This image is a rendering of my Rocksim model. I worked off of the photos on pages 151 and 152 of Project Orion: The True Story of the Atomic Spaceship, by George Dyson. I had never used Google Book Search before, and it was key to this effort. Still, my ability to get accurate measurements was limited. Since the frontal area of the Hot-Rod is probably most important, I should be in decent shape in this regard. I saw that it was 1 m in diameter and worked from there. The other item that is important to the model is the weight. It's reported weight is 230 lbs without the ballistic envelope (shroud), which was the flight configuration.
Coming up with an engine model was not as easy. From a Wikipedia search of 'explosives' I found the energy potential of PETN. After much searching, I decided to compute the thrust based on the pressure generated by a charge and apply it to the area of the pusher plate. Google came through again, and I found a formula in Explosive Loading of Engineering Structures, by P S Bulson. This formula uses the distance from the charge to the location of interest, and the equivalent pounds of TNT. I got the weight of the charges from Dyson and the relative strength from Wikipedia. It turns out that the equation is only good for certain ranges of the parameters, and this one is out of range. So, this approximation undoubtedly adds to the error. From what I've read, the actual pressure profile is generally determined experimentally, but I couldn't find any data.
This calculation yields a whopping 1.59 x 10^6 N of peak force. The curve is a step to this peak value, which should last from 0.1 to 0.5 msec. It then drops exponentially for a period of 5 - 30 msec. (I lost the reference links for these numbers). When playing around with these values, I found the model to be quite sensitive to what appeared to me to be small changes in the period of this pressure wave. The final issue was that the relative strength appears to be for pure PETN. Since Dyson referred to it as 'plastic', it undoubtedly was mixed with a binder in unknown proportions. I used 60%, which is on the low side. However, I knew by sims were coming up high anyway. The upshot is that this is pretty much a WAG on my part - and the results I mentioned in my previous post bear this out.
This is a work in progress, however, I suspect I'll hit diminishing returns quite soon. For now, here are some sim results:
Hot-Rod - Simulation resultsProject Orion Hot-Rod Revisited, Part 1
[PETN-0] [PETN-0-1] [PETN-0-1]
Simulation control parameters
Flight resolution: 800.000000 samples/second
Descent resolution: 1.000000 samples/second
Method: Explicit Euler
Altitude: 0.00000 Ft.
Relative humidity: 50.000 %
Temperature: 59.000 Deg. F
Pressure: 29.9139 In.
Wind speed model: Calm (0-2 MPH)
Low wind speed: 0.0000 MPH
High wind speed: 2.0000 MPH
Wind turbulence: Fairly constant speed (0.01)
Frequency: 0.010000 rad/second
Wind starts at altitude: 0.00000 Ft.
Launch guide angle: 0.000 Degrees from vertical
Latitude: 1.571 Degrees
Launch guide data:
Launch guide length: 36.0000 In.
Velocity at launch guide departure: 84.9918 ft/s
The launch guide was cleared at : 0.037 Seconds
User specified minimum velocity for stable flight: 43.9993 ft/s
Minimum velocity for stable flight reached at: 1.2181 In.
Max data values:
Maximum acceleration:Vertical (y): 26850.951 Ft./s/sHorizontal (x): 0.362 Ft./s/sMagnitude: 26888.025 Ft./s/s
Maximum velocity:Vertical (y): 176.5814 ft/sHorizontal (x): 1.8050 ft/sMagnitude: 176.7507 ft/s
Maximum range from launch site: 40.44619 Ft.
Maximum altitude: 655.03609 Ft.
Engine ejection charge data:
Using a delay time of : 0.000 Seconds
Velocity: 167.0810 ft/s
Altitude: 264.07940 Ft.
Recovery system data
P: Parachute Deployed at : 7.606 Seconds
Velocity at deployment: 6.8688 ft/s
Altitude at deployment: 655.03609 Ft.
Range at deployment: -40.44619 Ft.
Time to burnout: 2.752 Sec.
Time to apogee: 7.606 Sec.
Optimal ejection delay: 4.854 Sec.
Project Orion Hot-Rod Revisited, Part 2
Project Orion Hot-Rod Revisited, Part 3
Project Orion Hot-Rod Revisited, Part 4