This is a continuation of a previous question posted a few months ago. If we consider a SSTO vehicle launching from a planet with an atmosphere, would it be fuel optimal to have a period of lowered thrust whilst going through the thickest part of the atmosphere (even if we ignore dynamic pressure constraints), in order to minimize the largest losses from drag? If so, would a fuel-optimal thrust profile for an ascent into orbit consist of an initial period of maximum thrust, a second period of lowered thrust, a third period of maximum thrust, a fourth period of zero thrust (coast phase), and a fifth and final period of maximum thrust in order to circularize the orbit?
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asked Sep 21, 2017 at 12:15
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Essentially, yes. Providing you can output enough thrust and the atmosphere is so dense that your atmospheric drag losses during that relatively short period would outpace gravitational drag losses over the whole ascent.
On Earth, with the kind of propulsion we have, this isn't the case: MaxQ is primarily a structural durability concern, air pressure drops rapidly over the first few kilometers, air drag becoming far less of an issue rapidly, and gravitational drag swallows nearly 1000m/s of delta-V, never mind higher pressure reduces performance of engines making such rapid acceleration difficult to achieve.
So, essentially, on our planet, with engines as they are, and rockets as durable against dynamic pressure as they are, the "reduce thrust to reduce atmospheric drag" constraint is never encountered. It might become an issue with ground-aided launches (e.g. a "space gun" that gives the rocket first 2km/s at ground level) or if trying to launch from Venus or such. Not with current propulsions though.
I wouldn't be entirely sure about "fifth and final period of maximum thrust in order to circularize the orbit". You need very little delta-V to circularize, you operate at very high TWR (engine acting at maximum vacuum thrust, fuel tanks mostly empty not weighing it down!) and you want to achieve your orbit with a decent precision. Therefore throttling down may be desirable for practical/safety purposes (completely apart from fuel-optimality).
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1$\begingroup$ Also remember the old adage: fuel is cheap, engines are expensive. It's usually better to load up some more delta-V by increasing wet mass (extra fuel) than to reduce delta-V losses (add engines, increase TWR). This is unlikely to change anytime soon, meaning we're unlikely to see this constraint triggered in a very long time. $\endgroup$– SF.Sep 22, 2017 at 7:13