NATIONAL BUREAU OF STANDARDS REPORT

bSlb

LANDING GEAR LOADS RESULTING PROM

TAXYING AIRPLANE OVER A PROJECTING

RUNWAY LIGHT

Progress Report 1

To

Equipment Laboratory

Wright Air Development Center

Department of the Air Force

<NBS>

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
U. S. DEPARTMENT OF COMMERCE

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NATIONAL BUREAU OF STANDARDS

A. V. Astin, Director

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NATIONAL BUREAU OF STANDARDS REPORT

NBS PROJECT NBS REPORT

0201-20-2331 March 1956 lj.574.

LANDING GEAR LOADS RESULTING FROM

TAXYING AIRPLANE OVER A PROJECTING

RUTWAY LIGHT

Progress Report 1

To

Equipment Laboratory

Wright Air Development Center

Department of the Air Force

NBS Lab. No. 6.I+/295, PR-1

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

TL Ll . Approved for public release by the

The publication, ref

' director of the National Institute of

25 .D.C. Suchper, Standards and Technology (NIST)

cal ly prepared If tt On October 9, 2015

n part, is prohibited

indards, Washington

lort has been specifiport for its own use.

LANDING GEAR LOADS RESULTING FROM

TAXYING AIRPLANE OVER A PROJECTING RUNWAY LIGHT

by

Wilhelmina D, Kroll

1. INTRODUCTION

Eor the modern airport, runways are being built wider in

order to accomodate the larger, heavier airplanes that are coming

into use. The need for better lighting of the runways has become more important with the increased traffic in night flight

and with the higher landing speeds of present aircraft. Flushmounted units have been used for runway lights so as to put no

obstacle in the path of the plane as it taxies for landing or

takeoff, A more efficient lighting system could be devised if

the lights were mounted so as to project slightly above the

runway surface. Although this type of light might be approved

for lights at the sides of runways in the expectation that the

airplane wheels would not run over them, they would not be used

to light a runway across its intersection with another runway

unless it can be shown that this would permit safe operation of

all airplanes using the runway. It was the purpose of this investigation to determine what the loads on the gears of an airplane would be if, while taxying on a runway, the airplane

taxied over a runway light of a particular shape and height, and

what the optimum shape of light would be.

As a result of an increased number of accidents caused by

collapse or failure of the landing gear, numerous studies have

been made to determine the loads imposed on the structure during landing of an airplane or taxying it on a runway ( references 1-8), Although some of these reports consider wing flexibility, it is pointed out in references 9 and 10 that slightly

conservative results are obtained when wing flexibility is neglected,., It was felt, therefore, that an analysis in which the

airplane is represented by a two-degree-of- freedom system as is

done in reference 7, would give, with sufficient accuracy, the

increase of load on the landing gear when the airplane taxies

over a runway light and would indicate the best shape for a projecting runway light without an excessive amount of computational

effort.

2. METHOD OF ANALYSIS

The airplane is represented by a single mass riding on a

system of springs and dampers with a small additional mass
iM •

I

I

I

II

II

(i
NBS Lab. No. 6.4/295, PR-1 page 2

representing the wheel. The two-degree-of- freedom system shown

in figure 1 represents one of the landing gears of the airplane

and the proportionate part of the airplane mass that it supports.

In figure 1, the portion of the airplane mass carried by

one landing gear is m-^. The shock strut between the airplane

and the wheel is represented by a spring and a damper. The

spring constant k-j_ is obtained from the load- stroke curve of

the strut for slow closure, and the damping constant c from

drop test data of the oleo strut, m2 is the mass of the wheel

including the parts of the shock strut that participate in the

motion of the wheel. The tire is a simple spring whose constant, k2 , is given by the load-deflection curve of the tire.

W is the vertical force, other than the impact force, acting

on the airplane (airplane weight minus lift). W^, then, is the

part of W attributed to one landing gear.

For an airplane taxying down a smooth runway, the differential equations of motion of the masses are?

where

m2^2 + k2X2 - k]_( x]_“ x2) - = ^

l-^x^ + k-j_( X]_“X2 ) + c( x^-X2 mn ) = W-^

X1 is the

x

2 is the

X1 is the

f • x2 is the

2 ) is the

2

) is the

is the acceleration of mass m,

(la)

(lb)

Other symbols are defined above,

If the airplane, while taxying, hits an obstruction on the

runway such as a light projecting above the runway surface, the

term ^2X2 in equation (la), which is the force on the tire,

would have to be replaced by k2 [x2+h(t)], where h(t) is the

height of the light at time t, or

NBS Lab, No 6.1+/295, PR-1 page 3

m2^2 + k2^ x2 + h(t)] - k

i( xi~x2

^ " c( x ]_- x

2

) = 0 ( 2a)

mlx

l + k-^C x

i"x2

) + c( x2“x

2

) = ( 2b)

At some time during or following the run over the light,

the value of [x^+hCt)] may become zero or less than zero*

This would indicate that the wheel was no longer in contact

with the light or the ground but the oleo would still be partly

closed. The equation to use instead of (2a) would be

m2x*2 - k

1(x1 -x2

) - c(

x

1 -x2

) =0 (3)

as the force on the tire would be zero* Equations (2b) and (3)

would be solved simultaneously for the motion of the masses until [xp 4- h(t)] became greater than zero again, when equations

( 2a) ana ( 2b) apply.

If the stroke of the oleo strut ( xi~xp) becomes zero or

less than zero during the time the motion of the airplane is

being studied, it would mean that the oleo strut was fully extended and the airplane was air borne. For this condition, the

equation to be satisfied is

ra l^l = W1 (4)

At time t=0 when the airplane wheel would be at the edge

of the light and before it had started to run over it, the deflections of the masses are

X1

and

x2 = Wl^>

(5)

(6)

With these values of displacement as the initial values, a modi

fi cation of Newton’s method was used to solve the differential

equations after replacing the first and second derivatives by

the following difference equations given in Appendix B of reference 11

NBS Labe No. 6.4/295? PR-1 page 4

(7)

Xt = fltF 2X

t

‘ 5Xt-At

+ ^t-2At -X

t-3At (8)

and defining h(t) by a particular shape of light. By this

method, a time history of the motion of the masses and of the

loads on the landing gear was obtained.,

The 6 different shaped lights shown in figure 2 were used

to determine which was the optimum shape® Each light had a center portion 6 inches long and 3 inches high with fairings

to the center section in the shape of a triangle, circular arc,

ellipse, parabola or sine curve. The lengths of the trapezoidal-shaped lights were determined by varying the base angle

from 5 degrees to 45 degrees in 5 degree steps. The 9 lengths

of light corresponding to these angles for the trapezoidal

light, table 1, were then used for the remaining shapes of

light. The lights drawn in figure 2 have a length of 18.8? in.

which is the length of the trapezoidal-shaped light with a

base angle of 25 degrees and a maximum height of 3 inches.

The load-deflection curves of the tire and of the shock

strut for a particular airplane were used in the computation.

The damping constant was determined from the drop test data

for the landing gear of the airplane. The strut stroke and

the force on the oleo as a function of time were read from the

records of a particular drop test. The spring force was read

from the load- stroke curve of the shock strut for slow closure.

The damping force is the difference between the oleo force and

the spring force. The velocity of closure was obtained from

the slope of the stroke-time curve. In reference 12, the damping force in an oleo strut was found to vary as vl«4&. For

our purpose, it was believed to be sufficiently accurate to

consider the damping force proportional to v-*-°5 0 Although it

is realized that the oleo strut exhibits different characteristics in extension than it does on compression, it was assumed that the strut would have the characteristics associated

with its compressive action at all times.

3. ANALYSIS FOR REAR MAIN GEAR OF THE B-4? AIRPLANE

As the data needed in our study were available for the B-47

airplane, reference 13 9 it was decided to use this airplane in

our first study. The data are given in table 2. The load-

NBS Lab. No. 6 . 4/295 , PH-1 page 5

deflection curve for the tire, and the load-stroke curve for

the shock strut are given in figures 3 and 4., respectively.

The curves of figures 5 and 6 were used to obtain, in conjunction with figure 4 , the damping constant as a function of

stroke. With the data from these curves and from table 2 , the

time histories of the displacements of the masses were obtained

in SEAC, Standards Eastern Automatic Computer.

4 . RESULTS FOR B -47 REAR MAIN GEAR AND DISCUSSION

Figure 7 shows the time history of the compression of the

tire, X2 + h(t), as the airplane taxies at 10 miles per hour

over a rectangular- shaped light of the dimensions given in

figure 2 . The corresponding loads on the tire are obtained

from the load-deflection curve of the tire, figure 3.

Figure 8 shows the time history of the compression of the

tire as the airplane taxies over the series of trapezoidalshaped lights of the lengths given in table 1 . Results for

the other shaped lights, circular arc, ellipse, parabola, and

sine, were very similar to those for the trapezoidal light,

the only difference being in the slope of the curve from time

0 to the maximum value of tire deflection.

The loads corresponding to the maximum compression of the

tire are given in table 3. Although these loads are quite

high, particularly for the shorter length lights, they are

below the values that would cause tire bottoming and it is

assumed, therefore, that the landing gear could safely take

these loads.

It is noted from table 3 that for the longest light, the

trapezoidal shape seems to be best as the load on the tire is

least for that light. For all other lengths of light, the

maximum difference in impact load for the shapes studied did

not exceed 3 percent. This would indicate that the shape of

the light was not important and that any of the shapes investigated could be used. This result agrees with that of reference

14 where it was found that the obstacle edge had little effect

on the vertical loads in the main gears when taxying a B-36

airplane over obstacles from 1.5 to 4*5 inches high.

In a later series of tests on the B-36 airplane, reference

15, it was reported that taxying over a platform obstacle (20

ft long) produced a more severe loading condition than taxying

over a short obstacle (1 ft long). From our analysis, the

loads seem to be more severe for the short obstacle but are of
- : rfi
NBS Lab, No, 6.4/295, PR-1 page 6 *

shorter duration. See figure 8. However, a comparison of the

time histories of the displacements of the airplane and wheel

masses for the longest and shortest trapezoidal lights, figure

9, shows that taxying over the longer light causes a greater

rebound of the masses. This could result in undesirable loading, particularly if the airplane taxied over a series of these

lights as was done with the B- 36 .

5, ANALYSIS FOR THE NOSE GEAR OF THE F-86H AIRPLANE

After completing the analysis for the B-47 airplane, it

was decided to make a similar one for the nose wheel of a

fighter aircraft. The F-86H airplane was chosen for this

study. As it was found in the previous work that the shape of

light has little, if any, effect on the loads on the tire as

the airplane taxi es over the light, it was decided to limit

our study on the F-86H to the trapezoidal shape of light.

Four heights of light were used, 0.75, 1.00, 1.25, and

1.50 inches. A base angle of 14 degrees was used to determine

the length of lights for these heights. This value of base

angle was decided upon since it had been used in a preliminary

design of a runway light and would be about the largest base

angle that could be tolerated because of other considerations

such as snow removal from runway, et cetera. The dimensions

of the lights are given in figure 10 which shows the relative

size of the 4 lights to be studied. Taxying speeds of 50, 80,

110, and 140 miles per hour were used for each light. For this

series of computations, it was assumed that the nose wheel

carried the entire portion of the airplane weight attributed

to it, i.e., lift was not taken into account. To determine

the effect of lift, however, four of the cases were repeated

in which ¥]_ had a value of 900 pounds, approximately half of

the weight used in the first computation. Other data for the

F-86H airplane (reference 16) are given in table 2. The loaddeflection curve for the tire is given in figure 11. The

damping coefficient and load-stroke curves were obtained, as

previously described, from data in references 16 and 17. The

time histories of the displacement of the masses were computed

in SEAC. Loads corresponding to the wheel displacement were

obtained from figure 11.

6. RESULTS FOR F-86H NOSE GEAR AND DISCUSSION

The results obtained for the lowest light, figure 10(a),

are shown in figure 12 for the 4 taxying speeds investigated.

I

NBS Lab. No. 6.4/295, PR-1 page 7

In taxying over this particular light, the compression of the

tire and therefore the load on it was approximately the same,

about 5,000 lb for all taxying speeds. After the wheel is over

the light, the shock strut extends slightly but soon returns

with small oscillations to its initial position when taxying.

The extension of the strut after the first compression is

largest for the slowest taxying speed.

A comparison of the maximum impact loads, table 4, shows

larger differences between the loads obtained for the lowest

and the highest taxying speeds as the height of light is increased from 0.75 inch to 1.50 inches. It is also evident from

table 4 and figure 13 that, as the height of the light is increased, the compression of the tire and therefore the load on

it, for any particular taxying speed is larger and the extension of the shock strut greater following its rolling over the

light.

The time histories of the displacement of the part of the

airplane mass attributed to the nose gear and of the wheel mass

are shown in figure 14 considering no lift or W]_ = l8ll lb.

These are for taxying speeds of 50 and 140 mph. In order to

determine the effect of lift, these cases were recomputed assuming that the part of the airplane mass attributed to the

nose gear was only about 50 percent of its previous value or

WX = 900 lb. A comparison of the figures shows that lift of

this order of magnitude on the airplane would reduce the tire

deflection by about 0.24 in., or the load by about 1,000 lb

and, at the lower speed of taxying, would cause the wheel to

lift off the ground. It is to be noted that the time histories

of the displacement of the airplane mass show a very slight

movement, much smaller than it was in the case of the main

rear gear of the B-47 airplane, figure 9. This would indicate

that all of the reaction of a nose wheel running over a light

of 0.75 in. in height was taken by the shock strut with little

discemable reaction on the airplane. One would not expect a pitching of the airplane even though the nose gear raised off

the ground.

6. CONCLUSIONS

From the preliminary studies made on the main rear wheel

of the B-47 airplane and the nose wheel of the F-86H airplane,

the following conclusions seem to be indicated regarding the

landing gear loads resulting from taxying an airplane over a

raised runway light:
-
NBS Lab. No. 6.1j./295, PR-1 page 8

1. The height of light is an important factor in the

magnitude of the landing gear loads but the shape of the

light edge has little, if any, effect.

2. At high taxying speeds, there is little reaction of

the F-86H airplane when its nose wheel taxies over a raised

runway light of moderate height.

3. At high taxying speeds, the landing gear loads increase as the height of the light is increased, and, somewhat

less, as the taxying speeds increase. The latter may be offset

by an increase in lift at the higher taxying speeds.

On the basis of the results obtained, it is recommended

that:

(1) Analyses be made of other representative landing

gears using the SEAC code developed for the present study.

(3) The application of the analysis to the landing condition be investigated.

7. RECOMMENDATIONS

For the Director,

B. L. Wilson,, Chief UUi.01,

Engineering Mechanics Section,

Division of Mechanics.

Washington, D. C

March 1958
IIIIiiI
NBS Lab. No. 6 . 1+/295 , PH-1 page 9

REFERENCES

1. McBrearty, J. F.

A Critical Study of Aircraft Landing Gears

Jour. Aero. Sciences, Vol. 15, No. 5, o. 263, May 1

2. Lindquist, D. C.

Effects of Wing Lift and Weight on Landing - Gear Loads

NACA TN26J+5, March 1952

3. Anon

Flexural Transients in Model Wing Following Vertical

"Landing Imoact” at Point Below Center of Gravity

NBS Lab. No. 65l8l, PR-1, 19ij.6

ij.. Kroll, W. D. and Levy, S.

A Step-by-Step Method of Determining the Dynamic Response

of Aircraft in Landing

NBS Lab. No. 6 .l+/l-l 8 l, PR- 6 , 19l;9

5. Milwitzky, B. and Cook, F. E.

Analysis of Landing Gear Behavior

NACA TN 2755, 1952

6. Stevens, J. E.

Nose Gear Loads and Airolane Motion During Arrested

Landing of Model 7FN-1 Airnlane

Chance Vought Aircraft Reoort 8l7U> 19li9

7. Fliigye, W.

Landing - Gear Imoact

NACA TN27I4.3, October 1952

8 . Houbolt, John C. , Walls, James H. and Smiley, Robert F.

On Spectral Analysis of Runway Roughness and Loads Developed During Taxying

NACA TN3 I4

. 8I4., July 1955

9* McPherson, A. E. , Evans, J. Jr., and Levy, S.

Influence of Wing Flexibility on Force Time Relation in

Shock Strut Following Vertical Landing Impact

TN1995, November, 19i|9

10. Bisplinghoff , R. L., Isakson, G. , Plan, T. H, H.

,

Flom enhoft, H. I. and O’Brien, T. F.

An Investigation of* Stresses in Aircraft Structures under

Dynamic Loading

MIT reoort for Bureau of Aero. Contract No. N0a(s) 8790,

191+9 po • I 36 -II4J4

.

NBS Lab. No 6 .I4./295 , PR-1 page 10

11. Houbolt, John C.

A Recurrence Matrix Solution for the Dynamic Resoonse of

Aircraft in Gusts

NACA TN2060, March 1950

12. Durand, H. P. and Rosenberg, R. M.

A New Approach to the Design of Metering Pins in Oleo

Struts

University of Washington Exoeriment Station Bulletin No.

113, 19£L

13. Data for B-lj.7 Airolane

Communications from Wichita Division, Boeing Aircraft

Como any

ll|.. Anon

B-36 Taxi Tests over Obstacles at High Airplane Gross

Weights

Conrair Reoort FZS- 36-293, December 1952

15. Anon

B-36 Taxi Tests over Obstacles at High Airplane Gross

Weights

Convair Reoort FZS-36-293 Addendum 1 November 1953

16. Data for F- 86 H Airplane

Communications from North American Aviation, Inc.

17. Prescott, D. B.

Model F- 06H Airplane, Main Gear - Aerol No. 9203, Nose

Gear - Aerol. No. 9202

The Cleveland Pneumatic Tool Company Reoort 9203-02 DT

for North American Aviation, Inc. October 20, 1952
fl
NBS Lab. No. 6. 4/295 , PR-1 l page 11

Table 1. Lengths of light used in study

of B-I4.7 rear main landing gear.

Case

Base angle,

degrees

Length,

inches

1 5 74.58

2 10 40.02

3 15 28.40

4 20 22.48

5 25 18.87

6 30 16.39

7 35 14.57

8 40 13.15

9 45 12.00

Q

NBS Lab No. 6.4/295, PH-1 page 12

.

Table 2. Data for B—14.7 and F-86H airplanes.

B— 1|_7 Airnlane - Rear Main Dear

Unsprung weight - 2200 lb

Weight of airnlane - 100,300 lb

Weight support by rear main gear - 100,200 lb or 54,

per wheel

At t ime t=0, under weight supported by rear gear

= 15.01 in.

X

2 = I].. 11 in.

Taxying speed - 10 miles/hr or 176 in. /sec

W-j_ = 48,700 lb (weight supported by wheel reduced 10

to account for lift)

F-86H Airplane - Nose Wheel

I

lb

nose wheel, W-, = l8ll lb

weight supported by nose wheel

in.

in.

Unsprung weight - 60

Weight attributed to

At time 0 *\ -p II under

X

1 = 6.845

x

2 = 0. 665

For W^ = 900 :lb

x

i = 4.53 in.

Xp = 0.43 in.

100 lb

percent
rrr
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NBS Lab. No. 6.4/295, PR-1 page ll|

Table 4* Maximum loads on nose wheel of F-86H when taxying over

trapezoidal light

Case

Height of

light,

in. W-, , lb

Veloc

air

mi /hr

ity of

•plane

in. /sec

Maximum

deflection

of tire

in.

Maximum

load on

tire, lb

la 0.75 1811 50 880 1.360 4860

lb 1811 80 1408 1.375 4910

lc 1811 110 1936 1.393 5010

Id 1811 1^0 2464 1.390 4990

le 900 50 880 1.108 3740

If 900 llj.0 2464 1.153 3930

2a 1.00 1811 50 880 1.530 5630

2b 1811 80 1408 1.625 6070

2c 1811 110 1936 1.620 6040

2d 1811 140 214.6U. 1.645 6150

3a 1,25 1811 50 880 1.760 6690

3b 1811 80 1408 1. 800 6870

3c 1811 110 1936 1.870 7200

3d 1811 1^0 2464 1.895 7300

4® i.5o 1811 50 880 1.895 7300

4b 1811 80 1408 2.04.3 8000

U-C 1811 110 1936 2.070 8130

k& 1811 IkO 2464 2.092 8230

ke 900 50 880 1.590 5900

hr 900 80 1408 1.787 6820
1
Fig. / Representation of airplane.

t

I]

]

Rectangle

Fig. 2 Shapes of tights investigated

.

Fig. 3 Load- deflection curve for tire of B-47 rear main gear.
Il

0

n

Q

I

I
Fig. 4 Static load -stroke curve for B-47 rear mam gear.

Fig.

5

Dynamic

load

-

stroke

curve

for

B-47

rear

main

gear.

Fig.

6

Velocity

-

stroke

curve

for

B-47

rear

mom

gear

.

I Dn

Fig. 7

Time

history

of

compression

of

tire

due

to

airplane

taxymg

over

square 

shaped

light.

Height

of

light - 3

in.
[r![[iI[l1
GD

CVJ

III

I!

II

>1

II

II

I

l 9j(4 jo uojssajduuoo

Fig.

8

Time

history

of

compression

of

tire

due

to

airplane

taxying

trcpezoidai-shoped

fights.

Maximum

height

of

tight

=3

in.

Light

length,

in.

)

c*

"v. k

Ul ^USUUSODldSIQ

Time,

sec

Displacement

of

airplane

,m

/t

and

wheel

,m

2t

of

6-47

when

foxy

mg

over

trapezoidal

light,

3

in.

high,

at

10

mph

f •

01

ill

If

II

II

II

I

I!

II

II

II

I

i - Fig. IO Lights used in F-96H nose gear study.

(Dimensions in inches)

I

Fig. II Load -deflection curve for tire of F-86H nose wheel.

DD

I0*> U

|]

IJ

|]

\J i i)

IJ

N I

Time,

sec

Fig.

12

Time

history

of

deflections

of

nose

wheel

tire

when

taxying

F-86

over a

run

way

light

0.75

in.

high

at

various

speeds.
f[ .
II

11 .

Fig. 13 Deflection of tire of nose wheel as F-86

airplane is taxied over trapezoid lights of

different heights at 1 10 mph.

ia

€

JJ
(I

.
Taxying

speed

,

mph

140 O

in

CD CD

ui ‘ssduu auD|djio

uojioaijao

Fig.

14

Displacement

of

airplane

and

of

wheel

when

taxying

over

trapezoidal

tight

0.75

in.

high.

IV,

=1811

lb.

jo- uoijoaijaa

;§

N

&

fe

<b

Fig.

15

Displacement

of

airplane

and

of

wheel

when

taxymg

light

0.

75

in.

high.

W,

=

900

lb

THE NATIONAL BUREAU OF STANDARDS

Functions and Activities

The functions of the National Bureau of Standards are set forth in the Act of Congress, March

3, 1901, as amended by Congress in Public Law 619, 1950. These include the development and

maintenance of the national standards of measurement and the provision of means and methods

for making measurements consistent with these standards; the determination of physical constants and properties of materials; the development of methods and instruments for testing materials,

devices, and structures; advisory services to Government Agencies on scientific and technical

problems; invention and development of devices to serve special needs of the Government; and the

development of standard practices, codes, and specifications. The work includes basic and applied

research, development, engineering, instrumentation, testing, evaluation, calibration services, and

various consultation and information services. A major portion of the Bureau’s work is performed

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or program. Published papers appear either in the Bureau’s own series of publications or in the

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which provides data for determining the best frequencies to use for radio communications throughout

the world. There are also five series of nonperiodical publications: The Applied Mathematics

Series, Circulars, Handbooks, Building Materials and Structures Reports, and Miscellaneous

Publications.

Information on the Bureau’s publications can be found in NBS Circular 460, Publications of

the National Bureau of Standards ($1.25) and its Supplement ($0.75), available from the Superintendent of Documents, Government Printing Office. Inquiries regarding the Bureau’s reports and

publications should be addressed to the Office of Scientific Publications, National Bureau of

Standards, Washington 25, D. C.
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