March 2009 

NASA/TM-2009-215701 

Mars Aerial Regional-Scale Environmental 

Survey (ARES) Coordinate Systems Definitions 

and Transformations 

Christopher A. Kuhl 

Langley Research Center, Hampton, Virginia 
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March 2009 

NASA/TM-2009-215701 

Mars Aerial Regional-Scale Environmental 

Survey (ARES) Coordinate Systems Definitions 

and Transformations 

Christopher A. Kuhl 

Langley Research Center, Hampton, Virginia 
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757-5802 

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constitute an official endorsement, either expressed or implied, by the National Aeronautics and Space 

Administration. 
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TABLE OF CONTENTS

TABLE OF CONTENTS .......................................................................................................................... i

TABLE OF FIGURES.............................................................................................................................. ii

1.0 Introduction....................................................................................................................................1

2.0 ARES Primary Coordinate Systems ............................................................................................2

2.1 Airplane Design Axis System......................................................................................................3 

2.2 Aerodynamic Database (ADB) Axis System...............................................................................4 

2.3 Quarter Scale Wind Tunnel Model Axis System.........................................................................4 

2.4 Airplane Body Axis System.........................................................................................................5 

2.5 Coordinates for Moveable Surfaces.............................................................................................6 

2.5.1 Left Wing / Right Wing Axis Systems ................................................................................6 

2.5.2 Tail Axis System..................................................................................................................7 

2.5.3 Angles sign convention........................................................................................................8 

2.6 Local Axis Systems......................................................................................................................8 

2.7 Aeroshell Axis System.................................................................................................................9 

3.0 Spacecraft (Cruise Stage) Axis System ......................................................................................10

4.0 Launch Vehicle (Delta 2925) Axis System .................................................................................11

4.1 Launch Vehicle Axis System.....................................................................................................11 

4.2 Payload Static Envelope Reference ...........................................................................................12 

5.0 ARES Transparent Coordinate Systems ...................................................................................13

6.0 Primary Coordinate Systems Comparisons ..............................................................................14

7.0 Transformation matrices.............................................................................................................15

7.1 Definition: Local to Global Axis System...................................................................................15 

7.2 Aerodynamic Database Axis System to Airplane Design Axis System....................................16 

7.3 Left Wing Axis System to Airplane Design Axis System.........................................................16 

7.4 Right Wing Axis System to Airplane Design Axis System.......................................................16 

7.5 Tail Axis System to Airplane Design Axis System...................................................................17 

7.6 Wind Tunnel Model Axis System to Airplane Design Axis System.........................................17 

7.7 Aeroshell Axis System to Airplane Design Axis System..........................................................17 

7.8 Spacecraft Axis System to Airplane Design Axis System.........................................................18 

7.9 Spacecraft Axis System to Aeroshell Axis System ...................................................................18 

7.10 Launch Vehicle axis system to Aeroshell aXIS sYSTEM.........................................................18 

7.11 Airplane Body Axis System to Airplane Design Axis System..................................................18 

8.0 APPENDIX A: Airplane Nose Location ...................................................................................19

9.0 APPENDIX B: EXCEL Tool for Coordinate System Transformations................................20
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TABLE OF FIGURES

Figure 1. ARES Coordinate Systems and Interdependency .......................................................................2 

Figure 2. Airplane Design Axis System .....................................................................................................3 

Figure 3. Aerodynamic Data Base Axis System.........................................................................................4 

Figure 4. Body Axis System convention ....................................................................................................5 

Figure 5. Airplane folding sections Axis Systems......................................................................................6 

Figure 6. Left Hand Wing Hinge Axis System...........................................................................................6 

Figure 7. Folding sections angles sign convention .....................................................................................7 

Figure 8. Left Hand Wing Stowed configuration angles ............................................................................8 

Figure 9. Aeroshell Axis System ................................................................................................................9 

Figure 10. Aeroshell Axis Relative to Airplane Design Axis.....................................................................9 

Figure 11. Spacecraft Axis System...........................................................................................................10 

Figure 12. Delta 2925 Vehicle Axes.........................................................................................................11 

Figure 13. Payload Static Envelope 2.9-m Fairing, Three-Stage Configuration......................................12 

Figure 14. Primary Coordinate Systems Comparison...............................................................................14 

Figure 15. EXCEL Tool for Coordinate Transformation .........................................................................20
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1.0 INTRODUCTION 

This document defines the formal coordinate systems for the Aerial Regional-scale Environmental 

Survey (ARES) flight systems, subsystems, and assemblies. The purpose of a formal coordinate 

systems document is to ensure the reliability and compatibility of the various ARES flight systems 

design and analyses activities. The systems specified herein apply to the ARES Flight Spacecraft, 

including the Cruise Stage, the Entry, Descent, & Landing (EDL) system, the Atmospheric Flight 

System (AFS). 

The coordinate systems are direct (right-handed) orthogonal axis system. All references to aircraft and 

spacecraft coordinates are made using millimeters, with indication of dimensions in inches in brackets 

[]. 
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2.0 ARES PRIMARY COORDINATE SYSTEMS 

ARES has multiple coordinate systems in use for design and analysis purposes. Several of these coordinate 

systems are interdependent as shown in Fig X. The primary coordinate system for interdisciplinary 

communication is through the Airplane Design Axis System, which is ultimately transposed to the Aeroshell then 

the Launch Vehicle coordinates for reference. 

X Y X Y

Z Z

Wing < 0 φ RH Wing < 0

LH: Left Hand 

RH: Right Hand 

Y

X

Y

X

Right Hand Wing 

Axis System

Left Hand Wing 

Axis System

Y

Tail 

Axis System 

X

X

Z

θ Tail < 0 φ

Wind Tunnel Model 

Balance Moment Center

Aerodynamic Data Base 

Reference Point 

Xa

Za

X

Z

Chord line of the kink airfoil

ADB Axis System (Xa, Ya, Za) 

Design Axis System (X, Y, Z) 

Cg

Zb

Yb

Xb

Figure 1. ARES Coordinate Systems and Interdependency 
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2.1 AIRPLANE DESIGN AXIS SYSTEM 

The ARES Airplane Design Axis System is used for all engineering drawings, CAD models, mechanical and 

thermal analysis results, tracking mass properties, in the manufacturing of aircraft structure, mechanical systems. 

It is common practice to name the X, Y and Z axis respectively Fuselage Station (FS), Butt Line (BL) and Water 

Line (WL). For reference, the Airplane nose is located at FS(x) = 143.334 mm and WL(z) = 194.505 mm. The 

Airplane Design Axis is defined by: 

X-axis: orthogonal to the main spar forward face, positive towards the aft 

Y-axis: orthogonal to the Airplane symmetry plane, positive towards the right wing 

Z-axis: completes a right hand system (positive out the top of the airplane) 

Figure 2 shows the axis origin located at: 

X0: 1311.4 mm in front of the Main Spar tooling face 

Y0: on the Airplane symmetry plane 

Z0: 116.662 mm below the intersection of the main spar forward face and OML at Y0

Figure 2. Airplane Design Axis System 
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2.2 AERODYNAMIC DATABASE (ADB) AXIS SYSTEM 

The Airplane’s aerodynamic data sets are contained in the Aerodynamic Data Base (ADB) established by NASA 

LaRC. The Axis System used in the Aerodynamic Data Base, subscript a, is defined by: 

Xa-axis: aligned with the chord line of the kink airfoil, positive forward 

Ya-axis: orthogonal to the Airplane symmetry plane, positive out the right wing 

Za-axis: completes a right hand system, positive down 

Figure 3 shows the ADB Origin is located along with Design Axis BL, -41.6 mm below the Design Axis Origin 

WL, and +10.4457 mm ahead of the Design Axis Origin FS pitched 177.925°. The ADB Axis Origin relative to 

the Airplane Design Axis Origin is given by: 

For reference, the Airplane nose is located at xa = -141.35 mm, ya = 0 mm, za = -231.1386 mm. The 

coordinates of Aerodynamic Data Base Reference Point in the ADB Axis System are: xa = -1266.9 mm, ya = 0.0 

and za = -313.1 mm. 

Figure 3. Aerodynamic Data Base Axis System 

(ABD Axis Origin shown in blue) 

2.3 QUARTER SCALE WIND TUNNEL MODEL AXIS SYSTEM 

The Wind Tunnel Model is a quarter scale (1/4) model of the ARES Airplane used for wind tunnel 

testing. The aerodynamic forces and moments are measured at the Balance Moment Center (Figure 3). 

The coordinates of the Balance Moment Center in the Wind Tunnel Model Axis System are: 

x = 234.315 mm, y = 0.0 mm, z = 65.8876 mm 

The Wind Tunnel Model Axis Origin Relative to Airplane Design Axis Origin is given by: 

Translation: 

Fuselage Station (x) = 0.28857 mm 

Butt Line (y) = 0 mm 

Water Line (z) = -6.452435 mm 

Rotation: 

Yaw (ψ) = 0° 

Pitch (θ) = 0 ° 

Roll (φ) = 0° 

Translation: 

Fuselage Station (x) = 10.4457 mm 

Butt Line (y) = 0 mm 

Water Line (z) = -41.6 mm 

Rotation: 

Yaw (ψ) = 0° 

Pitch (θ) = 177.925° 

Roll (φ) = 0° 
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2.4 AIRPLANE BODY AXIS SYSTEM 

The Body Axis System convention is used for aircraft-related technical communications regarding Aerodynamics, 

Flight Controls, Dynamics, Flight Software, and Modeling discussions. 

The Body Axis System, subscript b, is the Aerodynamic Data Base (ADB) Axis System translated to the Airplane 

Center of Gravity. The Center of Gravity is chosen at the state where the airplane has a full propellant load with 

the Mass Spectrometer inlet cover in place (the Mass Spectrometer cover is ejected after extraction and prior to 

flight). 

The Airplane Body Axis System, shown in Error! Reference source not found., is defined by: 

Xb-axis: aligned with the chord line of the kink airfoil, positive forward 

Yb-axis: orthogonal to the Airplane symmetry plane, positive out the right wing 

Zb-axis: completes a right hand system, positive down 

The axis Origin, located at the airplane center of gravity, is: 

Airplane Center of Gravity: To Be Chosen during Phase A Study. 

For purposes of analyses, The Airplane velocity components with respect to the Body Axis System shall follow 

the following convention: 

U velocity along the axis Xb

V velocity along the axis Yb

W velocity along the axis Zb

p roll rate along the axis Xb (positive to the right) 

q pitch rate along the axis Yb (positive nose upward) 

r yaw rate along the axis Zb (positive nose right) 

Figure 4. Body Axis System convention 

Body axis system (Xb, Yb, Zb)
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2.5 COORDINATES FOR MOVEABLE SURFACES 

The master geometry CAD model is used for definition of the movable control surfaces Axis Systems. The Flight 

Control Unit specification [TBD] shall be used for convention of the movable control surfaces deflections. 

2.5.1 Left Wing / Right Wing Axis Systems 

Aeroshell packaging requires the wings and the tail of the Airplane to be folded to accommodate the space 

allocated to the Airplane. An Axis System is defined for each folding section: Left Wing, Right Wing and Tail. 

The Right Wing is defined by the wing located on the positive Y-Axis of the Airplane Design Axis System (see 

Section 1.1). 

The Left Wing/Right Wing Axis System, shown in Figure 5, is defined by: 

X-axis: along the wings hinge axis, positive forward 

Wing Y- and Z-axes define planes that intersect the Airplane symmetry plane through a common line. 

Z-axis: positive down 

The direction of the X-axis is chosen to ease transformation to the ARES Airplane Body Axis System. 

The axis origin, X0, is located at the Main Hinge center (See ). 

The Left Wing Axis Origin Location Relative to Airplane Design Axis origin is given by: 

Translation: 

Fuselage Station (x) = 1328.84 mm 

Butt Line (y) = -1119.02 mm 

Water Line (z) = 131.104 mm 

Rotation: 

Yaw (ψ) = 23.1° 

Pitch (θ) = 177.875° 

Roll (φ) = 0°

Y

X

X

Y

Right Wing Axis 

System

Left Wing Axis 

System

0,0 X

Y

-23.1°

Figure 5. Airplane folding sections Axis 

Systems Figure 6. Left Hand Wing Hinge Axis System 
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The Right Wing Axis Origin Location Relative to Airplane Design Axis origin is given by: 

Translation: 

Fuselage Station (x) = 1328.84 mm 

Butt Line (y) = 1119.02 mm 

Water Line (z) = 131.104 mm 

Rotation: 

Yaw (ψ) = -23.1° 

Pitch (θ) = 177.875° 

Roll (φ) = 0°

2.5.2 Tail Axis System 

The Tail Axis System, shown in Figure 7, is defined by: 

X-axis: aligned with the ABD Axis System longitudinal axis.

Y-axis: along the tail hinge axis, also orthogonal to the Airplane symmetry plane 

Z-axis: completes a right hand system, positive down 

With the Origin located at: 

Y0: on the Airplane symmetry plane 

The Tail Axis Origin Location Relative to Airplane Design Axis origin is given by: 

Translation: 

Fuselage Station (x) =2383.97 mm 

Butt Line (y) = 0 mm 

Water Line (z) = 167.478 mm 

Rotation: 

Yaw (ψ) =0° 

Pitch (θ) = 177.925° 

Roll (φ) = 0°

Figure 7. Folding sections angles sign convention 
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2.5.3 Angles sign convention 

The following sign convention is used for the folding sections: 

- Deployed angles = 0o 

- Stowed angles < 0o, measured from the deployed configuration 

The Wings stowed configuration is composed of two rotations; the first one around the Main Hinge axis and the 

second one around the lower rocket pin axis (See Figure 8). 

Figure 8. Left Hand Wing Stowed configuration angles 

2.6 LOCAL AXIS SYSTEMS 

Local Axis Systems may be defined for each specific Airplane sections (i.e. Wings, Tail, etc.) and movable 

control surfaces. Preferably, the Local Axis Systems should be extracted from the master geometry CAD model. 

A local coordinate system for hardware and components that are position sensitive or where position must be 

tracked (i.e. science instruments, cameras, etc) will be recorded in this document. Components that will contain 

local axis systems include: Airplane Thrusters, IMU-MIMU, Radar Altimeter, Radar Altimeter Antenna, Radar 

Altimeter Absorber, Air Data System Probes, CAS Actuators and Resolvers, CAS Position Transducers, Fuel 

Load, Oxidizer Load, Helium Load, Magnetometers, Context Camera, Video Camera, Mass Spectrometer, 

Neutron Spectrometer, Entry Data System. 

φ LH Wing < 0

Lower rocket pin

Left Hand

Wing

to Fuselage 

φ LH Wing overtravel < 0 

-10° preload (typical) 
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2.7 AEROSHELL AXIS SYSTEM 

The Aeroshell Axis System, shown in Figure 9, is defined by: 

XA-axis: orthogonal to the Aeroshell centerline, in the plane of the AES aft leg, positive towards the 

Airplane nose 

YA-axis: completes a right hand system 

ZA-axis: on the Aeroshell centerline, positive towards heat shield tip 

The axis Origin is located at: 

XA0 is on the Aeroshell centerline 

YA0 is on the Aeroshell centerline 

ZA0 is on the top surface of the Backshell Interface Plate (BIP) 

The Aeroshell Axis Origin Location Relative to Airplane Design Axis origin (Figure 10) is given by: 

Translation: 

Fuselage Station (x) =1219.20 mm 

Butt Line (y) = 0 mm 

Water Line (z) = 816.9046 mm 

Rotation: 

Yaw (ψ) =180° 

Pitch (θ) = 0° 

Roll (φ) = 0°

Figure 9. Aeroshell Axis System 

Figure 10. Aeroshell Axis Relative to Airplane Design Axis 
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3.0 SPACECRAFT (CRUISE STAGE) AXIS SYSTEM 

The Spacecraft Axis System is nominally identical to the Aeroshell Axis System with the origin and positive 

direction of each axis identical (Figure 11). 

The Spacecraft Axis System is defined by: 

XA-axis: origin location and positive direction identical to Aeroshell Axis System, Section 1.1. 

YA-axis: completes a right hand system 

ZA-axis: identical to Aeroshell Axis System, Section 1.1. 

The Axis Origin is located at: 

XA0 is on the Aeroshell centerline 

YA0 is on the Aeroshell centerline 

ZA0 is on the top surface of the Backshell Interface Plate (BIP) 

The Spacecraft Axis Origin Location Relative to Airplane Design Axis origin is given by: 

Translation: 

Fuselage Station (x) =1219.20 mm 

Butt Line (y) = 0 mm 

Water Line (z) = 816.9046 mm 

Rotation: 

Yaw (ψ) =180° 

Pitch (θ) = 0° 

Roll (φ) = 0°

Figure 11. Spacecraft Axis System 
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4.0 LAUNCH VEHICLE (DELTA 2925) AXIS SYSTEM 

4.1 LAUNCH VEHICLE AXIS SYSTEM 

The Delta II 2925 vehicle axes are shown in Figure 12. The vehicle longitudinal axis is inline with the 

vehicle centerline. Axis II is on the downrange side and axis IV is on the up-range side of the vehicle. 

The vehicle pitches about the I and III axes. Positive pitch is defined by the rotation of the nose of the 

vehicle upward, toward axis IV. The vehicle yaws about axes II/IV. Positive yaw rotates the nose to the 

right, towards the I axis. The vehicle rolls about the centerline. Positive roll is clockwise rotation, 

looking forward (from axis I towards axis II). The third-stage spin table also spins in the same direction 

as the positive roll direction. 

[Delta II Payload Planner’s Guide – July 2006, The Boeing Corporation] 

Yaw 

+ZLV

Pitch 

+YLV

Roll 

+XLV

I

II

III

IV

CL

Figure 12. Delta 2925 Vehicle Axes 
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4.2 PAYLOAD STATIC ENVELOPE REFERENCE 

Location of the payload is referenced to Delta II 2925 Station Number notation is shown in Figure 13. Station 

number units are in inches and measured along the X-axis of the launch vehicle coordinate system (station 

number is positive in the –XLV direction, see Figure 12). The origin of the launch vehicle station number notation 

is near the top of the mobile service tower. 

The Launch Vehicle Axis Origin Location Relative to Aeroshell Axis origin is given by: 

Translation: 

Station 0 (-XLv=0) =4000 mm 

YLV = 0 mm 

ZLV = 0 mm 

Rotation: 

Yaw (ψ) =0° 

Pitch (θ) = -90° 

Roll (φ) = 0° BIP Located at Station 10160 (TBD)

Figure 13. Payload Static Envelope 2.9-m Fairing, Three-Stage 

Configuration 
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5.0 ARES TRANSPARENT COORDINATE SYSTEMS 

ARES design and analysis tools as well as testing facilities utilize internal coordinate systems to develop design 

and/or testing data. These coordinate systems are used only by the software or test facility and transparent to the 

rest of the ARES design activities. All results from these sources shall be transformed back into the ARES 

Design Axis System. Transparent coordinate systems within various analyses tools include; Post Body Frame 

Coordinate System, Pro-Engineer Reference Frame, and NASTRAN Reference Frame. 
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6.0 PRIMARY COORDINATE SYSTEMS COMPARISONS 

AES aft leg

ZA

XAS

XS/C

XAFS

ZS/c, ZAS, ZAFS

Figure 14. Primary Coordinate Systems Comparison 
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7.0 TRANSFORMATION MATRICES 

7.1 DEFINITION: LOCAL TO GLOBAL AXIS SYSTEM 

According to Euler's rotation theorem, any rotation may be described using three angles. The convention used 

here is the yaw-pitch-roll convention, where the first rotation is by an angle ψ about the Z-axis (yaw), the second 

is by an angle θ about the new Y-axis (pitch), and the third is by an angle φ about the new X-axis (roll). 

Any rotation can be given as a composition of rotations about three axes: 

- a rotation around Z

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎣

⎡ −

=

0 0 1

sin cos 0

cos sin 0

ψ ψ

ψ ψ

RZ

- a rotation around Y

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎣

⎡

−

=

θ θ

θ θ

sin 0 cos

0 1 0

cos 0 sin

RY

- a rotation around X

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎣

⎡

= −

φ φ

φ φ

0 sin cos

0 cos sin

1 0 0

RX

and thus can be represented by a 3 x 3 matrix: 

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎣

⎡

− ⋅ ⋅

⋅ ⋅ + ⋅ ⋅ − ⋅ + ⋅ ⋅

⋅ − ⋅ + ⋅ ⋅ ⋅ + ⋅ ⋅

=

θ θ φ θ φ

ψ θ ψ φ ψ θ φ ψ φ ψ θ φ

ψ θ ψ φ ψ θ φ ψ φ ψ θ φ

sin cos sin cos cos

sin cos cos cos sin sin sin cos sin sin sin cos

cos cos sin cos cos sin sin sin sin cos sin cos

R

Then the total transformation can be given as a composition of a rotation and a translation: 

⎥

⎦

⎤ ⎢

⎣

⎡ = 0 1

R T

M with 

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎣

⎡

=

Z

Y

X

T

T

T

T a translation in the three directions, X, Y and Z

To be consistent, the coordinates of a point A are altered according to: 

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎣

⎡

=

1

z

y

x

A

A

A

A

The Local Axis is the coordinate system on which the original data points exist and the Global Axis is the 

coordinate system to which those points will be transformed. Angles and Translations are referenced to the 

Global Axis system. The transformation given below transforms Local points to Global points by first rotating 

then translating the Global Axis to the Local Axis. 

( ) Aglobal _ referenced R T Alocal _ referenced = ⋅ ⋅ r r

To transform from Local to Global, the transformation becomes: 

( ) Alocal referenced R T Aglobal _ referenced

1

_ = ⋅ ⋅ r r −
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7.2 AERODYNAMIC DATABASE AXIS SYSTEM TO AIRPLANE DESIGN AXIS SYSTEM 

Note: Transformation matrix returns results relative to the Global Axis System: 

 Local = “Aerodynamic Database Axis System” 

 Global = “Airplane Design Axis System” 

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎣

⎡

− ⋅ =

0 0 0 1

sin 0 cos - 40.2156

0 1 0 0

cos 0 sin 10.1117

θ θ

θ θ

R T r r in millimeters 

with θ = 177.925o 

7.3 LEFT WING AXIS SYSTEM TO AIRPLANE DESIGN AXIS SYSTEM 

Note: Transformation matrix returns results relative to the Global Axis System: 

 Local = “Left Wing Axis System” 

 Global = “Airplane Design Axis System” 

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎣

⎡

−

⋅ ⋅

⋅ − ⋅

⋅ =

0 0 0 1

sin 0 cos 131.104

sin cos cos sin sin -1119.02

cos cos sin cos sin 1328.84

θ θ

ψ θ ψ ψ θ

ψ θ ψ ψ θ

R T r r millimeters 

with ψ = 23.1o and θ = 177.875o 

7.4 RIGHT WING AXIS SYSTEM TO AIRPLANE DESIGN AXIS SYSTEM 

Note: Transformation matrix returns results relative to the Global Axis System: 

 Local = “Right Wing Axis System” 

 Global = “Airplane Design Axis System” 

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎣

⎡

−

⋅ ⋅

⋅ − ⋅

⋅ =

0 0 0 1

sin 0 cos 131.104

sin cos cos sin sin -1119.02

cos cos sin cos sin 1328.84

θ θ

ψ θ ψ ψ θ

ψ θ ψ ψ θ

R T r r millimeters 

with ψ = -23.1o and θ = 177.875o 
Mars Aerial Regional-scale Environmental Survey (ARES) Coordinate Systems Definitions and Transformations 

NASA/TM-2009-215701 

17

7.5 TAIL AXIS SYSTEM TO AIRPLANE DESIGN AXIS SYSTEM 

Note: Transformation matrix returns results relative to the Global Axis System: 

 Local = “Tail Axis System” 

 Global = “Design Axis System” 

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎣

⎡

− ⋅ =

0 0 0 1

sin 0 cos 167.478

0 1 0 0

cos 0 sin 2383.97

θ θ

θ θ

R T r r millimeters 

with θ = 177.925o 

7.6 WIND TUNNEL MODEL AXIS SYSTEM TO AIRPLANE DESIGN AXIS SYSTEM 

Note: Transformation matrix returns results relative to the Global Axis System: 

 Local = “Wind Tunnel Model Axis System” 

 Global = “Design Axis System” 

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎣

⎡

⋅ =

0 0 0 1

0 0 1 - 6.452435

0 1 0 0

1 0 0 - 0.045434

R T r r millimeters 

7.7 AEROSHELL AXIS SYSTEM TO AIRPLANE DESIGN AXIS SYSTEM 

Note: Transformation matrix returns results relative to the Global Axis System: 

 Local = “Aeroshell Axis System” 

 Global = “Airplane Design Axis System” 

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎣

⎡

−

−

⋅ =

0 0 0 1

0 0 1 131.104

0 1 0 -1119.02

1 0 0 1328.84

R T r r millimeters 

with ψ = 180o 
Mars Aerial Regional-scale Environmental Survey (ARES) Coordinate Systems Definitions and Transformations 

NASA/TM-2009-215701 

18

7.8 SPACECRAFT AXIS SYSTEM TO AIRPLANE DESIGN AXIS SYSTEM 

Note: Transformation matrix returns results relative to the Global Axis System: 

 Local = “Spacecraft Axis System” 

 Global = “Airplane Design Axis System” 

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎣

⎡

−

−

⋅ =

0 0 0 1

0 0 1 131.104

0 1 0 -1119.02

1 0 0 1328.84

R T r r millimeters 

with ψ = 180o 

7.9 SPACECRAFT AXIS SYSTEM TO AEROSHELL AXIS SYSTEM 

Note: Spacecraft Axis System and Aeroshell Axis System are identical. 

Transformation matrix returns results relative to the Global Axis System: 

 Local = “Spacecraft Axis System” 

 Global = “Aeroshell Axis System” 

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎣

⎡

⋅ =

0 0 0 1

0 0 1 0

0 1 0 0

1 0 0 0

R T r r millimeters 

7.10 LAUNCH VEHICLE AXIS SYSTEM TO AEROSHELL AXIS SYSTEM 

Note: Transformation matrix returns results relative to the Global Axis System: 

 Local = “Launch Vehicle Axis System” 

 Global = “Aeroshell Axis System” 

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎣

⎡ −

⋅ =

0 0 0 1

1 0 0 0

0 1 0 0

0 0 1 4000

R T r r millimeters 

with θ = -90o 

7.11 AIRPLANE BODY AXIS SYSTEM TO AIRPLANE DESIGN AXIS SYSTEM 
Mars Aerial Regional-scale Environmental Survey (ARES) Coordinate Systems Definitions and Transformations 

NASA/TM-2009-215701 

19

8.0 APPENDIX A: AIRPLANE NOSE LOCATION 

The airplane nose is located at the following positions on various coordinate systems: 

Airplane Design Axis System 

 x = 143.334 mm 

 y = 0 mm 

 z = 194.505 mm 

Aerodynamic Database (ADB) Axis System 

x = -141.35 mm 

y = 0 mm 

z = -231.1386 mm 

Body Axis System 

x = 0 mm 

y = 0 mm 

z = 0 mm 

Left Wing Axis System 

 x = 1526.10 mm 

y = 564.19 mm (Right Wing y = -564.19 mm) 

z = -120.07 mm 

Tail Axis System 

x = 2238.19 mm 

y = 0 mm 

z = -108.14 mm 

Aeroshell Axis System 

 x = 1075.866 mm 

 y = 0 mm 

 z = 1011.410 mm 

Launch Vehicle Axis System 

x = -2988.590 mm (Station 2988.590) 

y = 0 mm 

z = -1075.866 mm 

Spacecraft Axis System 

x = 0 mm 

y = 0 mm 

z = 0 mm 

 
Mars Aerial Regional-scale Environmental Survey (ARES) Coordinate Systems Definitions and Transformations 

NASA/TM-2009-215701 

20

9.0 APPENDIX B: EXCEL TOOL FOR COORDINATE SYSTEM 

TRANSFORMATIONS. 

A Microsoft® Excel 2003 tool was created to assist in coordinate system transformations. The 

transformation matrices listed in this document are implemented into this tool. Figure 15 shows the 

main worksheet of the excel tool. The original points are entered as x, y, z coordinates and the original 

and subsequent transformation coordinates are selected from the columns above the points. 

Not every coordinate system combinations have direct transformations. Consequently almost all 

transformations most pass through either the Airplane Design Axis or the Aeroshell Axis. If a 

particular transformation does not exist, the spreadsheet will display an error. 

The second worksheet in the excel tool comprises the majority of the transformation calculations. This 

sheet acts as a database of the transformation coefficients between two coordinate systems, which are 

rotations of yaw, pitch, and roll listed in degrees, and translations Tx, Ty, Tz listed in millimeters. The 

program determines if the transformation is “forward” or “reverse” based on the axis chosen on the main 

page. 

Figure 15. EXCEL Tool for Coordinate Transformation 
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Mars Aerial Regional-Scale Environmental Survey (ARES) Coordinate 

Systems Definitions and Transformations 

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14. ABSTRACT

This document defines the formal coordinate systems for the Aerial Regional-scale Environmental Survey (ARES) flight 

systems, subsystems, and assemblies. The purpose of a formal coordinate systems document is to ensure the reliability and 

compatibility of the various ARES flight systems design and analyses activities. The systems specified herein apply to the 

ARES Flight Spacecraft, including the Cruise Stage, the Entry, Descent, and Landing (EDL) system, the Atmospheric Flight 

System (AFS). 

15. SUBJECT TERMS

ARES; Airplane; Coordinate; Mars; Transformation

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