The CD of around 3.0 at high altitude is correct. Its caused by the very low Reynolds numbers at high altitude.
When you run Aero Plots for the rocket, it uses a default of Sea Level for each of the Mach numbers for the aero data. When the rocket is run at Sea Level (the default) on Aero Plots, notice that at very low Mach numbers (very low Reynolds numbers, which can be found in the tabular output on the far right-hand side), the rocket CD begins to increase very rapidly in an exponential fashion. This is due to the low Reynolds numbers, although not nearly as low as at high altitude.
For a 10 ft tall rocket at Sea Level, at;
50 ft/sec
Reynolds Number (Re) = 2,840,287
RASAero has a feature where you can vary the altitude for Mach number points on the Aero Plots. This feature was built in for comparisons with wind tunnel data, but its use is applicable here. See Page 32 of the RASAero Users Manual for the Mach-Alt Input feature. On the Main Input Screen, under Options, select Mach-Alt.
For example, you can put in
0 90,000
25 90,000
To have all of the Mach numbers in the Aero Plot plots (Mach 0-25) be at 90,000 ft.
Note how low the Reynolds numbers gets at this altitude at low velocities:
10 ft tall rocket
Alt = 90000 ft
Velocity = 50 ft/sec
Re = 85,258
Note that compared to Sea Level, the Reynolds number has gone from 2.8 million to under 100,000 at 90,000 ft. These very low Reynolds numbers, which can go under 10,000 or even under 1,000 at very high altitude, create very high CDs. Its like really backing up that exponentially increasing portion of the CD versus Mach plot at low Mach numbers that you saw at Sea Level.
If you put in Mach-Alt points from your flight into the Mach-Alt input screen, then the CD versus Mach plot from the Aero Plots will match the trajectory data. You saw two different CDs, because the default (Sea Level) was used for Aero Plots, but the trajectory was from 90,000 ft. If you put Mach-Alt points from the trajectory into the Mach-Alt input, then the Aero Plots will match the trajectory data.
There was a bug associated with this effect which was corrected in the latest version (Version 1.0.2.0) of RASAero. As noted on the RASAero Software Download page:
- Made corrections to fix error where on very high altitude flights (above 200,000 ft) extremely low Reynolds numbers would cause unrealistically high drag coefficients. Correction added a low Reynolds number cut-off to avoid very low Reynolds numbers (under 10,000) at high altitude.
Note that the current version of the RASAero software is for ground launch, and was checked out for Launch Site Elevations up to Mount Everest. You can put in a Launch Site Elevation of 90,000 ft, but youll also need the temperature at 90,000 ft to have the correct Launch Site atmospheric density. The temperature at 90,000 ft (Standard Day) is -56.57 deg F.
The CD versus Mach number, and the other aero data versus Mach number, for altitudes of 90,000 ft to 200,000+ ft generated by Aero Plots, and the trajectory data starting from a ground launch to altitudes over 200,000 ft, have been checked out. Doing a balloon launch using a launch site elevation of 90,000 ft, with a launch site temperature of -56.57 deg F has not been checked out, as this wasnt an intended use of the software. And of course RASAero shows the altitude above the ground, so if you put in a Launch Site Elevation of 90,000 ft, then for the altitude above the actual ground level, you have to add 90,000 ft to the altitude. Additionally, your rocket will land at 90,000 ft.
Summarizing; the current version of RASAero can generate the Aero Data for a balloon-launched rocket, but was not designed for a balloon launch in terms of the flight simulation. It will have at least the limitations for this use noted above (there may be more), and has not been checked out for the flight simulation portion of a balloon launch.
Chuck Rogers
Rogers Aeroscience
