NASA/TM-1999-209531

Taxiing, Take-Off, and Landing Simulation

of the High Speed Civil Transport Aircraft

Mercedes C. Reaves and Lucas G. Horta

Langley Research Center, Hampton, Virginia

December 1999

https://ntrs.nasa.gov/search.jsp?R=20000011601 2018-05-14T14:09:35+00:00Z
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NASA/TM-1999-209531

Taxiing, Take-Off, and Landing Simulation

of the High Speed Civil Transport Aircraft

Mercedes C. Reaves and Lucas G. Horta

Langley Research Center, Hampton, Virginia

National Aeronautics and

Space Administration

Langley Research Center

Hampton, Virginia 23681-2199

December 1999
Available from:

NASA Center for AeroSpace Information (CASI)

7121 Standard Drive

Hanover, MD 21076-1320

(301) 621-0390

National Technical Information Service (NTIS)

5285 Port Royal Road

Springfield, VA 22161-2171

(703) 605-6000
Table of Contents

1. Introduction .......................................................................... ............. 2

2. Airframe Model ............................................................................. 3

3. Equations of Motion .............................................................................. 3

3.1 Mode Selection Approach .............................................................. 6

4. Landing Gear ...................................................................................... 6

.

4.1 Runway Model ......................................................................... 7

System Integration / Numerical Simulations .................................................. 8

6. Simulation Results ................................................................................. 8

6.1 Aircraft Response During Ground Operations ...................................... 8

6.2 Taxiing Simulations .................................................................... 9

6.3 Rejected Takeoff Simulations ......................................................... 9

6.4 Landing Simulations ................................................................. 10

6.5 Frequency Comparison of the Various Ground Operations ..................... 10

6.6 Human Response to Vibration ...................................................... 11

7. Concluding Remarks ........................................................................... 11

8. References ....................................................................................... 11

9. Tables ............................................................................................ 13

10. Figures .......................................................................................... 15
1. Introduction

The High Speed Civil Transport (HSCT) has been identified as a means to extend the role

of the United States as the leader in aerospace well into the 21st century. However, the

unique configuration of the aircraft and its operational requirements present numerous

technical design challenges. The HSCT airframe, driven by aerodynamic design

constraints and design considerations, has relatively low stiffness compared to subsonic

aircraft. Also, the nose gear is well aft of the flight crew deck creating a long overhang.

Previous supersonic transport aircraft configurations, such as the Concorde and XB-70

aircraft, all exhibited excessive fuselage dynamic response during ground operations. 1_

NASA Langley Research Center has initiated a research effort to assess the problem of

ground-induced vibration for this new HSCT configuration. Being able to identify such a

problem in the early stages of the design process will enable designers to address the

problem early.

Computer simulations have been conducted to study the HSCT vibration levels during

taxiing, landing, and takeoff roll-out. A linear modal math model of the airframe with no

landing gear is constructed by combining the symmetric and antisymmetric modes of the

airframe. The landing gear dynamics, including inertia, damping and stiffness properties,

are introduced as external nonlinear forces. Software capable of detailed nonlinear

simulation of an aircraft and/or its landing gear and all associated sub-systems is available

3,4 and could be used in future studies or advance design stage. In the present work

SIMULINK 5 , a commercial computer simulation program, is used to numerically

integrate the equations of motion and to postprocess the data. The profile for a runway at

San Francisco airport (commonly used by the FAA for airplane certification ) is used as

input to the simulation. Displacement and acceleration time histories are obtained at the

cockpit and at various fuselage and wing locations for forward speeds ranging from 30

knots to 175 knots. Although the model contains simplified landing gear system

information, e.g., no specific oleo strut mechanics or dynamics (piston, metering pin, etc.)

have been modeled, the simplified model of the gear, nonlinear spring and damping forces

as a function of stroke, proved to be adequate to assess the vibration problem.

This document describes the aircraft configuration in terms of structural and mass models,

defines the analysis approach, systems models, computer simulation, and discusses results

from the simulations.
2. Airframe Model

The HSCT weights and finite element models used in this investigation are based on the

Boeing HSCT 1080-920STR model E configuration, Ref. [6], with the landing gear

deployed. A sketch of the aircraft, an aft tail / four engine configuration vehicle, is shown

in Fig. 1 with the landing gear in the stowed position. The original finite element model

created by Boeing using ELFINI 7, a general purpose FEM software package, was

translated into MSC/NASTRAN s format using a translator developed in-house. The HSCT

FEM, Fig. 2, represents the (symmetrical) right half of the aircraft and contains 38,444

degrees of freedom. This finite element model is divided into fourteen sections as shgwn

in Figure 3. Table 1 contains a description of each section. The primary structure which is

modeled consists of skins, chords, spar webs and landing gears posts, trunions and drag

braces. Secondary structure, such as windows, passenger doors, access doors, etc., is not

modeled because it is not necessary for strength or flutter analysis. Symmetric and

antisymmetric configurations are represented by applying the appropriate boundary

conditions to the degrees of freedom in the vertical plane of symmetry of the aircraft.

A data base of lumped masses representing the airplane mass distributions for the primary

and secondary structures with combinations of on empty weight (OEW), payload and fuel

weights were supplied by Boeing, Ref. [6]. Depending on the analysis to be conducted

(e.g., flutter, ground operations, etc.) the appropriate set of lumped masses can be obtained

from the data base and included in the structural t'mite element model as lumped mass

elements at specific grid point locations. The mass cases used in this investigation are

designated mass case MO5 and mass case M14, Ref. [6]. MO5 is a representation of the

airplane at maximum taxi or takeoff weight of 646,454 lbf with full wing fuel and with

e.g. located aft of the OEW (on empty weight) c.g. location. For landing simulation mass

case M14 was selected, for a total weight of 388,584 lbf which includes the OEW, aft body

full tank, and payload for an aft c.g. location. These conditions are considered the worst

case scenarios for ground operations.

3. Equations of Motion

To develop dynamic models for aircraft response analysis during taxiing, take-off, and

landing, it is required to combine airframe flexibility with landing gear dynamics.

Airframe structure is routinely modeled using finite element model (FEM) approaches

whereas landing gears are often modeled using equations obtained by semi-empirical

3
approaches.A f'mite elementdynamicmodel of the airframeleadsto a set of matrix

differentialequationsof theform

MJi(t) + Kx(t) = bu(t) (1)

where x(t) is a response vector order n x 1, M and K are the mass and stiffness matrices,

respectively, of order n x n, b is a direction cosine matrix locating external forces or

moments, and u(t) is a vector of applied forces or moments. The integer n is the total

number of degrees-of-freedom (DOF) used to construct the model, often a very large

number. For dynamic simulations it is important to reduce the size of the system in Eq.

(1). Typically, modal reduction techniques are used to reduce the size of the model. One

approach solves for the eigenvalues A2 and corresponding eigenvectors P such that

prMp = I, and prKp = A2. Assuming that the computed eigenvector matrix can be

partitioned into groups of symmetric and antisymmetric modes such that P - [_ W],

where • are the symmetric and Ware the antisymmetric modes, and substituting the

coordinate transformation x = Pr/ into Eq. (1) yields a decoupled set of equations as

follows

where r/r = [7/, r/,,land A == dtag(¢_o, " =,co_,). = The subscripts 's' and 'as' refer to the

symmetric and antisymmetric parts of the equation. Model reduction is accomplished by

retaining only a selected number of modes, normally fewer that the total available, for

analysis. So far it has tacitly been assumed that the full airplane configuration is modeled

and that an eigenvalue solution is computed. However, this is not necessary if one can take

advantage of symmetry, as discussed in Ref. [9]. By judiciously positioning the reference

coordinate system in the vertical plane of symmetry only half of the airframe structure

actually needs to be modeled, Fig. 2. The symmetrical and antisymmetrical eigenvectors

and eigenvalues can be computed by imposing the boundary conditions which are

consistent with the symmetry conditions. For example, the symmetric case requires the

degrees of freedon in the vertical plane of symmetry to be restrained from yaw, roll and

lateral translation, whereas the antisymmetric case requires restraining the degrees of

freedon in the vertical plane of symmetry from vertical translation, pitch rotation, and

forward translation. To recover information for the left-half of the airframe, the mode

shapes are expanded according to symmetry conditions, for example, _(I)= _(-l) and

4
Ig(1)= -V(-I) andwhencombinedwith timehistoriesof thegeneralizedcoordinatevector

r/(t) allows computation of the airframe left-half response.

To take advantage of existing numerical integration tools, the first-order form of Eq. (2) is

needed. Def'ming a new state vector z = [n, n_, h, h_,] r, Eq. (2) can be wdtten in

first-order form as

_(t) = Az(t) + Bu(t)

x = Cz(t) + Du(t)

°/i]t°0t o o

o o

c=[a, v o o]

D=0

m

(3)

where Q represent a null matrix with the proper dimensions. Equation (3) allows

calculation of responses in terms of the symmetric and antisymmetric modal coordinates

due to arbitrary inputs to the airframe. If acceleration responses are also needed, the

output vector in Eq.(3) must be augmented as follows

y = = Q 0 _ z(t)+

-_og-wo_ Q _ oo u(t) (4)

t_rb + tI_rb

and D is not null. The equations presented so far dealt with the airframe flexibility as

derived from the FEM. To incorporate landing gear dynamics, the approach is to use

empirical representations of the landing gear force versus stroke response and stroke

versus damping coefficient directly in the simulation. In its most general form, the landing

gear forces can be conceptually represented as

u(t) = f(y, Y, tS(t)) (5)

where the newly-defined parameter tS(t) corresponds to time variation of runway elevations

provided as input to the simulation program. Although Eq. (5) is deceptively simple, a

significant amount of time must be devoted to the experimental characterization of the

landing gear system if one expects to obtain high fidelity models using an empirical

approach. Typical experimental curves for Eq.(5) are presented in a later section.
3.1 Mode Selection Approach

The symmetric and antisymmetric vibration modes of the Boeing HSCT 1080-892STR-E

model with a 'rigid stick model' of the landing gear in the extended position and M05 mass

distribution were calculated using MSC/NASTRAN. A customized NASTRAN/DMAP

sequence was used to compute the kinetic energy associated with the vibration modes in an

effort to differentiate local modes from global modes to be used in the simulations.

Boeing-defined sections (fwd. fuselage, control surfaces, etc.) 1° were used to divide the

model into physically meaningful sections. A sample portion of the kinetic energy results

obtained for the HSCT with symmetric boundary conditions and MO5 weight distribution

is shown in Table 2. Since all sections are included in the list, the total kinetic energy is

100%. Figure 4 contains contour plots of the kinetic energy for the symmetric and

antisymmetric modes. Based on these results, the symmetric and antisymmetric global

airframe modes with the highest kinetic energy were selected for inclusion in the mode sets

_and _F .

In all, a combination of 8 symmetric modes ( 3 rigid modes , 5 flexible modes) and 7

antisymmetric modes (3 rigid modes and 4 flexible modes) in the frequency range between

0.0 and 6.67 Hz were chosen to represent the airframe flexibility for taxiing, takeoff and

landing conditions. The flexible mode frequencies and mode shapes corresponding to

equivalent modes from mass cases M05 and M14 are shown in Figures 5 through 13. The

symmetric rigid-body modes represent the aircraft vertical translation, pitch rotation, and

forward translation. The antisymmetric rigid-body modes represent the aircraft yaw, roll,

and lateral translation. The first two flexible modes appeared at relatively low frequencies

1.3 Hz and 1.5 Hz for the symmetric and antisymmetric cases respectively, compared to

3.6 Hz for a typical commercial transport configuration, Ref. [11].

4. Landing gear

It is important to distinguish between the landing gear structural model and the landing

gear dynamic model. In this document the term 'landing gear structural model' refers to

the finite element 'stick model' of the nose and main gear systems, Fig. 14, with stiffness

properties used to transfer loads into the fuselage correctly. The dynamic model refers to a

SIMULINK nonlinear mathematical model of the landing gear system described in this

section. The landing gear mass distributions included in M05 and M14 were modified to
separatethe"staticmassitems", e.g., braces,posts,etc., from the moving massitems,

e.g.,tires,wheelsand shockstruts. Table3 lists theweightsof themaincomponentsof

thenoseand mainlanding gearsfor the BoeingHSCT 1080-892STRE model. Forty

percentof thetotalweightof thenosegear,821.1 lbf, correspondsto moving massand

fifty-five percentof thetotalweightof onemain gear,4352 lbf, correspondsto moving

mass.Themovingmasswas takenout of theM05 andM14 massdistributions usedfor

FEM eigenvaluecalculations,andthenincludedin the SIMULINK airframe/landinggear

modelfor transientresponsecalculations.

Thenoseandmain landing gear dynamics models consist of a simple mass-spring-damper

system excited by the ground-induced motion of the support point as shown Fig. 15.

Nonlinear spring and damping gear forces are modeled as a function of stroke using the

empirical curves shown in Figures 16 and 17. Data points used as a basis for the faired

curves are denoted by open circles. Stiction and friction forces in the oleo strut mechanism

have been neglected. The moving mass of the gear is represented by a lumped mass and a

nonlinear spring in contact with the ground represents fire stiffness. Tires are represented

having a single point of contact with the ground, therefore no tire footprint information is

used. The tire model for the main gear is based on the load-deflection characteristics of the

Michelin 50X20-20 radial belted main-gear tire for the Boeing 777 transport aircraft. Nose

gear tire stiffness characteristics are based on H37X14-15 tires. Figure 18 shows the load

versus deflection curves for the nose and main gear tires. These curves represent the sum

of parallel springs, 2 springs for two nose gear tires, and six springs to represent the six

tires on each main gear. The damping characteristics of the tires were not available.

4.1 Runway Model

Figure 19 shows the elevation-versus-distance profile for a 3100 ft runway section in San

Francisco which is commonly used by the FAA for airplane certification. The runway

elevation is measured with respect to sea level. A 10,000 ft long runway profile is

constructed for the simulations by appending the 3100 ft runway section every 3100 ft

resulting in a periodic profile. This runway profile is the only one used in this

investigation. HSCT runway x-coordinate time histories (runway x-coordinate defined

along the length of the runway) in conjunction with the 10,000 ft San Francisco runway

profile are used to generate elevation-versus-time histories for various ground operations.

As an example, runway x-coordinate time histories for a rejected takeoff (RTO) simulation
areshownatthetopof Fig.20with theresultingRTOrunwayelevationtimehistory at the

bottom.

5. System Integration / Numerical Simulations

SIMULINK, a computer simulation program, was used to combine and integrate the

airframe/landing gear systems described in the previous sections. The system dynamics

described in Eqs (3-5) are represented in SIMULINK blocks depicted in Figure 21.

Blocks labeled "nose" and "main" contain tabulated information for the nonlinear response

of the main and nose landing gears. Displacements and velocities of the airframe at the gear

locations and the runway elevations are input to these blocks and gear forces are output

from the blocks. These gear forces are then input into the block labeled "State-Space" and

airframe displacements and velocities are the output. The SIMULINK diagram shows the

interconnection between the different systems. The additional blocks shown are for

decomposing vectors (Demux- turns vectors into scalar quantities) or assembling (Mux)

vectors.

Since the equations of motions are nonlinear, the first step in the solution process is to

determine the equilibrium states. Equilibrium states are computed when the rate of change

of system states are zero after all forces have been applied. Initially, the airframe weight is

applied to the landing gear producing an equilibrium state in which the landing gears are

compressed. All further simulation results are generated about this equilibrium state.

Aircraft responses are displayed at thirteen locations on the aircraft as indicated in Fig 22.

6. Simulation Results

6.1 Aircraft response during ground operations

The mathematical model described above has been used to simulate the HSCT response

during ground operations on a San Francisco runway. Ground operations simulated are

taxiing, rejected takeoff, and landing. Aerodynamic lift forces have been neglected for all

cases.
6.2 Taxiing simulations

Taxiing simulations were conducted for a forward speed of 44 fffsec (30 knots). Figures 23

and 24 show the vertical and angular response at the cockpit location for a time interval of

80 seconds. Peak half-amplitude vertical displacements at the cockpit with respect to the

runway profile range from 0 to 3.5 inches with peak accelerations ranging from 0 to 0.38

g's. Pitch angular displacements of +0.24 degrees are also observed at the cockpit

location. The rigid-body heave and pitching motions as well as contributions from higher

frequency modes can easily be seen on the time histories. Figures 25 and 26 show the

maximum vertical displacements, normalized with respect to the runway prof'de, and

accelerations at the 13 sensor locations On the airframe. Although the maximum

displacement and acceleration on the fuselage occur at the cockpit location, the

displacement and acceleration at the mid and aft sections of the fuselage also show

considerable response.

6.3 Rejected Takeoff simulations

A rejected takeoff (RTO) scenario was chosen over a normal takeoff because it is

considered the worse-case scenario in terms of pilot workload. For the RTO simulation the

aircraft accelerates from 0 to a maximum of 170 knots in 35 seconds, an engine failure or

some other aircraft malfunction then causes the pilot to abort the takeoff and decelerate to

zero speed in 20 sec. The forward speed profde used for the RTO simulation is shown in

Fig. 27. For the given runway elevation profile aircraft responses have been computed at

all sensor locations described previously. Response time histories at the cockpit location

are presented in Figures 28 and 29. Vertical displacements at the cockpit reached a

maximum of 6.5 inches (half-amplitude relative to the runway profile) with peak

accelerations of 1.4 g's. Pitch angular displacements of +0.35 degrees are obtained at the

cockpit with angular accelerations ranging from 0 to 70 deg/sec _. Again, the participation

of the rigid-body heave and pitch modes and flexible modes to the total response is evident

in the time histories. Maximum displacements and accelerations over the airframe, Fig. 30-

31, are all of considerable magnitude. Maximum response occurs at the wing tip (location

11).

A separate RTO simulation using only rigid-body modes of the airframe was conducted to

assess the contribution of the rigid body modes to the total response. Results showed that

9
60 to 70% of thetotalresponseis dueto rigid-bodymotion and30to 40% is due to the

elasticresponseof theairframe.

6.4 Landing simulations

Landing simulations of the HSCT were conducted at a landing weight condition of 388,584

lbf, mass case M14, for a time interval of 20 sec after nose gear touch down. The forward

speed prof'de for the simulation is shown in Fig 32. The simulation starts with the aircraft

on the ground at a maximum forward speed of 120 knots and continues with the aircraft

decelerating to a complete stop. Aerodynamic lift effects are neglected. Results are

summarized in Figures 33 through 36. Heave and pitch motions are dominated by the lowfrequency aircraft modes, with maximum vertical displacements relative to the runway of

4.3 inches and a maximum rotation of +0.25 degrees. Peak acceleration at the cockpit

reached a maximum of 1.2 g's. Again, displacements and accelerations at other locations

on the airframe are all of considerable magnitude but in this case the cockpit had the highest

values.

6.5 Frequency Comparison of the Various Ground Operations

The Power Spectral Density function (PSD) was computed from the acceleration time

history at the cockpit location and RMS values calculated at various frequency bandwidth

intervals in the frequency range from 0 to 22.6 Hz. Figure 37 shows a summary of the

cockpit squared RMS acceleration for all three ground operations. Based on the squared

RMS one can estimate the RMS responses at a given frequency by computing the square

root of the plotted value. During taxiing the rigid body vertical and pitching motions and

the first two flexible symmetric and antisymmetric airframe modes are the largest

contributors to the RMS response. Cockpit acceleration levels for the RTO case show

RMS acceleration levels in excess of 0.28 g's around 2 Hz which coincide with some of

the airframe flexible modes. The contribution of the rigid and flexible modes in the

frequency range of 0.7071 to 1.4104 is also noticeable. Cockpit acceleration levels for the

landing case showed RMS acceleration levels of about 0.14 g's around 2 Hz.

10
6.6 Human Response to Vibration

The results of some early studies on human tolerance to vibrations which were presented

in Ref. [12] are reproduced here in Figure 38. Note that levels of 0.5 g's are considered

intolerable in the low-frequency range between 1 and 5 Hz. The HSCT acceleration levels

at the cockpit during taxiing, RTO, and landing discussed in the previous sections are all

within the intolerable range. Pilot-in-the-loop simulator studies made by the Boeing Co.

have shown that vibration amplitudes exceeding 2 inches at low frequencies are considered

unacceptable. A need for active vibration suppression is evident based on this results.

7. Concluding Remarks

Numerical simulation of the Boeing High Speed Civil Transport 1080-920STR Model E

configuration during taxiing, take-off, and landing operations have been presented. Linear

finite element models of the airframe are used and combined with nonlinear landing gear

models to provide a simulation model which is used to examine dynamic response to

ground input conditions. A commercial computer simulation program was used to

numerically integrate the equations.

Simulation results showed vertical displacements and RMS acceleration levels at the cockpit

location and passenger cabin exceeding safe acceptable human response levels. Since the

aircraft response is dominated by the heave and pitch rigid-body modes and the first lowfrequency flexible modes, some type of actively or semi-actively controlled landing gear

should be employed to improve the ride quality of the aircraft during ground operations,

Ref. [11].

8. References

1-Mitchell, C.G.B., Some Measured and Calculated Effects of Runway Unevenness on a

Su_rsonic Transport Aircraft. Symposium on Nonlinear Dynamics, Loughborough

University of Technology, March 1972.

2- Irwin, K.S. and Andrews, W.H., Summary. of XB-70 Airplane Cockpit Environmental

Data. NASA TN D-5449, October, 1969.

11
3- Shepherd,A., Catt, T. and Cowling, D., The Simulation of Aircraft Landing Gear

_. International Council of the Aeronautical Sciences, Beijing, People's Republic

of China, pp. 21-25 September, 1992.

4- Doyle, G.R. Jr., A Review of Computer Simulations for Aircraft -Surface Dynamics, I.

Aircraft, Vol. 23, No. 4, April 1986.

5- $IMULINK User's Guide, August 1995 Revision, The MathWorks Inc., Natick, Mass.

6- Dawdy, J. R., Dornfeld, G.M., Phillips, B.A., High Speed Civil Transport Reference

H-Cycle 1 Simulation Database, NASA Contract NAS1-19360, Task Assignment No. 49.

7- ELFINI Basic User Guide, Vertsion 6.4, Avions Marcel Dassault-Brequet Aviation,

June 1990.

8- MSC/NASTRAN Basic Dynamic Analysis User's Guide,V68, First printing December

1993, The MacNeal-Schwendler Corporation, Los Angeles, California.

9- Hurty W.C. and Rubinstein, M.F., Dynamics of Structures, 2nd Edition, Prentice Hall,

Inc., Englewood Cliffs, N.J.

10- Mitchell, P.M., Advance Finite Element Weight Estimation Process on the High S_ed

.C,,j._L.T.I_I!,_. Society of Allied Weight Engineers, Inc.. SAWE Paper No.2169.

Category No. 23. May 1993.

11- Catt, T., Cowling, D. and Shepherd, A., A_tive Landing Gear Control for Improved

Ride Ouality During Aircraft Ground Roll. AGARD Specialists Meeting on Smart

Structures for Aircraft and Spacecraft, AGARD CP531, Lindau Germany, 1992.

12- Goldman, D.E., and von Gierke, H.E., Effects of Shock and Vibration on Man,

Shock and Vibration Handbook, Vol. 3, Chapter 44, 1961.

12
Table 1.HSCT model sections and offsets

Boeing Num.

E14

E03

E04

E05

E06

E07

El2

El3

E08

E09

E01

El0

Ell

E02

Section

Description

nosecone

fwd body

mid body

aftbody

vertical tail

horizontaltail

rudder

elevator

inboardcng

outboard eng

inboardwing

inb. controls

outb. controls

outboard wing

Section ID

nc

fb

mb

ab

vt

ht

rud

el

ie

oe

iw

ic

OC

OW

Base

Node

0

1000

50O0

10000

15000

16000

17000

18000

20000

22000

25000

30000

32000

35000

Base

Elem

0

1000

5000

10000

15000

16000

17000

18000

20000

22000

25000

30000

32000

35000

Base

Prop

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

Base

Mat.

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

Table 2. HSCT sample component kinetic energy summary table

Section

E14-nosecone

E03-fwd body

E04-mid body

E05-aft body

E06-vertical tail

E07-horizontal tail

E12-rudder

E13-elevator

E08-inboard eng

E09-outboard eng

E01-inboard wing

E10-inb. controls

E 11-outb. controls

E02-outboard wing

Total energy (%)

Mode

4

1.3 Hz

Mode

5

2.0 Hz

Mode

6

2.6 Hz

Mode

7

2.7 Hz

Mode

8

3.1 Hz

.3 0.0

50.1 1.4

2.1 0.8

0.1

6.2

4.0

0.0

0.1

0.1

0.1

5.6

3.6

13.2 12.6

2.7 2.9

8.5 10.6

0.8 0.9

1.7 2.5

1.4 2.3

1.4 24.7

17.3

0.2

0.1

0.3

6.9

0.3

7.2

26.8

100.0

5.6

1.6

7.2

0.5

2.1

9.2

3.5

18.4

0.5

9.7

31.3

0.1

0.0

0.2

0.0

0.0

97.6

0.1

0.6

0.0

0.3

0.8

0.3

0.0

0.2

0.0

0.1

4.1

49.5

16.5

0.3

4.8

14.8

100.0 100.0 100.0 100.0

Mode

9

3.1 Hz

0.0

2.2

1.4

0.1

0.0

0.1

0.0

0.0

1.0

88.3

6.3

0.1

0.1

0.3

100.0

13
Table3. HSCT1080-892Landinggearweights

NoseLandingGear

Wheels

Tires

Air

Dragstrut

Sidestrut

Shockstrut

Attachmentfittings

Miscellaneous

Nosegearsteering

Nosegearretraction

Emergencysteering

Weight

(INside)

101.1

178.4

7.3

67.2

38.2

375.7

12.6

15.0

145.0

87.5

12.1

Total 1040.0

Main Landing Gear

Wheels

Tires

Air

Brakes

Drag slruts

Side struts

Trucks

Oleos

Axles

Torsion links

Oleo fluid

Attachment fittings

Truck positioners

Miscellaneous

Retraction systems

Brake operating system

Emergency extension

Elec. operating mech.

Weight (Ib/side)

334.9

448.8

22.2

490.8

464.4

73.3

210.7

833.1

187.6

105.6

50.8

286.6

51.9

45.6

257.1

57.0

19.5

21.9

Total 3962.0

Note : These weights are for a halfmodel representation of the airplane

14
Figure 1. High Speed Civil Transport (aft tail/four engine configuration)

:m

Figure 2. HSCT Finite Element (symmetrical right-halO

15
0

L_

CS_

L_

16
Hz

13.5 Hz

13.o Hz

11.7 Hz

I1.1 Hz

_10.2 HZ

9.4 HZ

8.4 Hz

6,5 HZ

5.3 Hz

-3.8 Hz

Hz

Hz

1.3 Hz

m90-1001

m80-90 I

D70.80 I

1160-70 I

1150-60 I

1140.50 I

030-40 I

[320-30 I

1110-20 I

II0.10 I

a) Symmetric boundary conditions

10.7 Hz

10.1 Hz

9.8 Hz

8.5 Hz

7.9 Hz

6.2 Hz

Hz

2.0 Hz

0.0 Hz

0.o Hz

b) Antisymmetric boundary conditions

Figure 4. Modal kinetic energy data, MO5

17
d

Figure 5. Mode 4, f=1.308 Hz, MO5 symmetric

f=1.2703 Hz, M14 symmetric

Figure 6. Mode 6, f=2.641 Hz, MO5 symmetric

f=2.6878 Hz, M14 symmetric

18
Figure7. Mode 11,f=4.736Hz,MO5 symmetric

f=4.721Hz, M14 symmetric

Figure8. Mode 13,f=6.218Hz, MO5 symmetric

f=6.674Hz, M14 symmetric

19
Figure 9. Mode 14, f=6.546 Hz, MO5 symmetric

no equivalent, M14

Figure 10. Mode 4, f=1.555 Hz, MO5 antisymmetric

f=1.412 Hz, M14 antisymmetric

20
Figure 11. Mode5, f=2.035Hz, MO5 antisymmetric

f=2.129Hz, M 14antisymmetric

Figure 12. Mode 6, f=2.146Hz, MO5 antisymmetric

noequivalent,M14

21
Figure 13. Mode 10,f=3.545Hz, MO5 antisymmetric

f=3.650Hz, M14 antisymmetric

22
16R

I N2273

N2272

N2275 I N2271

12 ft

Figure 14. Nose gear structural 'stick' model

Landing gear

damper

!

Ground input

Figure 15. Landing gear dynamic model

23
5_x105

Nose gear

vertical spring

force (lbf)

4

3

2

1

0- -.- v O

-1 I ! ! ....! I ! I

-25 -20 -'15 -10 -5 0 5 10

Gear stroke (inches)

I

15

8 x105

Main gear

vertical spring

force (lbf)

6

4

2

v

m

-2 ! I I ! I I

-25 -20 -15 -10 -5 0 5

Gear stroke (inches)

O

I

10

!

15

Figure 16. Nose and main gear load-stroke curves

24
Nose gear

damping

coefficient

lb/in^2/sec^2

80

7O

60

50

40

30

20

10

0

-25 -20 -15 -10 -5 0

Vertical stroke (inches)

60 -

Main gear

damping

coefficient

Ib/inA2/sec^2

50

40

30

20

10

I , I I I

-20 -15 -10 -5 0

Vertical stroke (inches)

Figure 17. Nose and Main gear damping force coefficient curves

25
Nose gear tire

spring force

(Ibf)

5

1.4 xlO

1.2 _

.1 --

.8 --

.6 --

.4 --

.2 --

0 -

-°2

-10

I I I I I

-8 -6 -4 -2 0

Tire deflection (inches)

Main gear tire

spring force

0bf)

6

5-

4-

3-

2-

1-

0-

-1

-8

5

xlO

I , I I I ,,, I I I I

-7 -6 -5 -4 -3 -2 -1 0

Tire deflection (inches)

Figure 18. Nose and main gear fires spring curves

26
Runway

elevation

(inches)

10

5

0

-5

m

I

3100 ft section

=..._1

-10 I

0 2000

I

I

i

I

I I I

4000 6000

I I

8000 10000

Runway distance (ft)

Figure 19. San Francisco runway elevation with respect to sea level profile

27
x-coordinate

fit)

10000 -

8000

6000

4000

2000

0

0

I

10 20 30 40 50 60

time (sec)

RTO runway x-coordinate time history

Runway

elevation

(inches)

4

0

-4

-8-

0

I I I I I I

10 20 30 40 50 60

time (sex)

RTO runway elevation time history

Figure 20. Rejected takeoff time histories

28
i--mmm

o

lu

cp_

Vm4

29
0

0

e,i

3O
Heaveat

cockpit

(inches)

I0

0

-5

-10 0

m

I

t_ _ Resp°nse I

_/_ _ -----Runway I I_

I I I I I I I

10 20 30 40 50 60 70 80

time (see)

Heave accel.

at cockpit

(g's)

20 30 40 50 60 70 80

time (see)

Figure 23. Taxiing vertical response at cockpit location

31
0.3

0.2

0.1

Pitchrotation

atcockpit 0

(degrees)

-0.1

-0.2

I I I I I I I I

-0"30 I0 20 30 40 50 60 70 80

time (sec)

Pitch accel.

at cockpit

(deg/sec^2)

20

15

10

5

'0

-5

-10

-15

10 20 30 -20

0 40 50 60

time (sec)

70 80

Figure 24. Taxiing pitch response at cockpit location

32
3.5

3

2.5

Max. 2

Vertical

disp.

(inches) 1.5

0.5

0

1 2 3 4 5 6 7 8 9 10 11 12 13

Sensorlocation

Figure25. Taxiingmaximumverticaldisplacementsat 13sensorlocations

Max.

Vertical

accel.

(g's)

°7r

0.6

0.5

0.4

0.3

0.2

0.1

0

1 2 3 4 5 6 7 8 9 10 11 12 13

Sensor location

Figure 26. Taxiing maximum vertical accelerations at 13 sensor locations

33
Forward

speed

(kts)

200

150

100

50

0

0

! I I i

10 20 30 40 50 60

time (sec)

Figure 27. RTO forward speed profile

34
Heaveat

cockpit

(inches)

-5

-10

-15

15F

10

5

0

n

I I I

0 10 20 30

Response

Runway

time (sec)

I I I

40 50 60

1.5

1

0.5

Heave accel.

at cockpit 0

(g's)

-0.5

-1 -

-1.5 I

0 10 20

I I I

30 40 50

time (sec)

I

60

Figure 28. RTO vertical response at cockpit location

35
0.5

Pitchrotation

at cockpit 0

(degrees)

-0.5 ] !

0 10 20

I I I I

30 40 50 60

time (sec)

100

50

Pitch accel.

at cockpit 0

(deg/sec^2)

-50

-100

0

I I I I I I

10 20 30 40 50 60

time (sec)

Figure 29. RTO pitch response at cockpit location

36
7

6

Max. 4

Vertical

disp.

(inches) 3

0

Figure30.

1 2 3 4 5 6 7 8 9 10 11 12 13

Sensor location

RTO maximum vertical displacement at 13 sensor locations

m

3.5 --

3-

2.5-

Max.

vertical

accel. 2 -

(g's)

1.5-

0.5

0

1 2 3 4 5 6 7 8 9 10 11 12

Sensor location

13

Figure 31. RTO maximum vertical accelerations at 13 sensor locations

37
Forward

speed

(kts)

150

100

50

0

0

Nose gear

touch down

I

5 10 15 20 25 30

time (sec)

Figure 32. Landing forward speed prof'de

38
Heave at

cockpit

(inches)

8

6

4

2

0

-2

-4

-6

-8

-- L_ A/q A [ ResponseI

t Ai[\ l- -- -Runway

vt _ -v - " V

I

\\

- \

I I I I

0 5 10 15 20

time (sec)

Heave accel.

at cockpit

(g's)

0.5

0

-0.5

-1

m

I I I

5 10 15

time (sec)

I

20

Figure 33. Landing vertical response at cockpit location

39
Pitchrotation

at cockpit

(degrees)

0.3 --

0.2

0.1

0

-0.1 -

-0.2 -

-0.3

0

!

m

l1 h J_

Jw_ 1

! I

10 15

time (sec)

I

20

Pitch accel.

at cockpit

(deg/sec^2)

lO0[-

50

o

-50

-lO0 0 5 10 15

time (sec)

I

20

Figure 34. Landing pitch response at cockpit location

40
Max. 3

Vertical

disp.

(inches) 2

0

1 2 3 4 5 6 7 8 9 10 11 12 13

Sensorlocation

Figure35. Landingmaximumverticaldisplacementsat 13sensorlocations

1.2

0.8

Max.

vertical

accel. O. 6

(g's)

0.4

0.2

0

1 2 3 4 5 6 7 8 9 10 11 12 13

Sensor location

Figure 36. Landing maximum vertical accelerations at 13 sensor locations

41
RMS

acceleration

squared

(g's^2)

0.08

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0

[] Taxiing

[] RTO

[] Landm_

1 2 4 8 16

Central frequency (Hz)

Figure 37. HSCT response at cockpit location during ground operations on the San Francisco runway

Peak acceleration

(g's)

1.0

0.10

+._ ( Typical )

m

Intolerable

Unpleasant

0.01

0.001 I I

1 2 5 10 20 50 100

Frequency (Hz)

Threshold of

preception

Figure 38. Human subjective response to vibration

42

Form Approved

REPORT DOCUMENTATION PAGE OMBNo.0704-0188

]Public reportingburden|or thiscollectionof information is estimated1oaverage1 hourper response,includingthe timeforrev4ewinginstructions,searchingexistingdata sources,

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1. AGENCY USE ONLY (Leave blank) 12. REPORT DATE 3. REPORT TYPE AND DATES COVERED

I

December 1999 Technical Memorandum

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Taxiing, Take-Off, and Landing Simulation of the High Speed Civil

-v,_'rrans"o"Aircraft WU 537-06-22

6. AUTHOR(S)

Mercedes C. Reaves and Lucas G. Horta

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center

Hampton, VA 23681-2199

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

8. PERFORMING ORGANIZATION

REPORT NUMBER

L-17901

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA/TM- 1999-209531

11. SUPPLEMENTARY NOTES

12a. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited

Subject Category 05 Distribution: Nonstandard

Availability: NASA CASI (301) 621-0390

12b. DISTRIBUTION CODE

13. ABSTRACT (Max/mum 200 words)

The aircraft industry jointly with NASA is studying enabling technologies for higher speed, longer range aircraft

configurations. Higher speeds, higher temperatures, and aerodynamics are driving these newer aircraft configurations towards long, slender, flexible fuselages. Aircraft response during ground operations, although often overlooked, is a concern due to the increased fuselage flexibility. This paper discusses modeling and simulation of the

High Speed Civil Transport aircraft during taxiing, take-off, and landing. Finite element models of the airframe for

various configurations are used and combined with nonlinear landing gear models to provide a simulation tool to

study responses to different ground input conditions. A commercial computer simulation program is used to

numerically integrate the equations of motion and to compute estimates of the responses using an existing runway

profile. Results show aircraft responses exceeding safe acceptable human response levels.

14. SUBJECT TERMS

High-Speed Civil Transport; High-Speed Supersonic Transport; Supersonic transport;

Simulation; Cockpit vibrations; Finite elements

17. SECURITY CLASSIFICATION

OF REPORT

Unclassified

II

NSN 7540-01-280-5500

18. SECURITY CLASSIFICATION

OF THIS PAGE

Unclassified

19. SECURITY CLASSIFICATION

OF ABSTRACT

Unclassified

15. NUMBER OF PAGES

48

16. PRICE CODE

A03

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