Building Efficiency and Math

Lets Do The Math!

In this section of the blog i will be going over the the math and equations needed for space flight. What will be discussed is the thrust to weight ratio, how the equation works and how simple it is to build an efficient rocket following these steps.

Basically, it's the result of dividing your thrust (in newtons) by your weight (in kilograms times acceleration, i.e. kg*m/s², so... well, also in newtons). Thrust is what gets you up, weight is what keeps you down. And if thrust > weight, i.e. if your thrust-weight ratio is more than 1, you go up. If thrust < weight, you can put your engines into overdrive and you won't move an inch. For the record, the Saturn V first stage rocket engine had a TWR of 94.1. In other words, it could have lifted itself over 94 times. Beat that!

What does that mean for our space vehicle? Basically, it means that whatever we put as rockets behind our craft, it has to overcome the total weight of the craft. Which also means that, if you have multiple stages, the upper stages are just dead weight at start. Yes, yes, there are rockets in there and they might have a lot of punch, but they do not add to the thrust at start. Thrust is always only the thrust you ACTUALLY apply, not the thrust your rocket can eventually do in total.

Note that every rocket engine has a TWR of more than one. By definition. Engines below a TWR of 1 need some kind of aerodynamics on the craft to get it off the ground. The question is, though, whether the dead weight sitting on top of it STILL keeps that equation above 1. The F1's 94.1 TWR doesn't mean that the Apollo craft got shot into orbit at 100g. It means that there was a friggin' HUGE rocket sitting on top of that engine and hence it could barely get the whole behemoth up into an orbit!

My guess is that Kerbin has a gravity of about 10 m/s² (much like earth), meaning that a rocket engine rated at 200 max thrust (like the non-gimballed stock engine) can lift 20 units of mass (or 8 stock liquid fuel tanks). Given that a rocket of 1 stock command center, 7 fuel tanks and 1 engine (totalling a mass of 20.5, 7*2.5+2+1) can't get off the ground but with 6 fuel tanks it can, I'd say that should be about right. So when building your rocket, always add up the mass of the parts you assembled, multiply by 10, then divide by the thrust of the engines, but ONLY the engines that actually thrust. The more you get out of that, the faster your rocket will climb. Considering that engines seem to overheat more readily if they're operated at the TWR limit, try to get to a TWR of at least 1.7 in your first stage. My Mun rocket has a first stage TWR of 2.2, which is plenty but not overdoing it to the point where the g-forces become unmanageable.

Also, keep in mind that you will use up fuel as you climb. Your fuel tanks will get emptier with every second your engine fires, making them lighter, meaning, less weight has to be lifted. Plus, gravity decreases with distance squared, which also makes the pull of Kerbin less and less with every inch you climb. Not as much as one would wish, though.