AeroDRAG & Flight Simulation 7.0
V-2 Rocket 2-D Flight Analysis
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The following AeroDRAG & Flight Simulation validation analysis uses widely available V-2 rocket physical characteristics and flight performance information to compare range, apogee of trajectory, velocity at burnout, velocity at impact, burnout altitude, acceleration at burn out and acceleration at liftoff to actual V-2 rocket flight performance information.



INPUT DATA:
Table-1 to Table-4 display the required V-2 airframe dimensions, fin dimensions and flight input data required for flight analysis. 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 for the A-4/V-2 rocket.


Table 1:  Airframe Dimensions
Data Input Airframe Source
Body Diameter [in] 65.0 A-4/V-2 Resource Site
Ogive Nose Length [in] 208.5 A-4/V-2 Resource Site
Body Tube Length [in] 327.9 A-4/V-2 Resource Site
Finish Quality Good A-4/V-2 Resource Site
Base Shape Boat Tail A-4/V-2 Resource Site
Boat Tail Diameter [in] 40.9 A-4/V-2 Resource Site
Launch Lug None N/A


Table 2: Fin Dimensions
Data Input Fin-Set 1 Source
Number of Fins 1 A-4/V-2 Resource Site
Fin Edge Shape Streamlined A-4/V-2 Resource Site
Fin Thickness [in] 4.9 A-4/V-2 Resource Site
Root Chord [in] 158.7 A-4/V-2 Resource Site
Fin Span [in] 41.1 A-4/V-2 Resource Site
Fin Profile Tapered A-4/V-2 Resource Site
Tip Length [in] 102.6 A-4/V-2 Resource Site


Table 3: Flight Input Data
Data Input Stage-1 Source
Motor burn time [sec] 65.0 A-4/V-2 Resource Site
Propellant weight [lb] 18982 A-4/V-2 Resource Site
Number of motors 1 A-4/V-2 Resource Site
Total loaded weight w/motors [lb] 28219 A-4/V-2 Resource Site
Reference diameter [in] 65.0 A-4/V-2 Resource Site
Coast time [sec] 262 N/A
Time increment [sec] .042869 N/A
Nozzle expansion ratio (Ae/At) 18.2:1 A-4/V-2 Resource Site
Initial (Sea Level) thrust (lb) 55,100 A-4/V-2 Resource Site
Final (Vacuum) thrust (lb) 70,107 Encyclopedia Astronautica
Wikipedia Encyclopedia


 Table 4: Launch Conditions & 2-D Flight
Data Input Stage-1 Source
Temperature at launch location [deg F] 80.0 N/A
Elevation of launch location [ft] 0.0 N/A
Flight path angle at insertion [deg] 49.0 A-4/V-2 Resource Site
Time from lift-off to roll initiation [sec] 5.0 A-4/V-2 Resource Site
Time from lift-off to Flight path angle insertion [sec] 54.0 A-4/V-2 Resource Site
Lift to drag ratio [1] 0.0 N/A


Table-5, AeroDRAG Flight Results Compared to V-2 Flight Data
Flight Data AeroDRAG V-2 Flight Data % Difference
Range (miles) 189.5 199 -4.8%
Apogee of trajectory (miles) 59.8 56.0 +6.8%
Velocity at burnout (ft/sec) 5,290.6 5,249.3 +0.8%
Velocity at impact (ft/sec) 2,927.8 3,608.9 -18.9%
Burnout altitude (miles) 18.3 17.4 +5.2%
Maximum Acceleration at burnout (G's) 6.6 7.0 (a)(b)(c) -5.7%
Acceleration at lift-off (G's) 0.95 0.90 +5.6%
Apogee, 90 degree lift-off (miles) 120.0 (d) 114.0 +5.3%

a) G modified using: G = F/W - 1, That is, V-2 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.
d) This AeroDRAG apogee result is compared to the approximate maximum altitude achieved by the V-2 rocket for vertical flight when used as a sounding rocket. This result is achieved by performing a one-dimensional flight analysis with the flight path angle set to 90 degrees from the horizontal. Burn time was increased to 70 seconds corresponding to the maximum burn time of  the V-2 rocket motor.


PROPELLANT WEIGHT:
The V-2 rocket used 3,710 kg of Ethyl Alcohol (75%) and 4,900 kg of Liquid-oxygen for a total of 8,610 kg or 18,982 lb of propellant consumed during the 65 second burn of the rocket motor for this example.


THRUST-TIME PROFILE:
The V-2 rocket motor developed 25,000 kg (55,100 lb) of thrust at sea level where the atmospheric pressure is approximately 14.7 psia. Also, when the ambient pressure is reduced to the near vacuum of space a V-2 rocket motor developed 31,800 kg (70,107 lb) of thrust because the low pressure of high altitude flight allows the nozzle to expand more efficiently from the nozzle exit to low ambient pressure. The thrust curve is constructed using these design conditions to define the thrust-time plot in the Thrust-Curve Generation screen. The thrust-time curve (saved as an FVT file) is used in this analysis to approximate the thrust profile of the V-2 rocket. Please see Figure-1 (below) for the input screen used to generate the thrust-time curve for this example.


FLIGHT RESULTS
(AeroDRAG 7.0): Comparison between AeroDRAG & Flight Simulation results and actual V-2 flight data compare well for range, apogee, velocity at burn out, impact velocity, burn out altitude, acceleration at lift-off and finally the maximum altitude achieved by the V-2 rocket for vertical flight. Please refer to Table-5 where these results are compared. For example, the range predicted by the simulation for the V-2 rocket was 189.5 miles compared to 199 miles for the published V-2 range data for a difference of 4.8 percent. These results include the effects of Cd verses Mach number, air density verses altitude, propellant weight as a function of time and Cd verses rocket shape and Mach number. However, wind velocity, Earth curvature and other perturbations are not included in the 2-D analysis at present. Please note, the effects of Earth curvature may be neglected for ranges less than 500 km (310.7 miles). Finally, please refer to Figure-2, Figure-3, Figure-4 and Figure-5 for more information concerning the procedure required to generate program output.


Figure-1, Thrust-Time Profile - Manual Input screen and Free-Form Input screen



AeroDRAG & Flight Simulation Input Data and Results Screen Shots


Figure-2, Drag Screen and Summation of Input Data
 


Figure-3, Flight Screen and Results
 


Figure-4, Launch Point Specification Screen
 


Figure-5, Altitude and Axial Acceleration Plot Screen

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