1DOF sounding rocket

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:
  1. mdot = Fthrust/Isp(x)/g;
  2. 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. 

Altitude and velocity vs. time

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. 

Program for getting a lot of Cd vs. M points out of this plot. Click on the curve and the data appears in the table to the left. 


Cd “data” in blue and Cd values used in simulation in black.

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