Step-by-Step dV calculation?

[Vectura]

I am trying to make a small utility to calculate dV of a single stage. I just wondered: what variables will it need, and what is the step by step mathematical process to get the final number? Sorry if this is the wrong forum section

[EtherDragon]

You need to know the following pieces if information:

The vessel's dry mass - that is it's mass without any fuel loaded.

The vessel's wet mass - that is it's mass with a full load of fuel.

The Isp of the rocket motor.

With these infos you can run the numbers through a rather simple equation to find its delta-v.

The real difficulty comes down when you have multiple stages. You need to do the same calculation for each stage to determine the vessels total effective delta-v.

For reference - here is a link to Tsiolkovsky's rocket equation.

[Vectura]

Thanks. I assume that with the calculations for lower stages I should include the wet mass+part mass of all the stages above?

[Rune]

That's really easy. You need the initial and final masses of your rocket (for each stage on a multistage design, of course), and the isp of the engine. Let's call those Mi, Mf, and Isp. DeltaV (dV) would be:

dV=9.81*Isp*Ln(Mi/Mf)

As simple as that, Ln is the natural logarithm (base e). Any calculator can do that in a second! The only laborious part is adding and subtracting masses around. And of course, Mi and Mf are before and after a rocket burn, you have to consider the whole rocket as it does the burn, upper stages included.

Rune. Shouldn't be hard... but a bit redundant, given KER and the like.

[Vectura]

Thanks! Simpler than I thought

[EtherDragon]

Thanks. I assume that with the calculations for lower stages I should include the wet mass+part mass of all the stages above?

Hint dropped and picked up, good job!

Yes, you are exactly correct. Given an arbitrary number of stages the dry mass for stage N is always equal the dry mass for stage N plus the total mass of stage N+1.

Specific example - a two stage rocket

Stage 1 has 15/10 wet/dry masses (not counting stage 2)

Stage 2 has 10/5 wet/dry masses (not counting stage 1)

Your delta-v calculation would consider stage 2's wet mass as part of stage 1's dry mass, thus the actual values are:

Stage 1 = 25/20 wet/dry* mass (*includes wet mass from stage 2)

Stage 2 = 10/5 wet/dry mass

Then you calculate each stage based on the Isp for the engine available. For instance Stage 1 might run at 250 Isp, but stage 2 might run at 800 Isp.

So you plug those into the rocket equation (thanks Rune for posting it!) and you end up with

dVs1 = 9.81*250*Ln(25/20)

dVs2 = 9.81*800*Ln(10/5)

Since Total dV = dVs1 + dVs2 you end up with

dVt = 9.81*250*Ln(25/20) + 9.81*800*Ln(10/5)

[numerobis]

g0 is 9.82 in KSP, not 9.81 (or 9.806... IRL).

[pincushionman]

Thanks! Simpler than I thought

It's not very complex, in the strictest sense. The difficulty and complexity come from making sure you correctly account for all your sources of mass and properly carry them through your stages, approptiately identifying your Isp (especially with mixed engine clusters), and the like. THAT part can be tedious and error-prone, and that's why so many players prefer tools to do the heavy lifting for them.

So it's a really straightforward MATH problem, but it CAN BE a difficult BOOKKEEPING one.

[GoSlash27]

If you're looking to calculate the DV for one stage, you would only include the wet mass of stages that are being treated as payload.

So here's the process for doing it:

Mp is your payload

Me is your engine mass

Mt is the mass of your empty fuel tanks

Mf is the mass of your fuel

Mp+Me+Mt+Mf= Mw; your wet mass

Mw-Mf= Md; your dry mass

Mw/Md= Rm; your mass ratio

LN(Rm)= Cdv; your delta v coefficient.

Isp= the specific impulse of your engine.

Cdv*9.82*Isp= DV; the total delta v for that stage.

Best,

-Slashy

Edited December 12, 2014 by GoSlash27

[justidutch]

I gets a little funner if you happen to have a stage with different engines though. Then you have to calculate the weighted average of their ISPs first.

I too built my own DV calculator - a great little project to do at work instead of working.

[LethalDose]

If you're looking to calculate the DV for one stage, you would only include the wet mass of stages that are being treated as payload.

So here's the process for doing it:

Mp is your payload

Me is your engine mass

Mt is the mass of your empty fuel tanks

Mf is the mass of your fuel

Mp+Me+Mt+Mf= Mw; your wet mass

Mw-Mf= Md; your dry mass

Mw/Md= Rm; your mass ratio

LN(Rm)= Cdv; your delta v coefficient.

Isp= the specific impulse of your engine.

Cdv*9.82*Isp= DV; the total delta v for that stage.

Best,

-Slashy

You go on a tear about how calculating dV isn't complicated, and then you start inventing superfluous notation to complicate dV calculation...

Ignore the Cdv and Rm terms above. The notation clarifies nothing and isn't used anywhere else. Just stick to the equation:

9.82 * Isp * ln(Mw/Md)

since it's recognizable as the actual equation.

[GoSlash27]

You go on a tear about how calculating dV isn't complicated, and then you start inventing superfluous notation to complicate dV calculation...

Ignore the Cdv and Rm terms above. The notation clarifies nothing and isn't used anywhere else. Just stick to the equation:

9.82 * Isp * ln(Mw/Md)

since it's recognizable as the actual equation.

Know how I know you didn't read the actual OP?

The man asked for a step-by-step process and variable names to use in his utility and this is what I gave him.

More reading, less being snotty please and thank you.

-Slashy

[Pecan]

You have all the information you need, here's how NASA explains it. There's a load of interesting stuff on that site, as you'd expect.

[LethalDose]

Know how I know you didn't read the actual OP?

The man asked for a step-by-step process and variable names to use in his utility and this is what I gave him.

More reading, less being snotty please and thank you.

-Slashy

No, I read the OP, the equation should be presented as a one-step process. It's why I didn't say anything about the separate mass terms, which are useful.

PS Learn to take your own advice. Especially before starting threads that insult large swaths of the community.

[Basketcase]

Here, I did this real quick. It should be accurate minus a few absolute value and dot indications.

[Vanamonde]

Please don't make this personal, folks. Talk about the math and leave each other's personalities out of it.