DeltaV estimate for an LKO rendezvous @ 100km

[vosechu]

I'm trying to do a challenge with a very constrained weight budget and I'm trying to figure out if there are any ways to estimate how much deltaV I should be using for a rendezvous in LKO. I know that I can just track it, but I'd love to know if there is any math or rules of thumb that I could be using for the estimate?

Thanks in advance!

Edited April 27, 2014 by vosechu

[Pecan]

From where?

"LKO" usually means 75 - 100km above the surface, so you know the orbital velocity there (~2,200m/s, but depends on your specific altitude).

If both ships are in the same orbit then the deltaV is zero or infinite, depending on how you look at it. They'll both be going at the same orbital velocity so the distance between them will never close.

So the 'other' ship must be in a lower orbit (=slower orbital velocity) or higher (=higher orbital velocity).

The difference between the LKO orbit and the 'other' one is the amount of deltaV you need to bring the orbits together (plus or minus).

Hohmann transfer should be half that to reduce your periapsis (if coming from above) or raise your apoapsis (from below) and the other half to circularise once the ships actually meet.

So pretty simple, if you know the two orbital velocities. In practice, of course, your rendezvous won't be perfect so you'll need a little bit to bring the ships close together but - go slowly! - that'll be insignificant compared to the orbit-changes (say 10m/s per km).

[Taki117]

hmm, for a 100km orbit you will need about 500m/s dV in addition to whatever you need to get into orbit.

[Amagi82]

// Delta V to reach orbit around a body with no atmosphere, from sea level, r1 is the equatorial radius

public static double getToOrbit(double gravParameter, double r1, double orbitHeight, double siderealRotationVelocity) {

double r2 = r1 + orbitHeight;

return Math.sqrt(gravParameter / r1) * Math.sqrt((2 * r2) / (r1 + r2))

+ (Math.sqrt(gravParameter / r2) * (1 - (Math.sqrt((2 * r1) / (r1 + r2))))) - siderealRotationVelocity;

}

// Additional Delta V to reach orbit around a body with an atmosphere

public static double getToOrbitAtmo(double surfaceGravity, double scaleHeight, double terminalVelocity) {

return (4 * surfaceGravity * scaleHeight) / terminalVelocity;

}

// Get terminal velocity at a specific altitude.

public static double getTerminalVelocity(double surfacePressure, double altitude, double scaleHeight, double planetMass, double equatorialRadius) {

double G = 6.67e-11; // Gravitational constant

double r = equatorialRadius + altitude;

double atmosphericDensity = 1.2230948554874 * surfacePressure * Math.exp(-altitude / scaleHeight);

return Math.sqrt((1250 * G * planetMass) / (r * r * atmosphericDensity));

}

For Kerbin:

Double toOrbit4 = (getToOrbit(3.5316000e12, 600000, 69078 + mClearanceValue, 174.53) + getToOrbitAtmo(9.81, 5000, 100.2));

For a 69,079m orbit, the absolute minimum possible with a flawless ascent, this returns just over 4,338.2 dV

For a 100km orbit, mClearanceValue = 30922, so with a perfect ascent, to a circular 100km orbit, this returns: 4389.4 dV

Edited April 26, 2014 by Amagi82

[MockKnizzle]

I'd estimate 4700 m/s, allowing 4500 for a comfortable human-controlled ascent and another 200 for rendezvous maneuvers.

[cantab]

If you've got two ships both in basically the same orbit - for example 100 km equatorial prograde around Kerbin - then you can use as much or as little delta-V as you want to rendezvous. It's a tradeoff between how much delta-V you want to use and how many orbits you want to wait before you get the rendezvous.

Now if you have initial differences in the orbits you'll have some minimum delta-V needed. But as long as you don't launch either ship into an excessively high or inclined orbit, the requirement will be low. A couple of hundred m/s should be more than enough.

[vosechu]

Thank you all so much, I hadn't really thought about the difference of velocities being the approximate dV. It's amazing how simple dV is, I forget a lot!