To achieve fuel economy during orbital launches (for a particular orbital altitude), do we select the first stage (its thrust), in such a way so as to achieve the desired altitude above the Karman line, (with all the payload - such as that of the hardware for all the stages) with the least acceleration, and then once at the desired altitude, fire the rockets (may be second stage) to impart enough tangential velocity in that orbit (e.g. 24000 kilometers /hour)? I might have elaborated more than required, but that's because my experience is people tend to comment more on the letter than the spirt of the question. - So, sorry for that.
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Fuel economy is absolutely imperative in rocket launches. The rocket equation is such that we have no wide margins in getting stuff to space.
But we have some (sometimes opposing) parameters to keep in mind and balance them against each other to get the optimal launch profile for each mission.
- We want to accelerate as fast as possible to minimize gravity losses
- We want to turn horizontal as early as possible to minimize gravity losses (in the end, everything that counts is horizontal velocity for orbital flights)
- We want to leave the dense parts of the atmosphere as quickly as possible to minimize aerodynamic losses (and reduce aerodynamic stresses)
- We need to keep the speed inside the atmosphere within certain limits to not overstress the structure
- We need to keep the acceleration within certain limits the whole trip to not overstress the structure and the payload
About the karman line: It has no meaning at all for our purposes here.
So your idea of going vertical as quickly as possible to get above most of the atmosphere and than turn horizontal fulfills some points some points in the list above but contradicts with others. It would also be very hard to turn a rocket quickly and impart high loads on the structure.
So every rocket start is a question of finding the optimal parameters the get as much payload to the destination with as little fuel as possible while staying within the structural limits of the system and with the performance available from the rocket motors.
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$\begingroup$ :My idea is NOT to go vertical ASAP. On the contrary, I was thinking of having minimum speed for going up, & thus avoid spending more fuel to save time. The intention of crossing the Karman line & then imparting horizontal velocity is to minimize atmospheric drag (practically no atmosphere above Karman line). As you said correctly, for an orbital flight, all that matters is the horizontal velocity. So, I was thinking of saving fuel for the same instead of wasting the same to save time. As such with lower accelerations, many problems (3,4 &5) are over. Your views please. $\endgroup$– NiranjanCommented Aug 15, 2022 at 10:48
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$\begingroup$ Further, what is the minimum acceleration required in order to keep us climbing upward, till we cross the atmosphere? Do we need to have just more than 9.8, or is that dependent on other factors too? It need not be a straight vertical path, it can be curved one also, but upwards, eventually to touch a part of the orbit, it would take. I believe that the thrust will depend on the mass of the entire rocket. $\endgroup$– NiranjanCommented Aug 15, 2022 at 10:56
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4$\begingroup$ Let's play a mind game: you want a rocket, which is "standing" in the air on a constant altitude. This rocket would use much fuel and achieve nothing. Thrust would be equal to the mass of the rocket. Now go next step an increase the thrust a tiny bit. Your rocket would keep going up, but most fuel would be burned to keep fighting gravity. Optimizing trajectories is not about saving time, it's about wasting as less fuel as possible working against gravity. That is why we try to get into less dense atmosphere as fast as possible: to avoid working against gravity. $\endgroup$ Commented Aug 15, 2022 at 12:20
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4$\begingroup$ @Niranjan what CallMeTom said... Climbing slowly increases your gravity losses. If you're hovering, your gravity losses are infinite (you're spending fuel but not gaining any hight/energy). Because of that, climbing slowly is a really bad idea. It's exactly what happened to this astra rocket when it lost an engine... what Scott Manleys Video: youtube.com/watch?v=x2jU5W4ehPE $\endgroup$ Commented Aug 15, 2022 at 13:41