How to find the optimum balance between amount of fuel and number of engines?

I'm coming from a background of Kerbal Space Program, so I'm not 100% sure all of this applies to real-life but I'm asking in the hopes someone might tell me that. Yes, I know, it's not real space travel and it doesn't accurately simulate all physics perfectly, but it's a good approximation and the core concepts are unchanged, so I consider it a good way to get introduced to concepts which one can then go and research further.

One thing that becomes pretty apparent from the start is that to get to orbit you need engines. To power these engines you need fuel, but fuel has mass, so you need more fuel and eventually things get pretty large and expensive. Each engine has a specific impulse and a craft (as we understand it to be a collection of payload, fuel, and engines) has a certain amount of delta-V, or the change in velocity possible.

Every maneuver, ascent, or powered landing the craft makes eats away at this budget of velocity change. From playing around it seems to be that making the following changes has the following effects:

• The thrust to weight ratio decreases. In orbit this doesn't appear to matter, but when landed it must be greater than 1 to have enough thrust to lift the craft.
• The amount of time the engines can burn for increases, but does this mean the delta-v only increases if you assume you are not ascending/landing and therefore do not need a TWR > 1?
• The TWR increases The thrust increases (and this usually increases the TWR, but not if the engine is exceptionally heavy in relation to the thrust produced), but the amount of time the engines can burn for decreases as more fuel is burnt in the same amount of time.
• I am unsure how delta-v changes here. It seems like adding more engines without adding more fuel does not increase it, it just means the same amount can be expended in a shorter time.

So when constructing a spacefaring vehicle (in reality), is there a mathematical or "proper" way to determine the optimum balance between fuel and engines? Furthermore, is such a method dependant on the celestial body/bodies you are within the Hill sphere of?

• Since you don't mention it...do you know about the rocket equation? en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation – Organic Marble Feb 28 '17 at 14:08
• Oh god, all that maths. I can't even say it's not rocket science. So I take it (I have no strong maths background) the rocket equation can be rearranged to allow me to find out the optimum balance of engines/fuel if I have a set of available existing engines with known properties? – Leylandski Feb 28 '17 at 15:01
• @Leylandski: While you don't need to know all that math, you need to know $\Delta v =v_e ln { m_0 \over m_f }$ and $v_e = I_{sp} g_0$ - these two are all that binds high school level physics with rocket science; you can solve 90% of problems involving maths on this SE site with these and Newton's 3 laws + conservation of momentum. – SF. Feb 28 '17 at 16:27
• Mandatory related XKCD – Gallifreyan Feb 28 '17 at 21:28
• Related – Max Q Lagrange Feb 28 '17 at 21:36

You're correct that the thrust level doesn't affect delta-v at all -- the rocket equation (which is not very much math at all, really) doesn't have a thrust term. The only variable factors in it are the mass ratio $\frac {m0} {mf}$, which is maximized by carrying a lot of fuel, and the exhaust velocity $v_e$, which is a property of the engine type. In KSP, exhaust velocity is indicated via the specific impulse figure for an engine, which when multiplied by 9.81 gives the exhaust velocity in meters per second.
The other part of the rocket equation is the natural logarithm function $ln$ which reflects the diminishing returns of carrrying more fuel.