I used the thrust to weight ratio of 2.12 to determine the thrust my spacecraft needs for a lunar liftoff, Apollo Lunar Ascent Stage Thrust to Weight Ratio. Is this a proper way of determining and sizing my spacecraft based on the Thrust needed using the thrust to weight ratio of the Lunar Ascent Module?
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$\begingroup$ Lunar surfact gravity is 0.17 g. that means that a craft with a thrust to weight ratio of more than 0.17 can lift off. Is that your question? $\endgroup$– Rikki-Tikki-TaviCommented Feb 19, 2019 at 20:39
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$\begingroup$ If my spacecraft weight for example is 45,000 kg. How much thrust does my engines need to produce? I know you mentioned the gravity. However does my spacecraft also need to satisfy the T/W=2.12, similar to Lunar Ascent Moduls T/W ratio of lunar module. $\endgroup$– user28833Commented Feb 19, 2019 at 20:46
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$\begingroup$ When you say T/W, by "W", do you mean the weight on earth, or the weight on the moon?` $\endgroup$– Rikki-Tikki-TaviCommented Feb 19, 2019 at 21:01
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$\begingroup$ Yes, mass*lunar gravity(1.62 m/s^2 ) $\endgroup$– user28833Commented Feb 19, 2019 at 21:05
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1 Answer
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You don't need exactly 2.12:1 thrust-to-weight; if you have less, you'll need a little more ∆v to reach orbit, because you'll lose more altitude to gravity on your slower ascent, and if you have more, you'll need a little less ∆v. Obviously you need something more than 1:1 or you won't move until you've burned off enough fuel to drop your weight below your thrust.
The exact performance you need is dependent on a large number of engineering factors, but around 2:1 initial thrust to weight is good rule of thumb for lunar liftoff.
(Taking off from Earth you can get away with something like 1.2-1.4:1 initial T/W instead, which is comparable in initial acceleration.)
For a 45 ton spacecraft, to produce 3.4m/s^2 of acceleration (about 2.1:1 TWR), Wolfram Alpha tells me you need 153kN of thrust.
You can check this against the Apollo Lunar Module ascent stage, which was about 4.7 tons (10.4% of the weight of your spacecraft) and had an engine producing 16kN (10.5% of the thrust of my answer).
answered Feb 19, 2019 at 23:16
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$\begingroup$ Is there a different approach to take or an equation to determine the thrust required, if I had the Delta-V for Lunar liftoff and mass of my spacecraft? $\endgroup$ Commented Feb 20, 2019 at 19:05
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$\begingroup$ Without the thrust and trajectory information, you don't know the ∆v to reach lunar orbit. You'll need to iteratively simulate launch to determine whether you have an appropriate combination of thrust and specific impulse; there's no simple equation for it. What are you actually trying to accomplish? $\endgroup$ Commented Feb 20, 2019 at 19:57