AeroDRAG & Flight Simulation 7.0 Validation
SpaceShipOne Flight, October 4, 2004


1:48 Scale SS1 Wind Tunnel Model
SpaceShipOne Wind Tunnel Test Results
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Built By John Cipolla/AeroRocket
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The following AeroDRAG & Flight Simulation validation analysis uses widely available SpaceShipOne physical characteristics and flight performance information to predict maximum altitude, maximum Mach number and maximum acceleration during ascent (lift-off) and descent (re-entry). The AeroDRAG flight simulation predictions were then compared to data collected during the record setting flight of SpaceShipOne on October 4, 2004 when the winged sub-orbital spacecraft designed and built by Scaled Composites of Mohave, California achieved a maximum altitude of 367,463 feet and a maximum speed of Mach 3.09 during its ascent into the atmosphere and finally into space.

Physical dimensions for this analysis were derived from a completed SpaceShipOne card model built from plans made available by Currell Graphics. The 1:48 scale model of SpaceShipOne used for this flight validation analysis may be downloaded directly from Currell Graphics. SpaceShipOne represents a real break through for the commercialization of space travel for individuals.


Please Note: SpaceShipOne is a registered trademark of Mojave Aerospace Ventures.



INPUT DATA:
The following tables display the required SpaceShipOne airframe dimensions, wing dimensions and flight input data required for flight analysis. All dimensional data was derived from the SpaceShipOne model and verified by other sources when possible. Flight input data was derived from articles published by Aviation Week & Space Technology and verified by other sources such as the Science Channel's October 4, 2004 documentary called BLACK SKY, THE RACE FOR SPACE. Please refer to Figure-3 for a screen shot of the drag analysis screen and a summation of the input dimensional data and Figure-4 for a screen shot of the flight results. Finally, please refer to Figure-8 and Figure-9 for screen shots of altitude verses time, Mach number verses time and acceleration (G) verses time plots.

Please note: This analysis is an approximation based on the best information available.


Table 1:  Airframe Dimensions
Data Input Airframe Source
Body Diameter [in] 59.84 1:48 scale model
Ogive Nose Length [in] 96.0 1:48 scale model
Body Tube Length [in] 214.4 1:48 scale model
Finish Quality Good 1:48 scale model
Base Shape Boat Tail 1:48 scale model
Boat Tail Diameter [in] 25.6 1:48 scale model
Launch Lug None No Launch Lug


Table 2: Wing Dimensions
Data Input Fin-Set 1 Fin-Set 2 Fin-Set 3 Source
Number of Fins 2 2 2 1:48 scale model
Fin Edge Shape Streamlined Streamlined Streamlined 1:48 scale model
Fin Thickness [in] 9.6 6.4 3.07 1:48 scale model
Root Chord [in] 134.4 204.8 51.2 1:48 scale model
Fin Span [in] 70.4 51.2 70.4 1:48 scale model
Fin Profile Tapered Tapered Tapered 1:48 scale model
Tip Length [in] 96.0 32.0 19.2 1:48 scale model


Table 3: Flight Input Data
Data Input Stage-1 Source
Motor burn time [sec] 83.9 Aviation Week & S.T., 10/11/04, page 35 
Propellant weight [lbf] 4,200 Aviation Week & S.T., 06/28/04, page 28
Number of motors 1 Aviation Week & S.T., 06/28/04, page 28
Total loaded weight w/motors [lbf] 6,800 Aviation Week & S.T., 11/11/04, page 35
Reference diameter [in] 59.84 1:48 scale model
Coast time [sec] 275.0 AeroDRAG Input
Time increment [sec] 0.05 AeroDRAG Input
Nozzle expansion ratio (Ae/At) 25:1 Aviation Week & S.T., 04/21/03, page 69


PROPELLANT WEIGHT:
The June 28, 2004 issue of Aviation Week & Space Technology states on page 28 that "The flight was loaded with 3,600 lb. of oxidizer and 600 lb. of rubber." Therefore, the weight of propellant used during the 83.9 second burn is approximately 4,200 pounds and is the weight of propellant weight used in the AeroDRAG & Flight Simulation analysis to determine maximum altitude, maximum velocity at burnout and maximum altitude at burnout, etc.


THRUST-TIME PROFILE:
The SpaceShipOne thrust-time profile was approximated from the hybrid rocket motor chamber pressure (Pc) verses time plot presented on page 45 of the August 9, 2004 issue of Aviation Week & Space Technology. The Pc verses time plot was isolated from the other plots and repeated in Figure-1 below. In the magazine's presentation, the vertical pressure scale of the plot is defined by the spike in chamber pressure stated to be approximately 600 psi. The horizontal time time scale of the plot is defined by the 76 second total burn time of the flight. The pressure-time plot for the October 4, 2004 flight is simply extended to 83.9 seconds by using the same slope of the curve at 76 seconds. During the scaling process the Pc verses time plot was "smoothed" by using the average pressure in the vicinity of the oscillations and continuing down the curve to the 83.9 second cut-off point.

Estimated thrust verses time is computed from actual SS1 hybrid rocket motor chamber pressure (Pc) verses time data from Figure-1 using the MathCAD analysis at the end of this report. First, an iterative process is used to determine altitude (H) verses time corresponding to chamber pressure (Pc) verses time from Figure-1. One or two flight simulation runs is required to determine altitude (H) verses time for entry into Appendix-A of the MathCAD analysis. Then, the isothermal model of the atmosphere between the release point (47,100 feet) to the maximum altitude is used to determine atmospheric pressure (Pa) verses time for entry into the main part of the MathCAD thrust-time analysis. Please note that AeroDRAG & Flight Simulation uses the U.S. Standard Atmosphere to define atmospheric properties as a function of altitude and not the simpler isothermal assumption used in the MathCAD analysis. Once chamber pressure verses time and atmospheric pressure verses time are defined the pressure coefficient (Cf) and thrust (F) are determined using the equations for an ideal rocket motor. Finally, the efficiency factor (h) for the thrust coefficient (Cf) is used to modify the thrust verses time curve to better match comparison between AeroDRAG prediction and actual flight data. This SS1 thrust verses time MathCAD analysis required a thrust coefficient correction factor of 0.982, well within the normal range of 0.92 to 1 as recommended by reference 8.


Figure-1, SS1 Chamber Pressure vs. Time, AW&ST 8/9/2004 page 45


Figure-2, Thrust-Time Profile - Manual Input screen and Free-Form Input screen
 

FLIGHT RESULTS (AeroDRAG 7.0): Comparison between AeroDRAG & Flight Simulation results and actual SpaceShipOne flight data compared well for maximum altitude, maximum speed during ascent and maximum acceleration during ascent. Maximum altitude predicted by AeroDRAG 7.0 was 367,846 feet compared to the actual flight altitude of 367,463 feet. This represents a 0.1% difference. Maximum speed predicted by AeroDRAG 7.0 was Mach 3.05 compared to the actual maximum speed during ascent of Mach 3.09. This represents a 1.3% difference. Finally, maximum acceleration predicted by AeroDRAG during ascent was 1.71G compared to a gravitationally corrected maximum acceleration during ascent of 1.70G. This represents a 0.6% difference. However, for re-entry the comparisons were not as good because AeroDRAG & Flight Simulation assumes ballistic re-entry while the actual winged SpaceShipOne used a "feathered" configuration to increase drag and reduce the re-entry speed and acceleration. The high drag "feathered" condition was achieved by folding the wing at the mid-point during re-entry. The "feathered" configuration has a higher Cd verses Mach number than the initial low-drag shape required for high speed flight. Future releases of AeroDRAG & Flight Simulation may have provisions for increased rocket drag during re-entry by specifying an altered drag coefficient (Cd) when a specified altitude during re-entry is reached.


Table-4, AeroDRAG Flight Results Compared to SS1 Flight Data
Flight Data AeroDRAG SS1 Flight Data % Difference
Maximum Altitude [ft] 367,846 ft 367,463 ft +0.1%
Maximum Speed During Ascent Mach 3.05 Mach 3.09 -1.3%
Maximum Speed During Decent Mach 4.05 (Ballistic) Mach 3.26 (Feathered) +24.5%
Maximum acceleration During Ascent 1.71G 1.70G* +0.6%
Maximum acceleration During Descent 5.75G (Ballistic) 3.7G* (Feathered) +55.4%
a) G* modified using: G = F/W - 1, That is, SS1 published values have been reduce by 1G.
b) When coasting vertically in space in a gravitational field, G = -1 when F ~ 0 and W = SS1 final weight.
c) Acceleration due to gravity of a particle in space is G = - g0 * R^2 / r^2, where r is the distance from the center of the earth to the particle, R is the radius of the Earth and g0 is the acceleration due to gravity at the surface of the Earth.



AERODRAG & FLIGHT SIMULATION SCREEN SHOTS
SpaceShipOne Validation Analysis


Figure-3, Drag Screen and Summation of Input Data
 


Figure-4, Flight Screen and Results



Figure-5, Airframe Input Data Screen



Figure-6, Fins Input Data Screen



Figure-7, Launch Point Specification Screen



Figure-8, Altitude and Mach Number Plot Screen



Figure-9, Altitude and Acceleration (G) Plot Screen


THRUST VERSES TIME FROM CHAMBER PRESSURE VERSES TIME
MathCAD Analysis By John Cipolla






References
1) Aviation Week & Space Technology, April 21, 2003
2) Aviation Week & Space Technology, June 28, 2004
3) Aviation Week & Space Technology, August 9, 2004
4) Aviation Week & Space Technology, October 4, 2004
5) Aviation Week & Space Technology, October 11, 2004
6) Aviation Week & Space Technology, October 18, 2004
7) Rocket Propulsion Elements, By George Sutton
8) Design of Liquid Propellant Rocket Engines, By D.K. Huzel and D.H. Huang
9) Wikipedia free on-line encyclopedia
10) Flight Mechanics of Manned Sub-Orbital Reusable Launch Vehicles with Recommendations for Launch and Recovery



SpaceShipOne
SUBSONIC WIND TUNNEL TESTING

Figure-1, Rear-mounted SpaceShipOne (1:48 scale model)
AeroRocket Wind Tunnel used for CD and CL measurements
 

A 1:48 scale model of SpaceShipOne was tested in the AeroRocket subsonic wind tunnel. Drag coefficient (CD) at 0.0 degrees angle of attack and aerodynamic center (hac) for pitch and yaw were measured. Drag coefficient is referenced to the maximum airframe cross-sectional area and hac is normalized by airframe length. Results of this investigation are presented in Table-1. Please refer to Figure-4 and Figure-5 to see how the model was mounted in the wind tunnel for determining drag coefficient and Figure-2 and Figure-3 to see how the Low-Friction Caliper was used to determine pitch and yaw aerodynamic centers. Please Note: SpaceShipOne is a registered trademark of Mojave Aerospace Ventures.

Table-1, SS1 Wind Tunnel Test Results
Aerodynamic Coefficient Description Coefficient Reference Quantity Value
Drag Coefficient, AOA = 0.0 degrees CD Maximum Airframe
Cross-Sectional Area
0.610
Yaw Aerodynamic Center From Nose Tip hac_yaw Airframe Length, L 0.635
Pitch Aerodynamic Center From Nose Tip hac_pitch Airframe Length, L 0.588
Reynolds Number (U = 47 ft/sec) Re U, L, r, m 142,375


Figure-2, SS1 yaw (nose side-to-side) aerodynamic center measurement
using Low-Friction Caliper set just ahead of the yaw aerodynamic center


Figure-3, SS1 pitch (nose up-down) aerodynamic center measurement
using Low-Friction Caliper set just ahead of the pitch aerodynamic center


Figure-4, close up of SS1 model in the AeroRocket
wind tunnel during drag (CD) and lift (CL) measurements


Figure-5, SS1 model in the AeroRocket wind tunnel
during drag (CD) and lift (CL) measurements

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