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Take the Vega rocket launcher for example. Its first three stages are solid rocket engines and burn at a relatively short time. If I were to change its first stage into a liquid rocket engine, can this theoretical engine have the same thrust as the original one? Or would it make more sense to have a thrust-to-weight ratio greater than one but have a longer burn time?

Possible constraints are:

  • Same diameter
  • Same mission profile (bring upper stages + payload up to 53 km of altitude)
  • Same optimal expansion pressure
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  • $\begingroup$ Given what constraints? In general a solid motor or liquid engine can be designed to have any thrust you want - but the really high thrust levels are usually motors. $\endgroup$ – Organic Marble Dec 19 '20 at 13:12
  • $\begingroup$ Sticking to the example of the Vega rocket, the constraints could be that it should maintain it's diameter, same mission profile (bring upper stages up to 53 km of altitude), same optimal expansion pressure. $\endgroup$ – Miguel Dec 19 '20 at 13:37
  • $\begingroup$ You should edit those constraints into your question. $\endgroup$ – Organic Marble Dec 19 '20 at 13:40
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    $\begingroup$ the speed is more important than the altitude. $\endgroup$ – user20636 Dec 19 '20 at 18:54
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Solid rockets have very high "density specific impulse," that is, they produce a lot of thrust per unit volume, so an equivalent liquid stage of the same diameter would be somewhat longer, but not prohibitively so.

There are a few extant liquid-propellant engines that produce similar thrust to the Vega first stage that could be used. The hydrogen-oxygen RS-68 produces sufficient thrust in a 2.43m diameter engine, but due to hydrogen's low density, you'd need big propellant tanks, yielding a very long and skinny stage. The BE-4 and Raptor are also in the same general thrust class.

The very largest solid rocket boosters -- the shuttle's SRBs, and the similar 5-segment SRBs intended for use on the SLS -- are more powerful than any single liquid propellant engine built thus far (such as the 4-chamber RD-170 and the Saturn V's F-1), but much larger liquid engines have been considered.

Among engines in production today, the RD-191 would probably be the best candidate for a liquid engine to replace the Vega P80 first stage. At the same mass as the solid first stage, it would have slightly initial lower acceleration off the pad, which would be balanced out by the increased mass-specific impulse (311 seconds at sea level, versus the P80's 280). I estimate the stage would be about 14 meters long, just a little longer than the P80 solid stage.

Vega is quite small, as orbital launchers go, but at that scale, liquid engines are competitive with solids by mass and volume.

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The high-thrust limit for a solid rocket engine would be something resembling an explosively formed projectile. This is obviously not something you can equal with a rocket feeding liquid propellant from tanks. Of course, it's also not something you'd realistically use for orbital launch...you'd be compromising its functionality as a rocket to give you more thrust than you can use.

Vega's P80 first stage isn't anything exceptional in terms of thrust though. It produces 3037 kN of thrust and is 3 m in diameter. The Falcon 9 booster is 3.7 m in diameter and produces a total of 7605 kN, with slightly higher specific impulse and longer burn time. A liquid-fueled booster could easily make a drop-in replacement for the P80.

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The five F-1 rocket engines of the first stage of the Saturn V had a thrust of 35,1 MN ( all 5 engines together).

The two boosters of the Space Shuttle had 25 MN (both boosters without liquid fuel engines).

The diameter of the first stage of the Saturn V was 10 m, the solid fuel boosters diameter was 3.7 m each. A single F-1 engine had a diameter of 3.7 m too.

The thrust of a single F-1 was 6.77 MN, a single booster 12 MN.

So if we compare single engines only, the solid fuel had about 75 % more thrust.

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