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Originally Posted by niky
Your acceleration rate would stay the same until relativistic effects increase the mass enough to blunt accelerative force. There is no drag in space, so acceleration will not taper off.
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Hi niky,
I am using the word power to mean power, in the exact specific physics sense: P = F x V
None of NASA's graphs show power they show acceleration. In the case of big rockets the power generated at lift-off is lower, because the nozzle is poorly coupled to the atmosphere for low speed - it's low efficiency. By design they are built to deliver maximum efficiency near the expected burn-out altitude and speed. Each rocket nozzle is designed to get good efficiency over a specific speed range. Faster and you lose a lot of thrust. Since all the propellant will be used, and for various engineering legacy reasons, rocket designers never talk about power, it is irrelevant to the design. Specific impulse and thrust are what is tossed around.
But just for fun consider: The main engines on the Shuttle: near the point of normal shut off, that is over 100 miles up, and at about 17,000 mph with the fuel almost used up, the mass of the Shuttle was about 250,000 lbs. Because of mechanical and human limits, acceleration was generally below 3 g, the engines were throttled back to about 750,000 lbs of thrust. So 750,000 lbs x 17,000 mph/375 = 34 million horsepower. Full power (or 109% throttle - the allowed maximum) is where the maximum amount of fuel that can be pumped is being burned and the nozzle is near 100% efficiency. Fuel cannot be pumped faster, the engine is at peak power.
If you had more (weightless) fuel and continued to run the engines, your acceleration would fall off. So at around 140,000 mph they would just be able to make about 1 g. That's because the engine cannot produce ever increasing power. As you go faster engine-nozzle efficiency falls off too. Of course, as you mention fuel isn't weightless and the effect of throwing off mass is important.
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It doesn't matter what speed you're going. Applying force x in one direction causes x acceleration in the other, along any vector, no matter what your velocity is on the other vectors.
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This makes me think you are confusing force and power.
Every engine has a maximum power output. For a rocket that happens at the maximum fuel use rate and maximum nozzle efficiency. When it is at that output the force (thrust) the engine makes is exactly the power divided by the speed. As the speed increases the thrust decreases. If you want to continue accelerating at a constant rate, you need to add more power (which can't happen) or throw off more mass.
-mort