TECHNICAL
MECHANICAL
REPORT
PROPERTIES
WITH
SPECIAL
MODERN By ROBERT
OF PNEUMATIC REFERENCE
AIRCRAFT
F. SMILEY
R-64
TIRES
and WALTER
Langley Research
Center
Langley Field, Va.
TO
B. HORNE
TIRES
CONTENTS Page
SUMMARY
.........................................................................................
l
INTRODUCTION ................................................................................... SYMBOLS ..........................................................................................
1 2
DEFINITIONS RATED
..................................................................................... PRESSURE .............................................................................
3 4
AND
4
RATED SLIP TIRE
BOTTOMING
RATIO
DEFLECTIONS
.....................................................
....................................................................................
4
CONSTRUCTION AND NOMENCLATURE (See GENERAL DISCUSSION ........................................................................ SPECIFIC
NOMENCLATURE
PROPERTIES
OF
PURE
A
LOADING
Geometric Properties Footprint length Footprint Gross
width footprint
Net Pressure
Rise
OR
NONROTATING
(See
also
figs.
also
figs.
Vertie-d Lateral COMBINED General
Center
also
Vertical Sinking Circumferential COMBINED
Force
Vertical-Force PROPERTIES OF ROLLING
14.) ......................................
9
variation
(See
also
figs.
1i
to
13.) .....................................
10
also
fig.
23.)
also
(See
also
10 and
14.) ..................................
12
(See
also
13 13
figs.
17 to
25.) ........................
14
21.) ................................................. figs.
17 and
22.)
14
.......................................
17
.............................................................
figs.
26
(See
figs.
Length) (See TWISTING and
also
27.)
also
18
also figs. 17, ._[OMENT
24, and 25.) ..................... (See ,dso figs. 26 to 29.)
18 19
............
..................................................
and
figs.
(See
AND
34
to
19
29.) .............................................. LOADING (See also figs.
31
and
figs.
30
30
to
20 21
33.) ..................
32.) .......................................... ,_nd
22
33.) .....................................
24
TILT
(See
Effect
of
Vertical
Effect
of
Braking
(See
Length
Relaxation
(See
Length also
figs.
Deflection
(See 40
(See
(See
24 24 als0
figs.
34
to
37.)
............................
25
36.) ..........................................................
LENGTIIS Relaxation
RADIUS
and
figs. 34 TIRE also
figs.
also
fig.
Mso
fig.
25
and 37.) ....................................... (Sec also figs. 38 to 59.) 38
30.)
and
39.)
26 26
.........................
.....................................
26
38.) ............................................
26
..............................................
27
42.) ......................................................
also
figs.
40
-rod
41.)
28
............................................
28
............................................................................
(See
also fig. 42.) ................................................................ CIIARACTERISTICS (See also figs. 43
Observations
Steady-State Normal
figs.
LOADING 18 to
Center of Pressure (See also ROLLING 0}2 ROTATING
Y,_wvd-l_olling
Effect of Yaw YAWED-ROLLING
also
figs.
LOADING
RELAXATION
General
(See
LATERAL
of Pressure
'flso
Unyaw(,d-Rol]hlg I{OLLING
8
to
............................................................................. Distortion ....................................................................
(See A
7
10
Constant
VERTICAL
Later'd
7
figs.
(See
Center
7.) .................................................
also
(Static Relaxation LOADING AND
Spring
6
(See
of Pressure
(See
Vertical-Force
6
...............................................
9.) ...........................................................
Spring Constant (See also figs. 28 VERTICAL AND FORE-AND-AFT
Fore-and-Aft
..................
Variations
(See
Observations
Torsional COMBINED
2 to 37.)
..............................................................
8 and
AND
Deformation VERTICAL
figs.
5.) .....................................................
6 and
variation
Constant
Sinking
I6.)
also
(See also fig. 15.) ...................................................... (Set' also fig. 16,) ......................................................
VERTICAL
Vertical-Force
figs.
area
Pressure Pressure
Spring
2 and
also
Dynamic-force-deflection
L'tteral
2 to
(See
7
also (See
Static-force-deflection
COMBINED
figs.
5
TIRE
(See
Vertical-Force-Deflection
Gross Footprint Average Bearing
4 4
6 6
footprint
(See
1.) ....................................
of Footprint Area (See also figs. 2 to 7.) ..................................... (See also figs. 2 to 4.) ...................................................... area
or bearing
fig.
..................................................................
STANDING
VERTICAL
also
(See
Conditions force (See
Cornering
force
Cornering
power torque
Pneumatic
easter
Coefficient
of
fig.
to
30 30
52.) ...................................
43.) .........................................................
30
(See also figs. 44 to 52.) ................................................. also figs. 44, 46, and 47.) .................................................
(See
Self-alining
also
28
also
(See (See (See
friction
fig.
also also also (See
30 30
45.) ...........................................................
figs. fig. fig. also
48
and
33
49.) ..................................................
33
50.) ........................................................
35
51.) ......................................................... fig.
35
52.) ......................................................
37 III
CONTENTS
PROPERTIES
OFAROI,LING
OR
BRAKING
F()RCE
TURNING ROLLING
MOMENT FOR CIIARACTERISTICS
Lateral
FOR
Force
(Se_
also
Turning Moment (See VERTICAL-FORCE-DEFLECTIC)N
effects
Drag and ltysteresis Illustrative
fig.
55.) fig.
TIRE
Preliminary
TIRE
Lateral
Prcrotation
tests
wsts
(See
.dso
Drop
(See TIRE
also
also
fig.
(See fig.
60
(See
37 38 40
56.) ......................
40 57
to
59.)
41 42
..........................
42 ,12 -13 43 43
also
also
figs.
17 and
of
Torsional
REMARKS A--SAMPLE
APPENDIX
B--MEASUREMENTS C--I)ETERMINATION
also
figs.
58
and
59.)
.....................
45
65.) .....................................
4,5
figs.
45
60
and
61.) .............................
62
to
65.)
46
................................
47
17.) ........................................................
fig.
rh (See
62.)
also
figs.
i9
62
to
65.)
.............................
49 49
...................................................
63.) ...............................................................
value of r/x ........................................................................ of Vertical Hysteresis Parameter _7_ (See
Evahmtion
(See to
44 41 -t4
..................................................
Paramct('r also
T_sts
figs.
RADIUS (See
IIyst(,resis
of Fore-and-Aft
REFERENCES
........................................... (See also figs. 55 and
.................................................
PROPERTIES
(Sec
APPENDIX
IV
OF
Evaluation
APPENDIX
for
INERTIA
Free-vibration Mean Ev,duation
54.) ............................
Slow Rolling (See a]so fig. 57.) ...................................... I,anding Impact (See also fig. 58.) .................................
PROPERTIES of
Static
53 and
...............................................................
PROPERTIES
Discussion
Evahmlion
l'age
figs.
56.) ............................................................. VARIATII)N (See also figs.
...........................
GROWTH
IIYSTERESIS
CONCLUDING
for for
Varialion
ANI)
also
Tire Doflections ......................................................... Variation ...............................................................
TIRE
CENTRIFUGAL W[IEEL
Continued (See
side-lo'M effects ................................................................. effects ...................................................................... data (See also fig. 58.) .........................................................
Foree-Defloction MISCELI,ANEOITS
RATIOS
CURVILINEAR ROI,I,ING OF A TILTED TIRE
Variation Variation
Inertia
TIRE
SLIP
also
Apparmlt and Effcctivc St atic-Forcc-Dvfloetion Force-Deflection Force-Deflection
ROTATING
SMALI,
Itystcresis Itysteresis
Parameter Parameter
also
"q_ (See
50 50 fig. also
64.)
.................................
fig.
65.)
50
............................
51
"q.................................................
51
....................................................................... OF
METIIOD
OF OF
OF
TIRE
GROWTIt
IIYSTERESIS
...................................................................................
52
DETERMINATION
OF DVE
CONSTANTS
TO
EMPIRICAL CENTRIFUGAL
FROM
EQUATIONS FORCES
FREE-VIBRATION
..... ........ TESTS__
53 5,1 55 56
TECHNICAL
MECHANICAL
SUMMARY A .,'tudy i._ pre._ented of mo._t of the propertie.; q/ pneumatic tires which are of i.terext to aircraft de•_igner,_. The principal topic,s di,_eu,_._ed are tire vertieal:foree-d_fleetion eharaeteristie,_; lateral, foreand-aft, aim tor._ional ._pring eonxta_ts; footprintarea propertie,_; rehtxation length,_'; rolling radiu,_; cornering f.rce, cornering power, ,_elf-alining torque, and pneumatic caster .tim yawed rollD_g condilion,_; _fleets q[ wheel tilt; a.d tire radial growth under the i.fluenee of eentr(fugal.force,_. For each tire property eon,_idered, ,_emiempirieal equation,_ are set up which lake i_+to aecou.t tt+e major factors pertine,_t to the property. Wl_ererer po,_sible each equation is compared with the arailable c,rperimental data to exlablish il,_'degree of reliability. A ,small amount _!f preciou,dy unpublished experimental data i._ i_cluded, mo.stly o7_ the subjects of tire tilt,.fore-an :t-aft st(fine,% and con tr(fugal grmeth. INTRODUCTION In ordt, r to cope adequately with the landing atul taxiing problems of present-day aircraft, those engaged in landing-gear design need inforination on a large nmnber of pneumatic-tire properties. At present some information can be obtained from such sources as referenees 1 to 64 flw a number of or foreign types of tires and for a few American tires. Ilowever, it is doubtful the landing-gear designer will find in the experimental data which are directly to the particular tire or tires in which he
is interested. Moreover, the scale laws which tire properties obey have not been thorougldy investigated, and, for at least a few important tire i ,%lpersedes
NACA
R-64
PROPERTIES OF PNEUMATIC TIRES WITH TO MODERN AIRCRAFT TIRES 1 By ROBERT F. StaLEr
obsolete modern whether literature pertilwnt
REPORT
Technical
N*oie 4110 by
"Robert
F. Smile5"
and
Walter
and
WALTER B.
SPECIAL
REFERENCE
ttORNE
properties, these scah, laws are not at all obvious; in some cases, simph, and accurate scah, laws apparelltly cannot be estal,lished at all. Consequently, the air('raft desio_ner cannot confidently scah, the results of tire tests in order to apply them to tires in which he is interested. Some useful studies have been made in regard to theoretical i lfformation on tire properties; most of these studies are contained or summarized in references 18 and 46. llowever, these l|leoretical studies, although enlightening in some respects, are usually based on oversimplified concepts and, almost inevitably, involve some empirical constants which have not. yet been evahtated. Th(,se
observations
indicate
a need
to assess
tim
present state of the art for prediction of tire properties I)3" a. comprehensive study of the awfilable theoretical and experimental information on tire properties. The present paper presents such study which has as its primary aims the determination of the most important variables which influence the various tire properties and the establishment of some simple quantitative equations for most of these properties. Since it is improbal_le that many readers of tiffs paper will be interested in all the properties discussed herein, each tire property is considered in a separate section with as little cross-correlation between sections as appears necessary. For each tire property considered some equat ion is obtained, either from a previous paper, by a crude theoretical deriva.tion, or by purely empirical means. (For example, see appendix A.) Values calculated by these equations are then compared with the available experimental data, which are B. IIorne,
1958. 1
TECHNICAL
REPORT
R-64--NATIONAL
AERONAUTICS
used to establish any empirical constants needed in the equations. It should be emphasized that the theoretical derivations that are presented are intended largely to give some idea of the basic phenomena, to demonstrate the major variables involved, and to suggest some promising form for empirical equations. In general, the equations resulting from these derivations are far from rigorous; however, by judicious insertion of empirical constants into these equations, it is believed that most of them can give at least a fair correspondence to reality. Although ahnost all the discussion in this paper deals with previously published experimental data, a small amount of new data is presented princi-
G,Fz F_
pally on the sul>jects of centrifugal-growth effects.
F:,o F+
tire
tilt,
braldng,
and
SYMBOLS
F_ F_._ F_,,,_ Fu,_ F_,, F_,x F,
f_,r _,r,e
ratio
of net
print vertic_d
area, A,j.'lg sinking of
distortion _oss footprint net footprint
Ag .(t
footprint
_t
b
_x
area tire
to gross
per
unit
footlateral
H
steady-state normal force half-length of tire-ground (footprint) tire radius minus rim radius
of inertia of tire and tubo axle (excluding solid wheel
parts) polar moment wheel about
of inertia of tire, wheal axle
change in lateral position pressure of vertical force wheel tilt
lv,_
kw
d
D,( )
differential
operator
with
respect
to time,
k,
dt base of natural
[2.4[( force
)-_-0.216( )-- C'.]
and
3,:'/z_w_ r/_ w
fore-and-aft spring constant torsional spring constant
K,
lateral force per radian tilt standing tire with Xo=O
K,, _
lateral
logm'ithms
)2/C,
tube,
circumferential decay length radius of g3.'ration of tire and tube about the wheal axle, _7_. ,/m, radius of gyration of wheel and tire _tbout the wheel axle, _:}_, w/mw radius of gyration of wheel and tire about an a:vis perpendicular to the wheel axle,
force
per radian
tilt
angle
angle
spring
constant
L
relaxation
L,.
unyawed-rolling-force
L,
static
L_
yawed-rolling-relaxation
length
relaxation
relaxation length length
for
for roll-
ing tire lateral
)=t0.96(
of inertia of wheel and tire perpendicular to the wheel
K, If_
d( )
F
area
polar moment about wheel
of of
fat
contact
Iv,t
change in lateral position of center pressure of vertical force per unit lateral distortion braking-force coefficient cornering-power coefficient vertical-force coefficient (see eq. (24)) outside diameter of free tire
e
drag forces for two narrow couph, d wheels instantaneous drag or fore-and-aft force (ground force parallel to direction of motion) lateral or cornering force (perpendicular to direction of motion) lateral force resulting from wheel tilt for standing tire lateral force resulting from wheel tilt, for rolling tire lateral hysteresis force lateral spring force lateral force resulting from elastic and hysteresis effects vertical force acting on tire from ground average or reference verlic_d force normal force (ground force perpendicular to wheel plane) instantaneous normal force
width of tire-ground contact area (footprint) change in fore-and-aft position of center of pressure of vertical force per unit of fore-and-aft deflection
J let
c_ c.
ADMINISTRATION
polar moment about axis axle
of of
CX
SPACE
I_,_ area area
of center per radian
C- t
AND
length
MECHANICAL
Lx
m_ D'l t
M,
31,, _ n
N
PROPERTIES
cornering
power,
po
tire inflation (gage) tire inflation
_b
P_ P_
pressure
at zero vertical
load
pressure
at zero vertical
load
forces
pn
average F)An
Pr
tire rated inflation pressure tire parameter defined by or (97)
P q r ro Ar
tire-ground
re re,o
rolling
re.Dre,2
R 8 81
t _o V_
V qJ) X
Y
bearing
pneumatic caster, _ll,._/F¢._ outside fi'ce radius of tire initial tire radius increase in tire trifugal-force rolling radius radius
a .y 8 8o _, 82 80 8_ 8_
(ix
(absolute) tire bursting pressure average gross footprint pressure, FjA_ additional pressure resulting from centrifugal
TIRES
\_/_--_
tire inflation pressure pressure rise, P--Po
,a
PNELVMATIC
unyawed-rolling-deflcction relaxation length mass of tire, tube, and wheel mass of tire and tube turning or twisting moment about a vertical axis through the wheel center turning moment rcsulting from path curvature turning moment resulting from wheel tilt, polytropic exponent
P Ap
po
OF
pressure,
equation
for unyawed
rolling rolling radii for wheels radius of curvature peripheral distance
two
from
and
w n, n. yx O O_ K
drag coefficient maxinmm drag locked-wheel
u_,_
sliding-drag eocfi3cient locked-wheel tests
_+
yawed rolling coefficient of friction tilt paramctcr (sce rcf. 53) lateral-spring-constant coefficient N yaw-angle parameter, _ _b yaw angh,
path 4' _b
peripheral displacement vertical velocity at ground horizontal rolling velocity inside volume of tire initial volume of tire
_oo contact
maximum width of undcflccted tire displacement in fore-and-aft direction in direction of motion perpendicular
to
direction
distortion
of tire-ground
of friction coefficient tests
con-
of friction of
friction
for for
wheel angular velocity, radians/see wheel angular velocity for unbraked rolling, radians/sce
Subscripts : max maximum st static or
narrow
vertical sinkiug of tire resulting from application of fore-and-aft ground force vertical sinking of tire resulting from application of lateral ground force elongation strain produced by drag force elongation strain produced by vertical force (always negative) fore-and-aft hysteresis parameter vertical hysteresis parameter torsional hysteresis parameter lateral hysteresis parameter wheel rotation, radians peripheral angle, deg pressure-rise parameter lateral distortion of tirc equator lateral distortion of tire equator at center of th'e-ground contact area
g_ .....
cen-
vertical
vertical deflection at tire bottoming effective vertical tire deflection rated vertical tire deflection
fore-and-aft tact area,
slip ratio time
displacement of motion
vertical tire deflection for pure loading conditions (F_= F_=0) vertical tire deflection for two coupled tires
X_
coupled
rolling tire
tire twist, angle tilt of wheel pla, ne, radians vertical tire deflection
....
rx of tire around
TIRES)
X Xo
unbrakcd
narrow
AIRCRAFT
(96)
or 3[,._.JFt
radius resulting effects
_ E_
(MODERN
value
DEFINITIONS The following terms are defined parts of this paper. Other terms
for use in many which arc used
4
TECHNICAL
only locally ill the priate plaees.
REPORT
text
RATED
Inasmuch
as the
are
R
defined
64
-NATIONAL
at
the
AERONAITTICS
appro-
AND
SPACE
tire carcass
BOTTOMING
ADYIIXISTRATION
some idea of the practical vertical-deflection for the data in these figures. SLIP
PRESSURE
stiffness
is a factor
of some importance in understanding the behavior of pneumatic tires, some numerical index of this carcass stiffness which could be used readily in establishing empirical equations for tire properties appears desirable. Somewhat arbitrarily, this paper adopts the quantity "rated pressure" as this standard. The term "rated pressure" (denoted by the symbol p,) is defined as one-quarter of the bursting pressure p_ of the tire. (The minimum bursting pressure for eun'ent tires can be found in refs. 63 and 64.) The rated pressure p, thus defined is, for current Mneriean tires, ahnost always exactly equal to the inflation pressure listed in tire specifications (refs. 62 to 64) ; however, the operating inflation pressure of tires may be eonsider_bly different, from the specified or rated pressure. For example, some tires are operated at pressures less than one-half the rated pressure, and others may be operated a! pressures in excess of the rated pressure. For calculations in this paper which required numerical values of the rated pressure, the following procedure was followed: For recent American tires the rated presmlre was calculated from the minimum bursting pressures given in references 63 and 64. For some German tires (for which little bursting-pressure data were availabh,) the rated pressure was considered to be equal to the customary inflation pressure according to indirect evidence in German tire specifications (for cxaml)h, , fig. 23 of ref. 51). For a few tires, for which no better estimate could be made, the rated pressure was considered to be equal to the tire inflation pressure. RATED
AND
DEFLECTIONS
The term "r,,_ted deflection" (denoted by the symbol _,) is used to refer to the customary operating vertieM deflection of a tire as specified by references 62 to 64. "Bottoming deflection" (denoted by the symbol ito) refers to the maximum vertical deflection which a tire can sustain before the rim begins to cut into the tire carcass. Both rated and bottoming deflections are indicated in most figures in the present paper in order to give
The "slip ratio" a rolling unyawed defined t_s follows:
o.os :
!
,_
s.sl ............
{ .16
i
,
_
o lOx3-R49
'
0 15x6-RSO-B , _'_1 ,5 tSx6_-_RSO-BF(~Type
_,
i I)
i4 I _ .... Ka
(n+u_Pr) w ..... - ...... 7i9(go/d_O.Oi )
• _ v
....i
I tires. III
!
',
e...... i
2.0 (a) Type
_
'_'
L
45x15-14PR(15.50-20)R21
0
16 26x66-12PR-R25-B
/ 0 40xte-14PR-R24-A I 6 40Xi2-I4PR-R24-B I =I `5 56x16-24PR-R21 / 56xl632PR-R21
',
&/P," 2.4
t
i
1.6
_
vertically loaded tire ati a an initiM vertical tire (h'flec-
tion ao is subjected to a fore-and-aft or drag force F:, the tire experiences a corresponding drag deformat.ion at. the ground Xx, a vertical sinking 6_, and a shift of the vertical-force center of l)ressure c:X:. (Sec fig. 30.) The available experimental data pertinent to these quantities, to the corresponding fore-and-aft spring constant /t_, and to the corresponding distortion of the tire equah)r are summarized and anal?,'zed in this section.
'
28xg-IOPR(27-inch)R21E2 44xl5- IOPR[44- inch)R21
1%e.4 o
I 5
E2
3.2
_cu
l.t
a stationary load F. and
I
.:=-
When vertical
_;o,¢
tire. 1.5
Fret-RE rameter
29.--Varia, wit,h
tion vertical
of
st-itie deflection
torsional for
stiffness paseveral aircraft |.0
tires.
"-
,_
{ ' /i/_
O
Type I
to coililiin no simph' equalions at all for the torsional spring constant, these equal,ions should a,t, least be useful as a first approxinnition, The wide variation of the data from the calculation is due in part to the neglect of lhe apparently important amplitude effect mentioned previously. Seine additional static-test data on torsional 54190S
61--
4
!
.5 (d) --3
i "_ I I .02 .04
"-Typesrrf .06
ond'_Zl] .08
Vertical-deflection (e) (d) Figure
Type
VII
German
.t0 parameter, tires.
tires.
29.--Concluded.
I i .12 8old
I
.14
.16
22
TECHNICAL REPORT R--64--NATIONAL AERONAUTICS ANDSPACE ADMINISTRATION Tire
for
Kx
# 0
Tire
for
fx
: 0
20
x
I03
&
....
0 0
d 16
o
°°
z3
E2
Po/Pr 0.7
o 0
.S
0
LO
&
I,i
=
o
I
I
I
2
I
3 Verficol
FIGI'RE for
a
with 56X16
_o,
variation
vertical 32PR
4 deflectlon,
31 .--Experimental
constant
I
I
I
5
6
7
in.
of fore-and-aft
deflection VII
I
and
tire.
inflation
(Data
from
spring pressure
ref.
21.)
In view of the preceding analysis of lateral and torsional stiffness, it appeared reasonable to expect that the fore-and-aft stiffness could be described by a similar
o Experimental data from reference 3
equation
of the
A'_ = lqd(p
type (46)
+ k_p,)f(_o/d)
u
x--;i e
d
c
b
o
g
Circumferentiot
f
e
position _._$_
FIc_r_E
30.--Sketch bined
illustrating
w, rt.ieal
and
FORE-AND-AFT
Before
the
distortion
fore-and-aft
SPRING
available
spring-constant noted that the
tire
com-
CONSTANT
experimental
data are discussed, available fore-and-aft
tion data from which be determined consist
for
loading.
fore-and-aft it should be force-deflec-
such spring constants almost entirely of the
can first
quarter-cycles of force-deflection hysteresis loops, and, as was mentioned pre_qously in the discussion of the lateral spring constant, because of hysteresis effects, such spring constants are sometimes of questionable accuracy. Sample experimental fore-and-aft spring-constant data from the investigation of l'efercnce 21 are shown in figure 31 for a 56XI6-32PR-VII tire. These data slmw that the fore-and-aft spring constant tire vertical slightly pressure.
tends to increase with increasing deflection and to increase only
(or not
at
all)
with
increasing
where k_ and k2 are numerical constants, tlowever, since t.be fore-and-aft stiffness does not depend strongly on the inflation pressure (see fig. 31), it wouhl be expected that k2>>l; thus, to a first approximation, prce have been discussed by Ratio. (See ref. 45 or 46.) Rotta has also made some theor('tical calculations of this tilt force, which are reproduced
-.._
(3--t ,
'_ v 0
.084| .094) .t 16| .J25/ .137 / .0771
26x
6.6-12PR-R23
tires
Equation (871
,
.2
o
.08
' I
.2
.4
I
.6
.B
I
(c)
"
"L%2
50.
=l/
--
[] 0 o
,o[_
.062 .066 0.056
0 A
.08/ .09}
l'me
M.:
Airer.tft
Army
Air
Rep. Forces,
K. W.: Aircraft Load-Deflection
Boeing
der
Wheel
translation
Inertia TSELA-
Sept.
30,
Wheel Inertia Characteristics.
28_
FederNorm-
of Stand._rd 388, Deutsche E.V.
English
TN
3I.tr.
deutscher
Luftfahrt,
An Ob-
Predicting
Co.,
Ermitthmg
Characteristics PB Nr.
No.
Jr.: for
Stiffness.
Fhtgzeugreifen
far
Memo.
3152,
NACA for
Lateral
Boeing
Kranz,
Loads. Method
and
(Available in ATI No. 23005.) W.:
Kinemaiic A.D.
Philip M., Melhod
Drag
(The Elasticity Aircraft Tires.)
Div.
on
No.
and Edge, Accelerometer
Forec_
yon
K.
Work
NACA
1940.
D-11719,
II.,
of IIysleresis Shimmy.
Rep.
lmnding-Gear 1954.
Thorson,
Wheel
Shimmy.
Theisen, Jerome Evaluaiion of
Zahrt, Tire
Paul: Der Fahrl)ahn.
499-50-t.
F,
Robert
Temple,
ATSC,
27061.)
Weichsh'r, Rad und
Shimmy.
and
(Berlinlransla-
1957.
Snfiley,
Zahrt,
No.
der
English
Aircraft
F.: Correlation, Linearized Thearies
Smih'y, Robert Force-Defleelion
Fng.
1947. McKay, Forces
1365,
ATI
NACA
Adlershof). ASTIA as
129-141.
Translations
as
140
(Av-dlal)le
Zeilschrift,
1935,
gr6sse. German
Summer
Ing.-Archiv,
Ileps.
IIall, Albert W., Sawyer, James M.: Study of
as
Vcrsuchsanstalt
Luftreifens.
(Des-
ASTIA
Bericht
Capacity
and
kennbilder
1955.
Statik
Alighting.
R.A.S.,
Forces.
Anniversary
10. TM
ASTIA
Wheel
Doe. 195l. 59.
Cornering
Golden
12-17,
Jour.
A.-G.
from
Frage des Reifvnauflmus yon Flugzeugreifen.
Load
Smiley, Robert Extension of
Tire
no.
1085-1094.
Speed
Properties
and
pp.
SAE
Heft
Off
of
8
Robert, zwisehen
25,
taining 3247,
of AutoTheir R('-
and
from
Schuster, sehluss
Brilish
Apl)lied
Rep.
Zur Mechanik des Pneumalie Tires.)
Tires.)
NACA
and
and
Potter,
32-16.)
Bull.
Slate
of
NACA TN
1154, 56.
Study
Acre.
Jan.-Mar.,
vcrsehiedemu'liger
pp.
:ts
Effects on TN 400l,
Amdysis
C., and
1,
Motorenwerke,
Various
Schrode: Beitrag zur der Belaslungsfiihigkeit
39O9,
English
Rep.
of
Inch-Diameler Tests With
55.
NACA 2755.)
TN
yon
E.:
Large
Wheels.
no.
R.: of
availabh!
Sleifigkeiten
(Supersed,'s
translation
Francis
and
1941,
and
ZWB,
(The Problem Z.F.M., Rd.
Characterislics Surfaces
Coefficients
Dec.
No.
J.:
53.
8, 1934.
Meeting,
Bd.
Cook,
L'mding.
Iowa
C.:
II.:
Oct.
in
3,
Dietrich, Mechanics
Flugzeug-
ntol)il_echnische
English
2,
1932. (Available TM 689.)
XACA
IIighway
Station,
Robson,
Rotta,
I[eft
English
Experimental in
52.
Spornradflalof Tail-Wheel
and
vol.
FB N,'. 1235, Deutsche Luftfahrtforsehung Adhws'nof), 1940. (Av'dlal)le in English
15,
Abmesmmgen
I,indquist,
An
B., and (The
(Translation
Schrode,
lion
8, Aug.
a
(Supersedes
45-52.
Von Schlil)pe, Imftreifens.
siruelion
yon L.G.L.,
Wheel.)
Tires
A.S.M.E.,
translation 51.
54.
R. A.: Skidding Tires on Roadway
print
45.
in
"Behavior. NACA
(Supersedes
httion
43.
7,
der
and
Loads
1956.
10,
Bd.
Frage
Benjamin,
Dexter
Air
in 36989.)
Thcorie des the Theory
Berichte,
Benjamin,
Exp.
10, IIcft
(Also available as ATI No. 1o
of L.mding-Gear I953. (Supersedes
42.
Bd.
zur
Zur
13,
Mihvitzky,
U.S.
Airplane
Trans.
I,G.I,.,
Flugzeugrad.
fiir Flugzeuglaufriider. Sizes for Airplane Wheels.)
23, Nr. translation
AirTech.
Airphme
59 70. (Awdlable TM 1380.)
Imftreifen of Tire
41.
schwenkbaren
Z.W.B.,
Tech.
Michael,
Center,
Swivellable
M.: Beitrag (Contribution
Shimmy.)
40.
the
229-238. from ASTIA
1940, pp. as NACA
Dev.
of
Seitenbeanspruchungen Bericht 169 der
am
of
1943, pp. translation
39.
der
19 -27. Probleme
Berichte
Melzvr, terns.
Friction WADC
1955.
(Pr'obhmls
38.
Air
Mater, E.: Zur Frage Fhlgzeugfahrwerken.
F.:
(Stiffnesses
R.: Coefficient of Concrete Ilunways.
of
1958.
L55E12e.)
H. pp.
Impacts 4247,
105296.)
TM 1365, pp. 31-40.) 35.
R.XI
Schil)pel,
sau).
pp.
NACA
TN
Junkers
Tire.
1941,
-Landing
NACA
1931,
10, -19.
in
During
Airl)lane.
Eng.,
Conno.
Measured NACA
13,
93-98.
Kraft, P.: Die Kriifleverteihmg fliiche zwischen Reifen
and
Kraftim
G.m.b.II. (Berlin), 1938. [Tse of Motion Pictur_es
Studies.
1954,
am
I(raftfahrtforschung
Reichs-Verkehrsnainisteriunas.
Verlag V. I.:
t'mt
34.
Deutsche
57
Drag 2B-4263
(Berlinfrom Loads. 46
4,
1944. Drag Loads. Engr. Div.
58
TECHN'ICAL
Memo.
Rep.
ATSC, avail'tbh"
Army from
62.
Anon.: 1955.
Ye-lr
63.
Anon.: matic
Military Tire.
Sept.
REPORT
No.
TSEAL2
R-64--NATIONAL
4263-46
Air Forces, Apr. ASTIA as ATI No.
Book,
The
Tire
and
4,
AERONAUTICS
ADD.
20, 1945. 169885.) Rim
Assoc.,
2,
64.
16,
1949;
Amendment-2,
Feb.
Aircraft MIL
Tire. C 550,
Inc.,
8, 1951.
PneuC 5041,
Anon.: ings;
(Also
65. SpecificationCasings; Military Specification,
AND
Scanlan, duction Flutter.
SPACE
ADMINISTRATION
Army-Navy Aircrafl Army-Navy Dec. 20, Robert to
Aeronautical I,anding, 1946; It.,
the
The
Specification
Nose,
T.dl
Aeronautical Amcndmont-l,
and Study
Macmill.m
Aircraft Co.,
CasBeaching
Specification, June 16,
Rosenbaum, of
and
1951.
Robert: Vibration
AN1947. Introand
