Why do rockets fall apart on the way up? Because the rocket equation is brutal — and dropping dead weight in stages is the only way to reach orbit.
Rocket StagingLive
beating the tyranny of the equation
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The rocket equation grows delta-v only with the logarithm of the mass ratio, so a single stage hauling empty tanks all the way up is hopelessly inefficient. Staging drops dead weight along the way: each stage contributes ve·ln(mass ratio), and their sum easily clears the ~9.4 km/s needed for low Earth orbit.
Reading this result: 2 stages at Isp 350s and mass ratio 4 each sum to 9.5 km/s — past the ~9.4 km/s LEO budget, since every stage adds ve·ln(ratio) after dropping dead weight.
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How it works
The Tsiolkovsky equation gives delta-v as exhaust velocity times the log of the mass ratio, so a single stage carrying empty tanks all the way is hopelessly inefficient. Staging jettisons spent structure, and each stage adds its own ve·ln(mass ratio). Summed, they clear the roughly 9.4 km/s needed for low Earth orbit.
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