Splitting long burn on maneuver node

[Thanny]

So the maneuver nodes work on the premise that you're velocity is changing instantaneously. Hence the advice to straddle the node, doing half the burn before, half after.

But half of what? Half of the total burn time, or half of the delta V? For a long burn, those will be two notably different answers, as the acceleration is higher near the end of the burn than near the beginning, on account of fuel mass being reduced.

As an example, consider a 350 tonne ship that needs to do a 2500m/s burn using twenty nuclear engines (thrust = 1200kN, Isp = 800s). The total time of that burn will be 624.53 seconds, making the time midpoint 312.27 seconds. However, the delta V will reach the halfway point of 1250m/s at 337.06s into the burn.

So which do you think would provide the least deviation from the intended maneuver node result, starting the burn at -05:12 or at -05:37?

Edited October 10, 2014 by Thanny

[mckamx]

My thinking, which MechJeb seems to agree with, is to split the delta-V.

[Jimbimbibble]

It would be a better approximation to split the dV, but the analytical solution is pretty complex. Either way, you're going to be making correction burns.

[Red Iron Crown]

Split the delta-V++.

For short burns it doesn't really matter much, but for long ones like the example given splitting the dV gives a better approximation. A ten minute burn like that might be better split into two or more separate burns depending on the initial orbit, as well.