Circularization Efficienty

[SiliconPyro]

Say I have a rocket with poor acceleration. It has staged its primary lifting stage and is in a sub-orbital trajectory with an 85km apoapsis. My intent is to keep the apoapsis at 85km. Is it more efficient to start my circularization burn as soon as I reach 70km and steer below the horizon to keep my apoapsis from rising, or burn later and risk passing the apoapsis during circularization, possibly requiring me to steer higher?

Obviously a circularization stage with a higher acceleration is ideal, but in this case, I'm just wondering what the most efficient option would be.

[lincourtl]

Seems to me that the optimal solution, assuming you haven't just flown straight up thus requiring 1,500 m/s to circularize, would be to set a maneuver node at apoapsis, note the est. burn time, then start your burn at 1/2 that early. Keep your nose on the node while doing the burn.

[SiliconPyro]

Seems to me that the optimal solution, assuming you haven't just flown straight up thus requiring 1,500 m/s to circularize, would be to set a maneuver node at apoapsis, note the est. burn time, then start your burn at 1/2 that early. Keep your nose on the node while doing the burn.

Seems simple enough, but I don't know if maneuver nodes really calculate for efficiency. It would tell you how to burn to keep your apoapsis below a certain altitude though.

[rkman]

I don't know if maneuver nodes really calculate for efficiency

They don't, they just give you the burn time and delta-v. Burn time is useful because it allows you to estimate how long before the node you should start the burn. That then ends up being close to the most efficient circularization burn.

[Alshain]

To answer the original question. Achieving 70km and then Altering your orbit from 70km to 80kim is more efficient than achieving orbit of 80km...technically. However with those numbers it's minimal.

Where it really matters is if your trying to achieve a higher orbit, let's say 1000km. Pushing your apoapsis from 0 to 1000km and the circularizing is the same as flying straight up to get an orbit. Your fighting gravity. However, circularizing just out of the atmosphere and then burning on the prograde, which will be on the horizon, to raise your orbit is much more efficient because your burning laterally and not fighting gravity.

[KerikBalm]

Actually, the most efficient way to get into an 80 km orbit, is to go into an 80x80 orbit directly.

Or a 80x70km orbit, and then burn at apoapsis to turn it to 80x80.

Just like any other hohman transfer.

For practical purposes, just split burn pointing at the horizon until your PE is at 70km (use a maneuver node so its half before, and half after apoapsis). If your apoapsis goes up a little more than you'd like, a tiny burn at PE should fix that (or even only raise your PE to 65-68km depending on how much over 80 you went).

Once in a nearly 70x80km orbit, it should be trivial to circularize to 80 x 80km

[Laie]

Say I have a rocket with poor acceleration. It has staged its primary lifting stage and is in a sub-orbital trajectory with an 85km apoapsis. My intent is to keep the apoapsis at 85km.

If raising the periapsis with a low-TWR stage is even an option, you must still be deep in the atmosphere when you start burning. So your apo won't stay at 85km anyway. Point towards the horizon and have an eye not only on apoapsis altitude, but time-to-apoapsis as well.

When I had that problem recently, I had (after many tries) great success with a somewhat counter-intuitive flight profile: point towards horizon at first, then ever more upward as apoapsis came nearer. In effect, I was using pitch to control the climb rate -always ever so slightly positive- thus keeping apoapsis just a few seconds ahead of me.

This sounds wasteful, but given that all other attempts ultimately failed, it can't have been that bad.

[Sirrobert]

Seems simple enough, but I don't know if maneuver nodes really calculate for efficiency. It would tell you how to burn to keep your apoapsis below a certain altitude though.

What does efficiencie have to do with low acceleration in this scenario?

[Laie]

What does efficiencie have to do with low acceleration in this scenario?

Because if he had an high acceleration, he could just do a short burst near apoapsis and be done with it. Low TWR means that he has to keep burning for a long time; and all the while, he wants all the energy to go towards the periapsis. As I understand the OP, "efficiency" means "not wasting any fuel on the apoapsis, as it's already high enough".

[regex]

As far as efficiency is concerned, I'm not sure what's the best way. When faced with such a situation (low TWR, apoapsis already at apoapsis, circularize) I generally end up burning radially part of the time to preserve the apoapsis and that's not exactly optimal.

[Sirrobert]

Make a manouver node at apoapsis, burn towards prograde instead of towards the manouver node marker

[Red Iron Crown]

I would make the gravity turn sharper to add more horizontal velocity before getting to the circularization stage if possible. That will give a longer window in which to complete circularization.

[z26]

Actually, the most efficient way to get into an 80 km orbit, is to go into an 80x80 orbit directly.

Or a 80x70km orbit, and then burn at apoapsis to turn it to 80x80.

Just like any other hohman transfer.

AFAIK hohman transfers often refer to go from a circular orbit to a larger or smaller, also circular orbit. Like, 70-70 -> 80-70 -> 80-80. Its probably more efficient to go for the smallest orbit that avoids air drag, then circularise to wherever you want. (maybe not in op's case, since with a low twr if your apoapsis is too low, you might not have enough time to circularise before reentering the atmosphere.)