Tried to do Delta V calculations... help?

[Superewza]

Well over the past few days i\'ve been trying to churn out some numbers that might help me to better design ships. I can work out the ?v of a ship and all the separate stages, what i have trouble with is actually calculating the requirements of a maneuver.

Using the equations ?vo = sqrt[ (G * Pm) / Pr ], ?vd = gp * tL, tL = ?vo / A, ?va ? 610 (not sure how accurate this estimation is for Kerbin but without knowing more about the atmosphere i don\'t think there\'s much you can do about it) and of course ?tvo = ?vo + ?vd + ?va i managed to come up with an estimation for reaching orbit, assuming about 2Gs acceleration of around 4250m/s. I also figured i should probably take 100 off that due to the rotation at the equator but it can\'t hurt to overestimate a little.

Then for starters i tried to work out the combined requirements for a mission to the Mun. Using Hoffman orbits i think there should be about six independent maneuvers (Kerbin orbit, Munar transfer burn, Munar insertion burn, Munar de-orbit burn, Munar descent burns and the Munar ascent/Kerbin transfer burn).

Respectively, i assume to work out each i would have to use the value i already have (which i am aware doesn\'t take into account altitude, so i assumed 100km above surface), the first Hohmann transfer equation (on wikipedia, although i was a bit thrown off with the Gravitational parameter given in the wiki for Kerbin being in km^3/s^2, so i used all km values and came up with an answer of 0.842km/s). Then... i got lost. I assume you would have to know how fast you would be travelling at the point in the transfer orbit where you got captured, and the orbital velocity of the Mun. Then is it just the difference of the two? Problem being i have no idea how to work out velocity at any given point in an orbit. I could probably do the rest using what i already know plus suvat.

So i guess what i\'m asking is - how do you work out velocity at apoapsis (which i believe is also the semi major axis?), are the figures i have anywhere near right/what anyone else has and also, with regards to Minmus, are the calculations much the same if you just rotate the craft on the launch pad? Just because i\'m pretty sure that changing your orbital inclination is one of the most fuel-intensive burns you can do... what sort of angle are you looking for then, or does nobody know.

Thanks to anybody that can help/understand what the hell i\'m on about (i barely can). I have to say i never thought i would be using this stuff in a game, and actually enjoy it

References:

http://www.projectrho.com/public_html/rocket/mission.php

http://en.wikipedia.org/wiki/Hohmann_transfer_orbit

[semininja]

If you know your velocity and altitude at periapsis and your altitude at apoapsis, you can use the equations for conservation of mechanical energy and solve for final kinetic energy.

[Superewza]

Hmm, well velocity at periapsis should be initial orbital velocity plus the change in velocity required for the transfer burn, right? You wouldn\'t happen to have a link to somewhere i can read up on these equations, would you?

[The_Duck]

Your figures for delta-V for ascent and for trans-munar injection are quite accurate. MechJeb will record how much delta-V is expended during automatic ascents if you want hard numbers. It will also tell you how much delta-V is required for various orbital operations, including TMI.

I believe the most efficient way to land on the Mun is to adjust your Munar periapsis so that it is just above the ground, then when you reach periapsis do one big burn to kill all your velocity and drop a few meters to the surface. When I do this I usually find that my velocity at periapsis is around 800 m/s, so that\'s the delta-V required to land this way.

It\'s a little complicated to predict that 800 m/s figure from first principles. If you know your velocity at the apoapsis of your transfer orbit, you can subtract the Mun\'s orbital velocity to get your velocity with respect to the Mun at the moment when you enter the Mun\'s SOI. But then the Mun accelerates you toward it, so you\'re going faster when you reach the deorbit burn.

To find your velocity at one altitude given your velocity at another altitude you can use conservation of energy. Your orbital energy per unit mass is

E/m = (1/2)v^2 - GM/r

where v is your orbital velocity, GM is the body\'s gravitational parameter, and r is your distance from the center of the body. E/m is conserved, so if you know your velocity at one value of r, you can compute E/m, then solve the above equation for v, plug in a new value of r, and find your new velocity at the new r. With this you should be able to calculate how much the Mun will accelerate you as you fall toward it.

It\'s true that plane changes are expensive. You can calculate the cost of a plane change as dV = 2 v sin(theta/2) where v is your velocity and theta is the angle by which you rotate your plane. For small theta this is approximately dV = v * theta if theta is measured in radians. Since v is large in low orbits, plane changes are especially expensive at low altitudes.

One way to avoid that cost when going to Minmus is to launch into an initial Kerbin parking orbit that lies in the same plane as Minmus, instead of launching into an equatorial parking orbit and then doing a plane change. (This requires launching at the time of day when the launchpad passes through Minmus\'s orbital plane).

[UmbralRaptor]

So i guess what i\'m asking is - how do you work out velocity at apoapsis

What semi-ninja said. Both orbital energy and the vis-a-vis equation will work.

(which i believe is also the semi major axis?)

Only for circular orbits. For elliptical orbits, average the two apses together to get the semi-major axis. (Just keep in mind that KSP gives altitudes, rather than the 'actual' apoapsis/periapsis figures.)

are the figures i have anywhere near right/what anyone else has and also, with regards to Minmus, are the calculations much the same if you just rotate the craft on the launch pad?

The figures are in the right area. From what I\'ve flown, efficient ascents tend to LKO be ~4300-4400 m/s. Less efficient ones may be 4500-5100 m/s. The descent figure also sounds about right. Timing for launching into Minmus\' orbital plane is slightly hard at the moment, but the low inclination (6°?), means that there are times when you can reach it from a 0° orbit. (eg: with a fresh persistence file)

[Superewza]

Right, well using everyone\'s suggestions i came up with this:

What it doesn\'t take into account is the delta-v you need to not crash into the surface of the Mun or Minmus after your de-orbit burn, which depends largely on your distance above the surface (v^2=u^2+2as, where u=0). Also the gravitational drag you need to overcome to get back into orbit from the surface. Oh, and also the fact that piloting skills can be less than perfect. But i can calculate all those - what i can\'t is a maneuver between the Mun and Minmus.

How does it look? Anything drastically off? Thanks!

[DavidSJ]

I did some calculations tonight for some maneuvers. I got:

Mun landing -> Low Munar Orbit

575 m/s*

Low Munar Orbit -> Mun/Minmus transfer orbit (assuming orbital plane alignment obviates need for change of inclination)

294 m/s (provides 308 m/s in hyperbolic excess velocity, resulting in 850 m/s at periapsis and 217 m/s at apoapsis)

3d 2h 24m transfer time, launch 90.5 degrees clockwise from Minmus

Low Munar Orbit/Minmus transfer orbit -> Minmus landing

57 m/s burn to eliminate hyperbolic excess velocity

307 m/s burn to land*

Minmus landing -> Low Minmus orbit

217 m/s*

Low Minmus orbit -> Kerbin

166 m/s burn (provides 229 m/s in hyperbolic excess velocity, resulting in 45 m/s at apoapsis and <3254 m/s at periapsis, in atmosphere)

2d 6h transfer time

* Actual cost will be somewhat higher; depends on thrust/mass ratio.

[DavidSJ]

Haven\'t checked all your numbers but note that the most efficient way to get to Kerbol is a Munar slingshot for Kerbin escape followed by a bi-elliptical transfer to Kerbol. I\'d guess you save about 5 km/s vs. a simple Kerbin escape followed by Hohmann transfer.

[maltesh]

Munar slignshot doesn\'t help for a bi-elliptic sundive. You\'re far better off taking advantage of the Oberth Effect and doing your burning for the outbound leg in low Kerbin orbit.

You gain velocity on a slingshot by being bent closer to the travel direction of the body you\'re slingshotting past, and when moving at 4+km/s, even a Munscraping flyby doesn\'t bend you much.

[DavidSJ]

Ah, that is a good point. A burn in LKO buys you far more energy than a Hohmann to Mun and slingshot/burn there.

[PakledHostage]

Low Munar Orbit -> Mun/Minmus transfer orbit (assuming orbital plane alignment obviates need for change of inclination)

294 m/s (provides 308 m/s in hyperbolic excess velocity, resulting in 850 m/s at periapsis and 217 m/s at apoapsis)

3d 2h 24m transfer time, launch 90.5 degrees clockwise from Minmus

It is nice to see new members who share my enjoyment of pre-planning missions. Welcome to the forums! Can you provide more details about your planned trajectory? You seem to be using a hyperbolic Munar escape trajectory and then bleeding off the excess later in the flight. Have you tried planning your Munar escape burn using an elliptical trajectory with apoapsis outside the Mun\'s SOI, instead?

I calculated (and later verified with an actual mission) that 185.1 m/s Delta-V was sufficient to transfer from a 50 km circular, prograde orbit about the Mun to a ~100 km orbit about Minmus. Delta-V for a typical plane change manoeuvre would add between 0 and about 30 m/s to that if done correctly, and depending on the timing of the window.