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In other words, why was the F1 rocket engine programme stopped? Is there a sense that solid motors can take care of high thrust cases in a better way? Or is it an unfortunate fallout of the end of the space race?

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It's likely a mix of both factors.

First, there's little demand at present for 100-or-more-ton-to-orbit launchers like the Saturn V. Robotic exploration of the solar system is cheaper and safer than crewed missions, and requires payloads less than a tenth the size. New Horizons, for example, massed only half a ton. For the vast majority of space launches, the payload is under 20 tons. Very large engines like F-1 aren't needed for rockets that size.

Second, solid rockets provide much more thrust per dollar in expendable systems than liquids, so the large solid booster + medium liquid sustainer first-stage strategy is preferred for large uncrewed launchers, and even some crewed ones (shuttle and SLS), though many people challenge the wisdom of using unstoppable solids for crewed flight.

SpaceX believes that reusability can reduce the cost of large liquid-fueled launchers to a point where latent demand manifests, but they haven't proven this.

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    $\begingroup$ Plus, SpaceX goes the route of using many small engines instead of few large ones. F1 had combustion stability issues, G9H/BFR/IPS will have to prove the can cope with pogo oascillations from that many engines. Furthermore, F1-B was part of the liquid booster design that was under consideration for SLS. $\endgroup$ – Polygnome Jul 31 '17 at 20:04
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Most of the rocket engine producers and consumers seem to have bought into the idea that more engines means more chances of failure without considering the many other things that affect reliability, such as good engineering that provides adequate testing and accounts for all factors that affect reliability and ample testing and evaluation of flown engines to preclude unknown factors that affect reliability.

One of the major innovators in rockets is SpaceX and their choice to use many small engines was wise. Unlike NASA, they saw that reducing cost was very important and made two important decisions to reduce cost which also improved reliability.

The first choice was reusable rockets. This returns the rocket engines to the factory for inspection. It is much easier to analyze an intact engine for developing flaws (cracks that have started but are not a failure yet) than an engine that has exploded and burned.

The second choice was a production line that was as automated as possible. In addition to greatly reducing labor costs, it also means more consistent quality, especially for machine welds instead of hand welds.

Finally, the availability of multiple rocket engines means potential redundancy but the engine controller must be able to use them well. In the days of the Russian N30, the controllers were very limited in their ability to respond to engine failures. SpaceX has shown that today's computer systems can do remarkable things.

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The other answers here are wrong. They provide good explanations for why there isn't more demand for large liquid engines, but there is demand since there is one that is still in active use. The RD-171 has 7% more thrust at sea level then the F-1 had. It is used on the Zenit rocket. Which has launched as recently as December of 2017.

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    $\begingroup$ Although I prefer more neutral wording like "I would not agree" instead of "wrong" - yes, big engines are not undemanded in fact. The Russian rd-171 is also planned for Soyuz-5 rocket (=upgraded russian-built Zenit). China is considering design of YF-660 engine for superheavy CZ-9 rocket, although maybe has not decided finally is it better than multiple small engines or solid fuel boosters. $\endgroup$ – Heopps Sep 25 '18 at 7:50
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    $\begingroup$ The difference between the RD-170 and F1 is that the former uses four combustion chambers and the latter uses one. I think most answers here assume that single-chamber engines were meant by the OP. Furthermore, while it has seen recent use, its an old design, and I think most people understood the question to mean why there isn't demand for newly designed engine in that power range. That being said you are right, there is demand. For example F1-A / F1-B was under serious consideration for the SLS as late as 2015. $\endgroup$ – Polygnome Sep 25 '18 at 14:43

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