The Multistage Rocket

Decide how to divide the job before designing any hardware.

1. Take a total delta-v requirement of 9.4 km/s and a two-stage vehicle.
2. Try splitting it 50/50, then 60/40, then 40/60, computing the total launch mass needed for a fixed payload each time.
3. Assume a realistic structural fraction — stage dry mass around 8 to 10 percent of its propellant.
4. Plot launch mass against the split and find the minimum.

There is a genuine optimum, and it is not an even split. The upper stage carries the payload all the way, so mass there is expensive; the first stage is thrown away early and its inefficiency matters less. The optimum usually gives the upper stage a larger share of the delta-v than a naive split would suggest.

Design the structure whose entire purpose is to stop existing on command.

1. Build a model two-stage vehicle with an interstage that carries flight loads between the stages.
2. Fit a separation system — at model scale, a spring-loaded pusher released by a servo or a burnwire.
3. Test on the bench, measuring the relative velocity the pusher imparts.
4. Verify the interstage carries the expected compressive load without the release firing prematurely.

The interstage must be strong enough to transmit the full thrust of the lower stage through the whole vehicle, and weak enough to come apart reliably on command. Those requirements point in opposite directions, which is why the mechanism is separate from the structure — a joint held by frangible bolts, clamp bands or explosive cord, rather than by something that must be broken.

Two philosophies, and they fail differently.

1. Sketch cold staging: lower stage shuts down, stages separate, upper stage ignites in the gap.
2. Sketch hot staging: the upper engine ignites BEFORE separation, its exhaust venting through an open lattice interstage, and the thrust itself pushes the stages apart.
3. Consider what happens in each case if the upper engine fails to light.
4. Consider what happens to propellant settling in each case.

Cold staging is cleaner and has a dangerous gap: during coast the vehicle is unpowered, propellant floats away from the tank outlets, and the engine may ingest gas when it does light. Ullage motors — small thrusters that keep a gentle acceleration during the gap — exist entirely to hold the propellant at the bottom of the tank.

Hot staging eliminates the gap and needs an interstage that survives being blasted by a rocket engine at point-blank range. Soviet designs used it routinely; the lattice interstage on the R-7 is visible in photographs as an open framework rather than a solid tube.

Test the separation in flight, at a scale where failure is a walk across a field.

1. Fly the two-stage model with the upper stage inert first, verifying separation alone.
2. Film from the ground at high frame rate.
3. Examine the footage for tumbling, recontact, or asymmetric release.
4. Only when separation is repeatable, fly with the upper stage live.

Separating one thing at a time is the whole method. A failure with both stages live tells you very little, because you cannot tell whether the separation or the ignition went wrong.

The failure modes to watch for are specific: a release that fires unevenly imparts a tumble; too little push allows recontact; and a stage that separates while still thrusting will chase the one above it.

More stages always help the arithmetic. Decide whether they help the mission.

1. Compute the launch mass needed for a fixed payload with one, two, three, four and five stages.
2. Now assign each separation event a success probability — say 0.98 — and each engine start likewise.
3. Compute overall mission probability against stage count.
4. Plot performance gain and reliability loss on the same axes.

Performance improves steeply from one to two stages, appreciably from two to three, and barely beyond that — while reliability falls with every added event. The curves cross somewhere around two or three, which is exactly where the industry settled without anyone decreeing it.

This is the honest shape of most engineering optimisations and worth naming: the quantity you can calculate improves smoothly, and the quantity you cannot calculate gets worse. The optimum sits where a confident number meets an uncertain one, which is why judgement rather than arithmetic decides it.