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Does the cost of every subsequent dV exponentially increase?


NaniByte
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In career mode you have a cost constraint to optimize for. I have noticed that certain rocket sizes are much cheaper then other ones. Using the Kerbal Optimal Rocket Size calculator,assuming a 10t payload and assuming it's correct, you would get values along these lines:

Total dV Total Cost Cost Next dV
9000 248630 /
8000 161570 87060
7000 88400 73170
6000 53160 35240
5000 30800 22360
4500 24470 6330
4000 21080 3390
3000 11200 9880
2000 7575 3625

As you can see from this, not very scientific, table the cost from going from 7000 dV to 8000 dV is much greater then going from, say, 5000 dV to 6000 dV. There is that strange anomaly around 3000 dV. There appear to be a brake-point somewhere when it becomes more cost effective to launch multiple rockets, for example a main one and a refuel one, then to launch just one single rocket. This also appears to get much worse the heavier the payload.

That is why I have been thinking about how a mining base on Minmus is a real gateway to the heavens. Allowing you to launch much smaller rockets because you can split the dV need for the mission and the initial to orbit and out of Kerbin's SOI.

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Such is the tyranny of the rocket equation.

Fuel is very inconvenient in that it has the gall to have mass.  When you add more fuel, and therefore more mass (in fuel and in tanks), you get less dV from the fuel you already had.  It's the reason staging exists.

 

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trying to be less cryptic than the other posters:

take you rocket, put a bit of fuel, you get some deltaV. Now add the same amount of fuel - for the same cost - you don't get twice the deltaV, you get less. That's because the new fuel must push also the old fuel; your rocket is effectively heavier. Worse, even after you spent all your fuel, those empty fuel tanks are still heavy, making - again - your rocket heavier. So the more fuel you add, the less it is convenient. Past a certain point, the weight of the fuel tanks alone is so much, that you stop gaining meaningful deltaV by adding fuel tanks.

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