Improving the USOFS software | Project planning and misc | Forum

Rocket-To-The-Moon said:The units for Mach is simply Mach. The speed of sound in air in meters per second is equal to s=20.1*[(air temperature in Kelvis)^(1/2)] and the mach number would be M=v/s where v is the rocket's velocity in m/s.

The Mach number is technically a dimensionless number (see the second sentence of the Overview section of the Wikipedia article).  Also, the speed of sound in air varies with air density, which varies with altitude.  The USOFS code takes this into account, however.

Thanks for making the changes, Craig, great work.  I hate to nit-pick, but having the times in units of seconds (e.g. t = 59.9s) would be a fantastic final tweak.

So, the issue of the bizarre simulation results is not so deep as I first feared.  There is no problem with the physics per se, rather with the data!

The default rocket specifications that are hard-coded into USOFS are stupidly inappropriate.  The thrust of 1000 N combined with the empty mass of 30 kilograms, the fuel mass of 100 kg and the payload mass of 5 kg means that, at the time of ignition, the rocket engine provides 1000 / 135 = 7.40 m/s/s of upward acceleration, which is of course not enough to counter the 9.8 m/s/s/ downward acceleration due to gravity.  Since USOFS has no crash-detection built in (since the simulations usually terminate at zenith), the rocket actually falls down through the ground, resulting in the observed negative altitude values.  Eventually, the mass of the rocket decreases sufficiently (as fuel is burned) for the net acceleration to be in the upward direction and the rocket flies back up, through the ground and into the realm of positive altitude, at about t=50s.  USOFS believes the air density at negative altitudes to be zero, which explains the extremely sharp spikes in Mach number and dynamic pressure at the time the rocket passes upward through the ground, and also the small drop in acceleration observed at the same time: there is an instantaneous switch from flying in a vacuum to flying through the densest part of the atmosphere at high speeds!

If one takes the simple step of setting the thrust to 2000 N, one gets much, much nicer looking graphs which are entirely within the realms of what is physically sensible. :)