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I'm working on a simple rocket flight simulation program, and am trying to reproduce aspects of Goddard's first successful rocket flight. My sources put the empty weight at 5.75-6lbs, loaded weight 10.25-10.4 lbs, and thrust 9 lbs (40N), using a fuel-rich gasoline/LOX propellant with Isp of about 150s. The rocket is supposed to have reached an altitude of 41' (12.5m) and turned to cover 184' (56m) horizontally in a 2.5 sec flight after burning 20 seconds without leaving the launch stand. Fully fueled, the rocket didn't reach 1:1 thrust-to-weight, so couldn't lift off; my calculations agree that 20-25 seconds of fuel consumption is about where the weight would have dropped to 9 lbs.; so far so good.

However, in order to reach 12.5m altitude in no more than 2.5 seconds, the rocket would have to accelerate at about 4m/s² on average (d = 1/2 at²), implying thrust-to-weight ratio of around 1.4; this thrust could be achieved only very briefly right before fuel-out, and that would leave no time at all for the fall (actually a powered dive!) from that peak altitude.

If we take the widely reported 41' altitude as counting the rocket's 10' height, that still leaves us with a 9.5m apogee to account for.

My simulation doesn't yet include rotation off the vertical, so my final apogee is much higher (Goddard's rocket had another 40 or 50 seconds of propellant available after liftoff; it flipped over and crashed quite quickly), but 2.5 seconds after liftoff I see only 0.04m of vertical travel, nowhere near the reported figure.

Am I overlooking something obvious? My model includes drag, but at the low speeds in the first seconds of travel, it's negligible.


Update:

My best guess at this point is that the nozzle burnthrough that caused the rocket to go off-course also greatly increased the thrust while decreasing the Isp (i.e. it let a lot of unburned propellant out of the combustion chamber in a hurry); if I change thrust to 100N and Isp to 50s right at takeoff, my simulation can reach the reported altitude at the required time. Does that seem plausible?

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    $\begingroup$ This needs far more research, because I'm not exactly sure which flight is shown ~ 10 seconds into this video, but it looks to me like the engine part separated from the stand on its own (well "something" is shooting up fast in a straight line, the 2+ frames and precise placement suggest it's not merely a scratch on the film), while leaving the stand with open fuel supply on the ground that burst into flames, causing the nearby tree and bushes to catch fire. If true, it could drastically change T/W for a few seconds. $\endgroup$ – TildalWave Aug 23 '14 at 16:28
  • $\begingroup$ I don't think that's the launch in question -- the launch I'm referencing had the motor at the top of the stack. $\endgroup$ – Russell Borogove Aug 24 '14 at 20:12
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It could be that what happened is a slight "Ground Effect". Essentially, the exhaust will push off the ground, which pushes off the rocket slightly as well. This normally isn't a big deal, but it does have an effect when a rocket stays near the ground for an extended period of time. I think what this would do in effect is to increase the acceleration for a period of time. This would also increase the time, as it would take slightly less fuel to push the rocket forward. The effect would be something like a 50% increase in thrust which falls off based on the height, although I don't know the specifics. Take a look at Wikipedia for more details.

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  • $\begingroup$ Interesting; ground effect is most often observed with vehicles that have a substantial horizontal area, though. Goddard's configuration had the engine at the top of the stack, with a conical cap on the fuel tank below, which would have tended to deflect the exhaust to the sides, so I'm skeptical that there would be substantial exhaust back pressure lifting the rocket (though I confess I'm ignorant of the physics involved there). In any case, a 50% increase in thrust isn't enough to account for it; it has to be more like a 150% increase. $\endgroup$ – Russell Borogove Aug 22 '14 at 18:06
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    $\begingroup$ Any downthrust within about 5m of the ground gets some ground effect, as the impact bounces off the ground and increases the surrounding pressure, and thus the pressure in the chamber. $\endgroup$ – aramis Aug 24 '14 at 6:55

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