Understanding Delta-V

[Mr Shifty]

TWR is always relative to local gravity. TWR 1 means you're just able to hover, i.e. you spend all your dv on fighting gravity.

If your TWR is higher, "1" of it always goes to fight gravity. So if your TWR is 2, half your dv is spent to fight gravity and half is used to ascend. If your TWR is 3, 33% is lost to fight gravity.

As you're getting to orbit, you are compensating gravitational pull by centripetal force generated by your horizontal speed. Thanks to that, your effective weight decreases and your effective TWR is growing.

Ignore the air for now. On an airless world, the most efficient way to reach orbit is to thrust sideways without losing altitude. Getting to orbit requires speed not altitude, and every extra bit of thrust you use to gain altitude is wasted on fighting gravity. If you have a TWR of 2, you can thrust sideways at an angle of 30° to the horizontal and still have enough upward thrust to maintain your altitude. At that angle, you still have a horizontal thrust of 1.732, so you're only wasting 13% of your thrust to fight gravity. Obviously, on an airless world, the higher your thrust, the more horizontal you can thrust and thus the more efficient your ascent will be.

Air, of course complicates the picture. Due to how air resistance is modeled in KSP, your most efficient speed in atmosphere is terminal velocity. (Note that this doesn't necessarily match how air resistance works IRL.) And you reach and maintain terminal velocity with a TWR of 2. Since your TWR increases as you burn fuel, it means that a starting TWR of slightly less than 2 -- 1.7 or 1.8 -- will give you the most efficient ascent. It also makes sense when you're ascending in atmosphere to get into thinner atmosphere as quickly as possible, so that your terminal velocity will be higher, which is why we have a vertical portion of the ascent before gravity turn.

[Nao]

Hell, did y'all think I was including the payload? I mean, the shoot the whole thing into space as one big piece with no decouplers whatsoever? No way...

Ohh that clears that out

Ignore the air for now. On an airless world, the most efficient way to reach orbit is to thrust sideways without losing altitude. Getting to orbit requires speed not altitude, and every extra bit of thrust you use to gain altitude is wasted on fighting gravity. If you have a TWR of 2, you can thrust sideways at an angle of 30° to the horizontal and still have enough upward thrust to maintain your altitude. At that angle, you still have a horizontal thrust of 1.732, so you're only wasting 13% of your thrust to fight gravity. Obviously, on an airless world, the higher your thrust, the more horizontal you can thrust and thus the more efficient your ascent will be.

100% correct... but! The more engine mass you take with you the less dV you will get by burning fixed amount of fuel.

On airless body, using nuclear engines, the most Mass efficient launch TWR is only ~1,25.