Calculating A Delta V Budget

[The Flying Kerbal]

So I've just finished another session of KSP (at 3.03am, lucky I'm off work today...) by putting the "John Glenn" satellite into a highly elliptical orbit.  As usual I had way too much fuel on board, I could probably go interplanetary and return to Kerbin with what's left.

The problem is I haven't got a clue how to calculate Dv for orbits specified in contracts for satellite launches.  Going to a moon or another planet - just look up a Delta V map and Bob's your uncle, but with a one off orbit for a satellite it's not so easy.

So the question, how do you calculate a Dv budget for such orbits so you don't end up hauling a truck load of fuel into space which is never going to be used?

Thanks everyone. 

[Foxster]

Well you can "run it in the simulator" first i.e. fly the mission, check the dV or fuel usage then revert the mission and remake it more economically. 

[Reactordrone]

You can also just pick a ship in low Kerbin orbit and place manoeuvre nodes to get it to the right orbit (without actually executing any of them) and then just add up the delta-v of the nodes.

[GoSlash27]

TFK,

 The proper way is to employ the vis- viva equation. Start with the DV to get to LKO, then add the computed DV to get into the desired orbit. Once you have established the desired DV, use the reverse rocket equation to design the stage. If you do it right, you will arrive in the desired orbit with little to no fuel remaining.

Best,
-Slashy

[Rauko]

3 hours ago, Reactordrone said:

You can also just pick a ship in low Kerbin orbit and place manoeuvre nodes to get it to the right orbit (without actually executing any of them) and then just add up the delta-v of the nodes.

I do this. (In fact, this is one of the very few real practical usages my LKO space station has)

[Snark]

14 hours ago, The Flying Kerbal said:

So the question, how do you calculate a Dv budget for such orbits so you don't end up hauling a truck load of fuel into space which is never going to be used?

Well, the way I generally calculate it is to just not care much about having some leftover fuel.    It doesn't cost much, and given how many launches I do, I'd sooner just pay slightly more than I need to and save myself the time of doing the calculations.

If you want to actually do the math, then the vis-viva equation is what you want, as @GoSlash27 points out above.

Depending on the situation, there may be some other little clever tricks you can do, which will give a more accurate idea than "just wing it", but are simpler and quicker than cranking through the vis-viva equation yourself.

One thing you can do (in some cases) is use a "proxy" for orbit calculations, as @Reactordrone describes above.

Another approach is to simply use a knowledge of limits to "box in" the dV you need.  Getting it approximately right is often good enough.  Specifically, here are some numbers to know about Kerbin, assuming you're already in LKO and coplanar with your target orbit:

• The cheapest target orbit to get to is "also LKO", which is close to zero dV.
• The needed dV climbs, up to a certain maximum, as the altitude of the target orbit increases.
• Getting to a circular orbit at 2700 km altitude will take about 1100 m/s of dV.
• The most expensive circular orbit to get to from LKO is roughly 9700 km altitude, at which point you need about 1230 m/s dV from LKO.
• Above that altitude, the needed dV goes down somewhat.  At the highest-possible circular orbit out around the bounds of Kerbin's SOI, the needed dV is about 1100 m/s.

So, what this tells you is that if you build a satellite that has about 1200 m/s of dV remaining after LKO, and you launch it into an orbit that's approximately coplanar with the target orbit, then you'll be able to match any orbit you like.  You never need more dV than LKO plus 1200 m/s.  That's a useful number to know. 

In other words:  for all target orbits between 2700 km and the edge of Kerbin's SoI, the needed dV is between 1100-1230 m/s.  That's a pretty darn narrow dV range for a very wide variety of target orbits.  So if you just give yourself 1200 m/s of dV after LKO, you'll have about the right amount for practically any orbit in that range, with no more "wasted" dV than 100 m/s or so.

If the target orbit is significantly lower than 2700 km, you'll need less than that.

[bewing]

I always need more tankers and spacetugs. So I make sure my "satellites" always have an extended lifetime after I complete the first contract. First, I wait until I have 3 or maybe 4 satellite contracts to complete, and then I build my rocket to complete all of them. And then make sure it has all the parts necessary to be a nice interplanetary tanker or spacetug after the satellite missions are complete. So, the more deltaV in LKO the better.

 

[Plusck]

I came to much the same conclusion as Snark, but from a slightly different approach:

Getting to the Mun requires at burn of "almost 900 m/s". Capturing at the Mun needs "about 250 m/s".
Getting to Minmus needs "almost 1000 m/s". Capturing at Minmus needs "a bit more than 150 m/s".

Therefore 1150 m/s will get you to to a circular orbit anywhere from the Mun to Minmus and beyond. Since you benefit a bit from the Oberth effect because of the size of the Mun, you'd need a bit more to circularise in an orbit sans Mun.
And closer in to Kerbin, it'll cost a bit more to change orbit. But grosso modo it looks like it comes to about 1150-1200 m/s whatever you do.

Next step: what if you need to change inclination?

Assuming you start off going the right direction, the biggest possible plane change burn is going to be the square root of two multiplied by your current orbital velocity (since you're doing a right-angle vector change with each vector being identical, so the hypotenuse is the square root of 2x each vector).
However, we know that we can go out to the SOI edge, change plane almost for free, then come back. Going to the SOI edge costs about 1000 m/s, so double that to get back and we have an absolute maximum of about 2000 m/s to change inclination.

SO...

If there is no change in inclination, you'll need about 1200m/s to get to any orbit.

If you need to change inclination and have time, you'll need about 2000 m/s to get to any orbit (out to SOI edge, plane change, return and circularise, 2x approx 1000 m/s).

If you need to get there quickly, the absolute maximum DV requirements of a ship in orbit around Kerbin is going to be 1.4 x 2300 m/s (LKO velocity) + whatever you need to raise your orbit. Since you can combine raising orbit with a plane change, that means (applying pythagoras again) that the absolute maximum is going to be the square root of (2300^2 + (2300+1000)^2)) (to get to SOI edge with correct inclination) + 1000 m/s (to return to low orbit). Now that is actually quite neat because (2300+1000)/2300 (to get back to units for the first burn) is almost equal to the square root of two. Therefore our pythagoras equation is the square root of (1^2 + (root 2)^2) = sqr.root (3) = 1.7. Therefore total expenditure is 2300 m/s x 1.7 = 4000 m/s.

SO....

No change in inclination: 1200 m/s
Change in inclination but no time constraint: 2000 m/s
Absolute maximum if in a rush: 4000 m/s.

[mystifeid]

5 hours ago, bewing said:

So I make sure my "satellites" always have an extended lifetime after I complete the first contract. First, I wait until I have 3 or maybe 4 satellite contracts to complete, and then I build my rocket to complete all of them.

This. And in addition, if you leave one sat in orbit around x there's a good chance you'll be offered contracts later to move it to a new orbit (and in the meantime they can be useful for "collect/transmit science data from space around x" contracts).

Edited June 2, 2018 by mystifeid

[The Flying Kerbal]

Sorry for not reading these sooner guys, I've been busy recently and KSP had to be put on the back burner.  Hopefully by the end of this week things will ease up a bit and I'll be able to launch a few rockets (ie blow 'em up on the launchpad).

Excellent answers as always, I really do need to look more closely at that vis-viva equation.

I too sometimes wait until I have a number of contracts for satellites, using the one launch to complete them.  And yes, I too use satellites to gain science from around x, although unless I'm really in need of funds I seldom take on contracts to reposition them; I don't know why, but for some reason this type of contract doesn't interest me.

Plusck has given me an answer which I'm going to have a look at more closely, really interesting and useful.

Using them as spacetugs is a novel idea, one I certainly would never have thought of myself, it is definitely one really useful way of using up that extra Dv.

All the answers are much appreciated and thanks to everyone for offering advice.