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. REPORT NO. 2. GWPINWiNT ACCESSlOU NO. 3. RECIPIEKT'S CATUOG NO. NASA CR-2287 . TlTLE AN0 SUBTITLE

Effect of Shear on Aircraf t Landing

r. AUTHORgS) James K. Luers and Jer ry B. Reeves

). PERFORMtNG ORGANW)ZATION MA- Am) ADDRESS

The University of Dayton Research I n s t i t u t e Dayton, Ohio 45469

2. SPOWSORING AGENCY NAME AND -SS

5. REPORT OITF

6. PERFORMlff i ORGANIZATION CCDE July 1973

M i l l &PERFORMING ORGANIZATION REPORT I

10. WORK UNIT, NO.

11. COIITRXT OR 6RMT NO. NAs8-26600

13, TYP!€ OF REWRY & PERIOD tOVEREC

July 1971 - N W . 1972 National Aeronautics and Space Administration Washington, D. C. 20546

17. KEt WORDS

wind shear a i r c r a f t response atmospheric boundary layer wind p r o f i l e

14. SPONSORING AGENCY CODE

18. DISTRISUIION STATEMENT

02

1s. SUPPLEMENTMY NOTES

This repor t prepared under t h e technical m n i t o r s h i p of the Aerospace Environment Division, Aero-Astrodynamics Laboratory, NASA-Marshall Space

t3. SECURITY CLASSIF. (d thL rapatr 20. SEClRlTY CL'SSIF. (Or tbh p...)

unclass i f ied unclassified

A simulation study w a s conducted t o determine t h e e f f e c t of wind shear on a i r c r a f t landings. The landing of various type of couunereial and m i l i t a r y a i r c r a f t was d i g i t a l l y simulated s t a r t i n g from an i n i t i a l a l t i t u d e of 300 f e e t . AsSuming no p i l o t feedback during descent, the deviation i n touchdown point due t o v e r t i c a l p rof i les of wind shear was determined. The v e r t i c a l p r o f i l e s of wind shear a r e defined i n terms of surface roughness, Zo, and s t a b i l i t y , L, parameters. on touchdown due t o Z and L have been calculated f o r the d i f f e r e n t type a i r c r a f t . Comparison: w e r e made between the following typesof a i r c r a f t : C-l30E, C-l35A, C-141, DC-8, Boeing 747, and an augmentor-wing STOL. I n addi t ion, t h e wind shear e f f e c t on touchdown resu l t ing from d i f f e r e n t locat ions of t h e center of gravi ty and gross weights was a lso analyzed.

The e f f e c t s

21. NO. OF PAGES 22. PRlCE

73 $3.00

.

FORSWORD

The motivation f o r the research reported i n t h i s document w a s t o delineate the adverse e f fec ts of wind shear on the landing f l i g h t phase of aeronautical systems. Once these e f fec ts are known, relative t o the t o t a l wind environment, i t is possible t o es tabl ish operational wind shear requirements and limits fo r observ- ing and reporting low leve l wind shear. wind shear, or t o grade wind shears r e l a t ive t o t h e i r e f fec t on aeronautical systems, a criteria must be established i n the context of aeronautical sysfem performance parameters. degree t o which a given shear environment adversely e f f ec t s the landing f l i g h t phase of aeronautical systems was assessed i n terms of the departure of the landing touchdown point from the touchdown point tha t would have occurred i n the absence of wind shear. wind environments w e r e selected f o r the analysis. The selected wind environments encompass a s ignif icant number of low level wind s i tua t ions tha t would be encountered during t h e l i f e of an operational aeronautical system. The ef fec ts of the wind environ- m e n t s on the a i r c r a f t touchdown point are presented i n terms of properties of t h e selected flow f ie lds . Anumber of new conclu- sions resulted from the study relative t o how the de ta i l s i n the wind pro f i l e can e f f ec t the landing f l i g h t phase. It is believed t h a t these r e s u l t s can have s ignif icant implications relative t o t h e aeronautical safety aspects of t h e landing problem.

To assess the e f f ec t s of

In- this study, t h e

A variety of a i r c r a f t types and a broad select ion of

This research w a s conducted by the University of Dayton Research I n s t i t u t e f o r the National Aeronautics and Space Administration, George C. Marshall Space Flight Center, Huntsville, Alabama, under the technical direct ion of Tk. George H. F ich t l and Dr. Stephen W. Winder of the Aero-Astrodynamics Laboratory. w a s provided by Mr. John Enders of the Aeronautical Operating Systems Division, Office of Advanced Research and Technology, NASA Headquarters.

The support fo r t h i s research

iii

TABLEOFCONTENTS

' SECTION

1 INTRODUCTION

2 AIRCRAFT LANDING MODEL

3 WIND SHEAR MODEL

4 ANALYSIS O F CONVENTIONAL AIRCRAFT LANDINGS

Headwind Landings Tailwind Landings Ground Effects Wind Shea r Effects on Touchdown Comparison of Different Types of A i rc ra f t Variation in A T due to Ai rc ra f t Weight Variation in AT due to Cg Locations

5 ANALYSIS O F -4UGMENTOR-WING STOL AIRCRAFT

Ground Effects of STOL Wind Shea r Effects on Touchdown

6 SUMMARY AND CONCLUSIONS

REFERENCES

PAGE

1

3

10

17

23 23 24 26 30 36 36

39

44 44

49

53

. APPENDIXA A-1

iv

LIST OF TABLES

Table

1 2

3

4

A. 1 A. 2 A. 3 A. 4 A. 5 A. 6

Init ial Flight Conditions and Aircraf t Physical Data Deviation f r o m Touchdown Point With and Without Ground Effects Deviation f r o m Touchdown Point for Various Locations of the Center of Gravity, B-747, Weight = 400,000 lbs Deviation f rom Touchdown Point With and Without Ground Effects f o r STOL Airc ra f t DC-8 Aerodynamic Data C-13SA Aerodynamic Data C-141 Aerodynamic Data C - 130E Ae rodynamic Data Boeing 747 Aerodynamic Data Augmentor-Wing STOL Aerodynamic Data

9

25

38

45 A-2 A -4 A-5 A -7 A-8 A-12

V

LIST OF ILLUSTRATIONS

Figure P a g e

1.

2. 3. 4. 5. 6. 7.

8.

9.

10.

11. 12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

Relationship Between the Various F o r c e s Acting on a n Ai rc ra f t . Unstable Wind Profi les . Neutral Wind Prof i les . Stable Wind Profi les . Very Stable Wind Profi les . Very Stable Wind Profi les . A i rc ra f t Descent T ra j ec to r i e s Through Unstable Wind Prof i les . A i rc ra f t Descent T ra j ec to r i e s Through Neutral Wind Prof i les . A i rc ra f t Descent T ra j ec to r i e s Through Stable Wind Profi les . A i rc ra f t Descent T ra j ec to r i e s Through Very Stable Wind Profi les . Very Stable Wind Prof i les . Deviation in Touchdown f o r DC-8 in Unstable Wind Profi les : Headwind, Deviation in Touchdown f o r DC-8 in Neutral Wind Profi les : Headwind, Deviation in Touchdown f o r DC -8 in Stable Wind Profi les : Headwind. Deviation in Touchdown f o r DC-8 in Very Stable Wind Profi les : Headwind. Deviation in Touchdown f o r Different Type Aircraf t in Unstable Wind Profi les : L = -300111. Deviation in Touchdown f o r Different Type Aircraf t in Neutral Wind Profi les . Deviation in Touchdown f o r Different Type Aircraft in Stable Wind Profi les : Z = 0. lm. Deviation in Touchdown f o r Differen? Type Aircraf t in Very Stable Wind P r o f i l e s . Deviation in Touchdown f o r B-747 in Very Stable Wind Prof i les w a h Different Landing Weights. STOL Descent T ra j ec to r i e s through Unstable Wind Prof i les .

5 12 13 14 15 15

18

19

20

21 22

27

28

29

31

32

33

34

35

37

40

LIST OF ILLUSTRATIONS (concluded)

Figure

22.

23.

24,

25.

26.

A-1

STOL Descent Trajectories Through Neutral Wind Profiles STOL Descent Trajectories Through Stable Wind Profiles. STOL Descent Trajectories Through Very Stable Wind Profiles. Deviation in Touchdown for STOL in Unstable and Stable Wind Profiles: Headwind. Deviation in Touchdown for STOL in Very Stable Wind Profiles: Headwind.

Some Geometric Parameters for Augmentor- Wing STOL Aircraft

Page

41

42.

43

46

48

A-1 1

vii

INTRODUCTION

Wind s h e a r is an important consideration in the landing of aircraft

and aerospace vehicles.

change in the horizontal wind will instantaneously effect the velocity of the

a i r c ra f t re la t ive to the air mass.* If the shea r is such that the relat ive

velocity of the aircraft increases , the lift force will increase and the air-

c ra f t will tend to rise above the glide slope. If the s h e a r causes a sudden

dec rease i n the relat ive velocity, the a i r c ra f t will respond by falling below

the glide slope and a potentially hazardous condition could result .

As an a i r c ra f t descends its glide slope, a sudden

Severa l r epor t s have been published which link shor t and long

touchdown to a sudden wind s h e a r occurrence during final approach (Ref-

e r e n c e s 1 and 2). Recent accident repor t s have found wind shea r t o be at

least a contributing cause t o seve ra l accidents (Reference 2). In addition,

it is believed tha t wind s h e a r has been responsible f o r many other accidents

though it remained undetected at the time (Reference 3).

The problem of quantitatively defining the effect of shea r of given

magnitude on an aircraft during descent has not been completely resolved.

Noteworthy s tudies that have investigated wind s h e a r and /o r turbulence

during landing include References 4, 5, 6, 7, 8 , and 9. The study under-

taken by the University of Dayton Research Institute (UDRI) was designed

to provide answers to th ree specific questions: a) what shape of wind

s h e a r prof i les are mos t c r i t i ca l to a i r c ra f t landing, b) which type of air-

craft are m o s t responsive to shea r , and c) what meteorological pa rame te r s

relate to those wind s h e a r s that provide critical landing problems. The

UDRI provided answers to these questions by a digital simulation model

f o r an a i r c r a f t landing in var ious wind profiles. The simulation model

is used by first calculating the touchdown point f o r a conventional-type

* The effect of ver t ica l a i r motions is not considered i n this report .

a i r c ra f t t r immed on a n init ial glide slope of 2. 7 deg rees (7. 0 f o r a STOL

a i rc raf t ) in a constant wind field descending f r o m a n altitude of 300 feet. The

landing simulation i s then repeated f o r a wind s h e a r profile input with init ial

I t rim conditions determined at 300 feet fo r the wind velicity at that alt i tude.

By determining the deviation in touchdown point f r o m the constant wind c a s e ,

the effect of the s h e a r on a i r c r a f t touchdown can be determined. Th i s s i m u -

lation model a s s u m e s a fixed s t ick model with no pilot o r autopilot control .

The wind s h e a r profile is defined in the sur face boundary l aye r

according to s imi la r i ty theory by the sur face roughness length, Zo; the

zeroplane displacement, d; the sur face fr ic t ion velocity, u*; and the sta-

bility parameter , Z/L.

the landing simulation model and the wind profiles used in the study.

The next two sections desc r ibe in fu r the r de ta i l

Throughout this repor t , Engl ish units are used to desc r ibe the

a i rc raf t - re la ted quantities while metric units are used to descr ibe the

meteorological quantities. On all f igures , a dual s y s t e m consisting of

both sets of units is used. The use of both unit s y s t e m s w a s necessi ta ted

to conform to the conventional s y s t e m s used by the aircraft and me teo ro -

logical communities.

2

AIRCRAFT LANDING MODEL

The aircraft t r a j ec to ry model employed in this study was der ived

based on the following assumptions.

a ) The e a r t h is f la t and nonrotating.

b) The acce lera t ion of gravity is constant (32. 2 f t / s e c ).

c ) Air densi ty is constant (0, 002375 s lug / f t ).

d) The airframe is a rigid body.

e ) The aircraft is constrained to motion in the ver t ica l plane.

f ) The a i r c r a f t has a symmet ry plane (the x-z plane).

g) The mass of the aircraft is constant.

h) Once the aircraft is t r immed, i ts throt t le setting and e l eva to r

deflection angle are not changed.

The aerodynamic stabil i ty der ivat ives are constant within the

alt i tude and Mach numbe r range experienced in this investigation.

2

3

i)

At the beginningof each t r a j ec to ry (300 feet altitude, H), the aircraft is t r i m m e d

by determining the values of angle of attack, throt t le sett ing, and e leva tor

deflection, which wil l resu l t in macce le ra t ed flight. The equations of motion

are then integrated numerical ly by a fourth-order Runge-Kutta scheme.

For a constant wind and no ground effects, the a i r c r a f t flies down the glide

slope at a constant velocity until it r eachs the ground. Upon introducing a

ver t ical ly-varying horizontal wind field, the aircraft no longer adhe res t o

the glide slope.

m e a s u r e of how s e v e r e the par t icu lar wind field is to t h e landing aircraft.

The result ing deviation i n touchdown point s e r v e s as a

. The influence of ground effects on the deviation in touchdown points

between constant wind and wind shear conditions was investigated f o r s e v e r a l

of the a i r c r a f t considered in this study.

r a t h e r small and therefore was not included in the final ana lys i s s ince

ground effects da ta was not available for all of the aircraft.

cussed f u r t h e r in the section describing the analysis of the data.

It was found that this influence was

Th i s is d i s -

3

The aircraft included in this study are the DC-8, C-135AJ C-141,

C-130EJ Boeing-747, and anaugmentor-wing STOL aircraft. The f i r s t t h r e e

are representat ive of the medium-weight turbojet t r anspor t s .

two are low-wing design while the third is a high-wing design.

is a lighter-weight t r anspor t powered by propjet engines. The Boeing-747 i s ,

of course , a la rge turbojet t ranspor t .

is i n the same weight category as the DC-8, C-135, and C-141. The aero-

dynamic d a t a f o r this a i r c ra f t is similar to that used by NASA A m e s

Resea rch Labora tory in the i r computer simulations of a n augmentor-wing

STOL a i rc raf t .

The first

The C-130E

The augmentor-wing STOL a i r c r a f t

The equations of motion of the aircraft w e r e der ived under the

assumptions stated above.

These include gravity (me), t h rus t of the engines (i' ), and the aerody-namically-

induced lift (L) , and drag (D) forces. The figure shows the orientation of the

forces with respec t to the velocity vec tor relative to the e a r t h (V), the velocity

vec tor relative to the air mass (Va), and the fuselage re ference line ( F R L )

of the a i r c ra f t .

ea r th ; the 2 is perpendicular t o the su r face of the e a r t h (positive downward).

F igure 1 shows the fo rces act ing on the a i r c r a f t .

T A A

-L

2

The X axis in F igu re 1 is para l le l to the sur face of the

Two of the equations of motion can be der ived by summing the 3

forces para l le l and perpendicular to V (the velocity vec to r re la t ive to the

e a r t h ) and applying Newton's Laws of Motion. The r e su l t is

. c o s ( 6 + a ) V = - g s i n y t - FT

T m - - - CIS C cos6

e- qs c sing . m D - m L

4

X

Figure 1. Relationship Between the Various Forces Acting on an Aircraft.

5

qs c sin6 - c o s y + - sin(6 +a) -- Y - ' V m V T m V D - FT

+ - '' C cos6 m V L B

where the dot r e f e r s to the derivative with respec t to time and

g

V

y

is the magnitude of the accelerat ion of gravity,

is the magnitude of the velocity re la t ive to the ear th ,

is the angle between V and the X-axis (the flight path angle),

is the magnitude of the thrus t vector ,

a

FT

OT

m is the a i r c ra f t mass,

is the angle between the th rus t vec tor and the fuselage reference line (FRL),

is the angle between V and the FRL,

is the dynamic p res su re which is equal to one half the air density ( p ) t imes the square of magnitude of the velocity

A

a

q -

relative t o the air mass (Va) , = 1 / 2 pVa 2 , S is the a i r c ra f t wing a r e a ,

6 is the angle between V and V,

is the drag coefficient, and

is the lift coefficient.

A a

a

cD

cL

The aerodynamic forces and the th rus t f r o m &he engines exert a

pitching moment on the aircraft.

accelerat ion is

The equation descr ibing the rotational

- - qsc

'm t- I F ~ L T

9 = 1 YY w

where

q is the time derivative of the pitching rate (q) ,

LT is the effective moment arm of the th rus t vector ,

c -

is the Mean Aerodynamic Chord,

6

( 3 )

I is the moment of iner t ia about the symmet ry plane of the aircraft, and

C is the pitching moment coefficient. m

Equations ( l ) , (2), and (3) f o r m the c o r e of the A i r c r a f t Landing

P rogram. These th ree equations along with . x = v cosy

Z = -V siny 0

o = q

are the six equations of motion of a n a i r c ra f t constrained to fly in the

vertical plane.

the X-axis.

. 0 is the time derivative of the angle between the FRL and

In o r d e r t o evaluate the above equations a t e a c h t i m e step, s e v e r a l

auxi l iary equations are needed. They aze

a' = O - y - 6 9

3. S g c o s ( y t 5 ) - - sin('; +at)--

a' = q + v , mVa T mVa

F T cL '

e

I

7

where W, is the horizontal wind speed, a

between Va and the FRL, and 6E is the e leva tor deflection angle.

indicated above, the aerodynamic coefficients are functions of a number of

var iables . are not the same f o r all

the a i r c r a f t considered.

tive data a r e presented in Appendix A .

(the angle of a t tack) i s the angle

As is

The express ions f o r C L, CD, and C m’ These express ions along with the stabil i ty de r iva -

The above s e t of equations compr i se the a i r c ra f t model.

conditions and a i r c r a f t physical data f o r each of t h e flights s imulated in

this study a r e presented in Table 1.

a i r c r a f t flights was 2. 7 degrees while its value f o r the STOL a i r c r a f t

flights was 7 degrees .

at two landing weights.

of-gravity locations of 1570, 25%, a n d 33% Mean Aerodynamic Chord.

a i r c r a f t was flown in a wide var ie ty of horizontal wind s h e a r conditions.

These a r e discussed in the following section.

The init ial

The glide slope f o r the conventional

A s noted in the table, the Boeing-?47 was investigated

Flights of this a i r c r a f t w e r e simulated with cen te r -

Each

8

0 0 4

0 4 0 4 o x

* m d I N s m O N N

. o - l n r n O O N m . m l n I n o N

e , , o . . . s o

I 9 0 0

9 0 0 ,

9 0

0 4 o x o m

c, 0 E

0 0

0 0 rn

P 0

I-

N d

d 3 0

I-

m

0 rcI

0 0 ln ln

I- - 4

0 - m m m d c 8

7 4 d >

W 0 m M

I

u

0 0 0

9 0 0

4

IC

O d

0 ln

9 9 -4

IC 0 0 m

N I 0 0 4 8

5 Q) u C m .d

9 0 0 0 4 o x - 0

o m I n . N e

* 0 0

0

0 N N N

4

e 4

I

u 0

0 0 m

0 b) N N rrl

I-

N I

0 0

4 E Q) P 0 c 0

0 0 N

8 3 ld > r4

4 ld E .d

E 0 E m s t.l * n

c, N

WIND SHEAR MODEL

The wind shea r model used in the aircraft landing simulation is

completely descr ibed in the document, "A Model of Wind Shea r and T u r -

bulence in the Surface Boundary Layer" (Reference 10). Only a c u r s o r y

description of the model i s presented here .

The wind shea r in the surface boundary l a y e r is considered to be l a function of surface conditions, stability conditions, and altitude. According

to s imi la r i ty theory, the mean wind speed fo r t h ree of the four stabil i ty

classifications is defined as a function of altitude by -

where Z is the surface roughness length, 0

u t is the surface fr ic t ion veloci ty ,

k

2 is the altitude above the re ference level, and

L is the Monin-Obukov stabil i ty length.

I is the Von Karman 's constant = 0 . 4 ,

In the unstable c lassi f icat ion, the function rlr is given by

Z Z/L

z /L Z

$(-iT) = 1 Z / L { 1- ( 1 - 1 8 Z / L ) -'I4 1 d (z)

The stability pa rame te r , Z / L , is related to the gradient Richardson

number f o r the unstable c lassi f icat ion by Businger 's Hypothesis:

R i = Z / L f o r Ri < 0 . For the neutral classification, Z / L = 0 and+(O)=O so that the wind speed,

given by Equation (4), i s a logarithmic function of a l t i tude.

10

For the s table condition, that is 0 42 R i <O. 2, the function is descr ibed - by

f (Z/L) = 5.2 Z/L

The relationship between Richardsons number and Z/L is s table air

is

for 0 < Ri < 0 . 2 R i

= l - 5 . 2 R i . Figures 2 , 3, and 4 show plots of typical wind prof i les fo r the unstable,

neut ra1,and s table catego rie s .

For the v e r y stable condition, when Ri>O. 2, t h e wind speed cannot

be represented by Equation (4).

adequately r ep resen t the very stable wind profiles.

conditions, turbulence tends t o diminish so that the l aye r s of the a tmosphere

become disconnected.

l ikely to ex i s t under inversions.

l eve l with a constant wind above th i s level.

profile is shown below the interface with a constant wind magnitude above

this level.

the interface w e r e considered in th i s study.

In fact, no analytic function has been found t o

Under s t rong inversion

F igu res 5 and 6 show two types of prof i les that are

Figure 5 shows a calm below the in te r face

In F i g u r e 6, a logarithmic wind

Seve ra l values of the interface leve l and the wing magnitude above

The wind direct ion in the sur face boundary l a y e r can be considered

constant with alt i tude except in the v e r y stable condition. In v e r y s table

air, the wind direct ion often changes by 45 degrees o r m o r e between the

eurface and 300 feet.

The wind input t o the aircraft landing simulation p rogram cons is t s

of defining the wind prof i le f r o m 300 feet altitude t o the surface. The

wind magnitude has been defined for the unstable, neutral , and stable

conditions by Equation (4). The pa rame te r s us , Zo, and L w e r e var ied

11

m l s e c

f t / s e c

1 . U* = 5 . o m / s e c Z o = 3. O m L = - 2 5 m

0. 5 m / s e c 2 . lJ* = Z o = 0. OOlm L = -300 m

3. U* = 0. 5 m / s e c Z o = 0. 01 m L = -300 m

4. U* = 1. 0 m / s e c Z = 1 . 0 m L 0 = -300 m

5 . u:c = 0 . 5 m/sec Z o = 0. 01 m L = - 2 5 m

6 . U* = I . O m / s e c Z o = 1 . 0 m L = - 2 5 m

U* = 1. 0 m / s e c Z o = 3 . 0 m L = - 2 5 m

7.

Figure 2. Unstable Wind Profiles.

12

No. 6 u*= 0.1 mlsec Zo= 0.001. m

300-

280 - t 260 -

240 -

220 -

200 -6

180 -

160-

.Z 140 -

120 -

100 - 80 -

'v I

4 + 2

2I 60 -

40 -

20 - 0- (

No. 3 No. 5 us= 1. Om/sec u*= 0 . 5 m/sec z,= 1 . 0 'm No. 2

u*= 1 . 5 m/sec

u*= l.Om/sec

I m/sec

0 10 20 30 40 50 60 70 ft/sec

5 10 15 I I 1 1 t 1 I

- u

Figure 3. Neutral Wind Profiles.

13

300 - 280 -

8 260 -

240 -

220 -

200 -6

180 -

160 - al .tl 3 3 140-

4 120

100 -

80 -

41 c, H

-

21 60 -

40 -

20 - 0-

No.6 No.5 No .4 No.3 No. 2 No. 1

1. U* = 0. 5 r n / s e c Z = 0 . 1 rn L = 100 rn

2. u* = 0. 1 r n l s e c z = 0 . 1 m L = l O m

3. U* = 0. 5 r n l s e c 2 = 0 . 1 rn

0

0

0 L = 300 IT^

4. U* = 0. 5 m I s e c Z = 1 . 0 m L = 300 rn

5 . U* = 0. 1 r n l s e c Z o = 0.001 rn ~ = 5 0 rn

6. u* = 0. 1 r n l s e c Z = 1 .0 rn L = 100 rn

7. u* = 0 . 1 r n / s e c 2 = 0 . 1 rn L = 5 0 rn

0

0

0

m l s e c

0 10 20 30 40 50 60 70 f t l s e c I I I I I I I I

- U

Figure 4. Stable Wind Profiles.

14

Variation in Wind Magnitude

I I t I

I I

i I

Figure 5. Very Stable Wind Profi les .

I--

- Variation in Shear Interface Level

I I I I

Figure 6. Very Stable Wind Profi les .

15

so as to include a l l reasonable wind profiles.

wind profiles of the type shown in F igu res 5 and 6 have been used.

wind direct ion is considered constant with altitude f o r a l l stabil i ty conditions.

In the landing simulation program, only headwinds and tailwinds have been

considered with the emphas is being on the m o r e conventional headwind

landing case .

F o r the v e r y s table condition,

The

.

ANALYSIS OF CONVENTIONAL AIRCRAFT LANDINGS

The init ialization conditions f o r the s imulated landings of conven-

tiona1 a i r c r a f t w e r e a 2. 7-degree glide slope with the descent beginning

at an al t i tude of 300 feet. (An augmented-wing STOL a i r c r a f t is discussed

in a later section. 1 This co r re sponds to a touchdown point 6361 feet down-

range f r o m where the descent begins. The a i r c r a f t is t r i m m e d at 300 f ee t

to maintain the 2.7-degree glide slope f o r the wind speed existing at that point.

Any var ia t ion in wind speed will cause the a i r c r a f t t o deviate from the glide

slope. The deviation in touchdown point is defined as the dis tance between

the actual touchdown point and the 2. ?-degree glide slope touchdown point.

That is, i f t he aircraft lands at a distance X downrange f r o m its init ial

descent point (300 feet alt i tude), then the deviation in touchdown point, AT,

is

AT = X - 6361.

Note that a posit ive A T indicates a long landing while a negative A T indi-

cates a s h o r t landing.

F i g u r e s 7, 8 , and 9 show the descent of the DC-8 through the un-

stable, neutral , and stable wind prof i les of F i g u r e s 2, 3, and 4. The num-

ber ing of the aircraft descent t r a j ec to r i e s co r re sponds t o the numbers on

the wind profiles.

headwind profiles.

constant wind) profile. The No. 9 and 10 trajectories cor respond to tail-

wind prof i les . In par t icu lar , the No. 9 profi le has the same shape as the

No. 6 prof i le but d i f fe rs in direct ion by 180 degrees .

profile is the same as the No. 3 profile except f o r direction.

true for the unstable, stable, and neutral wind profiles.

DC-8 landing through the very stable wind prof i les of F igu re 11. The No. 1

through 8 prof i les are headwinds, No. 9 is a z e r o wind, and Profi le No. 10

is the same as No. 5 b G t is a tailwind.

The t r a j ec to r i e s numbered 1 through 7 correspond t o

The No. 8 t ra jec tory co r re sponds to a z e r o wind ( o r

Similar ly , the No. 10

The above is

F igure 10 shows the

17

1; 0 0

-0 IC

0

In 9

0 0

-0 9

0 -0

Ln VI

0 -0 0 L n

0 -0

In * 0 0

-0 * 0

-0 Ln rr)

0 -0 0 m 0

-0 In N

0 -0 0 N

0

In

-0

-0

4

0 0

-0 4

0 -0

In

-0

0 (0 C 5 s M 7 0 k c t. m Q)

k 0 U Q)

.r.

w

*-

2 t. c, C 8 U m

B 2 c, w

U k .r.

4

b a, k 5 w) .r. crr

9) M C

c 2 i: Q

s3

sz atar

0 0

02

0 0 rz) IC

0 0 0 b

0 0 In 9

0 0 0 9

0 0 In In

0 0 0 tn

0 0 In * 0 0 0 -3

0 0 tn m

0 0 0 m 0 0 In N

0 0 0 N

0 0 m d

0 0 0 4

0 0 m

0

m al 4 .r( rcc -0 k PI co E

.r(

3 p" ;;

0)

Id

c M 7 0 k c f? m al

k 0 0 al

.d

+I

-7

d f? G b) u m

c1

a" c, w Id k u k .d

4

cI\

p1 k 7 M .d

6(

3 3 0 3 0 u

3 0 3

- 4 I n n o

3 2 s 4

' ' 0 "-0

. 0 Q 4 d W 0 k

P 4

0 0

-0 cc

-In 9

0

0 9

0 -0

In In

-0

-0

0 - 0

In 9

0 0

- 0 9

0 -0

0 - 0 0 m 0

-0 In N

0 -0

0 N

In 4

0 0

-0 4

0 - 0 tn

-0

a c T

c, W rd k U k .d

4

d 4

Q k 7 m i;I

300

-

3

2 50

200

+I

150 U

100

10

50

l o t 0

2

I I I in/sec 10 20 30

I I I I 1 I I I 1 f t / sec

-30 -20 -10 0 10 20 30 40 50

Tailwind Direct ion +- Headwind Di rec t ion

Figure 11. Very Stable Wind Profiles

22

Headwind Landings

For headwind landings, the unstable wind profiles show the least

A s the stability inc reases , the aircraft be- sca t t e r in touchdown point.

comes more effected by the wind prof i le causing l a r g e r deviations in

touchdown point.

from the des i red touchdown point, in one case over 3600 feet. In addition,

the actual t ra jec tory of the a i r c ra f t follows a s teeper slope as the stabil i ty

increases .

stable and ve ry stable conditions are significant and could lead to haza r -

dous landing conditions. This is especial ly t r u e s ince the simulation be-

gan at a n alt i tude of only 300 feet.

l aye r occurred above 300 feet, the effect on touchdown Gould cer ta inly be '

g r e a t e r than tha t shown in Figure 10. The same is not t r u e f o r the o ther

stabil i ty conditions. For the unstable, neutral, and s table profiles, the

s h e a r is close to the ground and little additional effect on touchdown point

would result fmm beginning the simulation above 300 feet. Consequently,

the very s table condition has the g rea t e s t potential fo r adversely affecting

the landing of a i rc raf t .

The ve ry stable prof i les produce v e r y l a rge deviations

The magnitude of the deviations in touchdown point f o r the

In the very stable case , if the s h e a r

-

Tailwind Landings

For a tailwind, a somewhat l a r g e r deviation intouchdown occur s

over the case of the same wind profile being encountered in the headwind

direction.

probably not as likely t o occur as one involving a headwind condition f o r two

reasons. First of all, landings are made in the runway direct ion that has a

headwind component whenever possible. As a resul t , tailwind landings, es - pecially with high wind magnitudes, are seldom required. Secondly, since

However, a landing accident involving a tailwind condition is

a tailwind implies overshoot, the pilot has a s lower descent rate and can

more eas i ly abor t the landing. In addition, a light tailwind s h e a r can pro-

vide the somewhat des i rab le effect of a natural flare maneuver.

23

At this point, it is well t o reca l l that the simulation model a s s u m e s

no fu r the r control of the a i r c ra f t a f t e r t r imming at the initial altitude of 300

feet for a constant wind field; that is, no pilot feedback o r automatic landing

s y s t e m is introduced. The deviation in touchdown point can therefore be con-

s idered as a wors t -case analysis i n that any pilot o r autopilot feedback during

descent would, hopefully, resul t in srr.aller deviations in touchdown point.

F r o m th is point of view, the Landing Simulation P r o g r a m is intended to se rve

as a standard which will indicate the areas in which fur ther r e s e a r c h is required.

Ground Effects

In addition t o wind s h e a r causing a n a i r c r a f t to depar t f r o m its des i r ed

2.7-degree glide slope, the ground effects on the a i r c r a f t aerodynamics nea r

the su r face will cause a small departure f r o m the glide slope.

deviation in touchdown due to ground effects, simulations of the DC-8 and

Boeing-747 landings were made with and without the inclusion of the ground

effects t e r m s for the wind prof i les of F igu res 2, 3, 4, and 11. Table 2 shows

the r e su l t s for the ex t r eme stabil i ty conditions, unstable and ve ry stable. F o r

headwinds, the deviation in touchdown point is near ly identical with and without

the ground effects included.

point is the largest but still l e s s than 100 feet.

stable a i r , l a r g e r changes in touchdown point occur; however, t h i s i s somewhat

misleading,

caused the a i r c ra f t t o touch down at AT = 891 feet; whereas , without ground

effects , the a i r c r a f t descended t o a n altitude of t h ree feet at AT = 1320 f ee t

downrange, then began t o rise, finally touching down at AT = 3779 fee t .

the pilot control, the actual difference between touchdown points would be

considerably less . Consequently, since ground effects cause r a t h e r small

deviations i n touchdown and s ince accu ra t e ground effect terms w e r e not ava i l -

able for all the a i r c r a f t used in th i s study, it w a s decided not t o use the

ground effects t e r m in any f u r t h e r ana lyses of conventional a i r c r a f t .

To estimate the

F o r the z e r o wind c a s e , the change in touchdown

F o r the tailwind c a s e s in un-

In C a s e 6 of the Boeing-747, f o r example, the ground ef fec ts

With

24

TABLE 2

With Ground Effects

DEVIATION FROM TOUCHDOWN POINT WITH AND WITHOUT GROUND EFFECTS

Without Ground Effects

Wind Id Ground With

Profi les Effects

- 91

- 553 - 834 - 809 + - 770

t 996 - 888

Zero Wind

No. 1 No. 2 No. 3

5 No. 4

II) No. 6 2 No. 7

No. 8 No. 9

+ $ No. 5 .w

0

- 492 - 786 - 767 +lo33

+3715 - 858

No. 1 No, 2

2 No. 4 * No. 5 x No. 6 No. 7 No. 8 No. 9

9) NO. 3

m k

- 90

- 566 - 852 + 738 + 891 -1314

-2651

- 821 - 890

- 859

-3671 +1854 -2048 -2685

-2758 -1641 - 715 - 333

-2992

747 Without Ground Effects

0

- 502 - 800 - 783 +lo49 - 881 +3779 -1317 - 858 -2652

-3677 +1833 -206 5 -2650 -2965 -2762 - 1644 - 709 - 299

25

Wind Shear Effects on Touchdown

The equation used to define the wind profile f o r unstable, neutral ,

and s table a tmospheric conditions is defined in t e r m s of the p a r a m e t e r s

u*, Zo, and L.

magnitude above the shea r level and the altitude at which the s h e a r occurs .

Landing simulations of the DC-8 have been made to de te rmine the influ-

ence of each of these pa rame te r s on touchdown point f o r headwind landings.

F igure 12 shows the resu l t s f o r the unstable case .

tation, the X-axis does not use the fr ic t ional velocity, u*, but r a the r the

wind speed at the initial height of 300 feet.

that the stability length, L, has l i t t le effect on touchdown point. The

l a r g e r negative values of L, which imply increased stabil i ty, produce

somewhat l a r g e r deviations in touchdown point.

length, Zo, however, causes a l a r g e r var ia t ion in touchdown point. Over

a ve ry smooth surface such a s mown g r a s s ( Z = 0.001rn) deviation in

touchdown point, A T , g r e a t e r than 1000 feet cannot occur even under a

very strong wind field. If, however, the runway is surrounded by l a rge

buildings, with associated roughness length of one to th ree m e t e r s , AT

inc reases by a fac tor of 2 t o 3.

The ve ry s table prof i les use as p a r a m e t e r s the wind

F o r ease of i n t e rp re -

F r o m Figure 12, it is observed

The sur face roughness

0

The neut ra l wind profiles, F igure 13, fo r headwind landings can

be considered as the limiting c a s e of the unstable profiles as L + - 0 0 .

Thus, f o r a given Zo, AT will be l a r g e r f o r the neut ra l than f o r the un-

stable cases .

neut ra l s t ab i l i t y .

AT f o r s ay Z =3m and AT f o r Zo=lm i s s m a l l e r fo r neut ra l than f o r the

unstable condition.

2, becomes less important while L e x e r t s g r e a t e r influence on AT

(Figure 14). Under highly s table conditions, with say L = 10, ve ry l a r g e

values of AT are produced. The t e r r a i n roughness has a lmos t no influ-

ence on these values of AT. It i s under these highly s table conditions that

hazardous landing situations a r e most likely to occur .

The effect of Zo on AT i s , however, somewhat ' l ess in

That i s , f o r a given wind speed, the d i f fe rence between

0

A s stabil i ty f u r t h e r i nc reases to the positive s ide ,

*

26

4m(

3601

320

280

24f tr 4 - Y E 4 g 201

i: C

71 c V 2 16 tr E

C 0

.d

-4 w 5 12 > z

e

1

I #

-1000

3 at 300 feet

Figure 12. Deviation in Touchdown fo r DC-8 in Unstable Wind Profiles: Headwind.

27

+r 0

f

* O o o f

36 1

32(

b a -- 28C E L

n" $ p" 240 E 0

b

* 1601

a"

120(

80(

400

0

1000

800

500

2 0 30 40 50 60 10 u at 300 ft.

Figure 13. Deviation in Touchdown f o r DC-8 in Neut ra l Wind Prof i les : Headwind.

z = 3 . 0 0

2 =1.0 0

28

4000

3600

3200

2800

tc a

a"

2 g 2000

. Y E - 2400

C

V

tc C

U 0

2 1600

Q

4

4

$

1200

800

400

0

,1000

800

,600

-400

L = 10

L = 50

zo= 1.0 zo= 0.1 zo= 0.001 2 = 1.0

2 = 0 . 1

0

0

z = 0.001

2 = 1.0 0

0

2 = 0 . 1 0

zo = 0.001

L = 300

I I I I rn/sec

I W s e c

51 IO 15 20 I I I I I

0 10 20 30 40 50 60 70 I

- u at 300 feet

Figure 14. Deviation in Touchdown for DC-8 in Stable Wind Profiles: Headwind.

29

The values of A T f o r ve ry stable profiles a r e shown in F igure 15

for headwind landings as a function of the altitude at which the shea r , o r

interface l a y e r occurs . The ve ry stable profiles cause a l a r g e r deviation

in touchdown point than the o ther wind profiles, especial ly when the s h e a r

for the ve ry stable profile occur s at a high altitude.

stable prof i les that cannot be predicted by a n analytical exp-ression in-

volving meteorological parameters .

conditions with Richardson number g r e a t e r than 0. 2, carefu l attention should

be payed to the n a t u r a l environment.

It is a l s o the ve ry

Thus, during ve ry stable a tmospher ic

Comparison of Different Types of Conventional A i r c r a f t

F igu res 16 through 19 compare the r e su l t s f r o m the DC-8 with that

of o t h e r aircraft.

weight, and landing speeds.

aircraft weight and l a n d k g speeds used in the simulation.

the var ia t ion in touchdown point, AT, i s not la rge ly dependent on the type

a i r c r a f t .

l a r ly to the o ther a i r c ra f t .

sensit ivity of different a i r c r a f t to a given wind field depends upon the wind

field. F o r example, a s table profile with Zo = 0. 1 and L = 10 (F igu re 18)

shows the C-130 t o produce the l a rges t values of AT and the C-135A the

smallest. However, by changing the value of L to L = 300, the r e su l t is

that the C-130 produces the sma l l e s t values of A T with the C-135A falling

in the middle range.

The a i r c r a f t considered span a l a rge range of s ize ,

Table 1 can be consulted f o r the exact

In genera l ,

Even the C-130 which is s lower and l ighter pe r fo rms ve ry simi-

It is interest ing to observe that the relative

The variat ion in AT result ing f r o m the s imulated landing of different

type aircraft is smaller than the var ia t ion in A T due t o sur face roughness

and t o stability. F o r prac t ica l considerat ions, the type of wind prof i le

that is hazardous to one type of a i r c r a f t is hazardous to a l l types - at

least within the range of a i r c r a f t d i scussed in this repor t .

30

Shear at

1000

/ Shear at 40 m

mlsec

I I I I 1 I I W r e c r

50 60 70 0 IO 20 30 K i t 30dOft.

Figure 15. Deviation in Touchdown f o r DC-8 in Very Stable Wind Prof i les : Headwind.

31

4000

3600

32 00

2800

t-l

5 2400

a

w c 0 1

; c 2000 .r(

C 0

(d * .d - ..I

1600

1200

800

400

0

. 1000

C-130 /C-141

Y/ C-141 I

10 15 20 1 I I I I

0 10 20 40 50 60 70

I lft/mcc 5

3 0 - u at 300 feet

Figure 16. Deviation in Touchdown f o r Different Type Ai rc ra f t in Unstable Wind Prof i les : L = -300

32

4000

3600

3200

2800

tc a

30

i : ZOO(

240C

Q r:

4

c 0 .L) +.

3 3 1604

1204

80(

401

(

- 1000

I , C-!41

- 800

B-747 -***I

C-135 DC -8

- 600

C-13%

DC-8 2 =0.001 i o - 400 B -747

C-141 C-130

C I

I I I I I I i0ft/se( 10 20 30 40 50 60

I I I I I mf sec IO 1s 20 - 0 5

u at 300 feet

Figure 17. Deviation in Touchdown for Different Type Aircraft in Neutral Wind Profi les .

33

4000

3600

3200

2800

rn

C

b

C

E 0

ld

-cI

.d w

5 160

a"

40

Figu

I

- 1000

' 8 0 0

,600

/ c-130 C-141

B -747 D C -8 C-135A

C -141 C-130

B -747 DC -8 C J 3 5 A

C-141 B -747

D C -8 C-135A

C-130

L = 1 0 m

L = 100 rn

L = 300 rn 1

I I 1 5 10 15

1 ml sec

' ftlsec 1 I

20 I I I I I

40 50 60 70 0 10 20 30 gat 300 feet

.re 18. Deviation in Touchdown f o r Different Type A i r c r a f t in Stable Wind Prof i les : 2 = 0. 1 m

0

34

400

360

320

280

I- 4

240 5 B s 0

200 E

c 0

a

d

4 @

rr.

2 160 n

I20

80

40

‘1000

* 800

c-*30C-141 B-747DC_g

/ / e c - 1 3 5 A

C-130 C-141

Shear at 8Om

Shear at 40m

Shear at 2Om I

8 I I I I J 5 10 15 20 m/sec 0

u at 300 feet

Figure 19. Deviation in Touchdown fo r Different Type Aircraf t in Very Stable Wind Profi les .

35

Variation in AT due to Aircraf t Weight

In s imulat ing the landing of an a i r c ra f t , the g r o s s weight of the

aircraft w a s chosen approximately midrange between i ts to le rance ex-

tremes. To de termine the influence of the g r o s s weight of an a i r c r a f t

on AT, Landings were s imulated fo r the Boeing-747 with g r o s s weights of

400,000 pounds and 550,000 pounds.

ma te ly to minimum and maximum landing weight l imitations fo r th i s air-

craft. F igu re 20 com5ares the values of AT fo r the ve ry s table profiles.

T h e difference between A'Tfor the two g r o s s weights is smal l ; generally

less than 200 feet. F o r the o ther stabil i ty c a s e s , the difference between

the AT'S are even smaller and hence not presented in th i s report .

s u m m a r i z e . the g r o s s weight of a n aircraft appea r s to have little effect

on touchdown point, especial ly when compared t o the effects produced by

su r face roughness and stabil i ty.

'These values cor respond approxi-

- T o

Variation in AT due to Cg Locations

The location of the c e n t e r of gravity, Cg, of an aircraft depends

upon the gross weight and weight distribution of the aircraft.

the previous simulations, the Cg location was chosen approximately midway

between t h e tolerance extremes. To observe the influence of the C g l o c a -

t ion on touchdown point, s imulated landings of the Boeing-747 w e r e made

with t h r e e d i f fe ren t Cg locations:

Mean Aerodynamic Chord; and 3370 Mean Aerodynamic Chord. The 1570

and 3370 Mean Aerodynamic Chord are the extreme allowable to le rances .

Table 3 shows the resu l t s f o r t he unstable and v e r y s tab le profiles. The

d i f fe rence between AT values f o r the th ree Cg locations i s negltgible in

all cases.

found to be in te rmedia te between the unstable and v e r y s tab le ex t r emes .

Thus , the C g location s e e m s to have little influence on the deviation in

touchdown point due to wind s h e a r s .

In m o s t of

15% Mean Aerodynamic Chord; 2570

The differences in A T for neut ra l and s tab le prof i les w e r e

36

4000

3600

3200

2800 e a

g 2400

- C

.cI E V 1 0 e -E

0 ; 2000

3 * i6oa

4

* e

1200

80C

40C

(

2(

. loo0

- 800

/ Wf= 400,000 Ibs

Shear at

WT = 550,000 lbs

Shear at 60m

= 550,000 lb

Shear at 4om

- 600

W - 400,000 lb. I/ / / / T-

L I I I 1 20

5 10 15

0 10 20

W = 550,000 Ib. T Shear at

20 m

WT= 400,000 lb W - 550,000 lb

Shear at T-

1Om

I \ I m/sec

ftlsec - u at 300 feet

Figure 20. Deviation in Touchdown fo r B-747 in Very Stable Wind Profi les with Different Landing Weights

37

Wind Prof i les

No. 1 No. 2 No. 3

a NO. 4 5 No. 5 $ No. 6

No. 7 No. 8 No. 9

No. 1 No. 2

a No. 3 2 No. 4 c, NO. 5 h N o . 6 E No. 7 * No. 8 No. 9

Id [A

TABLE 3

DEVIATION FROM TOUCHDOWN POINT FOR VARIOUS LOCATIONS O F THE CENTER O F GRAVITY:

B-747, Weight=400,000 pounds

Cg= 1570 Mean Aerodynamic

Chord

- 463 - 737 - 731

' t 951 - 856 t2877 -1 323 - 849 -2887

~~ ~ ~

C g= 2570 Mean Aerodynamic

Chord

- 462 - 736 - 731 t 942 - 855 t2985

- 847 -2845

-1317

-4028 t1164 -2370 -2936 -3212

-1854 - 824 - 352

-3031

38

-3953 t1126 -2299 -2884 -31 77 -2985 -1827 - 818 - 352

Cg=j370Mean Aerodynamic

Chord

- 463 - 737 - 731 t 942 - 849 t3633 -1299 - 837 -2781

-3854 t1260 -2204 -2821

-2932 -1797 - 813 - 351

-3138

ANALYSIS O F AUGMENTOR-WING STOL AIRCRAFT ,

The landing of the augmentor-wing STOL aircraft descr ibed in the

Ai rc ra f t Landing Model Section was simulated f o r the same unstable, neutral ,

stable, and v e r y s table wind prof i les identified in t h e Analysis of Conventional

Ai rcraf t Section.

slope with d e s c e n t again beginning at 300 feet.

The trim conditions were defined fo r a 7-degree glide I

Under these conditions, the I

resulting touchdown point f o r a constant ( o r ze ro ) wind field would be (ignoring I I

f o r a moment the ground effects on the a i rc raf t ) 2443 feet downrange.

21 through 24 show the landing of the STOL a i r c r a f t in the unstable, neutral ,

stable, and v e r y stable prof i les previously presented as F igures 2, 3, 4, and

11, respectively. For s e v e r a l of the tailwind prof i les , in par t icu lar those

f o r which the wind velocity exceeded 17 ft/sec, it was impossible t o trim the

F i g u r e s

I

a i r c r a f t t o follow a 7-degree glide slope by controlling only the th rus t magni- ~

tude and elevator .

tive th rus t would L e required f o r the STOL a i r c r a f t t o descend t h e 7-degree

glide slope at a constant velocity relative to the air of 118f t / s ec .

r e su l t s f rom those runs where negative thrus t was assumed have been d i s -

carded.

from the glide slope but the na tura l response of the aircraft eventually br ings

it back toward the glide slope.

T ra j ec to ry No. 10 of F igu re 24 are good examples of th i s phenomenon. These

oscil lations arise f r o m the Phugoid mode of the aircraft.

STOL trajectories, the aircraft was fur ther f r o m the glide slope at some point

p r i o r to touchdown than it was at touchdown. This was not t rue of the conven-

t ional aircraft flights. In the latter case , the period of the Phugoid oscil lation

w a s much l a r g e r so that touchdown occurred before the first quarter-cycle

of the flightpath oscillation.

The solution of the initialization subroutine showed a nega-

Thus, the I

I For s e v e r a l wind f ie lds , the shear causes the a i r c r a f t to depar t

Tra jec tor ies No. 1 and 10 of F igure 23 and

In seve ra l of the

F o r most of the STOL t r a j ec to r i e s in which the above phenomenon

w a s present , AT was not great ly less than the maximum deviation f r o m the

glide slope during the flight. Nonetheless, the AT'S observed f o r the STOL

39

S.I

0

0 0

-0 +

.c u) 5 0 k

d

r\l

Q) k 7 M

f4 .d

40

3 3 0 3 0 u

3 0 3 i n 0 d m

0 g : d

- 0

* o &--g Cn-

d 0 0 0

>

.e

0 k

9

0 0

-0 t-

-In 9

0 0

-0 9

0 -0 In In

-0

0 -0

In * 0 0

-0 * 0

-0

0 -0 0

g 0 N

-0 In d

0 0

-0 d

0 -0 m

40

m a"

N N Q k

41

0 - 4

U co 0 .n 0

A 0 hl 0

0 0

9

0 0 0 :1' 9

z l n o i" 4 l n

I- O 0 0 4

0 0 VI

~ 0

7 0 k s t.c m P)

k 0 U

.d

+I

a i rc raf t cannot be interpreted in quite the same manner as they w e r e f o r

the conventional aircraft.

deviation f r o m the glide slope f o r a given wind shear .

The STOL AT'S only approximate the maximum

Ground Effects of STOL Ai rc ra f t

The landing of the augmentor-wing STOL a i r c ra f t was simulated

both with and without ground effects t e r m s to de te rmine the degree to which

the a i r c ra f t groupd effects influenced touchdown point.

deviation in touchdown fo r the very s table and unstahle wind profiles f o r

the simulations with and without ground effects.

the ground effects causes a touchdown 180 feet beyond the 7-degree glide

slope touchdown point. This cont ras t s with the 90-feet-short touchdown

point for the Boeing-747 and DC-8 aircraft.

ground effects causes a deviation in touchdown point on the o r d e r of 150

to 200 feet.

are much smaller.

influence when the wind s h e a r is light and the a i r c r a f t ' s descent follows

a path near i t s des i red glide slope.

influence of ground ef fec ts on touchdown is general ly less than 200 feet ,

ground effects are not an important considerat ion in o u r study.

Table 4 shows the

F o r the z e r o wind field,

F o r the unstable profiles, the

F o r the very stable profiles, the deviations in touchdown

In general , the ground effects provide the l a r g e s t

Since,even under these conditions, the

Wind Shea r Effects on Touchdown

Figure 25 shows deviation in touchdown, AT, f o r selected s table

and unstable wind profiles when the landing approach is in the headwind

direction.

the parameter L.

small (not shown in F igure 25).

in AT is g r e a t e r with respec t to Zo than with r e spec t to L.

s is tent with the previously observed var ia t ions i n AT with Zo and L for

F o r the s table wind prof i les , AT shows the m o s t var ia t ion with

F o r a fixed value of L, the var ia t ion of AT with Zo is

For the unstable prof i les , the var ia t ion

This is con-

44

TABLE 4

DEVIATION FROM TOUCHDOWN POINT W I T H AND WITHOUT GROUND EFFECTS

FOR STOL AIRCRAFT

Wind Prof i l e s

Zero Wind No. 1 No. 2 No. 3

2 N o . 4 P cdNo. 5 $No. 6 DNo. 7

No. 8 No, 9

c,

No. 1 No. 2 No. 3

-No. 4

*No, 6 &No. 7 $No. 8

No. 9

0)

D $No. 5

x

Augme nto r - W ing STC

AT W i t h AT Without Ground G round Effects Effects t180 0 t125 - 91 t 32 -161

+349 +190

Negative Tnrust Needed 1 -113 -280

+ 57 -145

- 8 -179

- 49 -189 -599 -713

-1 -1299 + 157 - 683 - 975 -1141 - 1024 - 623 - 189 t 54

-1303 t 137 - 701 - 978 -1 141 -1025 - 639 - 123 - 290

1 Difference i 1 180

216 193 2 02 159 171

i Trim 167 140 114

4 20 18 3 0 1 16 101 177

45

2800

2400

E- Q 2000

8 -

C

'FI c 0

1600 E- d

C 0

.CI

.CI

2 1200 4 * a"

800

400

800

600

-

-

-

-

-

-

-

0-

1 4 0 0

/ 0 L = 10m 0

0 /

M

0

, Stable, Zn= 0. l m - - 200

Unstable, L = 300m - -- L = 25m

=O.Olm 0

I I *m/eec 10 15 20 _ _

1 I I I 0 10 20 30 - I I I 1 f t l sec

40 50 60 70 u at 300 feet

Figure 25. Deviation in Touchdown for STOL in Unstable and Stable Wind Prof i les : Headwind.

46

conventional-type aircraft. The variation of AT in neutral wind profiles, though

not shown in F igu re 25, lies intermediate between the resu l t s f o r the s table

and unstable wind profiles.

stable wind profiles.

f o r the STOL aircraft than f o r the conventional aircraft.

STOL resu l t s t o that of t he conventional a i r c ra f t , it mus t be remembered tha t

t he simulated landings fo r the STOL aircraft were down a des i red glide slope

of 7 degrees as compared to a 2. 7-degree glide slope f o r the conventional air-

craf t .

the glide slope in a s h o r t e r length of time which apparent ly accounted f o r the

much smaller deviations in touchdown observed with the STOL. On the o the r

hand, since a 2. 7-degree sl ide slope is typical f o r a conventional a i r c ra f t , and

Figure 26 shows the var ia t ions in AT f o r the v e r y

The values of AT are approximately th ree times smaller

In comparing the

The difference in glide slope angle allowed the STOL aircraft t o descend

7 degrees typical f o r a STOL, the comparison between the two is valid when

considering the effect of wind s h e a r on typical landing conditions at a given airf ie ld .

Landing of the augmentor-wing STOL aircraft in a tailwind presents

a problem if the tailwind is g r e a t e r than 17 ft/sec.

z e r o th rus t is requi red to maintain the 7-degree glide slope with a relative

air velocity of 118 ft/sec. F o r a tailwind in excess of 17 f t / s e c the seven-

degree glide s lope cannot be maintained without increasing the speed of the

aircraft as it descends. If it becomes necessa ry t o land this STOL aircraft

in a l a rge tailwind, the pilot should probably d e c r e a s e his glide slope angle

to two o r t h r e e degree s if Dossible-

With a 17 ft/sec tailwind,

0 - c -

47

I

+a e rl:

2800-

2400-

2000-

1600-

120c-

800-

40C-

W

0 & a 0

J

800

600

400

200

Shear at 80m

Shear at 60m

Shear at 40m

I I I I I I I 0 10 20 30 40 5 0 6 0

Gat 300 feet

Figure 2 6 . Deviation in Touchdown f o r STOL in Very Stable Wind P ro f i l e s : Headwind.

48

SUMMARY AND CONCLUSIONS

The three -degrees -of -freedom a i r c ra f t landing simulation study has

determined the types of wind s h e a r profiles tha t can produce potentially

hazardous landing conditions.

into the simulation.

sulting f r o m variat ion of the horizontal wind during the final 300 feet of

descent have been observed under wind shear conditions that are not unrealistic.

The influence of ground effects, cen te r of gravity location, and g ross weight

of the a i r c r a f t on the deviation in touchdown point due t o wind s h e a r s has a l s o

been investiaged. The specific conclusions result ing f rom this study are:

No pilot o r auto-pilot feedback was introduced

Deviations in touchdown point i n excess of 3000 feet re-

a) Stable (OcRi<O. 2) and ve ry stable (Ri>O. 2) conditions are

most likely t o produce hazardous landing conditions. Deviations

in touchdown of 2000 to 4000 feet have been observed f o r conven-

t ional aircraft. Neutral and unstable wind profiles seldom cause

deviations in touchdown point i n excess of 2000 feet f o r conven-

t ional aircraft and 600 feet fo r the augmentor-wind STOL.

b) The deviation in touchdown point, AT, is m o r e dependent upon

the t e r r a i n roughness, Zo, than upon the stabil i ty length, L,

under unstable and neutral wind conditions.

conditions, the r e v e r s e is t rue .

c) F o r ve ry stable conditions, AT is mos t dependent upon the

alt i tude at which the shear layer occur s . Very stable wind

prof i les are highly unpredictable and are not dependent upon

the su r face p a r a m e t e r s (Z

stabi l i ty conditions.

d) For the a i r c r a f t considered here , the var ia t ion in touchdown

due t o the ground effects on the aircraft is small in comparison

to the variat ion which can r e s u l t f r o m the wind s h e a r s investigated.

Under stable wind

u*,L) that cha rac t e r i ze the o ther 0’

49

e) F o r a given wind profile, a tailwind direct ion produces a

slightly l a r g e r deviation in touchdown than does a headwind

direction.

f ) F o r the conventional a i r c ra f t , the s ize , type, and the landing

speed of the aircraft has some influence on AT but th i s influence

is considerably less than that due to sur face roughness and

stabil i ty length.

t h e C-l3OE, C-l35A, C-141, DC-8, and B-747.

g) 'The landing of the augmentor-wing STOL in a given wind field

produced a much smaller value of AT than the landing of con-

ventional a i r c r a f t in the same wind field. In par t icu lar , AT

values f o r a STOL landing were 3 to 6 times smaller than the

corresponding AT values fo r a conventional landing.

glide slope angle fo r the STOL (7 degrees ) allowed it to land

i n less time and was a m a j o r reason why AT was smaller f o r the

STOL. Under all but the mos t e x t r e m e s h e a r conditions, values

of AT f o r the STOL a i r c r a f t did not exceed 1000 feet.

h) The difference in touchdown points betweenthe landing of a fully

loaded a i r c r a f t and a n empty a i r c r a f t was found to be small.

a i r c ra f t analyzed was the Boeing 747.

The types of conventional aircraft studied we re I

The l a rge

The

i) The difference in touchdown point resul t ing f r o m a shift in the I

Cg, within operat ional to le rance , w a s found t o be negligible. The

aircraft analyzed was the Boeing 747. In par t icu lar , th i s indicates

that the Boeing 747 was well designed with r e spec t to its response

t o wind shea r .

Aeronaut ical Safety Conside rat ions

This r e s e a r c h program has provided r e su l t s tha t have d i rec t application

to aeronautical safety at a i r p o r t s .

landing conditions a r e likely t o occur under the s table and v e r y s table

It has been shown that the mos t critical

50

I

atmospheric conditions. Unfortunately, t he wind profile under ve ry stable

conditicns cannot be determined f rom a single wind measu remen t knowing the

sur face roughness and stabil i ty pa rame te r s .

during the night under s t rong tempera ture inversions.

height and magnitude of the s h e a r can only be determined by empi r i ca l m e a s u r e -

ments.

provide the capability of measur ing a ver t ica l profile of shear. A f i r s t - o r d e r

s h e a r approximation could be derived by a simple two-point shear, calculated

f r o m a n a i r p o r t sur face wind measurement and a n onboard a i r c r a f t wind speed

measurement .

remote sensing techniques present ly under development.

~

I

Very s table conditions often occur

Under these conditions,

I Thus, a n important consideration in improving a i r p o r t sa fe ty is t o

I

A m o r e refined profile could perhaps be derived by some of the

A second safety consideration relevLnt to air traffic control is the o b s e r -

vation that a seve re s h e a r condition effects all a i r c r a f t (at leas t those within

the range of s ize and type considered in th i s repor t ) to approximately the same

degree.

it should be assumed that a l l - s ize aircraft will experience similar landing

problems.

Thus, if one aircraft r epor t s landing difficulties due to wind shear,

A th i rd conside ration related to a i rpo r t safety concerns the homogeneous

t e r r a i n that immediately sur rounds different a i rpo r t s .

roughness pa rame te r , 2 , shows little influence on touchdown points under s table

and v e r y stable conditions, the roughness of the t e r r a i n surrounding the air-

port is not a n important consideration fo r determining which a i rpo r t s experience

the critical s h e a r prof i les .

s ince the wind prof i les defined i n this study a s sumed the t e r r a i n t o be homo-

geneous of a given roughness length. A t many a i r p o r t s , a s the a i r c r a f t descends

the glide s lope, the roughness of the t e r r a i n that regulates the profile changes

SO that more s h e a r could possibly be introduced into the wind profile. A study

should be d i r ec t ed toward the change i n t e r r a i n problem before a firm con-

c lusion delineating the t e r r a i n effects of a i rpo r t surroundings can be made.

Since the surface

0

This s ta tement needs some qualification, however,

51

A fourth safety consideration is related to pilot training and automatic

landing sys tems. A wide var ie ty of wind prof i les represent ing t h e var ious t e r r a i n

roughness and stability conditions should be used as input to flight s imula to r s

where pilot response o r pilot training is required. The same var ie ty of wind

prof i les should be used for the evaluation of a n automatic landing sys t em.

A final safety considerat ion has application to those involved in STOL

a i r p o r t design.

should provide pre l iminary guidelines fo r the runway length safety f ac to r

needed to allow fo r touehdown d ispers ions due to wind shea r .

The deviations in touchdown observed f o r the STOL aircraft

Suggestions fo r Additional R e s e a r c h

This study has provided some basic resu l t s concerning the amount of

d i spers ion in touchdown that is likely to occur fo r a n a i r c r a f t landing under a

specific set of assumptions. These assumptions limit the reali ty of the s i m u -

lation model to some extent since the actual si tuation is different when a pilot-

controlled aircraft descends the glide slope.

cluded in this study may be important and could be considered in a more defined

six-degree-of-freedom aircraft simulation model. A six-degree -of - f reedom

model could extend the analysis to cons ider c r o s s wind landings and landings

i n wind fields where the direct ion of the wind changes significantly ove r the

f inal 300 feet of descent.

introducing th ree -dimensional turbulence s t r u c t u r e into the mean wind prof i le .

F u r t h e r work is a l so needed in defining the wind profile along the glide slope

when a change in t e r r a i n roughness occurs .

f r o m sea to land t e r r a i n should a l s o be studied. A final recommendat ion is to

improve the reali ty of the simulation by introducing pilot feedback o r a n auto-

matic landing sys t em into the s imulat ion model.

c a n a completely real is t ic s imulat ion be anticipated.

as defined above would produce more definit ive r e su l t s under a much b r o a d e r

range of conditions.

Many fac tors which w e r e not in

The effect of turbulence could a l s o be studied by

The effect of t he roughness change

Only by introducing cont ro l

Such a r e s e a r c h p rogram

52

REFERENCES

I.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Melvin, W. W . , "Wind Shea r on the Approach", Shel l Aviation News, 393: 16 -21, (19fl) .

Kraus, K., "Aspects of the Influence of Low-Level Wind Shear on Aviation Operations", International Conference on Aerospace and Aeronautical Meteorology, Washington, D. C. , May 22-26, 1972.

Haskins, G. L., "The X in WX", Aerospace Safety, Apr i l , 1969.

Gera, J . , "The Influence of Ver t ica l Wind Gradients on the Longitudinal Motion of Airplanes", NASA TN-D-6430, September , l971.

Neuman, F., and F o s t e r , J . , "Investigation of a Digital Automatic A i rc ra f t Landing Sys tem in Turbulence", NASA TD-D-6066, October, 1970.

Skelton, G. B. , "Wind Gusts - 0-300 ft . Altitude - Homogeneous Terrain" . Aerospace Vehicle Flight Control Sys tems, SAE SP-358.

Johnson, W.A., and D. T. McRuer, "A System Model f o r Low-Level Approach", Journa l of A i rc ra f t , December 1971.

Fichtl , G. H., "Fluctuating Wind Shear in the Atmospheric Boundary L a y e r as Related to Ai rc ra f t Operations", accepted f o r publication.

Gerlach, O.H. , and J. Schuring, "Mathematical Model of Externa l Disturbances Acting on an Aircraf t During an I. L.S. Approach and Landing.'' Delft-The Netherlands, March 1970.

L u e r s , J. K., Surface Boundary Layer" , t o be published as NASA Cont rac tor Report .

"A Model of Wind Shear and Turbulence in the

53

The equations for the l i f t , drag, and moment coefficients (C C C ) L' D' m and the aerodynamic coefficient data f o r e a c h aircraft considered in th i s study

are presented below. The ground effects t e r m s f o r four of the a i r c r a f t (DC-8,

C-l35A, Boeing 747, and the STOL) are discussed. Ground effects data w e r e

not available f o r the C-130E and t h e C-141 aircraft.

presented cor responds to a given flap setting and, where applicable, a given

horizontal tail setting.

The aerodynamic data

The data includes the effects of the landing gear .

DC -8

The express ions f o r the aerodynamic coefficients of the DC -8

aircraft are:

C L =

CD =

c = m

C + C L a '+ L O a

CD, + CD, a '

Cmo+ Cnh a '

where the usual notation is

c a' C t A C L~~

2 t C D ~ ~ a ' t ACDGE

used f o r the var ious stabil i ty der ivat ives . The

last term in e a c h of the above equations is the ground e f f ec t s term. The

values of the stabil i ty der ivat ives are given in Table A. 1 f o r a f lap setting

of 50 degrees . The ground effects terms fo r the DC-8 are:

'GE PCLCE Lm = 0.063 (C

= ( -0 .02 - 0.332a ') cGE ACDGE

'GE = -0.066 (C A C W E

A-1

TABLE A. 1

DC -8 AERODYNAMIC DATA

C

C

C

LO

La

L6E

cLq

CL&

cDO

‘Da

cD, 2

m6E C

9 C m

0.90

5.30/rad

0.0053/deg

7.68/rad

0 .0

0.140

0.501 / r a d

1. 818/rad2

-0.01

-1.062/rad

-0.0161 /deg

-12,30/rad

-4 .Ol / rad

A-2

where

-hi17 c = 0.972e GE

L' h is the wheel height, and C is the free stream value of C La,

C-135A

The express ions fo r C and C f o r the C-135A are the same as L m those f o r the DC-8. The express ion fo r the d r a g coefficient is

2

DGE c D = c D o + C D c ~ C L t A C

Table A. 2 shows the aerodynamic data-for a flap sett ing of 30

d e g r e e s and a horizontal tail deflection of -4 degrees .

terms are:

The ground effects

= (0.039 + 0.2292a ') eGE AcLcE 2

LJ 'GE = (0.119 - 0.357 C A C ~ ~ ~

2

'GE = (0.0228 - 0.1408 CL + 0.054 CL a, a, AcmG*

w h e r e

C-141

The expres s ions f o r the l i f t , d r a g , and pitching moment coefficients

f o r the C-141 are the same as those f o r the C-135A. Table A. 3 p resen t s

the aerodynamic data f o r a flap setting of 45 degrees and a horizontal tail

set t ing of -6 degrees .

terms.

No data w e r e available f o r C-141 ground effects

A -3

TABLE A . 2

C-135A AERODYNAMIC DATA

0 cL

a CL

L6E C

L¶ c

cDO

c m6E

0 . 6 1 2

4 . 0 1 /rad

0 .00376 /deg

0 . 0

0 . 0

0 . 0 6 8 5

0 . 0 4 7 3

0 . 0 9 2 2

-0 .765 /rad

-0 .0108 /deg

-14 .182 /rad

- 5 . 7 8 7 l r a d

A -4

TABLE A.3

C-141 AERODYNAMIC DATA

1.309

5.441rad

0.00443/deg

0.0

0.0

0.0835

0.0388

0.391

-1.351/rad

-0.0149/deg

-15.751rad

-5.17/rad

A-5

C-130E

The C-130E aircraft is powered by four propjet engines. For this

type of a i r c r a f t s e v e r a l of the stabil i ty der ivat ives depend upon the th rus t

coefficient TC defined as

- 2 TC = 2qd

- where F T ~ is the th rus t p e r engine, q is the dynamic p r e s s u r e , and d

is the propel ler d iameter . F o r the C- l30E , d is equal to 13. 5 feet. The

expressions f o r CL, CD, and Cm fo r the C-130E are the same as fo r the

C-135A except that C

dependence is shown in Table A. 4.

sett ing of 18 degrees .

, Cmo, and C L ~ depend upon Tc. This

The data in Table A . 4 i s f o r a f lap LO’ ‘La

N o ground effects d a t a w e r e available f o r this a i r c r a f t .

Boeine. 747

The express ions f o r

Boeing 747 are the same as

CD, and Cm used

those of the DC-8 with cL’ in this study fo r the

the exception t h a t a n

additional t e r m has been added to Cm to account fo r different c e n t e r of

gravi ty locations. This t e r m is:

CL ( c g - 0.25)

w h e r e C g is the location of the c e n t e r of gravi ty in terms of the mean

aerodynamic chord, c . above t e r m i s zero.

a flap setting of 30 degrees and a horizontal t a i l se t t ing of -4 degrees .

It was assumed that the inboard and outboard e l eva to r deflections are the

same. The express ions fo r the ground effects t e r m s are:

- - F o r a c e n t e r of gravi ty location of 25%c, the

The aerodynamic da ta presented in Table A. 5 is f o r

A -6

TABLE A.4

C -130E AERODYNAMIC DATA

C

G L8E

Lq

0.379 TC t 0 . 7 0 2

(3 .62 TC t 6. 70)/rad

6.59/rad

2. 52/rad

0.0638

0.0305

-0 .224 TC t 0 . 3 3 8

(2 .75 TC - 1.785) /rad cm,

C m6E

-O.O285/deg

C -20.061 rad m¶

A -7

TABLE A. 5

BOEING 747 AERODYNAMIC DATA

LO C

‘La

L6E C

L9 C

‘Da2

=m0

m6E C

9 C m

0 . 9 6 0

5 .735 / rad

5 . 6 8 / r a d 6 . 7 6 / r a d 4 . 8 8 / r a d

-6 .70 /rad

for c . g . = 2570 c for c . g . = 1570 c‘ for c . g . = 33% c

-

0 .1381

0. 5498/rad

2 . 1 9 0 / r a d 2

0 . 0 9 4

-1. 536lrad

-21. 50 /rad

- 3 . 4 0 l r a d for c . g . = 2570 - c - -3. 8 l / r a d - 3 . 0 9 / r a d

for c . g . = 15% c for c . g . = 3370 c

-

A -8

- (0.240) c o s [8.036(a t-0.00526)] A c ~ ~ - K~~

2 (2 .308a l 3 - 0,9796a - 0.1769a ' - 0.0384) A

AC

2 (2.736a ' - 0.621a.I - 0.115) *'WE = K~~

where A -6 3 -4 2

B

= 1.7034 x 10 h - 1.0736 x 10 h - 1.4813 x h + 1.0

= 3 . 7 9 0 6 ~ 1 0 h - 4 . 9 3 7 ~ 1 0 h + 2 . 8 0 7 ~ 1 0 h + 1 . 0

K~~

K~~ -6 3 -4 2 -3

The ground effects terms are included only during the last 82. 5 feet of flight.

STOL

The equations f o r the aerodynamic coefficients for t he augmentor

wing STOL aircraft are somewhat different than f o r the previously d iscussed

a i r c ra f t . Seve ra l of the stabil i ty der ivat ives are functions of the th rus t co-

efficient C

aerodynamic coefficients are expressed as:

In the present study, a value fo r C . of 0.75 was chosen. The j* J

8 t- c% +-c c a t CL = c + C L H ~ + C LHa a t + CLhE E 2v, Lq 2va L& LWB

1 Cm = Cmo + Cmaa ' + CLWB (Jcosat+ 3 - s ina 1 ) -

C C

+ C D - (-sinat 1W - - cosa ' ) ZW - + (C LHo + C LHa Q. ' + C L % ~ E )

ZH C C

- 0 - W E C t A C

c a ' c o s a t ) t 3 c +- s i n a ' -- 1H

(T - 2va mq 2va m;r C C

A-9

The subscr ip ts H and WB refer to the contributions f r o m the horizontal

tail and wing-body, respectively. C is the basic l i f t coefficient f o r LWB

the wing-body. The p a r a m e t e r s l w y Z w , .t and Z are d is tances which

relate the a i r c r a f t cen te r of gravi ty to the wing-body Cm reference point

and the 25% mean aerodynamic chord of the horizontal tai l .

The values of these p a r a m e t e r s are:

H’ H

(See F igure A . 1).

lw = 3 . 9 5 ft.

lH = 7 5 . 3 9 ft.

Zw= 0. 083 ft.

ZH = -24.75 f t .

The values f o r the var ious stabil i ty der ivat ives a r e shown in Table A . 6.

The flap sett ing i s 70 deg rees and the auxi l iary f lap is s e t a t 6 deg rees .

The descr ipt ion of the ground effects f o r the STM a i r c r a f t is much

The ground more complex than f o r the conventional aircraft investigated.

effects come into play at approximately 200 feet altitude.

point, C L ~ ~ is given by

P r i o r to this

a ’ - cLWBm - ‘LWB0 ’ GLWBa

The subscr ipt oodenotes the free s t r e a m value.

modified by ground effects according to the equation

The value of C is LWBm

where 1

¶km = 1

[ 1 t 16(- I 2 P 2

A-10

I ' i '

I

Ref CmWB e renc e

Aircraft Center -of -G ravity

Figure A. 1 Some Geometric Parameters for the Augmentor-Wing STOL Aircraft.

A- 11

TABLE A . 6

AUGMENTOR-WING STOL AERODYNAMIC DATA

CLWBo

CLWBa

C LHo

LHa C

C Lq

C L * a

c m O

m¶

Cmh

C

C mC j

4 . 2 7 4

4 . 4 9 8 / rad

-0 .124

0 .743 /rad

0 .00936 /deg

0 . 0

0 . 0

0 . 4 4 9

2 . 1 2 / r a d

-1 .245

0 .372 /rad

-0 .0265 /rad

0 . 0

2 . 2 0

0 . 1 7 0 9 a ' - 0 . 0 3 1

-0 .780

0 . 3 8 4 / r a d

A - 1 2

Aa 1 - - - - 123 h - cL 2nAR [ l t 16 (

R c-A

and AR is the wing a spec t ratio which has a value here of 6 . 5 .

equation does not apply if C

which f o r the present case is 6.74.

effects terms are:

The above

exceeds its maximum allowable value L w b

T h e drag and pitching moment ground

+ (1 - q/q ) c cj 00 DCj

Values f o r C Lcj, C D ~ . Cmc , and C' are presented in Table A . 6 ma

for a C - value of 0.75. j j J

A-13