Theoretical and experimental dynamic loads for a prismatic float having an angle of dead rise of 22 1/2°


Material Information

Theoretical and experimental dynamic loads for a prismatic float having an angle of dead rise of 22 1/2°
Alternate Title:
NACA wartime reports
Physical Description:
11, 4 p. : ill. ; 28 cm.
Mayo, Wilbur L
Langley Aeronautical Laboratory
United States -- National Advisory Committee for Aeronautics
Langley Memorial Aeronautical Laboratory
Place of Publication:
Langley Field, VA
Publication Date:


Subjects / Keywords:
Seaplanes -- Hydrodynamics   ( lcsh )
Aerodynamics -- Research   ( lcsh )
federal government publication   ( marcgt )
bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )


Summary: An application of a modified hydrodynamic impact theory is presented. Plots are given from which the maximum load, the time to reach maximum load, and the variation of load with time may be obtained for a prismatic float of 22 1/2° angle of dead rise for different combinations of flight-path angle, trim, weight, velocity, and fluid density. The curves cover the range of trim, flight-path angle, and weight-velocity relationship for conventional airplanes. Test data obtained in the Langley impact basin are presented and are used to establish the validity of the theoretical curves.
Includes bibliographic references (p. 10).
Statement of Responsibility:
by Wilbur L. Mayo.
General Note:
"Report no. L-70."
General Note:
"Originally issued July 1945 as Restricted Bulletin L5F15."
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 - 003638573
oclc - 71836436
sobekcm - AA00006267_00001
System ID:

Full Text



July 1945 as
Restricted Bulletin LF15

By Wilbur L. Mwyo

Langley Memorial Aeronautical Laboratory
Langley Field, Va.


!;ACA WA.RTIME REPORTS are reprints of papersorginallUy issued to prc.vide rapid distributic-n of
aoivance research results to an authorized group requiring them for the war effort. They were pre-
'.i usly held under a security status Lut are now unclassified. Some of these reports were not tech-
nial', .*dited. All have been reproduced without change In order to expedite general distribution.

L 70


RB No. L5F15

Digitized by the Internet Archive
in 2011 with funding from
University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation






By Wilbur L. Mayo


An application of a modified hydrodynamic impact
theory is presented. Plots are given which the maxi-
mum load, the time to reach maximum load, and the varia-
tion of Icad with time may be obtained for a prismatic
float of 22- angle cf dead rise for different combinations
of fli-:ht-path angle, trin, weight, velocity, and fluid
density. The curves cover the renge of trim, flight-path
angle, and weight-velocity relationship for conventional
airplanes. Test data obtained in the Langley impact basin
are presented and are used to establish the validity of
the theoretical curves.


During the past 15 yesrs numerous reports have been
written on hydrodynamic theory for the landing impact of
seaplane floats but none of these treatments has been
accepted for design purposes. An analysis (unpublished)
of available treatments (references 1 to 8) was undertaken
by the Langley Laboratory in order to determine the
validity and possibilities of the theory. This analysis
showed that the previous treatments did not properly take
into account certain hydrodynamic forces, particularly
those associated with planing action.

An application of a modified hydrodynamic innact
theory is presented herein for the case of a rigid pris-
matic float having an angle of dead rise of 22- The
validity of this theory is established experimentally by

NACA R3 No. L5F15

comparison with data for a rigid float tested in the
Langley impact basin. The theoretical solutions are
directly applicable to the calculation of the dynamic
response of elastic airframes, if it is assumed that the
variation of load vith time is not substantially affected
by the structural elasticity of the body. Experimental
verification of the rigid-body equations is significant
in that it establishes the validity of a basic hydro-
dynamic theory which is equally applicable to the deri-
vation of equations that involve modification of the force
history due to structural elasticity. Additional work is
planned to include the effect of the structural response
on the loading function.

A large number of force histories is given by three
plots from which the maximum load, the time to reach maxi-
mum load, end the variation of load with time may be
obtained. The equations used in obtaining the results are
given and the method cf solution is explained in an

p angle of dead rise, degrees

T trim, degrees

y flight-peth angle, degrees

"T weight of float

V resultant velocity at instant of first contact
with water surface

p mass density of fluid

g acceleration of gravity

tam elapsed time between instant of first contact with
amax water surface and instant of maximum acceleration

m mass of float

ni,,, impact load factor (maximum hydrodynamic load
"v ax normal to water surface divided by W)

NICA R3B No. 15F15 5

".T.ere units are not given, any consistent system of
units may be used.


Comparison of Theory and Experiment

Theoretical solutions made for a rigid Drismatic
float having an angle of dead rise of 22- were compared
with data obtained from tests of a float having the form
of the forebody shown in figure 1 and the offsets given
in table I. The agreement obtained in this commarison
indicates that the theory can be applied to floats which
do not differ from a prism more then the float in figure 1.
Figure 2 sho,'.s the variation of the impact-load-f-ctor
coefficient :with fli-ht-path angrle for trims ranging from
o0 to 120. The eauations, from which the curves were
obtained, were derived on the assumption that the ratios
of fluid compressibility, viscous forces, and gravity
forces to inertia forces are r.>-i ible. In tank tests
of seaplanes the ratio of the gravity forces to the inertia
forces (Froude's number) is the criterion for determining
the sirmilarity of the flow for similar hulls of different
size. The high speed associated with an impact tends to
increase the inertia forces and to decrease the relative
importance of the gravity forces; however, the tendency
to design lar-e airoplnes to have landing speeds of the
same order as small airplanes results in lesser acceler-
ation for the larger weights and greater importance of the
gravity forces. For a specific landing speed there is a
wei7r-t range above which the gravity forces may be of sub-
stantial importance.

Z:y.erimental data are included in figure 2 for the
two boundary values of trim investigated. The data were
obtained at widely different speeds for a float weighing
110C pounds. Even the points obtained in low-speed tests,
for which gravity forces are of greater importance than
for high-speed tests, show remarkable agreement with com-
putations made on the assii'-ition that the gravity forces
are negligible. For a full-scale lending speed of 70 miles
oer hour the experimental data represent airplanes weighing
up to 160,000 pounds. For higher l-ndinfc speeds, such as
may occur with military airplanes, the represented weight
is even greater. These interpretations of the experimental
check show that the theoretical computations presented

ITAC\ RB io. 15F15

herein will give gcod results for all present-day air-
planes. Pertinent data with regard to the weight-velocity
relationships for equal ratios of the gravity forces to
the inertia forces equivalent values of V T 1/6NT ) are
included in figure 2.

The fact that the curves in figure 2 intersect shows
that the variation cf maximum impact force with trim for
large flight-nath angles is the reverse of the variation
for small flight-oath angles. For small flight-path angles
the planing forces predominate and, since the effect of
increased trim is to increase the downwash angle of the
deflected stream, the resulting increase of the resultant
force for a specific draft at the step causes the impact
to be more severe than for small trim. For large flight-
path angles the increase of the virtual mass due to verti-
cal velocity dominates the impact force and, since the
effect of increased trim is to lower the rate of increase
of the virtual mass for a specific vertical velocity,
lesser force for a specific draft, and consequently a
less severe impact than for s-mall trim, occurs.

Figure 5 shows the variation of the time to reach
maximum acceleration with flight-psth angle for trims
ranging from 30 to 120. The plot is similar to figure 2
and therefore does not require further explanation.

Figure 4 is a plot of cceleraticn ratio against time
ratio for a widee range of fliht-oath angle and trim. The
ratios are based on the acceleration and time at any
instant as compared with the maximum acceleration and the
time to reach maximum acceleration. By interoolating
bet.' een the curves of figure 1+ an!d using the amolitude and
time plots of figures 2 and 3 to define the maximum accel-
eration and the time to reach rnximum acceleration, snr
number of time histories within the range of investigated
conditions can be constructed.

Because individual curves would be difficult to dis-
tinguish If all the solutions of the equations given in
thb appendix were clotted, so e of the solutions have been
grouped and the boundary linas for e-ch :.:.) plotted in
figure 4. The solutions that lie between the boundary
lin-s are tabulated in figure .t Although an approximate
inter-polation can be affected between the boundary lines
of fi ;1r l., the spacing is close enough to oprmit the use
of a line centered between those boundaries for practical


The equations used to obtain figures 2 to L assume
that the beam of the float is large enough to prevent'the
chine from coming into firm contact with the water. If
the chine does come into contact with the water, a discon-
tinuity occurs in the impact orocess and the conditions
specified by the equations of this report for the time of
chine contact must be taken as the initial conditions for
a different equation for the case of immersed chines. It
is planned that a later program will deal with such

Applicability to Flight Impact

The load values given herein are based on the assump-
tion that the chines do not become immersed; it should be
noted that early immersion of the chines can cause only
reduction of the maximum lead and hence conservative load
values. The variation of the impact force with draft,
which was obtained in the course of solving the equations
of the appendix for the force-time variation, was used
to determine the effects of beam loading, flight-path
angle, and trim on chine immersion. A comparison of the
data obtained in this study with available data for a
number of different airplanes was made. It was indicated
that the beam loadings of conventional American seaplanes
end flying boats are sufficiently light to ensure that
maximum load values given herein will not be unduly con-
servative. Some German airplanes, and possibly some
American flying boats with wartime overload, have high
beam loadings, which may cause the immersion of the chines
to be significant for high trims and steep flight-path

For small angles of dead rise and for large trims the
theory requires a different formula. Since the exact
manner of the transformation from the condition requiring
one formula to the condition requiring another formula is
not known, the formulas of the appendix should not be
applied indiscriminately.

The equations presented are for the absence of pulled-
up bow. The bow of the float tested is representative of
the bow of an actual flying boat; -greement between the
data obtained and the theoretical computations for the
prismatic float indicates that the effect of the bow is
not important for the conditions investigated.

E:iCA. R3 To. L5,15

Both the experimental data and the theoretical cal-
culations are for fixed-trim impact and therefore do not
indicate the effect of angular rotation during impact.
Various design considerations tend to locate the center
of gravity relative to the center of water pressure so as
to minimize angular acceleration. Even when substantial
angular accelerations are reached, the time to reach peak
load is believed to be short enough and the aver~g'- angu-
lar velocity small enough to keep large angular displace-
ment from being reached during this period.

The experimental data used in the present report were
obtained in tests of the flost shown in figure 1 with the
afterbody removed. Although exact evaluation of the
effects of afterbodyT leads is not possible at this time,
various design considerations ensure that actual airplanes
will have sufficient depth of the step and reduced trim
at the afterbody to be effective in promoting the shieldin:,
at impact speed, of the afterbody by the forebody and in
causing thereby the loads on the afterbody to be of rela-
tively small importance.

The experimental data used herein were obtained with
a float attached to a coasting carri-ce having a mass
about three times the mass of the float. This condition
involves slight reduction of the speed during impact,
whereas in the theoretical computations a constant hori-
zontal seed is assumed. By observing the relative magni-
tudes of the vertical and horizontal accelerations and
velocities for an impact and applying the laws of velocity
dissipation, even in the case in w-hich the float is
entirely free in the drag direction, the reduction in
horizontal seed during the impact can be seen to be of
small 1-. ortance. By using different constants in the
equations of the appendix, the reduction in horizontal
seed can be incorporated; however, it is felt that the
gain would be toc slight to warrant the additional com-

The curves of the present report are for smooth-water
impacts but they will give approximate results for rough-
water impacts if the flight-path n-le and the trim are
defined relative to the wave surface rather than relative
to the horizontal.

The equations in the appendix are based on the assump-
tion that the float is weightless (Ig wing lift). Devia-
tion of the wing lift of the actual airplane from lg will
affect the experimental results but the effect will
probably not be very lar:0.



Application of a modified hydrodvnsmric impact theory
to a rigid prismatic float with angle of dead rise of 22-
and an analysis of data made to determine the validity of
the theory indicate the following conclusions:

1. The effect of trim on load for large flight-path
angles is the reverse of that for small flight-path angles.
This reversal is due to a change in the relative importance
of the plening and impact forces and shows that both the
forces must be considered.

2. Tle agreement between experiment and theory was
good, and thus the theory was proved adequate for the
conditions investigated.

3-. Since hydrodynamic impact theory does not take
into account the effect of the gravity forces on the fluid
flow, the are--ment of this theory with experiment for the
range of weight-velocity relationships for landing impacts
of present-day airplanes indicated that the effect of
gravity on the flow pattern is not important in impacts
of such airplanes.

L4. Consideration of the factors involved in applying
the theoretical curves to actual airplanes indicated that
such Epplications will give good results.

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



0 0
O 0





'-,I I 0

0 -- -P

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0 f
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In equations (1) and (2)

A = 0.7p(- 2 + 0.79 ----
S23. tan p

B = 0.79- -
tan p

C =1 -tan
2 tan p

where p is measured in radians and

y draft of float at any instant

yo vertical velocity at contact
y vertical velocity of float at any instant

y vertical acceleration of float at any instant
Formulas (1) and (2) are not applicable when y is
negative, that is, after the float has rebounded from the
water surface. These solutions, which can be readily
obtained from equation (2), lie in the region where y
is negative. Efforts to obtain a solution giving the dis-
placement explicitly as a function of the time have not
been successful and, consequently, the following procedure
was used to calculate the curves presented herein:

1. Substitute arbitrary values of y in equation (1)
and solve for the corresponding values of y.

2. Substitute corresponding values of y and y in
equation (2) and calculate the corresponding values of y.

5. Repeat process for values of y selected to
define adequately the y-curves with a minimum number of

4. Plot the variation of l/y with y. For each
point on this curve the acceleration is known from the
previous steps. Th: time for each combination of y, y,
and y can be obtained by integrating the area beneath
and to the left of a particular point on the curve showing
the variation of 1/y with y. Determine such time
values for intervals that approximately define the
acceleration-time curve. Repeat the process for such y

NXCA RT3 No. T F15

and y combinations as a-e of greatest help in defining
the more critical portions of this curve.

The accuracy of the outlined method is dependent upon
the number of points for which solutions are made in order
to fair the various curves. After a certain amount of
experience with these solutions, the accuracy of a specific
solution may be approximated :v estimating possible errors
involved in fairing the curves through the limited number
of 2oirts. It has been found that after the constants for
equations (1) and (2) are computed curves giving the
relations between acceleration, velocity, and draft within
an accuracy of the order of 1 percent can be obtained by
one c'iputer in 3 or + hours.

PA ,-r- 7 "- 1 77.NC >

1. von TKarmsn, Th.: The Impact on Sonplane loats
during Landing. 'TAYC TN 1o. 21, 1929.
2. Past, "ilhel m: Theory of the Landing Imoact of
Se ilans. 'CT A TM No. 580, 1950.

2. Pabst, ;ilhelrr: Landing Impact of Seaplanes. 'ACA 7"1
Io. 624, 1931.

1. 'Wagner, Herbert: Landing of Seaplanes. NACA TM
No. 622, 1l.

5. "/agner, Herbert: Tber Stoss- und Gleitvortr'.ge an
der Oberflache von Flu'ssihkeiten. Z.f.a.M.M.,
?:1. 12, Heft 4, Aug. 1952, pp. 195-215.

6. Schmieden, C.: TUber den Landestoss von
'1Pugae-i chwirmmern. Ing.-Archiv., Bd. X, Heft 1,
Feb. 1959, pp. 1-15.

7. Sydo:, J.: Iber den Einfluss von Federung und
Kielung auf den Landestos.L. Jahrb. 1953 der
deutschen Luftfahrtforschunp, R. 01]dcnbourg
(Munich), pp-. I 29 I 3558. (Available as
British Air ""'-:stry Translation No. 861.)

8. .'r--s, R. T.: ExDcrimental Investigation of Tmonct
in Landing on afterr NACA TM T'. 10146, 194-5.

NACA RB :c. L5F15

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