shows an increase in friction coefficient on wet concrete
with a decrease in temperature, introduction of this fac-
tor would appear to constitute a refinement rather than a
fundamental revision.

By way of a general conclusion, it is believed from
this study that, on a well-maintained airport, a minimum
value of the coefficient of braking friction of 0.20









5


should be expected. Lower values, such as would exist on
newly formed ice prior to treatment, should be considered
as present under emergency conditions. Where ice is not
expected, the minimun value should be 0.30, provided the
surface has beeL properly chosen and is kept free of mud;
the minimum value may, of course, be still higher, depend-
ing on the particular surface used.


APPLICATION OF FRICTION COEFFICIENTS

TO CALOULATIOU OF LANDING DISTANCE


Two forces add together to stop the airplane: air
drag'and wheel friction. The manner in which thes' forces
change during the ground run is illustrated in figure 1.
In the proppraticn of figure 1 the airplane was assumed
to make the run at an angle of attack close to the stall,
and it was further as~uaed that a coefficient of friction
between .pels .nd ground of 0.4 P'as utili7ed throughout.
By a quiik reaction of the angle of attack of the air-
plane following cont.ict, greater use may be made of wheel
friction; this condition is plotted in figure ?. A com-
parison of figure 2 with figure 1 shows tha-t reducing the
angle of attack after contact sacrifices less in air drag
than it gains in ground friction force, for the conditions
assumed, and hence will produce the shorter run.

If the friction coefficient is sufficiently low, the
advantage will obviously lie in the reverse procedure;
that is, in making the greatest possible use of air drag.
Figure 3 was prepared to indicate the conditions under
which this result mi.ht be expected. It illustrates, for
the sample polnr shown in figure 4, the ratio of drag
change to lift change for any instantaneous change in
attitude between the limits represented by CL = 0 and
and CL = CLmx. Figure 3 was drawn for the polar for
max
flaps extended; for values of CL/CL lower than 0.5,
max
it also applies to the polr for flaps retracted. When
an increase in angle of attack gives a ratio of drag
change to lift change greater than the value of friction
coefficient available, the use of the higher angle of
attack will result in greater total deceleration. Like-
wise, if a decrease in angle of attack gives a ratio less
than the value of friction coefficient available, the use









6


of the lower angle of attack will result in greater total
deceleration. For example, assume that the choice is be-
tween an angle of attack represented by L/Lmax = 0.9

and an angle of attack represented by CL/CLma = 0.4.
Changing from one angle of attack to the other gives a
ratio of drag change to lift change of 0.13. If the fric-
tion coefficient is less than 0.13, the use of the higher
angle of attack will therefore result in a greater total
deceleration. Inasmuch as the lowest value of friction
coefficient expected on a well-maintained airport is 0.20,
the higher angle of attack will insure the quicker stop
only under emergency conditions. As another example,
assume that the friction coefficient available is 0.20 and
that a value of CL/CL of 1.0 can be used. Figure 3
max
shows that, if any value of CL/CLmax less than 0.5 can

be reached, the use of this lower angle of attack will pro-
duce the greater deceleration.

Examination of figure 3 shows that the greatest decel-
eration will always be present at one of the two extremes;
that is, either at the highest or the lowest angle of at-
tack that can be reached. This result will be true for
any polar that is concave upward throughout because oper-
ation at intermediate angles of attack is then equivalent
to operation near maximum L/D, an obviously undesirable
condition. With this fact in mind, the second example
given yields two interesting conclusions. First, since
an angle of attack below CL/CL = 0.5 can be reached
max
with most airplanes and since the friction coefficient is
nearly always above 0.20, it is concluded from figure 3
that only under extreme conditions will the magnitude of
the friction coefficient available affect the technique
required for obtaining the shortest ground run. In other
words, the best technique nearly; always consists in making
the greatest possible use of ground friction rather than
of air drag. Second, since an airplane seldom lands at
the lowest an:;le of attack that can be maintained during
the ground run, especially if the pilot keeps the approach
speed down for the sake of a short run, it is likewise
concluded that the landing attitude is rarely the attitude
for the shortest ground run.

It should be pointed out that, in the case of con-
ventional gear, another factor enters into the choice of
attitude; namely, the tendency of the airplane to nose












over. After the air forces have dropped off, it is desir-
able to have the tail low enough to permit fullest possible
use of the available wheel-friction force. This considera-
tion obviously does not arise in the case of the tricycle
landing gear.

Conclusions draw from the study represented by fig-
ures 1, 2, and ,3 are purely qualitative. Ir. order to
enable calculations to be mide of the ground-run distance
for any given v'.iue of friction coefficient, a general
eauation has been derived and a convenient form of chart
prepared. The equation anI the chart have been made to
include the effect of angle of attack directly. This
procedure was adapted not only because of the importance
of attitude sugesPtel by tie qualitative study but also
because considerable cl.ange in attitude following contact
is feasible, and some change inevitable, with the tricycle
landing gear.

The decelerating force at a given insta-nt ill be
the sum of the air force and the wheel friction force,



aL + (- L)



where

W weight

D drag

L lift

4 friction coefficient between airplane and ground

and

k ratio of lift at start of run to weight (L1/t.)

V velocity, feet per second

Assume CL and CD to be constant during the run. Use
the subscript i to rel.resent conditions at the start of
the run. T expression kcan be substituted for
the run. The expression kI d I can be substituted for









8



L, and D for D. This procedure gives


D(/ I kV
a = g + --
SV12



By substitution in the equation

V2
s = f VdV
J u
V=0


where s is the distance covered, and by integration,
the expression becomes



V7 -- + u ku

2c



For a gi"en value of L/'. or k the average de-
celeration, and hence the distance for an airspeed equal
to 1 for any given ratio of DI/W to i, is proportional
either to D1/W or w. The result is shown in figure 5,
in which the value of D1/W + p has been plotted against
the distance s' for V1 = 1 and p = 1; curves are
shown for values of angle of attack, as represented by k,
from k = 0 to k = 1.0.

A v-lue of ground-run distance can be calculated from
this chart as follows: First, calculate the ratio
DI/W + i. This step is most easily taken, as a rule, by
the use of the drag coefficient and the lift coefficient
that would be required for support at the initial speed,
or












D2/W CD


SCL ax


where V is stalling speed. Then, calculate the value
of !, which is simply the lift coefficient divided by
the lift coefficient that would be required for support
at the initial speed, or


L





Using thesr two values, read the value of s' from
the chart. Multiply s' by the square of the initial
speed and divide by the value of L. The answer is the
ground-run distance.

This chart should be useful for design e-stimates for
both airplanes and airports, inasmuch as it is possible
to examine the effect of Tha-nges in ground-friction coef-
ficient, air drag, and angle of attack, as well as initial
velocity, either singly' or in coLibination.


SAMPLE STUDIES


The significance of the ground-frictiun coefficient
and 3f the related problem of angle of attack during the
ground run cannot be precisely stated except for specific
cases. For this reason, the following sample study is
presented.

It is assumed that a efficient of friction of 0.4
is utilized between tires mnd ground. It is also assumed
that brakes are uq~d on all whels. The effect of the
time required to chspge the angl of attack following con-
tact has been indicated by making calculations for zero
transition time and for q 2-second transition period. The
conditions, the 0ncirnled numbers used to represent them,
and tne corresponding values of lift and Irag assumed are
as follows:









10


Airplane at stall; CL = 2.0, CD = 0.30
max
( Thrust axis horizontal, flaps not retracted;

CL = 0.93, CD = 0.12

O Thrust axis horizontal, flaps retracted;

CL = 0,33, CD = 0.025

When a transition from one angle of attack to another is
involved, both encircled numbers are used. (See fig. 6.)

Thus,. (2 means that contact was made at condition

Q and a transition made to condition j.

The runs with zero transition time were calculated
by means of figure 5 in the manner nlrealy explained,
using the lower angle of attack as the initial condition.
For the runs with 2-second transition period, the dis-
tance covered ?nd the velocity lost during this period
were calculated on the basis of two 1-second intervals,
assuming that hnlf tne decrease in angle of attack had
been attained during the first second. Successive ap-
proximations were used to determine the deceleration
during each second. The rest of the run was calculated
by means of figure 5, using the speed and the angle of
attack at the end of the 2-second period as the initial
condition.

The calculations were carried out over two ranges of
wing loading to indicate the effect of this factor. The
values obtained are plotted against effective wing load-
ing in figures 6 and 7. The effective wing loading I/oS,
where W/S is the wing loading in pounds per square foot
and C is the density ratio, was used so that a single
plot could be readily used for any density altitude. The
effect of change of angle of attack, and of transition
time required for this change, on ground-run distance is
summarized in figure 8, in which average deceleration is
plotted against reduction in lift coefficient following
contact for the lowest and highest wing loadings covered
by figures 6 and 7, respectively. The effect of a fixed
transition time is snown to be appreciably less at the
higher value of contact speed. Further, in every case
examined in this study, the effect of reduction in angle
of attack at or following contact is shown to be a reduc-
tion in ground-run distance.












CONCLUDING REMARKS


The values found for the braking friction coeffi-
cients of smooth-tread tires on various surfaces indicate
that such coefficients under adverse conditions, includ-
ing rain and snow, are commonly above 0.2 and that the
outstanding exception, fresh ice, can be raised to this
value by appropriate treatment. Values for smooth-tread
tires on wet surfaces commonly f-ll between 0.3 and 0,4.
Exceptions are common enough and the divergences in values
are wide enough to necessitate attention to specific val-
ues in designing or rating airports when the landing run
may be critical.

The analysis of the effect of lo-' values of braking
friction coefficient on the relative merit of tail-high
and tail-low,; attttuie during the ground run indicates
that, if tne friction coefficient available is greater
than 0.2, the tecu rique should be directed toward utiliz-
ing braking friction rather than air drag. For values
below 0.2 consideration of the individual case is neces-
sary.

The chart presented for estimation of *Cround-run
distance should facilitate quantitative stuly of the ef-
fect of changes in ground friction for specific cases.
Except where full knowledge of applicable assumptions
exist, however, it should be used chiefly to determine
relative rather than absolute values.



Langley Memorial Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley' Field, Va.








..-
12


REFERENCES


1. Moyer, R. A,: Skidding Characteristics of Automobile
Tires on Roadway Surfaces and Their Relation to
Highway Safety. Eng. Exp. Sta. Bull. No. 120, Iowa
State Col., vol. XXXIII, no. 10, Aug. 8, 1934.

2. Anon.: Committee on Winter Driving Hazards. 1940
Report to Street and Highway Traffic Section,
National Safety Council. Safe Winter Driving.
Nat. Safety Council, Inc., (30 N. Wacker Drive),
Chicago, Ill., 1940.

3. Anon.: Committee on Winter Driving Hazards. Lake
Cadillac Skidding and Tr..ction Tests. (Tech.
Supp. to reference 2.) Unt. Safety Council, Inc.







Figs. 1,2


Ai.rp/arn
makes In
concx e -- -


W 1e/-trc~, iI .I I I
Wheel/-ftir cor conr,buton if no 'ift


Tot al
T W'eel-fr. tin corttribd l

Sirdr contribution at contact c-s


l FO


PrcentQgye of trt ol tre of grojns run
'.e re /- V'r'.ao. ,of,' ?nc" "~.v.e/ fr f.a'r Forces dsr :;
cronstc-<: a ''e :f ator i.


A airplane
ioakes
contact


F/wjre h. n r/./b/ir
whb^n n7s/e f


/' ~ eel-friCeton cnncr e b or .
ro, ir a 'LL lL OL- >__ a
- To- to/ 'I i









2seconos a er conoct i _
50 C
,--"--------.--- ..- -'
.... = .. ---- --






Percentage If totai time of gr, "- run
o0a3/r SnC' rhPel /cN/eo7 f6.rce s azirr r ype/2.o
a.c'r- -s reduced" o'iewic^ a//e" ctntac .


NACA C








Figs. 3,6


,*P I t I for:
-- -to-- ,,,



It ItMAndI IM Tated lee;
P mud an consciut
9 CL/


S attitud 1.0
.1
n /

.2 .4 A /1
CLc
-.2

o --- -"


., i "..- i --,-
S .-_ I. /- ,_

o .2 .lj .6 .6 1.0
f for first attitude

i Figure 3.- Chart to frcilitate comparison of an7 two attitudes
between zero lift and the stall, for any given instant, to
show which attitude w111 give the greNter deceleration with
any assumed friction coefficent. See polar o figure 14.





At stall; Cl,,= 2.0; C)D= 0.0
__ t' Airplane velIa a no ______
retreated; Cl 2 0.9); C = 0.12
I Airplane level flal ^
500 r- ---r tg'et' n or4
C Calula te l Ivalus

CONCITIGI DURtNO RtN
100 'throughou--
,oo


S'XI, 2 4 ee t ans tion '
I ; \ -2 -cnds irans i on ," .'
5 002l sero tr"nettlon tl e- -
,1 12sero &oamsitimo e s- .
z e lift tUughiut -- ,

200 -



100 .



S 0o 1 8 12 16 20 -2. 28
Effective wing loading, .L lb per sq ft
Plgure 6.- Variation of grouqd-run distance over a range of low wing loadings for
several ground-run procedures. p = 0.4.









Fig. 4


CL/COIiax


0 .2


1.0


01- I I I I _-I I I I\-
0 .4 .8 1.2 1.6 2.0



Figure 4.- Polar curve assumanl for preparation of figure 3.






IACA Fig. 5


\-.9_ 1


AIM

5c L


.2!




.i -





.108
.07-- .. i\ ----- .. J..
.04 I
.-- -- -----

.082


.o .. ... -- -
S.0




.- .2.6 .8 -- -
.09. --- H -r --1 -- .

07- -- -,---- .-.--.--- -.----.--








.0
-^ -L- .. '



0 I i I




.01 A .LL_ ^-
100 150 200 250 o00 a, 4O0 500 600 700 x 10
Figure 5.- Chart for estimation of ground-run distance.







NJCA Figs 7,8




0NfO,,DIT',OA DL'OIAG A _UAI
T At to,/;' C.,= .0; C,=O.30 l i I
20 Airpone 'eve, fapsnot LI g oEv _c
,__ rer- cre CL =0.93; C,= 02 0
Airp/.ae ieve!, flaps retracted; I
6o C-= 0.33, Co= Co.025 ze- o ras o .
,Z, zero trasl 0n E -I '
S: |- ,zero tirocanr :"e





2 4, I 00----
I.'- I.


C 0 20 30 40 5' 6 70 0' C 00
Eect ve v r.- ood, 9,g b cer sq fr

Figure 7- Variaron of ground-run distc-ce over a 'oge ofc rq v .y .coo 5s -'Ic. sever.'
ground-run p.-rcedures. = OA 4




S!-- --- r-. i t



S- a. h



0 4 .8 .2 20






C, reoJuct -o- o3.;r rnr
o 'ece/Orabo ...__ ._ ,'-al.- Cc -""- -- Js c 5,horizonal veocit' r. rat contoc.

I I i ; ,

'I I I

0 .4 8 /2 ,.6 20
C. reductc'O" oir ry L'-,

F/j~'re f -EC'f{' of 6( r/defcd/an enA 0r /m r~dec/e/y fo/~''ow'g con'act ofr .i'eraye
deceerat/'ori o'-r/rff oroyn' 9r/o ,vn. < 3; c V horrzonrtol Lve'ocity at contact.




I








UNIVERSITY OF FLORIDA

3 1262 08106 564 0



UNIVERSITY OF FLORIDA
DOCUMENTS DEPARTMENT
120 MARSTON SCIENCE LIBRARY
P.O. BOX 117011
GAINESVILLE, FL 32611-7011 USA

























:isi






:.i '..i )




Full Text
xml version 1.0 encoding UTF-8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd
INGEST IEID EC28FRZDN_NOCRL6 INGEST_TIME 2012-03-02T22:46:32Z PACKAGE AA00009455_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES