HISTORICAL DRAWING · 1914

Multistage rocket

What ideal velocity budget results from two assumed stage mass ratios?

R. H. Goddard, US 1,102,653 "Rocket Apparatus", sheet 1 (multi-stage rocket)
R. H. Goddard, US 1,102,653 "Rocket Apparatus", sheet 1 (multi-stage rocket). View the original source and attribution ↗

A contemporary sketch model

Every number below is a modern illustrative assumption. The historical drawing supplies a question; the source model is an exercise in reasoning about it.

exhaustSpeed = 2000 m/s in 1500..2500 "Illustrative effective exhaust speed"
ratio1 = 3 "Assumed wet-to-final mass ratio for stage one"
ratio2 = 2 "Assumed wet-to-final mass ratio for stage two"
stage1 := exhaustSpeed*log(ratio1) [m/s]
stage2 := exhaustSpeed*log(ratio2) [m/s]
totalDeltaV := stage1+stage2 [m/s]
check budget: totalDeltaV >= 3500 m/s
sweep Exhaust: exhaustSpeed = 1500, 2000, 2500 m/s

Model limits

Ideal rocket equation only; no gravity or drag losses, burn timing, structural staging feasibility or trajectory integration.

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