Rocketeer's Lexicon: Delta-V

Simplified Rocket Equation

So for pretty much the entire narrative of this blog I've been talking about a quality of my spacecraft called Delta-V. I don't particularly like to type delta-v, but my alt-coding is not the best so I'm not actually sure how to type the actual Greek letter I am referring to. Oh well.

Anyway, delta-V, in simple physics terms, is the amount by which a velocity has been changed. There is one such formula for Delta-V based on a steady rate of acceleration over time that every high school student ostensibly knows and which most of you have forgotten, but that is okay because I'm not referring to it ever again. Delta-V in rocketry (whether real, sci-fi, or kerbal) refers to the amount by which a spacecraft can change its delta-V if you were to expend all of the propellant which it carried. Obviously, in staged rocketry this gets more complicated than single-stage rockets which is a part of the reason I occasionally miscalculate my delta-V budget and wind up doing stupid things like Barbara.

Delta-V is actually pretty easy to calculate manually, with a few known values and a good spreadsheet to keep track of the numbers you need. Alternatively you could use a few separate instances of the calculator app built into your computer, or a mod like Flight Engineer or MechJeb, which is my usual choice.

The formula above gives the formula for Delta-V given the velocity of the exhaust (v-sub-e), and the mass ratio (mass with fuel over mass without fuel) from which you take the natural log (ln). So the natural log of the mass ratio, multiplied by the exhaust velocity, gives you your total delta-v. Nominally.

Now, that only works for a single stage, so remember not to discount the fuel in any of the stages above it when you are calculating the dry mass (m-sub-i). This is part of the reason why it is in my view better to use a program like Flight Engineer or MechJeb for doing these calculations in Kerbal Space Program.

The delta-V calculation, or Tsiolkovsky's rocket equation, is one of the single most important equations in fundamental rocketry. If you play quite a bit of KSP or want to start making model rockets or are going to work for a major space agency (or space corporation) one day, you're going to need it. Advice from the interesting website Project Rho for aspiring hard-sci-fi writers is actually to have it on a poster or t-shirt. I simply memorized it as that was far easier.

Delta-V is so important because it is fundamentally the range of your spacecraft, which is to say a map of real distances in space is actually far less useful than a delta-v map showing the required delta-v to get from point-A to point-B. Making some exceptions for nifty things like the Oberth effect and aerobreaking, your fuel-based Delta-V is going to pretty well limit where you can go and what you can do once you've gotten there. Further, it's a useful measure of range because it already took into account the mass of a craft, so the delta-V of a TDRS satellite tells you exactly as much as the Delta-V of a Star Destroyer.

So, once you've got an idea of delta-v, it's helpful to have a map of delta-V values for the sorts of places you want to go in your world. If you are kerbonaut, there is an excellent one here. Happy Flying.