Then, I reconfigured the (simple) axial simulation, to exit when relative axial displacement reaches about 53.4 feet. This is the axial distance from the forward attach point to the external tank, to the inflection (strike point) on the left wing. Lastly I adjusted the drag coefficient (Cd) of the foam to yield 511 mph when axial displacement reached 53.4 feet. Cd = 0.65 did the trick. This is actually somewhat low. I would expect something more like 1.2-1.7, because the foam should be fairly ragged and thus draggy. However, higher values of Cd yield even higher deceleration and impact velocities. In this iteration, I mostly wanted to see if I could match NASA's number (511 mph). The table below shows that this goal was achieved.
Assumptions:
V0 = 682.5 m/s (reverse engineered from data at post #2341)
Accel_XB = 12.1 m/s2 (reverse engineered from data at post #2341)
Alt = 20 km (reverse engineered from data at post #2341)
Rho = 0.08823 kg/ms (from KCA-71 winter model for 20 km altitude)
Sref = 0.120492 m^2 (spherical approx for 1920 in^3 -- very conservative)
Mass = 1.211 kg
Cd = 0.65 (yields 511 mph Vrel at 53.4 ft axial displacement)
|
Time since separation (s) |
Relative axial velocity (mph) |
Relative axial displacement (ft) |
|
0.000 |
0.00 |
0.00 |
|
0.030 |
85.66 |
0.96 |
|
0.060 |
162.37 |
3.70 |
|
0.090 |
231.46 |
8.05 |
|
0.120 |
294.04 |
13.84 |
|
0.150 |
350.97 |
20.95 |
|
0.180 |
403.00 |
29.25 |
|
0.210 |
450.74 |
38.65 |
|
0.240 |
494.70 |
49.05 |
|
0.252 |
510.93 |
53.37 |
My initial velocity is slightly different from the 1570 mph stated by Dittemore. I chose to stay with this number because (A) it's consistent with other assumptions that I made and (B) I think that Dittemore was quoting inertial velocity which includes Earth rotation. Not that much difference between them anyway.