Apropos last weekend’s Exos launch, what does it take to build a reusable VTVL sounding rocket? Start w/ a 1DOF ascent-only simulation w/ a few realisms added:
- Time-varying mass
- Altitude-varying engine performance (LOX/ethanol at 350 psi and r = 1.1 from free version of RPA)
- Altitude-varying atmosphere (from 1976 atmo model)
- Drag coefficient (V2 copied out of Sutton) function of local Mach number
The 1DOF program needs to integrate these two differential equations:
- mdot = Fthrust/Isp(x)/g;
- xdotdot = 1/m(t) *(Fthrust – 0.5*rho(x)*Cd(M)*A*xdot^2 – m(t)*g);
For zeta = 0.45, TW= 1.1, and max thrust = 3.6 kN the max altitude is 16785 m (55069 ft). Definitely not the von Karman line, but probably enough of a challenge. A couple of the FAR university rocket challenges are to a similar altitude. I don’t know if a business case for a reusable sounding rocket closes – John Quinn said the sounding rocket stuff is a practice for their orbital program. And Blue Origin flies New Shepard only 3 times year, so probably can’t parlay a suborbital sounding rocket hobby into a business. Zeta = 0.45 is a lousy propellant mass fraction, but I’m pleasantly surprised it makes it past 50,000 feet.
I didn’t find a lot of drag coefficient data – I emailed this guy several times because his CFD software is cheap and looks easy to use, but he never replied. So I took the plot of V2 Cd vs. M and wrote a script that lets me click on the picture to capture a lot of points. The CdFxn() script does a crude nearest neighbor interpolation which is why you see the same drag coefficient for multiple Mach numbers in the plot below.