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.
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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.
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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.
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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.
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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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