NASA TECHNICAL

MEMORANDUM NASA TM X-62,333

https://ntrs.nasa.gov/search.jsp?R=19740008607 2020-07-10T13:26:48+00:00Z

:_ ABSTRACT

_. A set of computer programs has been developed to estimate the

" takeoff and landing maneuver of a given aircraft. The program is

applicable to conventional, vectored lift and powered-lift concept

aircraft. Portions of the program may also be used to evaluate the

static performance of these t)Tes of aircraft. The aircraft is

_ treated as a point mass confined to motion in a vertical plane,_-

_, and rotational dynamics have been neglected. The required input is/

described and a sample case is presented.

PReCeDING PAGE BLANK NOT FILMI_D

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1974008607-002

TABLE OF CONTENTS

,'_ INTRODUCTION iv

'_ NOTATION v

>%

_ SUBROUTINES

Subroutine TAKOFF I

;_ Program Inputs 2

Program Outputs 6

Subroutine LANDNG 7

Program Inputs 8

Subroutine ZERO 13

USER SUPPLIED SUBROUTINES

Subroutine ARODYN 16

Subroutine ENGINE 18

REFERENCES 20 _i

APPENDIX A -- EQUATIONS 21 _._

APPENDIX B --SAMPLE CASE 25 :

APPENDIX C - PROGRAM LISTING 27 _

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1974008607-003

COMPUTER PkOGRAMS FOR ESTIMATING AIRCRAFT

TAKEOFF AND LANDING PERFORMANCE

By Jeff V. Bowles and Thomas L. Galloway

Ames Research Center, Moffett Field, Calif. 94035

INTRODUCTION

A set of computer programs has been developed to estimate the

take)ff and landing maneuver of a given aircraft. The program is

applicable to conventional, vectored lift and powered-lift concept

aircraft. Portions of the program may also be used to evaluate the

static performance of these type aircraft. The aircraft is treated

as a point mass confined to motion in a vertical plane, and the

rotational dynamics have been neglected. The takeoff subroutines

are a modification and simplification of an unpublished program by

V. R. Corsiglia of Ames Research Center.

The user is required to provide two subroutines which compute

' the total force coefficients along and normal to the flight path, and

i determine various required engine characteristics.

This report describes the various subroutines and the required

t input, the equations used, and the computational techniques involved.L '-

,_ Also included J s a listing of the total program and an example case.

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1974008607-004

NOTATION

c

Symbol Fortran Name

a S(9) - acceleration normal to flight path (rad/sec 2)n

a t T(6), S(8) - acceleration along flight path (ft/sec 2)

C CX - force coefficient along flight pathx

Cy CY - force coefficient normal to flight path

ENP ENP - number of engines

g - acceleration due to gravity (ft/sec 2)

h PASS, S(7) - absolute aititude (ft)

:,_ i EYEW, EYEWNG - incidence of wing (deg)• • W ,.

_ LF XLF - load factor

'. _ q - dynamic pressure (ib/ft2)

': _' R/C S(ll) ROC, RTCL - rate of climb (ft/sec,fpm)

S SW, SWING - reference wing area (ft2)

T THRUST - thrust, net or gross, per engine (ib)

V T(4), S(4), VEL - aircraft velocity (ft/sec)

Vx S(IO) - horizontal component of V (ft/sec)

V S(II) - vertical component of V (ft/sec) 1Y

V V1 - engine failure speed, EAS (knots)I

VR VR - rotation speed, EAS (knots)

W W, WG - aircraft weight (ib)

Wf .,F,WFUEL - fuel flow (Ib/hr)

ALPHA - angle of attack (deg)

S(5), GAMMA - fllght path angle (rad,deg)

6 F DELFD - flap def!oction (deg)

Ii!!" 6S DELSPL "sp°iler d°flecti°n(deg)v

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1974008G07-005

0 THETAF - pitch attitude fuselage angle (deg)

ANGLE - vectored thrust deflection angle (deg)

p RHO - air density (slugs/ft 3)

MU - rolling coefficient of friction

_BRK XMUBRK - braking coefficient of friction

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1974008607-006

SUBROUTINES

Subro,atine TAKOFF

The subroutine TAKOFF simulates the takeoff maneuver of a given

aircraft. The program is applicable to conventional, vectored lift

and powered lift aircraft. The aircraft is treated as a point mass

confined in motion to a vertical plane and the rotational dynamics

are neglected. This simplification necessitates an estimation of all

rotational rates involved. These rates are either input by the user

or are approximated by a finite difference form.

The takeoff maneuver is divided into four basic segments: ground

roll and rotation, liftoff and initial segment climb, acceleration to

final climb speed at a constant rate of climb, and final!y, the pullup

maneuver to establish the final climb speed. Provisions in the program

: are made for gear retraction, flap retraction, changing of vectored

thrust angle and changes in the power setting.

t The ground roll is made at a specified setting and flappower

deflection. When the rotation speed is reached, the aircraft is

"rotated" by increasing the angle of attack linearly with time until

liftoff occurs or the tail scrape angle is reached. If the latter

occurs, the ground roll is continued with the fuse!age angIe equal to

the tail scrape angle.

'theflight path control is obtained by monitoring three dynamici

variables -- acceleration along flight path, load factor and fuselage

angle (pitch attitude), The aircraft is not permitted to decelerate

and the load factor and fuselage angle are restricted to values less

than or equal to a specified value. I£ any of these conditions are

violated, the angle of attack is reduced until all constraints are

satisfied.

1974008607-007

Once a specified altitude is attained, called the maneuvering

altitude, the aircraft is pitched down by a reduction in angle of

attack until a specified rate of climb is obtained. The aircraft

then accelerates at this rate of climb until the desired final climb

speed is reached.

hen the final climb speed is attained, the pullup maneuver is

executed in order to bring the aircraft to a zero rate of acceleration

along the flight path. This maneuver is accomplished by increasing

the angle of attack and pulling a load factor of 1.20, which will

result in an increase in the rate of climb to a final value at the

desired climb speed, It may be necessary to throttle the engines in

order to maintain the desired constant climb speed subject to the

i fuselage angle restriction.

Program Inputs

The inputs to subroutine TAKOFFare through the argument list,

input by NAMELIST and common blocks /UNIV/ and ]AERO/.

The call to TAKOFF is as follows: CALL TAKOFF (INPC, IDCN,

_ WGROSS,SWING, XENG, V1, VR, VEND) where

_,_:.: INPC - program control = 1 - input data loaded

., L.. = 2 - program executed

_:'i', = 3 - data input andprogram executed

IDCN - print control = 1 - no print out

• 9 - print outt

_,:" WGROSS - aircraft gross weight (Ibs)

,; SWING - reference wing area (sq ft) ,

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1974008607-008

XENC n_mber nf engines

V1 critical engine failure speed (knots)

VR rotation speed (knots)

VEND final climb speed (knots)

All speeds are indicated air speeds.

There are two namelist inputs to TAKOFF, /NM41/ and /NAM2/.

The namelist /NAMi/ input variables are as follows

CDGEAR - drag increment due to gear

DFLPDT - flap retraction rate (deg/sec)

" DTABS - temperature increment above 59°F (°F)

DTGR - time required to retract gear (sec)#

DTPDWN - throttling down rate (percent/sec){

_#, DTPUP - throttling up rate (percent/sec)

i DTVECT - vectored thrust angle reduction rate (deg/sec) ,EYEWNG - wing incidence angle (deg)

HAPT - airport altitude (it)

HGR - altitude at which gear retraction isstarted (it)

HMAN - maneuvering altitude (ft)

_t_X - takeoff termination altitude (it)

Iotrr - for engine out takeoff, set lOUT = 1

UM - rolling coefficient of friction

NPAGE - no. of lines printod per page

PMARG - pullup speed margin

RTCL - rate of climb during accelerate segment (fpm)

TI_rFLY - maximum allowable fuselage angle while airborne (deg)

S- THTSCP - tail scrape angle (deg)

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1974008607-009

XLFHAt - maximum allowable load factor

DTFAII, - time required for one engine to fail (sec}

The user may input all, some, or none of the above input variables.

The default values of these input variables are listed below:

CDGEAR = 0.0, DFLPDT = 3.0 deg/sec, DTABS = 0.O°F,

DTGR = 5.0 sec, DTPD_ = S.O percent/sec,

DTPUP -- 6.0 percent/sec, DTVECT = 10. de£/sec,

EYEHNG = 1.0 deg, HAPT = 0.0 ft, HGR = 25.0 ft,

I_ = i000. ft, IOUT = O, tim = 0.02, PMARG = 0.04,1

RTCL - 750. fpm, THTFLY = 15.0 deg,k

j _ THTSCP = 10. deg, XLFMAX = 1.15, DTFAIL = 3.0 sec

: If the default value cf CDGEAR is used, the program will calculate,

1 based on an empir, cal fo-:...ka, a value for the gear drag as a function

!

i of gross weight and wing area.

The second set of namelist variables, /NAM2/, constitute the

,.,- flap, throttle and vectored thrust schedules. These are tables that.-.}t'-:'. }

_'_h! manage the flap setting, power setting and vectored thrust angle as a

"_i "! function of the aircraft speed and altitude. These variables are

_': , ; arrays of dimension S.

XDELFD(1) - flap deflectio_ (deg)

_4FIAP(1) - flap retractiaa altitude (ft)

,:, XVFIAP(1) - flap retracticr_ speed (knots)

XPOWER(I) - power setting !

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1974008607-010

XHPWR(I) - power setting change altitude (ft)

XVPWR(I) - power setting change speed (knots)

XNU(I) - vectored thrust angle (deg)

XHVECT(I)- vectored thrust angle change altitude (ft)

XWECT(I)- vectored thrust angle change speed (knots)

All altitudes are absolute altitudes and all speeds ave indicated

air speeds.

These schedules are constructed as follows: If the s_eed or

altitude of the aircraft is equal to, say, XVFLAP(I) or XttFLAP(I),

respectively, then th- flaps are retracted to the value XDEI.FD(I).

The power setting and vectored thrust angle _anagement work in ae

similar manner. The power setting may either be increased or decreased.

"l_e flap setting and vectored thrust angle setting can only be reduced

i with speed and altitude. The values of XDELFD(1), XNU(1) and XPOWER(1) are

all for the _round run. The user is permitted four changes in flap,

power, vectored thrust ang:e settings during the airborne portionof

the takeoff.

tThe default values for /NAM2/ are as follows:

? - 100. percent throttle throughout takeoff :

b_

,_ - O. degrees recto, red thrust

- 15.0 degrees flaps d,,ri,_g ground roll,retracted to 5.0 degrees at 250 ftaltitude, retraction to 2.0 degrees at200 knots, and finally, complete

, retraction at 210 knots

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Again, the user may choose to use all, some, or none of the above

schedule values. No changcs to any of these settings are allowed

during the pullup maneuver.

Progre_ Output

The program output consists of a time hi_tory of several aircraft

and flight path parameters. See sample listing presented in Appendix B.

The variable DIST is the flight path track distance along the ground.

The variable TAS is the true airspeed and E_ is the indicated airspeed.

DALPH/DT and DTHTA/DT are the time rate of change of the angle of attack

,.nd fuselage angle respectively. In addition, the user may also obtain

the following values through the common block /EXO_G/:

SROLL - distance to liftoff (ft)

$35 - track distance to 35 ft (ft)

V35 - speed (EAS) cc 35 ft altitude (knots)

TSJ - ground distance covered by aircraft attime of engine failure

The variable TSJ may be used in conjunction with the subroutine

ROLL to calculate accelerate --stop distances.

The program will terminate normally when the end speed is reached

•_!_¢_" (VEND) or when the maximum specified altitude (_LAJ()is attained.

;_._ Abnormal termination will occur under several conditions:

' flight path constraints cannot be met byfurther reduction in angle of attack

• aircraft cannot accelerate at input rate :

of cliab (RTCL) }

- aircraft altitude goes negative t

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1974008607-012

- ground track distance greater than10. nautical miles

- ground run exceeds 90 seconds

- elapsed time greater than 300 seconds

For further definitions a-,d explanations refer to the listing of

TAKOFFand st, pporti_,g subroutines contained in Appendix C, and the

example case presented in Appendix B.

Subroutine LANDING

} The subroutine LANDING simulates the landing maneuver of a given

:_ aircraft. As in the TAKOFF subroutine, the airc,'aft is treated _- a

point mass confined to motion in a vertical plane and the rotationalk2

dynamics are neglected. The landing is divided into three distinct

|: phases: the approach, the flare to touchdown, and the rollout.

i The landing approach is made at the thrust and angle of attackrequired for zero acceleration along and normal to the flight path.

These values of thrust and angle of attack for the steady state-' approach may either be input by the user or calculated in subroutine

ZERO.

The flare is executed by incleaslng the angle of attack at a i

specified rate (DADT). The program iterates on the flare initiation 1

altitude until the rate of sink at touchdown equals a specified value1

(SINk'ro). !Flight path control during the fl_. _btained by monitoring

th_ load factor, fuselage angle and pi_ci_ r'__.e. These three variablesi

are all restricted to values less than or equal to values specified

by the user. If any of these conditions are violated, the angle of

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1974008607-01g

attack is reduced until all constraints are satisfied. Provisions are

made for spoiler retraction and increases in power setting during the

flare if desired.

After the touchdown, the rollour is then e_ecuted, with pro=

visions in the program for any pilot reaction or delay time, brake

application, deployment of spoilers and thrust reversing. The landing

_n terminates when the aircraft comes to rest.

Program Inputs

The inputs to subroutine LANDNGare through the argume;:t list,

common blocks /UNIV/ and /AERO/ and na_elist /NAM3/.

• he call to LANDNGis as follows: CALL LANDNG(INPC, _'_RITE,

; WfiROSS,SWING XENG, PWRSET, MODE, IZERO, IREV, NER) where

: INPC - program control - 1 input data loaded

s = 2 program executed

, ffi3 input data loaded

and program executed

i ', IWRITE - print control = 1 no print out

_:_": = 2 print out

__ = 5 iteration on HFLAREprinted out

_._t_::i_i WGROSS aircraft gross weight (Ibs)

' _ ,, SWING - reference wing area (sq ft)

XENG = number of enginese

-_ MODE = roll out option control (see below)- ;_ _

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IZERO - approach values of thrust and angle ofattack = 0 calculated by program .

= 1 input by user

IREV - reverse thrust control = 0 no reversethrust

= 1 reverse thrustused

NER - error indicator = 1 successful case

The user has two options for the ground roll calculations. An

; average deceleration rate and delay time may be input and the ground

roll distance determined by a single formula (MODE= 2). The second

_' option is the time step integration (MODE-- i).

!i The namelist /NAM3/ input variables are as follows:

ABAR - average deceleration (g's)

._. CDGEAR - drag increment due to gear

DADT - time rate of change of angle of attackduring flare (deg/sec)

DTABS - temperature increment above 59°F (°F)

DTDTMX - maximum allowable pitch rate during flare(deg/sec)

-. DTPENG - throttling rate (percent/see) "

_._,_ ! FAAFTR - field length factor

,/., HAPP - approach screen height (it)

,_-_',_:_!': HAPT - altitude of airport (it) :

.. HSPOIL - minimum spoiler retraction altitude (it) _:

IPOWER - throttle modulation control |

' I see below :':' ISPOIL - spoiler retraction control

_' ' PWRIDL - power setting at idle thrusti,? _"

-_'_' PWRNAX - maximum power setting _"

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, .., ..r, .............

_=4_-_: _ _ ___--_::1. _ _ _/--_v"- -,----' ................... . . .

1974008607-015

PWR_RG - power setting margin

SINKTD - sink rake at touchdown (ft/sec)

TDELAY - delay time after touchdown before anybraking action taken (sec)

THEMAX - maximum fuselage angle (deg)

TBRK - time before brake application (sec)

TFLP - time before flap retraction (sec)

TOFF - time before engine shut down (sec)

TREV time before reverse thrust applied (sec)

TSPL - time before spoilers deployed (sec)

kDIST de,lied landing distance (ft)

XMUBRK braking coeffient of friction

XLFMAX maximum allowable load factor

QUESS - see subroutine ZERO

HFLARE - initial quess of flare al. rude (ft)

STEP - step size for iteration on HFLARE

tn addition, the following are input through common block /LAND/

._._ .: COb94ON/LAND/ GAM_PP, VKAPP, ALP}_4X

';_S- i where

•._',' GAMAPP - flight path angle, measured positive

_._._.:., below horizon (deg)

•- VKAPP - true airspeed at approach (knots)

ALP_4X - maximum allowable angle of attack duringflare, sat equal to THEMAX in subroutine

_":" ZERO (deg)

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1974008607-016

The user may choose to input the approach speed (VKAPP) or input

the desired landing distance (XDIST) and the program wiii _alculate the

required approach speed. This calculated approach speed is based on a

constant load factor flare (XLF_t_X) and the input values of ABAR,

XLFbtAX, GAMAPP,SINKTD and TDELAY. To use this option, the user should

set VKAPP = 0. before the call to LANDNG.

. The approach values of thrust per engine and angle of attack may

be input (IZERO = i) through common block /AERO/ or calculated by

subroutine ZERO (IZERO = 0).

The quess for the flare initiation altitude can be input Dj *he1-

_ user or calculated by the pro£r_ (use default value of HFL_d_E). The

:

: _ variable STEP controls the step size in the iteration to find the proper

_ flare height. For powered - lift or any other aircraft that experience)

l, _ negative ground effects (suck-down), it is suggested that HFL_d_EandkI

STEP be input as 40.0 ft and 0.9 respectively.:

: For ISPOIL = 0, the spoiler deflection angle (DELSPL) remains _

constant throughout the flare, and for IPOWER= O, the throttle setting j

(PWRSET) is held fixed during the flare. For those aircraft experi-

f :encing negative ground effects, the spoilers may be retracted to obtain

-,.:_, 'l direct lift control (ISPOIL = I) and the power setting advanced during

_:_] the flare (IPOWER= 1) If the load factor during the flare should

_<_;o_ decrease, usually occuring when at or near maximum allowable angle of

.,-, : attack, the power setting will be advanced. Spoilers may be retracted

' when the air=raft is at an altitude of HSPOIL or when PWRMAX- PWRSET<

PWRMRG.

_ If the user chooses to use reverse thrust during the ground roll,

_:/ he must supply a subroutine REVRSE, which returns the total force

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4

coefficients along and normal to the ground roll veloci:y vector. It

is invisioned that this subroutine would be similar in structure to

subroutineARODYN, using the same common blocks to transfer required

variable values. When using reverse thrust, IREV = 1 must be input.

During the ground ro11, the user may select to apply brakes,

retract flaps, deploy spoilers, shut engines down or use reverse

t,_rust,or any combination thereof. Pollowing touchdown, there is a

delay of TDELAY seconds during which time no braking action is taken.

After this delay time interval has elapsed, the various braking

techniques listed above may be employed, with additional time delays

for each (TBRK, TFLP, TOFF, TREV, TSPL). Spoilers are extended at a?

rate of 90 degrees per second, 90 degrees being fully deployed, and

i ' flaps are retracted to zero degrees deflection at a rate of I0.0 degrees/t

'. sec. If no reverse thrust is used, the power setting is reduced to

. idle (PWRIDL) at the specified rate of DTPENG percent/sec. If reverse

! thrust is applied, the power setting is advanced to I00 percent at thei

i specified rate of DTPENG percent/sec. If the user desires the flap

_. settirg, spoiler deflection or throttle setting to remain fixed at the{

,:;_,_"'*"i value at touchdown, he should input a large value for the associated

;' _,;. l time delay interval (say, I00 seconds).

.:_:. The user may input all, some, or none of the input variables

_._i,," discussed above. The default values of these variables are listed below.

i

ARAR = 0.35 g's, CDGFAR = 0.0, DADT = 5.0 deg/sec,

DTABS= 0.0 °F, DTlYrMX• 7.0 deg/sec, DTPENG= 3.0 ,"

_ percent/sec, FAJ_FTR= 0.60, HAPP= 35.0 ft, HAPT

• 0.0 ft., THEMAX= 10.0 deg, TBRK - 0.0 sec, i

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1974008607-018

TFLP = 0.0 sec, TOFF = 0.0 sec, TREV = 0.0 sec,h

TSPL = 0.0 sec, XDIST = 5000 ft,

_4UBRK= 0.40, XLFMAX= 1.15, HFLARE= 0.0 ft,

STEP = 0.9

If the default value of CDGEARis used, the program will calculate

a value for the gear drag based on an empirical formula as a function

of gross weight and wing area.

: For further definitions and explanations refer to the listing

:i of LANDNGand supporting subroutines contained in Appendix C, and the

¢ example case presented in Appendix B.

_ f Subroutine ZERO_ .

i• Given the aircraft configuration, its velocity and flight path

i angle, subroutine ZEROdetermines the required values of thrust per

engine and angle of attack for zero acceleration along and normal to

the flight path.

The ma_.hematicalproblem entails driving two functions of two

I independent variables simultaneously to zero.

Let f(T,a) = dV/dt

_ :_ "" where

i

T - engine thrust

a - angle of attack

dV/dt - time rate of change of velocity along flight path

_-. '" d_/dt - time rate of change of flight path angle

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!

Subroutine ZERO generates the locus of f(T,a) = 0 and g(T,_) = 0,

and then searches for their intersection.

The values of thrust and angle of attack at this point are the

required value for the steady state approach.

_ ...........

\ Ji I

i .

! / -r_,, -1-;,,, "-i"i

1 The above figure shows a typical _lot of the f and g functions.

i The values aApP and TAp P are the desired values of angle of attack and

i thrust. The upper bound on the thrust is the static sea level thrust.

The search for al and a2 is made on the interval -amax _ i - _max'

_o,_ i = 1,2. The error is then defined to be the difference between _I and

i "" / ' a . The subroutine varies the value of the thrust until the error is

_i:_,-._, driven to zero, or aI • a . In varying the thrust, Ti �1• Ti times STEP,

,' where STEP is an input parameter, ususlly less than 1.0. The initial

quess at the value of tl'm_st is defin_l to be the sea level static

!i: thrust times the parameter Q_SS:

TI • TSL S *QUESS

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1974008607-020

It is suggested that the u_er make this initial quess of thet

thrust "high", so that the program does not search in areas where there

is no solution of f(a,T) = 0. Recommended values of QUESS are:

1) conventional aircraft- QUESS = 0.50

2) powered- lift --QUESS = 0.80

rhe default value for Qb£SS is 0.80. In the main calling program, the

user must specify a value for the total sea level static thrust (ST)

i:. before the call to IANDNG is made.

_: Subroutine ZEROmay also be used to determine the static perform-t

, _: ance of an aircraft, given its veiocity and flight path angle. Thei ,

: } flight path angle is measured positive below the horizon (i.e., if

: ,_ the aircraft is climbing at a flight path angle of 5.0 degrees, the

; _ call to ZEROwould be made with GAMAPP- --5.0).

i' The call to ZERO would be as follows:

,j

t CALL ZERO (NER, EN, ALT, DTABS, KENG, PWRSET, QU_SS) i

,° wher_

NER - error indicator = 1 successful case

I'_"I-,_- EN - aircraft Milchno

_:__,:,, ALl" - aircraft altitude (ft)

•",,-' DT&BS - temperature increment above Sg"F ('F) |

. _ |KENG = I i

.., PWRSET - power setting (returned)

_" QUESS - initial quess parameter :

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] 974008607-02 ]

The following con_non blocks must also be used:

/UNIV/ - passes ENP, ST, W, etc.

/LAND/ - passes GAMAPP, ALPHMX

/AP_O/ - passes QS, VEL, HABS

where

QS = product of dynamic pressure and wing area

VEL = aircraft speed (ft/sec)

HABS = absolute altitude of aircraft (ft)

Subroutines ENGINEand ARODYNare both called by ZERO. The call

: to ENGINE is made with KENG = 1 (see description of subroutine ENGINE).k

: The user may choose to work either with gross thrust or net thrust,J

i as long as he is consistent in the use of the variable "THRUST" in theI

; • definition of total force coefficients and power setting (PWRSET).

I

ii| Subroutines ARODYN and ENGINE

| The takeoff and landing subroutines described above require the

i_i_ user to provide two subroutines to compute total force coefficients:( and determine various required engine characteristics (e.g., thrust

_i_ _<.,'-_.,_.,_- _ per engine and fuel flow). The format and structure of these sub-

routines is left to the discretion of the user.

0

" I. Subroutine ARODYN

" This subroutine computes the total force coefficients along the

:_ flight path and normal to the fllght path as a function of angle of

_T attack and thrust. A force coefficient in a particular direction is !P - i I

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1974008607-022

defined to be the sum of all forces (excluding the weight component)

in that particular direction divided by the dynamic pressure times the

wing area.

e • Zx

Cx - qS

The transfer of the various computer variables to and from sub-

' routine ARODYN is through labeled common blocks /UNIV/ and /AERO/. Of

primary concern is the common block /AERO/:

/AERO/ VEL, QS, HABSj THRUST, TVECT, ANGLE, DELFD, DELSPL,

'_ ALPHA, CX, CY, CL, CD, RHO, GRCD, IFAST

fThe input variables from TAKO_F, LANDNG and ZERO are:

_" VEL - aircraft velocity along flight path (ft/sec)

QS - dynamic pressure time wing area (ibs) !

HABS absolute altitude of aircraft (ft)t

THRUST thrust (gross or net) per engine (ibs)J

TVECT - total vectored thrust (Ibs)

ANGLE angle of vectored thrust relative to aircraft _center llne, positive down (deg) i

DELFD - flap deflection (deg) )

!DELSPL - spoiler deflection (deg)

ALPHA - angle of attack Cdeg)

RHO - air density (slugs/ft 3)

GRCD - drag increment due to gear

%

The return froL ARODYN should be:

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1974008607-023

CX - total force coefficient along flight path

CY - total force coefficient normal to flight path

The output variable CL and CD are provided to the user as a means

to distinguish between pure aerodynamic coefficients and total force

coefficient3. The output variables CL and CD are printed out in the

time histories, but are not used in the actual calculations. If

desired, in subroutine ARODYN, CL and CD may be directly equated to

CY and CX, respectively.

There is a certain amount of redundancy among some of the input

variables. The user may utilize only those variables he desires andy

' disregard the cthers. Due to the wide range of velocities encounteredt

,_, during the takeoff and landing maneuver, there will be a _.orrespondinglyI

i large variation in the magnitude of the force coefficients which mustIv

e; be accommodated in s_broutine ARODYN.

!

| II. Subroutine ENGINE

This subroutine provides the various propulsion data to subroutines

i.. TAKOFF, ZERO and LANDNG,

The inputs to subroutine ENGINE are through the argument list and

labeled common blocks /AERO/ n.nd /UNIV/.

The call to ENGINEis as follows:

i

CALLENGINE (ALT, DTABS, EN, P_SET, WFUEL, KENG)

:" where ALl' - aircraft altitude I

-is- |

i

1974008607-024

EN aircraft Mach no.

PWRSET - power setting (see below)

WFUEL fuel flow (lbs/hr)

KENG - engine control parameter (see below)

The variable PWRSETis defined to be:

Net thrustPWRSET=

Net thrust available

g; and is the parameter used in controlling the thrust level. It is usedJ

r_ for power setting management during the takeoff (e.g. throttle cutback

•i _ for noise abatement), thrust modulatior,during the landing flare, and!_.

_ is calculated for the steady state approach.

j ' _ Used in conjunction with PWRSET is the variable KENG, the engine: i

i _ control parameter. For KENG = 0 or 2 (takeoff and landing respectively),

; the value of PWRSET is input and the thrust and fuel flow returned. InI

J the static performance calculations of subroutine ZERO, the call to

I ENGINE is made with KENG= I. Here, the thrust per engine is input andI

| PWRSET and fuel flow are calculated._,,

"" The user may choose to work with either the gross thrust per

., engine or the net thrust per .-ngine,provided he uses the variable:,,: :;.t: THRUSTproperly in the calculation of the total force coefficients.

K;/' For example, when using gross thrust per engine, the ram drag must be '

' _, included in the total summation of forces. If the gross thrust vector

and ram drag vector are colllnear, the user may choose i_,stead to work

,)_ simply with the net thrust.

;o Refer to the example case presented for an illustration of

__ I subroutines AKODYNand ENGINE.It

] 974008607-025

REFERENCES

J. Jim Webb, '-t2' - _!tN__G,The Iowa State University Press, Ames, 1971.

:. Sus_' E. 'Computer Programs for Estimation of STOL Takeoff,

t_nd_;lg, an:_ _tatic Performance", NASA TM X-62,217, December 1972.

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APPEhDIX A

£QUATIONSJ

Equations used in TAKOFF and LANDNG

1) Equation of motion along flight path

dVldt = (g/W)(-CxqS - Wsin 7)

2) Equation of motion normal to flig. pathi

' dy/dt = (g/WV''.CyqS"- W cos _)

t 1

3) Equation of motion during ground rollJ

':' i dr/dr - (g/W)[-Wu �qS(Cy_- Cx)lwhere

1 g - gravity cvnstantt

|

W • aircraft weight

q - dynamic pressure

-_ <. S _, win R area

- flight path angle

V = aircraft velocity

Cx - total force coefficient along flight path

• Cy • total force coefficient normal to flight path

!

' ' 41 Load factor _, Ii

|

112 • W cos _r

-2x-

1974008607-027

5) Constant rate of climb equation

Rate of climb _ ROC = V sin y

For ROC to be constant with time,

dROC_0dt

• drOC= d__(V sin Y)dt dt

; _ dV dy: _ sin _ + V cos y _-= 0

Substitute for terms dr/dr and dy/dt from equations I) and 2)

(g/W) (-CxqS - W sin y) sin

+ V cos _Cg/lCv)CCyqS - w cos _)cos y -- 0

"|1,

_, -CxqS sin y - I_sln2 y + CyqS cos y - W cos2 _,= 0

_ii! qs% _os_-& _in_ -W-0

i:;?-" 6) Rotational rate approxiwatlons by finite difference¢ . -_

L _

" " ' '_i 0 = Y + a " iw

_._:_ _ - flight path angle _,

., _ -22-

1974008607-028

- angle of attack

i w - incidence of wing

Differentiating with respect to time we Gbtain:

dO d_ dy

_ d"_= d-t+ d--_

dY is given by equation 2)._. where _-

g de,_. d-_is approximated by the finite difference form:

i

_. da - /_t_-_= (anow apast)

where

". _,

_, anow = current value of angle of attack

i apast = previous value of angle of attackAt = integration time interval

7) Simplified landing equations -for constant load factor (XLFmax), i

constant speed (VApP) flare !

i W 0 _'r_ _ _ _ , _r_pi' !! t

,-r

i

FIELO L._ NC_TI-t

1974008607-029

where: R =g (X,'.Fmax - 1. O)

VApp2(YApp2 " YTD2)hflare = 2g (XLF - 1.0)max

and

R YAPP <1 YTD 12:' 35.0 + .0

XDIST --tan YAPP 2 YAPP

VApp2+ _ _pp tDELAY +

2g *_

where

tDEI_ Y - delay time before braking

. _ - average deceleration Cg's)

1974008607-030

......... _- I - "]-*-I_ =. "'.." "_. "'- ' - -- - i_,_

APPENDIX B

SA_IPLE CASE

Shown below is an example of the input, calling format, sub-

routines ARODYNand .ENGINE, and the print out obtained for the takeoff

and landing programs.

The main calling program TEST1 is set up to do the takeoff and

landing of a Boeing 727-200. The required common blocks are shown,

_ but others may be added if required. Note that the spoiler _deflection

angle DELSPL has been set equal to zero before the call to TAKOFF. Also

note that before calling the landing program, the flap deflection

_ DELFD, the spoiler deflection DELSPL and the total static sea levelt

, _ thrust ST must be given values externally to IANDNG.

: _ The namelist input was as follows:

' i; 5

$NAH1 NPAGE= 48, RTCL = 530., THTFLY-- 20., tggAN= 2000. SEND

! SNAM2XPOWER{2)_- 0.75, XIIPI_'R.(2)= 7S0, XPOWER(3) = 0.95

1XHPWR(3) = 1750. SENDt

I_ $NAM3 DADT = 1.0, IPOffER= O, TFLP = 99., Pb'RIDL= 0.I0,

,:_} SINKTD = 3.0, TOFF -'-3.0, TSPL = 2.00, XMUBRK = 0.45 SEND

.... Subroutine AROD_ calculates the lift and drag coefficients of i

Ii _ the 727-200 as a function of angle of attack, flap and spoiler deflection.

-, Tha increments of lift and drag due to Flaps is determined in a table

-'__,_, look-up format. The increase in drag and loss in lift increment due to

-2s-

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1974008607-031

spoilers is assumed to vary linearly with spoiler deflection. Once the

lift and drag coefficients are computed, the thIust compcnents, normal-

ized with respect to dynamic pressure times wing area (QS), are adat.

in to deter.mi_e the total force coefficients CX and CY.

Subroutine ENGINE computes the thrust and fuel flow of the JT8D

engine, based on a simplified model. The thrust lapse is assumed to be

linear with Mach number, and the fuel flow assumed linear with power

setting. Note the use of the parameter PWRSET. The subroutine con-

sists basically of two sections. For KENG= 0 or 2, the power setting

P_SET is input and the thrust and fuel flow returned. For KENG= 1,

the thrust is input and PWRSETand fuel flow returned. No rcverse

thi_st was used during the landing ground roll and r _broutine REVRSE is

simply a dummy subroutine.

This particular run was made on the Lawrence Berkeley Laboratory

CDC 7600 and required a CPU time of 2.58 seconds.

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