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# Most efficient long burns?

## Question

Hi, I was wondering what the most efficient method for low TWR, high DV ejection burns is.

I thought pointing prograde is always best. But if you point prograde long before you are at periapsis the periapsis rises, so you lose DV because you can't use the oberth effect as much. To mitigate that problem, you can lower your periapsis to below the surface/ atmosphere, rising just high enough when you're eventually at periapsis.

But when burning the direction changes most in the beginning. Quickly the orbit becomes straight. So it's hard to estimate in which direction you'll eject exactly. Sometimes this even means you can't plan your orbit raising burns with the maneuver node system, because your periapsis moves to a point earlier in your obit/ the orbit points outward more than planned.
Some people (like turbopumped) do the suicide oberth burn. This seems like the best idea ever.

But other people use their hard earned fuel to burn pointing at the maneuver node marker. This seems to waste fuel because you are not pointing prograde, not all the fuel is used to increase your speed. Is it done this way only because it's easier to execute and plan the maneuver? Not everybody has the patience to retry their super long ejection burn 10 times?! Or does it just not matter that much?

Edited by kedrednael

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Prograde is always the most efficient. But without significant computation, you can't pre-plan the exact outcome of a pure prograde burn. Burning exactly with the maneuver node gets you a known outcome, but it is not maximally efficient. But your last statement is mostly correct -- it really does not make that much difference.  As I recall, the absolute worst-case result is the square root of 2 worse than an optimally efficient burn. (ie. 41%) And most burns are much better than that. Usually only a few percent worse than optimal.

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Okay thanks! That worst case is when you have to burn across half an orbit I assume. 41% difference sounds like a lot for some missions.

Perhaps in KSP 2 we will be able to do this computation, since low thrust high ISP engines get more support.

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1 hour ago, bewing said:

As I recall, the absolute worst-case result is the square root of 2 worse than an optimally efficient burn. (ie. 41%)

I doubt it. I mean, that's the result you get by integrating the cosine over the whole orbit. it assumes that, while you burn, you stay in orbit. which is not what's going to happen. especially with the orbital approximation of this game.

what actually happens is that, as you exceed escape trajectory, your ship is going to leave orbit entirely. and it's going to come out of your SoI pointing at a completely wrong angle. I'm too lazy to produce screenshots right now, but I can. I did send a spaceship with TWR 0.11 to jool. twice. unless you are talking about raising your orbit in a spiral, which is what is done with real life ion propulsion, but i'm fairly sure that's more than a 40% loss of efficiency.

in my experience, the best way to deal with low twr is with tricks. first one is raising periapsis peemptively. you have to burn for 2000 m/s, but you can burn the first 900 while still remaining in kerbin orbit. so, do that first, and then you only need to burn for 1100. which is still a huge amount with twr 0.1, but still manageable. if you have to go nearby, like to eve or duna, you can eliminate any problem with this strategy (actually, you can get there with a mun gravity assist without making long burns). It works best if you make your long burn in a long orbit, perhaps returning from a moon. maybe that's what you mean with suicide oberth burn? if that's the case, i can confirm that it is fairly efficient, as you will have a long time when prograde will coincide with the direction you want to burn.

another option is raising periapsis. it's something you normally want to avoid, you gain no benefit and you lose oberth effect, but it makes your orbit flatter, reducing cosine losses. can be worth doing in some cases.

but the best option by far is to avoid big burns by using gravity assists and other convoluted trajectories that only require correction burns.

last but not least, making manuevers in kerbol orbit is also a good way to avoid cosine losses. sure, you'll lose all oberth effect, but at least your orbit is so slow you can spend hours making your burn without any noticeable loss

In my case, i found that i needed over 2500 m/s to go to jool immediately, but i could lower it to 2200 by going to duna first, entering a high orbit that would put me eventually around ike, and then from ike fall back towards duna and make the bigger burn there.

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9 hours ago, king of nowhere said:

I doubt it. I mean, that's the result you get by integrating the cosine over the whole orbit. it assumes that, while you burn, you stay in orbit.

Well, @bewing called it the "absolute worst case" -- think of something like this, maybe even worse:

It is possible to create lots of maneuver nodes in a relatively short timespan if you interface with the API. Both kRPC and kOS will provide convenient ways to do so. The above represents a constant 40mm/s² burn... I think. It's been a while. I'm pretty certain that I didn't account for fuel consumption when making that picture, but you get the idea.

I've actually flown missions with that scheme: plotting lots of nodes only to figure out when to start the engines and begin the prograde-only burn. I guess one could also calculate it by other means, but I cannot.

I don't think any of my transfers ever took longer than 1/4 orbit, and the extra dV expenditure (compared to a short, high-TWR burn) was on the order of 15%.

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52 minutes ago, Laie said:

Well, @bewing called it the "absolute worst case" -- think of something like this, maybe even worse:

It is possible to create lots of maneuver nodes in a relatively short timespan if you interface with the API. Both kRPC and kOS will provide convenient ways to do so. The above represents a constant 40mm/s² burn... I think. It's been a while. I'm pretty certain that I didn't account for fuel consumption when making that picture, but you get the idea.

I've actually flown missions with that scheme: plotting lots of nodes only to figure out when to start the engines and begin the prograde-only burn. I guess one could also calculate it by other means, but I cannot.

I don't think any of my transfers ever took longer than 1/4 orbit, and the extra dV expenditure (compared to a short, high-TWR burn) was on the order of 15%.

that's quite a nice image, and it underlights the problem i was raising: if you actually do your burn like that, how can you predict where you'll end up? you started burning on one side of the orbit, and you exited on a completely different side. real space agencies have softwares to do those kind of calculations, and i'm sure some mods can allow the same. without access to those resources, though, that kind of manuever cannot be predicted accurately enough to be of any use.

1/4 of the orbit is still a manageable time. in my cases i needed a 20 min burn, and i got a result like the one in your picture, where i ended up pointing in a wrong direction.

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21 minutes ago, king of nowhere said:

how can you predict where you'll end up?

You save the game, do the burn once, write down all the numbers and angles, reload the game, and do it again "for real".

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15 hours ago, kedrednael said:

I was wondering what the most efficient method for low TWR, high DV ejection burns is.

Without any other consideration (aka time, hair available to pull out) I would think the "most efficient method" would be repetitive shorter prograde burns at the game calculated "in game, instantaneous" maneuver node - at least until you escape the local body's SOI, which would make every dV expended contribute to the most efficient trajectory (while keeping in mind that you need to be exiting the local body's SOI when the transfer window arrives). But like all things astrophysical, the caveat is that the point in the orbit where you perform these intermittent burns would change slightly each orbit according to the distance the body travels around Kerbol.

I think a reasonable compromise would be to, say, burn for 1/4 of an orbit, (1/2 before the node, 1/2 after) which would minimize cosine/wrong way losses to an acceptable point, and repeat in the next orbit with only an adjustment for the ejection angle change due to movement of the body you are orbiting.

[ Looking at some of the images, it appears that the burn might take, say, 3 orbits? maybe 4? ]

Edited by Wobbly Av8r
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Something to keep is mind is that the calculated perfectly efficient maneuver is instantaneous. That means the maneuver will be "inefficient" just because it takes a greater than zero time while you follow a curved trajectory. Even if you hold prograde the slight misalignment between your acceleration and your velocity will add some m/s to the cost of maneuver.

Just think about it. If you hold prograde while you burn, the first half of it will be slightly towards an "side" while the second half will be slightly towards the other "side". Don't it seems suspiciously like undoing the previous work?

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On 12/4/2020 at 12:04 PM, Laie said:

Well, @bewing called it the "absolute worst case" -- think of something like this, maybe even worse:

That's awesome! and terrible . Would love it if KSP could do that without separate maneuver nodes. We have mods like trajectories right, they iteratively calculate the changing orbit with aero drag. And the space combat simulator 'Children of a death earth' also takes into account burn time. In that game you can actually set up year long ion burns from Ceres to Mars for example.

On 12/4/2020 at 1:50 AM, king of nowhere said:

maybe that's what you mean with suicide oberth burn?

What I meant with the suicide oberth burn is what Hazardish does on 8:26 on the video: Wind the orbit up to a high apoapsis, low periapsis. Then before the final ejection burn when at apoapsis, lowering your periapsis below the surface. This would be suicide if your engine doesn't start again. When almost arriving at periapsis (and death) start the engine at the right time, pointing prograde, this raises the periapsis. When arriving at periapsis it has been just raised above the surface, so you are taking full advantage of the oberth effect, you are burning prograde and you can give a farewell high-five to people on the surface :).

On 12/4/2020 at 1:50 AM, king of nowhere said:

last but not least, making manuevers in kerbol orbit is also a good way to avoid cosine losses. sure, you'll lose all oberth effect, but at least your orbit is so slow you can spend hours making your burn without any noticeable loss

But I like the oberth and almost hitting the surface!

On 12/4/2020 at 1:50 AM, king of nowhere said:

In my case, i found that i needed over 2500 m/s to go to jool immediately, but i could lower it to 2200 by going to duna first, entering a high orbit that would put me eventually around ike, and then from ike fall back towards duna and make the bigger burn there.

Hm that sounds interesting.

On 12/4/2020 at 3:38 PM, Wobbly Av8r said:

I would think the "most efficient method" would be repetitive shorter prograde burns at the game calculated "in game, instantaneous" maneuver node

Yes you are right, the problem is the last ejection burn. For realism sake I don't want to make 50 year long manned missions with many gravity assists. I've created some missions in which I did more than 15 burns at periapsis to increase apoapsis before the final ejection burn. With an acceleration of 0.07G the ejection burn is still difficult.

On 12/4/2020 at 3:38 PM, Wobbly Av8r said:

point in the orbit where you perform these intermittent burns would change slightly each orbit according to the distance the body travels around Kerbol.

Yes I plan the ejection maneuver days in advance, then start burning at that maneuver node many times so the orbit has a very high apoapsis  when that planned maneuver occurs.

On 12/4/2020 at 12:04 PM, Laie said:

I don't think any of my transfers ever took longer than 1/4 orbit, and the extra dV expenditure (compared to a short, high-TWR burn) was on the order of 15%.

That still sounds pretty good!

On 12/4/2020 at 1:23 PM, bewing said:

You save the game, do the burn once, write down all the numbers and angles, reload the game, and do it again "for real".

Yes I should write the results down instead of guessing it 10 times in  a row.

22 hours ago, Spricigo said:

Just think about it. If you hold prograde while you burn, the first half of it will be slightly towards an "side" while the second half will be slightly towards the other "side". Don't it seems suspiciously like undoing the previous work?

It does seem like that, but I don't think so. Because at every moment in the burn you are pointing prograde, so at every moment all of the DV is being used to increase your speed.
If you burn prograde for 1 second to get a nice moon transfer, and then your orbit curves halfway around before you encounter the moon, that isn't undoing your work.

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39 minutes ago, kedrednael said:

If you burn prograde for 1 second to get a nice moon transfer, and then your orbit curves halfway around before you encounter the moon, that isn't undoing your work.

Evidently, you didn't get my point.

What you describe is doing nothing after the 1s burn. What I described two periods off active maneuvering or a lot more than two f we decide to break it down to 1s intervals.

In any case, some people have the patience to do the math demonstration. I consider that I can better use that energy into something else. If you don't think long burns are inherently inefficient , then I really don't care to convince you it is.

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On 12/4/2020 at 1:01 PM, king of nowhere said:

that's quite a nice image, and it underlights the problem i was raising: if you actually do your burn like that, how can you predict where you'll end up?

As mentione, I do it by plotting lots of small prograde-only maneuvers. Start at (guessd) time X, repeat until the desired exit velocity is reached, look where it goes. Discard all nodes and repeat with another start time.

That's the solution available to me, with my skill set. I won't promote it as the greatest best solution of them all.

On 12/4/2020 at 1:01 PM, king of nowhere said:

1/4 of the orbit is still a manageable time. in my cases i needed a 20 min burn, and i got a result like the one in your picture, where i ended up pointing in a wrong direction.

Well, I can only tell you what I know...

Below is the longest departure burn of which I can still find a screenshot, about 300m/s in ten minutes, for a maneuver that would have taken 270m/s if it had been instantaneous. Note that the nodes don't need to be all that closely spaced to get an accurate prediction. As the trajectory gets more straight, the nodes can be spaced ever further apart.

15 hours ago, kedrednael said:

For realism sake I don't want to make 50 year long manned missions with many gravity assists. I've created some missions in which I did more than 15 burns at periapsis to increase apoapsis before the final ejection burn. With an acceleration of 0.07G the ejection burn is still difficult.

Hmmm. 0.07g really isn't much, 1/6th of what I have in the picture above. Have you considered starting your mission from a high orbit? Within the constraints you set for yourself, it might be a totally acceptable solution:

1. bring the whole vessel into a very high orbit around Kerbin, Mun or beyond.
2. launch a resupply mission to top off the tanks, and bring aboard the crew.
3. then do your long burn there -- with an orbital period lasting 3+ days, even a three-hour burn will fit into a single node.

Departure from a high orbit is inherently more costly, but at your meager acceleration, it may not make that much of a difference in the end. And planning / execution will certainly be a whole lot easier.

Edited by Laie
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18 minutes ago, Laie said:

Departure from a high orbit is inherently more costly, but at your meager acceleration, it may not make that much of a difference in the end. And planning / execution will certainly be a whole lot easier.

While we often talk about the most efficient ways to do things, that is the kind of trade of trade off we regularly accept when actually doing thing.

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