Calculating true delta V aka more umph than I thought

[inigma]

Ok so after proving to myself that I can do the math for TWR and Isp and dV, I installed engineer redux. I planned a Munar mission but realized my third stage would still be burning through from atm to vacuum. Redux doesn't appear to calculate for this transition. How can I? I designed the third stage to boost me to almost LKO, but find that my total actual dV used for my entire mission is 300 more than I need. The culprit is that third stage and I hate over building my rockets, but I don't know how to calculate the atm to vac dV transition. I have a bad feeling it will not be a simple exercise.

Edited June 24, 2013 by inigma

[stupid_chris]

Usually, what I do is I consider 1000m/s being fully atmospheric delta V to get through the first 10km, then the rest being fully vacuum delta V. It's not 100% precise but it has proven to be suprisingly precise on my rockets.

Basically, lets say your first stage has 1500m/s in atmosphere and 2000 in vacuum. You substract 1000 from the atmospheric part, theres 500m/s left and in vacuum this is equivalent to about 666m/s. So your first stage would give you a total of 1666m/s approximately. Then you calculate the rest as vacuum delta V.

This is an approximative method, theres probably a mathematical way to do it but it depends on your ascent profile and all. If you have a good TWR (>1.6), this should be pretty precise honestly. When I use this and calculate exactly 4500m/s this way I'm usually left with ~100m/s at the end.

That's how I do it at least, probably other people will do it otherway but yeah, good luck!

[inigma]

You said 500 m/s atm is equivalent to 666 m/s in vac. How did you arrive at that?

I like the subtracting about 1000 dV bit, its what to do with the remainder that has me wondering the best guesstimate method.

What would you calculate a 5000 dV atm 7000 dV vac rocket's actual dV?

Edited June 24, 2013 by inigma

[stupid_chris]

Okay, I'll take a screenshot from what of my actual rockets and show you how I do it, I'll upload the pic in a sec, hold on.

[UmbralRaptor]

My rule of thumb is that any engine that burns all the way from surface to orbit gets 80% of its vacuum Isp. Eg: an LV-T30 (320 - 370 s) would get 360 s, and a Mainsail (280 - 330 s) would get 320 s.

For stages that burn only partway, it's more of a best guess thing, depending on what altitudes are involved, how many stages to orbit, etc. Anything that doesn't start burning until >10 km will get >90% of its vacuum Isp anyway...

[stupid_chris]

Alright here it goes. Screenhot of my rocket on the launchpad:

So let's do the math. Here, stage 4, 3 and 2 are used to get in orbit. So let's start with stage 4, who has 1476 of delta V in atmosphere and 1724 in vacuum. Thus, it has this 1000m/s to himself. So, if we take away, 1000m/s from the fourth stage atmospheric delta V, theres 476m/s left. 476/1476=0.32, meaning that 32% of the fuel will be left in the stage when it passes the "atmospheric limit". So, there will be 32% left of the vacuum delta V, so 0.32*1742=562m/s. So, for our first stage, wel'll get 1000m/s atmospheric + 562 vacuum, meaning we get a total of 1562m/s from our first stage. Then the other stages are considered vacuum, so 1562+1863+1197 = 4595m/s of delta V in total for our launch stage. To prove this out, I launched it with MechJeb to an altitude of 80k to have the most precise results possible:

Here we can see that the total delta V expanded to get into orbit is 4530m/s and there's roughly 125m/s left in the launch stage, so the total delta V of the rocket was actually 4655m/s, which is only 60m/s from the predicted 4595m/s. So yeah that's how I calculate my stuff. If you have multiple stages to get the first 1000m/s, just calculate the first as atmospheric and you do the same math as I did above to approximate the delta V of the one who goes through the limit.

The results will vary a bit depending on your TWR and such but it should usually be pretty darn accurate.

EDIT: To answer your question, that's how I calculated the 666m/s earlier: 1500-1000=500 --> 500/1500=0.33 --> 0.33*2000=666 --> 1000+666=1666

Edited June 24, 2013 by stupid_chris
extra info

[inigma]

Thank you. You sir are awesome. At least my head wont explode now.

[stupid_chris]

No problem, always glad to help!

[inigma]

Essentially:

Transitional AtmVac dV = [(dVatm-1000)/dVatm]×dVvac+1000

Very useful.

Edited June 24, 2013 by inigma

[metaphor]

I just ignore the atmospheric delta-v and only look at vacuum. I use 4600 m/s vacuum delta-v as a guideline from the surface to low Kerbin orbit, which works pretty well unless you're using nuclear engines near the surface.

Also if you have 300 m/s extra delta-v, that's very little. You're probably going to need that as margin in case your ascent or landing isn't perfect.