How to use math to calculate everything?

[TelluriumCrystal]

It's pretty obvious that math runs the universe. One can plan out entire space missions before launch and know exactly what is needed for said mission to succeed. This is what is done (usually quite successfully) in real life. I wanna know how to do it in KSP.

So my question it pretty simple: What math must I do to determine if my spacecraft is capable of launching to orbit on a given body, reaching other planets/moons, landing on a body, determine the max lifting capability of a launcher, etc.? Also, how might I use maths to make my spacecraft more efficient?

Don't be afraid to throw large complex formulas at me, I'll figure it out... probably.

Thanks in advance for any info!

Edited October 16, 2013 by Thrfoot

[Kosmo-not]

Trigonometry, calculus, and differential equations is what you need to know.

A lot of the equations you need can be easily derived. I taught myself basic orbital mechanics from where my physics classes left off.

[gmeine921]

wikipedia has a decent section on orbital mechanics.

launch basics

TWR at launch > weight (or you dont leave ground)

Marginal benefits of more fuel for a heavy spacecraft.

reduce weight in late stages to increase spacecraft effectiveness

in general, mr scott manley has some decent videos where he talks through some orbital mechanics. the maths needed may not be available in most high schools, but most community colleges and universities have classes that may help (differential eq/calculus)

[numerobis]

Trigonometry, calculus, and differential equations is what you need to know.

Eventually, but you can start with canned formulas and work your way up to deriving new things later. Perhaps the best way to start is reading this page on the wiki, which Kosmo-not cowrote but for some reason forgot to pimp!

[purpletarget]

There's plenty of good resources mentioned in The Drawing Board: A library of tutorials and other useful information, some of which contain some of the formula's, derivations, and some exceptions that exist only in the game itself. (*cough*Air Drag*cough)

Also, as not to miss a chance for shameless promotion, check the link in my sig as well.

And of course, plain old wiki can fill in a lot of blanks once you start hitting the right terminology to find what you're looking for.

[capi3101]

If you know Tsiolkovsky and can work it forwards and backwards, you can do pretty much anything. TWR is another good formula to know. Knowing how to calculate the Isp for a rocket with multiple engine types is handy, though almost always I have to look that one up still when it comes time to use it. There's also the full-to-dry mass relationship for most of the fuel tanks in the game (for every liquid fuel tank in the game except the Round 8 and the Oscar B, the tank weighs nine times as much full as it does dry, i.e. M = 9Md - this is a useful relationship to know when you're trying to solve Tsiolkovsky backwards, because with it and the knowledge of your deadweight, you can use it to calculate exactly how much fuel you need to produce a target amount of delta-V for a particular stage of a mission (and therein is the secret to making your rockets more efficient - why use three orange tanks per stack when for what you need you can get away with two oranges, an X200-32, a -16 and an -8?). Work your mission planning backwards.

[arq]

A mod like Engineer or Mechjeb is very helpful for designing rockets to specific missions. With one of these mods and a delta-v map (look around The Drawing Board, or just try searching for one), you can know whether or not a mission has enough thrust and fuel before you even hit the launchpad.

[Mr Shifty]

The two most central algebraic equations to the game are Tsiolkovsky (as capi mentioned) and the vis-viva equation, which you can use to figure out orbital transfers.

[Specialist290]

I'm going to second everything that's been mentioned in this thread, especially purpletarget's videos, because they're a great way to get in at the "ground floor" of applying actual rocket science to KSP and not at all because he already pimped my own little project for me... *innocent whistling*

On top of that, these three pages at Atomic Rockets are handy in breaking down some of the more complex aspects in a step-by-step way (and the rest of the site is worth a read, too, when you have the free time). I'm also going to recommend that you read the pages at MyKSPCareer.com as well, which aims to explain things in layman's terms specifically from a KSP player's perspective.

[TelluriumCrystal]

Wow, lots of advice. I've got some researching to do then!

I should point out that I'm a junior in high school, so I haven't got any experience with calculus or differential equations yet. I'll try to figure it out anyway.

[capi3101]

You can solve most of the necessary equations with algebraic methods. A good calculator helps, obviously...