How do you optimize a rocket or space vehicle liftoff?

Submitted by seriousnotshirley t3_1049w95 in askscience

I was thinking about the problem of lifting a space craft from the earth's surface to space and for some reason only just now realized that there's an optimization problem here (I think) and I'm curious what the model looks like for this and how it's performed. Suppose I want to lift a mass to an orbit of some altitude, I can compute what energy the system has to have once it's in orbit; what's the best way to generate that?

Suppose you launch with low power; then you spend more time in a higher gravitational field which means you're counteracting gravity for a longer period of time. I assume that minimizing the integral over time of the force of gravity on the vehicle would save you fuel, which saves weight which saves you fuel... (I assume this converges)

Suppose you launch with very high power; you accelerate quickly out of the gravitational force but then air resistance becomes an issue and with too much velocity any additional increase in velocity requires O(x^3) power. At some point it's not efficient to add more power because you'll need a lot more fuel.

In both of these cases the higher you are the lower those forces are; so maybe a launch system which has a lot more power early and cuts the power later is useful (SRBs are useful here).

Now, if you build a rocket or launch system with more engines you incur more weight that you're trying to move, also bad. Along with this is the weight of the fuel which goes down over time. The more fuel you have also starts to incur more non-usable weight for the fuel tanks.

I presume that the effects of wind resistance and gravity create non-linearities in the system since the forces acting at time t are functions of altitude. Is there a model that's used to get started and then iterated on once certain discrete parameters are figured in (that is, you can't add 0.5 engines)?

Edit: I’m familiar with both KSP and the rocket equation. The problem of designing the system seems like a optimizing a function described by a non-linear differential equation which I assume probably doesn’t have an analytical solution. I’m curious about what things get modeled and which don’t and how this is actually done in practice.

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mfb- t1_j347et8 wrote

A lot of simulations. There is essentially nothing that only has advantages or disadvantages, so you need to consider tons of options.

If you have a given rocket design and a fixed mission: Launch at full power - this is a very wasteful part of the flight and you want to gain speed as soon as possible. Acceleration will (almost) always be low because the rocket is still full of propellant. Tilt a bit to the side and follow an approximate gravity turn. Throttle down before reaching the maximum aerodynamic pressure if needed for safety. Typically this is only a pretty short period.

Some more things to consider, in addition to what you mentioned:

  • Different payloads have different requirements but you don't want too many rocket variants.
  • Making the rocket more robust against weather helps with launch opportunities but might reduce the performance.
  • Typically components are shipped from construction site to launch site, favoring a smaller diameter - but that makes it more susceptible to wind.
  • Launch site selection matters, too.
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aspheric_cow t1_j35n22k wrote

A faster ascent does take less energy - not because the gravity is stronger at lower altitude (the difference is pretty minor) but because the rocket spends more time fighting gravity. Think about the extreme case where the rocket is barely moving up - it will use up all fuel before it gets to any meaningful altitude. It's kind of like walking up a downward escalator - you have to expend energy just to stay in one place, and it's actually easier to run up quickly. Once you're at the top (in orbit), you can stay there without using any energy.

But there are limits on how quickly a rocket can accelerate, such as:

  • Quick acceleration requires more powerful engines. The engines themselves get heavier. This is mainly an issue with liquid-fuel rockets; solid fuel rockets don't really have an "engine" and you could design it to burn all the fuel very quickly if you want to.
  • The quicker you accelerate, the more G force & vibration the payload experiences. This is especially a problem if the "payload" is people.
  • If you accelerate hard, you end up traveling very fast through the dense low-altitude atmosphere, which means a lot of mechanical stress & vibration on the rocket.
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fliguana t1_j33uv8a wrote

Rockets launch at full power. The effect of air resistance comes into play for some, more fragile rockets which cannot withstand maximum frontal forces, so there is a point during ascend (maxQ), when engines are temporarily dialed back to reduce acceleration.

A few seconds later, the max power is restored in less dense atmosphere.

Why the let-off is stepped rather than gradual is a mystery to me, perhaps some optimization is available. Also relevant the path of the rocket - the more vertically it launches, the faster it clears the atmosphere, but then longer takes to gain lateral orbital speed.

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ncc81701 t1_j34xdbc wrote

I mean this is why rockets are staged and non single stage to orbit vehicles have been put into service. During early part of the flight you have massive engines/power and once you are at high speed and high altitude you drop your boost stage to dump the engine and Fuel/O2 tanks you don’t need anymore and continue to orbit using a much smaller second, 3rd or even 4th stage.

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fliguana t1_j34yvei wrote

Dropping unused fuel tanks is not unique to rockets, some military planes use it too.

In most cases, dropped stage also contains the engine(s), because replumbing inflight is hard, and because the next-stage thrust need is reduced. But not always. For example, the Space shuttle made do with oversized reusable engines and an add-on tank.

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aspheric_cow t1_j38aco0 wrote

Also, you want a larger nozzle at higher altitude (lower ambient pressure). An engine + nozzle optimized for low altitude would be very inefficient at high altitude, so you might as well drop it and switch to the high altitude engine. The Shuttle is an exception as you say, but actually the solid rocket boosters provided about 2/3 of the thrust at liftoff.

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[deleted] t1_j34cc0a wrote

[deleted]

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fliguana t1_j34nl3v wrote

Most engines are. Since liquid fuelrd rocket engines don't overheat, running them at less than top power would mean you are taking extra weight in orbit.

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Origin_of_Mind t1_j355ent wrote

In practice, this is done by numerical optimization, using ready-made optimization software.

A theory which was applied for designing the trajectory for the first "civilian" US space rocket "Vanguard", was presented in an article "Satellite launching vehicle trajectories" by Joseph W. Siry, published in 1959. The article was published in "Orbit Theory, Proceedings of the Ninth Symposium in Applied Mathematics", which unfortunately is slightly difficult to get a hold of.

More recent publications are easy to find, from lecture slides, to NASA technical reports, to various academic publications.

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