La ASDJR-68-56

AIRCRAFT BRAKE ENERGY ANALYSISPROCEDURES

DALE E. CREECH

TECHNICAL REPORT ASD-TR-68-58

OCTOBER 1968 -'

APIR 151969

This document hag been approved for publicrelease and sale;'its distribution is unlimited.

DEPUTY FOR ENGINEERINGAERONAUTICAL SYSTEMS DIVISION

AIR FORCE SYSTEMS COMMANDWRIGHT-PATTERSON AIR FORCE BASE, OHIO

Rep:eoduced by theCLEARINGHOUSEfor Federal Scientific & Techn.calInfornaton Springrold Va. 22151

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200 - March 1969 - C0455 - 70-1554

ASD-TR-68-56

AIRCRAFT BRAKE ENERGY ANALYSISPROCEDURES

DALE E. CREECH

Ic

I This document has been approved for publicrelease and sale; its distribution is unlimited.

ASD-TR-68-56

FOREWORD

The research described herein was accomplished through review of variousaircraft braking parameters during the time period of 1955 to 1968. Work was aaccomplished under System No. 139A. The author served as project engineer.

The report was submUed by the author on 12 August 1968.

The author wishes to acknowledge the assistance of personnel of theLanding Gear and Mechanical Equipment Division, Directorate of AirframeSubsystems Engineering, and of the Digital Computation Division, Directorate ofComputation Services, ASD, for significant contributions to the work presentedherein.

This technical report has been reviewed and is approved.

WM A HA ILTONChief, Landing Gear & Mechanical

Equipment DivisionDirectorate of Airframe Subsystems

Enginsering

ii

I ~ ASD-TR-68-56ABSTRACT

This report describes a standardized method for analyzing end calculatingaircraft brake energy requirements. The method is an adaptation of method IIof MIL-W-5013 and requires exaict inputs readily adapted to computer use.These methods have been used in an analysis of the C-5A, F-111, and AMSAaircraft brake energy requirements. Programming the equations into acomputer gave very satisfactory results. The methods can be used manuallyor by a computer to determine the braking energy requirements of any aircraft.

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ASD-TR-68-56

TABLE OF CONTENTS

SECTION PAGE

I INTRODUCTION 1

II DATA REQUIREMENTS 21. Data Requirement of MIL-W-5013 2

2. Requirements for Determining Braking Capacity 3

3. Landing Velocity Considerations 9

III DETERMINING BRAKING ENERGIES 13

1. Force and Distance Computations 13

2. Energy Computations 17

IV CONCLUSIONS AND RECOMMENDATIONS 19

REFERENCES 20

V

ASD-TR-68-56

ILLUSTRATIONS

FIGURE PAGE

1. Sample Plot of Net Thrust Versus Time 5

2. Sample Plot for Determining Coefficient of Drag Versus Time 6

3. Sample Plot for Determining Coefficient of Lift Versus Time 7

4. Sample Curves for Determining Percentage of Static Load onMain and Nose Gears Versus Time 8

5. Parameters for Calculating Brake Energies for Landingand Stopping Distances 10

6. Parameters for Reject Takeoff Type Stop 11

TABLES

TABLE

I Summation of Aircraft Forces and Distances ForSample Calculations 16

H Summation of Energies for Sample Calculations 18

vi

I _

ASD-TR-68-56

SECTION I

INTRODUCTION

The problems encountered in designing landing gear systems for aircraftare many and complex, and their solutions are both difficult and time consuming.The military brake specification, MIL-W-5013, gives two methods for determin-ing the necessary brake energies -- Method I, which Involves a simplifiedequation that provides a determination of the approximate brake energiesinvolved; and Method H, which gives more precise values by considering all theknown energy absorbers and additives associated with the process of landingand stopping an aircraft. Aircraft manufacturers normally use Method H1 inmaking their analysis. Over the past several years, most manufacturers havecomputerized many of the problems associated with this analysis because oftime and manpower considerations.

The aircraft manufacturers have little or no trouble in analyzing thebraking problems, because they have available the equipment and data neededto make the computations. The Air Force monitoring engineer, however, findsit both impractical and impossible to analyze the situation because of the timerequired and lack of appropriate data. While existing military specificationsrequire the manufacturers to submit specific analysis data, they do not requirecertain basic data needed as inputs for these calculations. In view of thisproblem, this report presents analysis procedures and a listing of standarddata requirements needed for making a braking analysis by Method II. Withthis information, the engineer can make adequate calculations to verify thecontractor's analysis of braking energy, stopping distance, velocity at touch-down, velocity at brake application, and rate of sink at touchdown.

To facilitate this analysis. data requirements as set forth herein should beestablished in the 6fficial specification so that the engineer can make anadequate analysis. Then for the first time, the monitoring engineer will havethe necessary tools at hand to readily determine braking energies and stoppingdistances.

T1

ASD-TR-63-56

SECTION II

DATA REQUIREMENTS

1. DATA REQUIREMENTS OF MIL-W-5013Military Specification MIL-W-5013, Method II, provides a method of

determining braking capacity by mathematical and graphical analysis based onprinciples of aerodynamic motion, The following are quoted from the specificationas items to be considered:

a. Actual energy of the mass of the aircraft at instant of touchdown.

b. An integration of the kinetic energy added to the aircraft by thrust ofthe aircraft's propulsion system during the stop.

c. An integration of kinetic energy absorbed by aerodynamic drag of theaircraft during the stop,

d. An integration of the kinetic energy absorbed by auxiliary brakingeffort, such as propeller reverse thrust, deceleration parachutes, or Jetreverse thrust during the applicable portion of the stop In accordance withtable I.

e. An integration of the kinetic energy to be absorbed by wheel brakesduring the stop.

f. Effect of wing lift in reducing the wheel load during the stop, therebydecreasing the torque which can be developed without skidding the tires.

g. Distribution of load and brake capacity among the various wheels.

h. Total stopping distance.

I. Static force avilable for holding aircraft stationary while runningup engines.

J. Appropriate ground winds, airport altitudes, and ambient atmospbericconditions.

k. Landing speed for aircraft shall not be less than aircraft designlanding speed as defined in 6.3. 5.

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ASD-TR-68-56

m. Brake retarding forces versus time curves and brake retarding forcesversus speed curves for each design condition.

n. A complete static and dynamic analysis shall be made by the aircraftmanufacturer of the main and auxiliary wheel loads. From this analysis, a loadingspectrum shall be prepared and submitted to enable design and testing of the

* wheels.

II2. REQUIREMENTS FOR DETERMINING BRAKING CAPACITY

This report presents a method of computing braking capacity that is moredefinitive than that presented in MIL-W-5013 and which Air Force engineerscan use to check the contractor's calibrations. For these computations, weneed inputs that are different from the factors listed in MIL-W-5013. For example,instead of the energy of the mass at touchdown (Item a above) we need data onthe actual gross weight, the c. g. position, and the touchdown velocity todetermine the energy at touchdown. Instead of Item b, we need the thrust of theengines versus time and vel-;clty to compute the energy added to or subtractedfrom the aircraft from a time one second prior to touchdown until it comes to acomplete stop. All of the factors can be computed in this way and comparedwith values submitted by the contractor. For these computations, the followingdata is needed and should be required from the contractor:

a. Time. The time, starting one second prior to touchdown for landingsand one second prior to brake application for rejected takeoffs in increments of0. 25 second.

b. Velocity. The speed listed in feet/second as follows:

(1) Touchdown - Unless otherwise designated, this velocity is1.1 Vspa , (1. 10% of the stall velocity with power on in the landing configuration).

(2) Rate of Descent - The vertical velocity during '9he approach ona 3* glide slope.

(3) Rate of Sink -. The vertical velocity after flare and at the instantof touchdown; In calculating braking energies and stopping distances, use4 ft/sec for all landings. (Note: 4 ft/sec is considered an average, but notthd maximum sink rate required by military specifications.)

3 4

4?i. ~ --

i ASD-TR-68-56s

are applied earlier for higher performance.

C. Thrust. Thrust in pounds is required in i.t least 3 quantities:(1) gross thrust per engine versus velocity, (2) net thrust per engine versusvelocity, and (3) net thrust for all englnes v.ersus velocity. Values shouldInclude the entire range of landing velocities. Values for net thrust in adirection parallel to the ground should be plotted versus time for the landingapproach, touchdown, and roll out, as shown in the example (Figure 1). If theaircraft has revetce thrust capability, values should also be included forreverse thrust net force. If more than one configuration can be used forreverse thrust (i.e., 2 out of 4 engines), values for these conditions shouldalso be given.

d. Coefficient of .Arcraft Prag (CD). Dimensionless units versus timeare required for landing approach, touchdown and roll-out configurations, asshown in the example (Figure 2).

e. Dynamitc Pressure (q). Pressure in lbs/ft 2 , for all altitudes andoutside air temperatur~es Lkpproprtate for the aircraft.

f. Effective Area (Sw). Units in square feet.g. Coefficient of Lift (CL). Dimensionless units versus time required,

as shown in the example (Figure 3).

h. Deceleration Chute D-,rag (D c), Deceleration force, given in pounds.

i. Deceleration Chute Drag Coefficient (Cc) Dimensionless units

rDC

plotted versus tim~e.

J. Effective Deceleration Chute Area. SC). Effective area of> deceleration chute(s), in square feet.

k. Percentage of Load -on Landing_.Gears. Percentages of weight versustime, as shown in ex ample (Figt 'e 4), for the main gear (PM) and nose

pear (P N)'

"' 4

ASD-TR-68-56

30 -

28-. Ref Runway Levl _i

" 26

24

20

-18--- --- _

0 1O146

.1 0o

0X . C- - --.

II 6-

to Complete Sto

-1 0 I 2 3 4 5 6 7 8 9 t0

Touchdown Time (Seconds)

Figure 1. Sample Plot of Net Thrust Versus Time

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ASD-TR-68-56

.13.

.12 - "I

.I -- _

.09 - _

.07

.06 1

.04 - _ -- - - - - - - - -

.03 .030 now Constant for- -

-Remainder of Stop.02 1 11

-I- -L - - - ___ -____

-I 0 I 2 3 4 5 6 7 8 9 "0I T.uth, ... Ti me (Seconds)

Figure 2. Sample Plot for Determining Coefficient of Drag Versus Time

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ASD-TR-68-56

1.2

.9 -

\A

Sample CurveK .8 -- - m u_.7ii: ~~~~~.6 -- - - .......

1;Constant for.3 -Re .- ___ mainder of Stop

--,

1 ft

-1 0 I 2 3 4 5 6 7 8 9 10Touchdown Time (Seconds)

Figure 3. Sample Plot for Determining Coefficient of Lift Versus Time

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ASD-TR-68-56

10011- -

PM Main Gear

* 90

80

00.2

50

_

30 - Nose Gear

-0 -

-I 0 2 3 4 5 6 7 8 9 10

Time (Seconds)

Figure 4. Sample Curves for Determining Percentage of Static Load on Mainand Nose Gears Versus Time

8

ASD-TR-68-56

3. LANDING VELOCITY CONSIDERATIONS

V The landing speed of the aircraft is not defined in MIL-W-5013, (Par 1,Item k above). Here we will define landing speed positively as touchdown speed,which is equal to 1.1 Vspa , where V is defined as the stall-speed-with-spa spapower-onlanding configuration, per MIL-A-8860. The kinetic energy to beabsorbed by the wheel brakes during stop is considered equal to 1.0 V s. If the

spa*velocity at brake application in a specific situation is greater than this value(due to operation of a specific aircraft), then the velocity should be increasedaccordingly.

Three basic conditions for which braking is required are considered in thisreport: normal landing, maximum gross weight landing, and rejected takeoff.These three conditions are described as follows:

a. Normal Landing

In a normal landing, the aircraft follows a 3* glide slope to point oftouchdown and has a gross weight of "landplane landing design gross," asdescribed in Reference 2. The rate of sink velocity, touchdown (forward) velo-city, and brake application velocity are provided, as required by Section H.All changes in configuration for the transition aroa are shown In Figure 5; ifadditional changes are required after the brakes are applied, these must alsobe indicated.

b. Maximum Gross Weight LandingMaximum gross weight landing conditions consist of an aircraft

following a 30 glide slope to point of touchdown with an aircraft gross weightof "maximum landing gross," as described in Reference 2. All other factorsare the same as for the normal landing situation.

c. Rejected TakeoffFor the rejected takeoff, the starting time begins at the point of

decision to abort or I second prior to brake application, whichever is earlier.The transition area includes all changes in configuration shown in Figure 6, plusany additional changes required for a specific aircraft.

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ASD-TR-68-56

0 a) 'DIn.0 - 0~

0 0 0i C0k0 0 )

C o 40.

000

ASD-TR-68-56

Transition Area

Velocity for Engine Set to Idle

Maximum Velocity Attained

Velocity for Brake Application

_______L.t fU or Engines at IdleBraked Stopping Distance

Velocity atDecision Point

Runway Length

The runway length is such as to result in the greatest velocity possible suchthat engine failure permits acceleration to takeoff in the same distance thattho aircraft may be decelerated to a complete stop @ 10 ft/sec 2 rate ofdeceleration by the brakes only.

Figure 6. Parameters for Reject Takeoff Type Stop

The rejected takeoff velocity is normally equal to 0.9 Vspa; however,the minimum abort velocity cannot be less than the maximum velocityresulting from critical engine failure (Reference 3). To determine themaximum abort velocity, V., we need values for the following factors:

an - acceleration with all engines for most adverse condition oftemperature and altitude commensurate with aircraft operation

a-_ 1 - acceleration with all engines minus one for most adverse conditionof temperature and altitude commensurate with aircraft operation

ad = deceleration during braking (deceleration rate for brakes only is10 ft/sec/sec, per Figure 6)

Vto = takeoff velocity

ASD-TR-68-56

For this computation, the time, t, from deciding to abort until the brakesare applied will be considered to be 3 seconds; during this time period, theaverage velocity has increased to 1.05 Vm . The abort distance, SA, then will be

(n+ad) Vm 2+ 2anadt1.O5 VmA2 an ad

and the takeoff distance after engine failure, Sn 1 , will be

(an- IV m + an (Vt 2o..VSn -i =

- - O iaJn-I

For maximum abort velocity, the distance to abort ideally should equalthe distance to takeoff after loss of one engine; thus,

Sn_ , = SA

or

aO 2 Y~ 2 2 2an-_Vr +On ( Yt -Vr = an+Od)Vm + 2 anqdjt1.O5Vman-i 2 anad

Therefore, the maximum abort velocity will be

2afnad[on.,Vml+ On (Vto - Vm)= an-n[(n+d)VmZ+21IanOd t Vml

12

ASD-TR-68-56

SECTION I

DETERMINING BRAKING ENERGIES

The following procedures are used for determining braking energies. Theequations used in solving the forces, distances, and energies are given, as wellas the inputs needed for use in these equations. A sample calculation is alsogiven using each equation. The results of these sample calculations for forcesand distances are presented in Table I. The results of the calculations forV4energies involved are presented in Table II.

1. FORCE AND DISTANCE COMPUTATIONS

The equation to use in computing each factor is given, follovd by a samplecomputation. For these computations, the time starts at -1. 00 second, andthe initial velocity is assumed to be 230 ft/sec. The thrust includes that providedby all engines corrected for horizontal alignment with the ground, as given inFigure 1.

a. Aircraft Drag (DA)

: DA =C O q Sw

where

CD = appropriate value determined from Figure 2

q 1/2 p V2 , and P = 0. 00238 at sea level

= 4000 ft2 (for. this example)

Therefore,

DA 0. 12 x 1/2 x 0. 00238 x 230 2 x 4000= 30,216 lbs

13

ASD-TR-68-56

b. Brake Drag, BD*

BDIL /PM)(G.w.- CL q SW) +(Ad) (C.G. Height)(G.W.)Nse to Main 13002.2))

+(_Thrust) (Height of Thrust Line))]+(Nose to Main Wheel Dist

wherep. = 0. 41 for this examplePM = appropriate value determined from Figure 4

G. W. = 240, 000 lbs (for this example)C = appripriate value determined from Figure 3L

P= 0. 00238C.G. Height = 150 inchesNose to Main Gear = 700 inchesHeight of Thrust Line - 140 inchesthrust = appropriate value from Figure 1

Ad and reverse thrust are accompanied by negative signs.

Therefore,41 [ (0. 85) (240, 000 - (0. 20) (0. 00238) (204. 9)2(4000)

+ (-1. 33) (150) (240,000)(700) (32.2)

+ (+160) (140,J= 68,855 lbs.(700) 1

Considering the initial velocity to be 230 ft/sec at time -1. 0 see. resulted In atouchdown velocity of approximately 226 ft/sec at t = 0. 0. Figure 5 Indicatesbraking application would start at a velocity of 204.9 ft/sec at t a 14.50 seconds.

c. Deceleration Chute Drag, DC (if applicable)

w DC = CDC 4 Sc N (x)wher,,

C DC and Sc are inputs provided by contractorN = number of deceleration chutesX = openiug shock effect

*Prior to brake application, this value can be based on main gear rolling resistance

calculated by MD = PM (G. W. - CL q % 0. 020 = 441.31 lbs for this example.After brake application, this drag Is nolonger appropriate.

14

7; 1 _ _1

ASD-TR-68-56

d. Nose Gear Drag, NDND = R/k [ (%,)(G. W,- C, S,,)

_(.-Ad)" (C.G. Height) (G. W.))[(( Thrust) (Height of Thrust) 1k(Nose to Main Dist) (32.2) )k(Nose to Main Wheel Dist) 1.1

where

P = appropriate value from Figure 4nRn _ _ = 0. 20 for tis exampleF = 2800 - 30216 = -27416 lbs.

A -27416) (32.2) = 3d (240, 000) * 8 ft/sec 2

AV = -3.68 (0. 25) - 0. 9196 ft/sec=(230 + (-0. 9196) (0. 25) = 57. 39

2

e. Algebraic Summation of Forces, 2 F_7F = T +DA+8D +DC +NU

Example: At t =1. 0 see

F = 2800 - 30,216 lbs = -27,416

f. Decelerttion, AdAd= IF.

Therefore

A = (-27,416) (32.2) - 3 68 ft/sec2d (240,000)

g. Incremental Change in Velocity, AV

AV=aAt

ThereforeAV = -3.68 (0. L) = 0.9196 ft/sec

h. Incremental Distance. Ad

Ad=(V + AV)At2

ThereforeAd = (2%0 + -0. 9196) (0. 25) = 57, 39 ft

2i. Total Distance Traveled ( d)

15

ASD-TR-68-56

CD -4 ) - ~ C 00 0 00

V ! t -D CD (D C D mto to to to 10 1 10 to 10

0) 0 m L- tD C C - " 1D ID I oo 00 0 0 t- q to

c; CD

a) 0D0 to 00 0) m 0 M -0) wD w 10 1o0 cD 0 V-f r-4

CD3 C; C; C; C; C; C; -

00 to V m to 00 I I Iz- "Ir W w c b- 0 O

Cq N~4 cq *q Q e 0) 1 C00 4J

r- .2 4 w 0P '0Z tJ' CD C -WDD 0

~~4-)

0 P c o uato0ca CC; 10 CD

I * 0 0 0CD 10

t00 H to mCDWt

MD m 00C mD mDC0 ~~~ 0 1. C

IC5 0 0 CDC D

0 0) 0C) HDC ) .Cm 00 00 0 OD 0 0

ODI I MD HD CD C CD3 to LD H o

;> CD CD CD CD CD CD CL CD0) C- 10 q 0 C D 0cq c

') 0 D CD C 0 to 0 t 0L- cq 0) cq CD v-I 044~ 0) 0 vI C D 1 ~ 4 C

go D CDI C ; ;C

16

ASD-TR-68-56

2. ENERGY COMPUTATIONS

The energy to be dissipated in the braking process can be determined bymultiplying the incremental forces (T, DA , BDo DC , and ND) by the incrementaldistances (A d) and summing for the total. Values for the example (aircraftwith a G. W. of 240, 000 lbs and an initial velocity of 230 fps) have been computedand are presented in Table H. Inputs for the various columns are as follows:

a. Time (t) - in increments of 0. 25 see, as in Table I.

b. Kinetic Energy (K. E.) - value determined from the following equation:G.W.

K.E.= '2 9c. Total Engine Energy - to include the total amount of thrust for thei given time period.

d. Total Aircraft Drag Energy

e. Increment of Brake Energy

f. Total Brake Energy

g. Total Deceleration Chute Energy

h. Total Nose Gear Drag Energy

i. Summation of Energies - to include the algebraic sum of columnsc, d, f, g, and h.

17

[,,

, i 17

ASD-TR-68-56

0 1 V-1 0 02 t

0~ ~ 0 a t"414 2 w0C

t- to LO4

t' I I

*4 q0

Cl0 b~ z z z z z z

0 0 0 w ;0o al L

*4* 0 0 t - t- copiI

0 0O 02 IN402o '4O4 oo2

(a ao 0 ; t

04 12 1

02 D2 o2 0 b4

46 0 b4 t

w2 m2 to '' 0 -

to Lo t- .-4 0o cato 02 0 m2 m 0D

;i 04 ?; ;C1- 4 0 -

m- 0 0 0 0 w'

18

ASD-TR-68-56

SECTION IV

CONCLUSIONS AND RECOMMENDATIONS

The procedures described in this report permit an accurate determinationof the braking forces and distances required for. stopping an aircraft. Theseprocedures require input data different from that required by MIL-W-5013.It is recommended that input data as specified herein be requitred of all AirForce aircraft manufacturers and that this data be used as described herein toevaluate aircraft designs.

1

IqIt

j 19

ASD-TR-68-56

REFERENCES

1, Military Specification, MIL-W-5013, "Wheel and Brake Assemblies;Aircraft."

2. Military Specification, MIL-A-8862. "Airplane Strength and RigidityLand Plane Landing and Ground Handling Loads."

3. Military Specification MIL-M-7700, "Manuals, Flight."

2

20

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DOCUMENT CONTROL DATA- R & D(Security claselflcation of title, body of abstract and Indexing annotation must be entered when the overall repoti s claa ified ,

I. ORIGINATING ACTIVITY (COrporte a luthor) Z. REPORT SECURITY CLASSIFICATIONDeputy for Engineering, Aeronautical Systems Division Unl_

_ifled

Wrigit-Patterson Air Force Base, Ohio ;b. GROUP

3. REPORT TITLE

AIRCRAFT BRAKE ENERGY ANALYSIS PROCEDURES

4. DESCRIPTIVE NOTES (Type of report end tnclualn dAtee)

I AU THOF(SI (FIrst name. middle Initial, last name)

Dale E. Creech

8. REP)ORT DATE 7. TOTAL NO. OF PAGES 17b. NO. OF REFSCletober 1 QAR 2I

IS. CONTRACT OR GRANT NO. 9a. ORIGINATOR'S AEPORT IJUMBER(S)

b. PROJECT NO. ASD-TR-68-56

c.System 139A 9b. OTHREPORT NOMS (An, unet number# that way be aaaldnedthis report)d.

I0. DISTRIBUTION STATEMENT

This document has been approved for public release and sale; Its distribution Is unlimited.

II SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY

Deputy for EngineeringAeronautical Systems DivisionWright-Patterson Air Force Base, Ohio

13. ABSTRACT

This report describes a standardized method for analyzing and calculating aircraftbrake energy requirements. The method is an adaptation of method II of MdIL-W-5013 andrequires exact inputs readily adapted to competter use. These methods have-boenjused in ananalysis of the C-5A, F-111, and AMSA aircraft brake energy requirements. Programmingthe equations into a computer gave very satisfactory results. The methods can be usedmanually or by a computer to determine the bratkng energy requirements of any aircraft. 1)I

:FORMIliI

DD 1 NOV J473 T.AS STF ...Security Classification

JWTLAqqFT1F-TSecurity Classification14. L INK A LINK 9 C

KEY WORDS RO LE WT RO,.E WT ROLE WT

Aircraft Landing Systems

Aircraft Braling Analysis I

IIiI!

UNCLASSIFIEDSecurity Classification

Dr:APToN 0 rHE AIR FORCE PP"

HIADQUARTL:RS ACRCNAJTICAl_ SYSTEMS DIVISION (AFSCP .- o

WRIGHT PATT.R:ON AIR FORCE BASE. OHIO 45433 A',' .

REPLY TO APR 9ATTN or ASNFL (Mr Creech) 2 9 w

SuIJECT ASD TR-68-56, Aircraft Brake Energy Analysis Procedures

T Clearinghouse for Federal Scientific & Tech Info IM" ,:Sills Building5285 Port Royal RdSpringfield, Va 22151 w,-" ...

SAttached hereto is the erraza sheet for pages 12, 14 and 15 of

the subject technical report.

14 WADLL" - I AtchActing Chief, Landing Gear and Errata Sheet

Mechanical Equipment DivisionDirectorate of Airframe Subsys Engr

CL F A R IN IiOUSEh^, ww , , e, I) ;, - f w1

ERRATA SHEET FOR ASD TR-68-56

1. On page 12:

a. The equations for SA and Sni equal the total field distance.

b. For the equation Snl the detiominator should be "2anan-l."Therefore, the final equation should read as follows:

2anad[an-iVm2 + an (Vto 2 - V m2)] = 2anan-l [(an+ad)Vm2 + 2.lanadtVm]

2. On page 14:

a. Change the "+" sinn to a "1-" sign as follows:

(tThrust)(Heiqht of Thrust Line))- ( Nose to Main Wheel Distance

b. The BD sample calculation has the proper answer but should readas follows:

85 -()(.238)(24.9) (1O).((l33)(l50)(24OOOO)D = "' [(.85)00)'= ) (0 .0 2 L (7 0 32 ' /

((+160) (140) I(700) )]= 68,855

3. Page 15, change the "-" sign to a "+" sign as follows:

+ (+tThrust)(Heiqht of Thrust)'\Nose to Main Wheel Distance/