# A question on the efficiency of a long burn

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I have a ship with low thrust, and i need to make a manuever with multiple apoapsis raising. pretty standard for this kind of ships. i'll start burning some 30 degrees before the manuever, and until 30 degrees after the manuever.

i'm wondering, though, if i should burn prograde all the time, or if i should burn according to the manuever instead.

Option A or option B? (sorry for my low graphic skill, but i think it's understandable)

On one hand, i think i should burn prograde all the time, because i need to increase my orbital energy and prograde is the only direction that does that.

on the other hand, i think that if i burn prograde, i have a component of my burn (would be vertical in respect to this page outline) that's cancelled between the times i'm before and after the manuever node.

my gut, which is generally very good with numbers, tell me that since both those arguments are good, in practice it won't make much of a difference; i suspect there is some mathematic demonstration that it makes no difference at all, you're just losing efficiency in different ways. so in the past i didn't worry about it.

now i'm curious, though. is option A more efficient? is it B? does it make no difference?

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You are fooling yourself a bit by drawing the orbits as circles. It helps to answer the question if you visualize the orbits as fairly eccentric ellipses, instead. If you burn in a direction other than prograde/retrograde, a significant portion of the energy that you are putting into your orbit is going into changing the orientation of your orbit, instead of just raising the Ap. So yes, at any instant you always want to be burning prograde, so that all your energy is going into the Ap. There is also the question of Oberth, so you only want to burn when you are really close to your Pe.  30 degrees before and after is a bit much for me. I'd limit it to 10 degrees at most.

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1 hour ago, bewing said:

You are fooling yourself a bit by drawing the orbits as circles. It helps to answer the question if you visualize the orbits as fairly eccentric ellipses, instead.

???

my starting orbit is circular, so i draw it as circular. i don't see how it changes the answer anyway, except for reducing the window in which i have small losses.

Quote

If you burn in a direction other than prograde/retrograde, a significant portion of the energy that you are putting into your orbit is going into changing the orientation of your orbit, instead of just raising the Ap. So yes, at any instant you always want to be burning prograde, so that all your energy is going into the Ap.

on the other hand, for a non-istantanous burn, burning prograde all the time also raises the periapsis. and raising the periapsis loses on oberth effect.

and on the other other hand, a higher periapsis means a longer time spent close to periapsis, a longer time when the ship can burn with limited cosine losses, thus less cosine losses on further orbits. so many variables...

Quote

There is also the question of Oberth, so you only want to burn when you are really close to your Pe.  30 degrees before and after is a bit much for me. I'd limit it to 10 degrees at most.

by 30 degrees i mean i am burning as long as the difference between prograde and manuever is less than 30 degrees. the cosine of 30 degrees is 0.87, so i'll be losing 13%. whether that is an acceptable loss depends entirely on what is the fuel budget, the actual thrust, and the time available before losing the launch window

Edited by king of nowhere
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Its an interesting question, and one to which I don't know the answer! I'll have a guess of my thoughts, and happy to be corrected by those more knowledgeable:

Burning prograde (ie towards the horizon) raises the Ap. If its at the Pe, then it doesn't raise the Pe and ALL the energy goes towards raising the Ap - the most efficient way to do it - which is well understood. However, case A, burning prograde NOT at the Pe, raises the Ap and also raises the Pe a bit.

Case B could be thought of as 2 components: mostly prograde, with a bit of radial in/out too. I'd have thought that this is even less efficient, 1) because the prograde component is less - and still "not at the Pe"; and 2) because the radial in is followed by a radial out later. I suspect the reason the manoeuvre node points you here, is that when you set up the desired orbit/escape, it had an unchanging Pe so the radial in/out component is included to prevent what would have been a purely prograde burn, also affecting the Pe due to its not being done exactly at the right time/place.

I know that in case B, the radial in/out would also contribute to the raising of the Ap in some way, but it would be an inefficient way. Better to have no radial at all, ie pure prograde burn even if its not at the Pe.

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My take on it: I think the answer lies in the Law of Conservation of Energy.

If you consider burning at Pe is the most efficient and therefore burning away from the Pe is less efficient. If, at Pe you burned prograde with a little radial in(?) you could rotate the orbit to keep yourself at Pe all the time and be super efficient yes? No, because some of the energy you appear to be saving by being at Pe is being spent burning radial instead (not what you want to increase Ap).

Therefore, with your examples working in the reverse of above, I believe it would actually be the same efficiency regardless as you're just moving the inefficient parts of the burn to a different place.

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Rather than 'Conservation of Energy' you might say 'you get exactly the Energy from the work that you put in'.

You can get quantitative with ΔE = GM/Dlow − GM/DhighΔv ⋅ v ;
the increase in orbital energy from and orbit with major axis Dlow to one with Dhigh,
is the same as the delta-v times the current orbital velocity v (multiplying with 'dot-product') summed over the whole burn.

The trouble is, v changes significantly through the burn, and in a complicated-enough way that I don't think you can make any useful conclusions by thinking and pencil-and-paper math.   If you stay always prograde, for example, you align the vectors  Δv and v  which you might think would maximize the product, but you also raise periapsis so v doesn't get as high as it would otherwise.

There was a thread long ago where I think they found from experiment that pointing prograde got you a bit more energy for your fuel, but it is easier to try in-game than to look up that thread.

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On the whole, pointing prograde gets you a more efficient burn, as you have no cosine losses (take this to the limit, if you burn prograde for a full orbit, you have more orbital energy than before, if you burn pointing at the manuver node, cosine losses cancel out all of your gained orbital energy).

The challenge becomes that its more difficult to keep the maneuver node precise when burning pure prograde.

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48 minutes ago, Lt_Duckweed said:

The challenge becomes that its more difficult to keep the maneuver node precise when burning pure prograde.

The technique I've used is to split it over 2 (or more) orbits, the first being a "steering" burn where you focus on accuracy of ArgPe rather than getting as much deltaV as possible. Of course, doing burns over 2+ orbits means that you need to plan ahead on the direction (ArgPe) required, some time in advance of the final orbit/burn that reaches the destination.

Because the more eccentric an orbit, the less the burning not-at-Pe influences the ArgPe (assuming we are starting from a circular orbit) it means that if you burned at T-1min to T+1min of the instantaneous ideal position, you'd be a little off. So you need to fudge this in and burn eg T-1min to T+1m15s the first orbit. In fact, after T you can come off the throttle, wait a bit, then burn again to 'push' it round. Or come off the throttle and not apply any after T, just wait for the next orbit, if 'pushing' it round is going in the wrong direction.

After the first burn, which should be small enough so the losses from not burning at Pe aren't too great, but big enough to make it quite eccentric, it becomes easier to do subsequent burns at eg T-2mins to T+2m10s or thereabouts.

Its a nice feeling once you have a handle of both the amount and when to burn, to 'drive' or 'steer' the orbit to the new one quite precisely.

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18 hours ago, king of nowhere said:

On one hand, i think i should burn prograde all the time, because i need to increase my orbital energy and prograde is the only direction that does that.

Yes, correct, you should do this, for precisely this reason.

18 hours ago, king of nowhere said:

on the other hand, i think that if i burn prograde, i have a component of my burn (would be vertical in respect to this page outline) that's cancelled between the times i'm before and after the manuever node.

If I'm understanding you correctly, I think you're saying "well, if I burn all the time, initially I'm thrusting slightly downwards in this picture, and later I'm thrusting slightly upwards, and those two things cancel each other out!", is that what you're saying?

If so, then no, that's not how it works, that's not a thing, nothing is "canceling" anything.  You're going "down" and then "up" (in that drawing" because the planet's gravity is curving your path, there's no loss.  You add energy by thrusting , and only the component adds to your orbital energy.  Any or component is wasted as cosine loss, so don't do that.

18 hours ago, king of nowhere said:

i'll start burning some 30 degrees before the manuever, and until 30 degrees after the manuever.

Probably will want to narrow that down by quite a bit.  When you're initially circular, this would mean you'd be futzing a lot with your Pe (since you should be thrusting ).  Later, after you've given it a few kicks to raise your Ap by a lot, this means that burning for 30 degrees on either side of Pe would mean doing a lot of the burn at high altitude and losing Oberth benefit.

So, best to keep your burns narrower-- 10 degrees on either side seems pretty reasonable.

15 hours ago, king of nowhere said:

on the other hand, for a non-istantanous burn, burning prograde all the time also raises the periapsis. and raising the periapsis loses on oberth effect.

Yes, it raises the Pe.  But as long as you only burn in a fairly narrow band on either side of Pe-- i.e. 10 degrees or less, not 30 degrees-- then it won't change your Pe very much, so the loss of Oberth effect should be minimal.

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The question of which approach to follow depends on which losses bother you more. Radial components are components not increasing your orbital energy. Thankfully trig is non-linear so a 10° angle only saps 0.5% of your prograde component when integrated.  Note: 30° robs 4.5% of your prograde component when integrated! Also note: these losses will worsen as eccentricity increases. A pure prograde burn will maximise the work of your dV, but it's harder to balance the burn correctly and control AoPe. Fixed heading burns tend to be slightly easier to execute while maintaining AoPe so can be more useful for precision maneuvers.

Edited by ajburges
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The manuver planner starts a long burn just forward of prograde, and finishes a bit behind (you may need to flip the words) so for a 5 minute burn, you would start burning at 2:30 from Ap, and burn basically to  Ap +2:30

Running a slightly retarded prograde, transitioning to a slightly advanced prograde seems to keep the Pe/new Ap  "still" (not sure what to call it, sorry) If you're flying manually, best to just go full prograde, and correct "longitude" if needed.

I like the little xenon motors, they are fun for long haul probes, but you have to think ahead for stuff going to eloo, you get about a third of the solar power that you get at kerbin. (which is very generous of the devs, BTW)

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On 3/27/2021 at 6:53 AM, king of nowhere said:

i'm wondering, though, if i should burn prograde all the time, or if i should burn according to the manuever instead.

If you are talking about maximum efficiency prograde all the time but then 30 degrees is a bit to early to start the burn if you are really trying to get the most out of your deltav. IMO you should start the burns later and just point at the maneuver node to keep it simple. The difference will not be noticeable.

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3 hours ago, dave1904 said:

If you are talking about maximum efficiency prograde all the time but then 30 degrees is a bit to early to start the burn if you are really trying to get the most out of your deltav. IMO you should start the burns later and just point at the maneuver node to keep it simple. The difference will not be noticeable.

yes, i toned it down to 15 degrees. also, i had to include a substantial normal component in the burn, and so it would be really difficult to keep that manually, so i just left the ship pointed towards the manuever.

kinda hard to figure out burn efficiency with a ship that's shedding drop tanks between burns while aiming for a mun gravity assist, but i estimate i have lost around 5% efficiency.

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6 minutes ago, king of nowhere said:

yes, i toned it down to 15 degrees. also, i had to include a substantial normal component in the burn, and so it would be really difficult to keep that manually, so i just left the ship pointed towards the manuever.

kinda hard to figure out burn efficiency with a ship that's shedding drop tanks between burns while aiming for a mun gravity assist, but i estimate i have lost around 5% efficiency.

I'm curious. Do you have a screenshot of you craft?

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1 hour ago, dave1904 said:

I'm curious. Do you have a screenshot of you craft?

many, as it will be my next big mission report.

the ship is intended to carry my second kerbalism grand tour, this time with the additional challenges of no isru and visit the green monolith on all planets

Spoiler

the part on top is the eve lander, including a disposable plane to explore eve

the second part is the habitation module. it is thin and narrow because then the engine/fuel module can shield it from direct radiation from the sun. it also has attached additional airplanes for laythe and kerbin, and disposable rovers for tylo and vall.

most of the ship then is nuclear fuel. there are 72 mk3 long fuselages that can be detached individually or in couples. also disposable engines, to keep twr roughly steady. the ship starts with 54 nervs and twr 0.07, but 36 engines will be gradually dropped with the spent tanks as the reduced ship mass will no longer justify carrying 150 tons of engines

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15 hours ago, king of nowhere said:

many, as it will be my next big mission report.

the ship is intended to carry my second kerbalism grand tour, this time with the additional challenges of no isru and visit the green monolith on all planets

Reveal hidden contents

the part on top is the eve lander, including a disposable plane to explore eve

the second part is the habitation module. it is thin and narrow because then the engine/fuel module can shield it from direct radiation from the sun. it also has attached additional airplanes for laythe and kerbin, and disposable rovers for tylo and vall.

most of the ship then is nuclear fuel. there are 72 mk3 long fuselages that can be detached individually or in couples. also disposable engines, to keep twr roughly steady. the ship starts with 54 nervs and twr 0.07, but 36 engines will be gradually dropped with the spent tanks as the reduced ship mass will no longer justify carrying 150 tons of engines

Haha you're crazy brother. Can you even use physics warp with that?

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1 hour ago, dave1904 said:

Haha you're crazy brother. Can you even use physics warp with that?

if you mean physics warp while burning, then no. i had the persistent thrust mod installed, and the first project of this ship was with ions, and much smaller. unfortunately, something broke, and after multiple attempts at making it work, i had to shift to nuclear

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9 hours ago, king of nowhere said:

if you mean physics warp while burning, then no. i had the persistent thrust mod installed, and the first project of this ship was with ions, and much smaller. unfortunately, something broke, and after multiple attempts at making it work, i had to shift to nuclear

Wait, you're using nerv's instead of xenon? Why dear and fluffy lord why? xenon is the only build I can stack 17km/s of usable thrust on a probe. (BTW, if you use tweakscale, it will cut the xenon thruster in half, 1Kn instead of 2Kn, making it totally useless)

I've had a good bit of playtime making long haul probes recently with xenon thrusters, one trick I can tell you is use the small radial xenon tanks instead of the stacking tanks, it greatly reduces the tankage weight factor, allowing far more Dv on the same fuel. The number 1 problem is balancing the electrical, followed closely by maximum acceleration.

The "mission constraints" (arbitrary standards) required the craft to sustain a 10 minute burn time, have over 1m/s acceleration, and over 10km/s in the gas tank. I can do that with xenon all day, but I've never gotten even close to that trying to use nerv's. (that could be me failing to pick the right gas tanks, but the ships with nerv rockets couldn't ever beat a decent terrier design.)

This is an interesting question, as using either tech to it's utmost requires some level of design juggling.

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5 hours ago, rynther said:

Wait, you're using nerv's instead of xenon? Why dear and fluffy lord why? xenon is the only build I can stack 17km/s of usable thrust on a probe. (BTW, if you use tweakscale, it will cut the xenon thruster in half, 1Kn instead of 2Kn, making it totally useless)

I've had a good bit of playtime making long haul probes recently with xenon thrusters, one trick I can tell you is use the small radial xenon tanks instead of the stacking tanks, it greatly reduces the tankage weight factor, allowing far more Dv on the same fuel. The number 1 problem is balancing the electrical, followed closely by maximum acceleration.

The "mission constraints" (arbitrary standards) required the craft to sustain a 10 minute burn time, have over 1m/s acceleration, and over 10km/s in the gas tank. I can do that with xenon all day, but I've never gotten even close to that trying to use nerv's. (that could be me failing to pick the right gas tanks, but the ships with nerv rockets couldn't ever beat a decent terrier design.)

This is an interesting question, as using either tech to it's utmost requires some level of design juggling.

i tried using xenon. 200 tons of xenon, over 40000 m/s of deltaV.

but the ship got bugged. the engines stopped working, despite having all the required resources. before you suspect me of some noob mistake, i opened a question with pictures, and no, it was a legitimate bug. i tried many times, i always got the same bug hit sooner or later. couldn't even leave kerbin orbit before it struck. I found that i could fix the bug only by removing persistent thrust. but without persistent thrust, burn time would be way too long, so i had to resort to the next best thing, nuclear.

Now, i see you mentioning 1 m/s of acceleration, so perhaps you think you can get away without using persistent thrust. Lol! You clearly have no experience with big ships.

Let me present some calculations. My ship is supposed to make a grand tour, with a life support mod, and land a rover on every planet. I have over 200 tons of Eve lander alone (and that's already a huge improvement over my previous eve lander, which was 400 tons and carried only one person). i have 50 tons of habitation module, which is already smaller than ideal - it also needs radiation shielding, which is heavy. over 10 tons of food, water, oxygen and supplies. And I have over 100 tons of rocket fuel, because ions would work in space but i still need to land on the various planets with regular rockets, and i can't use isru as part of the challenge.

so i have around 400 tons of weight i have to carry around. to which i need to add at least 200 tons of xenon to get a good deltaV. Around 600 tons.

Every dawn engine pushes 2 KN, so to get 1 m/s I'd need 300 dawns. But those would be 75 more tons, so now i'd need 40 more engines just to push the engines. so, 340 dawns. I'd also need trusses and structural parts to attach all those engines around, for extra weight, but let's ignore that for now. As each dawn requires about 9 electricity/s, I'd need around 3000 electricitry. Which I could supply with 100 gigantors at kerbin. But I have to go as far as eeloo, so i need rtgs; each one is 0.8, so I'd need 3600 of those.

Of course, since they weight 80 kg each, that would be 300 extra tons of rtgs. or, for 10 minutes of operation, we'd need 1.8 million capacity on a battery, which we could achieve with 90 tons of batteries. in any case it would require more engines, more fuel, etc.

To stay within a reasonable buget and part count, i had 24 engines, which could push my ship at an incredible acceleration of 6 cm/s. And I didn't even have enough rtg to power them full time; with kerbalism rtgs gnerate radiation, and too many of them will kill the crew.

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You're using mods?

I've found that yes, in theory, you can build a "big"* ship which reaches LKO, then the main burn to do the leaving of the Kerbin orbit and any deep space manoeuvres is a very low TWR. But in practice, you want a bit more of a TWR 1) so the "leaving Kerbin orbit" burn CAN be done more/less at the Pe, in 2 or 3 orbits at the most, with decent control on the direction and 2) so the deep space burns aren't 20+ mins, simply for sanity/boredom purposes.

Playing entirely stock, I've found the ideal engine is always selectable - although I might select the wrong one then be stuck with it on a trip!

In any of your mods is there a more powerful Xenon engine, so you aren't blighted with this ultra-low TWR/ultra-long burn time issue?

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39 minutes ago, paul_c said:

You're using mods?

I've found that yes, in theory, you can build a "big"* ship which reaches LKO, then the main burn to do the leaving of the Kerbin orbit and any deep space manoeuvres is a very low TWR. But in practice, you want a bit more of a TWR 1) so the "leaving Kerbin orbit" burn CAN be done more/less at the Pe, in 2 or 3 orbits at the most, with decent control on the direction and 2) so the deep space burns aren't 20+ mins, simply for sanity/boredom purposes.

Playing entirely stock, I've found the ideal engine is always selectable - although I might select the wrong one then be stuck with it on a trip!

In any of your mods is there a more powerful Xenon engine, so you aren't blighted with this ultra-low TWR/ultra-long burn time issue?

no mods for bigger ion engines, and i couldn't afford the power if i tried to keep them realistic.

50-odd nervs is the way to go. took me 5 or 6 apoapsis raising manuevers to leave kerbin, but that's still manageable. i could perform the eve capture burn at reasonable efficiency

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Are you using regular fuel tanks and just scrapping the oxygen? (been up a while trying to get a large scale xenon setup running, the current one looks like a camping stove, working out a good multi-angle solar geometry is proving a little much, given that it needs to launch from ground, but it's easy mode, so it won't snap if I breathe on it, mostly it's a question of scaling, so I'm not trying to press the rest of the situation. Just seeing how far I can bend it before it breaks, so far 48 engines at 91 tons and something like half of that is just fuel in the tanks it can dispense to other ships. I'll see if I can drive by eloo with a better solar geometry)

Edited by rynther
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I'm working at maybe 1/10th scale to the beast you're working on, but you've given me something to chew on, the rather flat response from the solar panels at eloo (and the 42 minute burn to get out to a test range) have put a crimp in my thrust budget, but that's only part of a grand tour, I'll have to spend a couple days cooking up some deviltry and testing it on a heavy ship.

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8 hours ago, rynther said:

Are you using regular fuel tanks and just scrapping the oxygen?

no, those are liquid fuel fuselages, they hold only liquid fuel. there is also at least one mod that lets you store any fuel you choose in any tank, and it would be advantageous because those Mk3 fuselages have a fuel/weight ratio of 7 instead of 8 of the normal tanks. but i don't want to install any more mods than strictly necessary.

1 hour ago, rynther said:

I'm working at maybe 1/10th scale to the beast you're working on, but you've given me something to chew on, the rather flat response from the solar panels at eloo (and the 42 minute burn to get out to a test range) have put a crimp in my thrust budget, but that's only part of a grand tour, I'll have to spend a couple days cooking up some deviltry and testing it on a heavy ship.

at eeloo and jool a gigantor makes less than 1 electricity/second. it's real hard to use ions on a large ship.

on the plus side, orbits are so slow, you can afford to have slow burns. i had a 6-days long burn on my return pod from eeloo, and it had 6 gigantors on a 15 ton ship (i.e. 10% of its total weight was solar panels). but the burn was efficient anyway. however, i'd nt be so crazy to try that long burn without the persistent thrust or a similar mod

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Well, I've already sank my teeth into the problem,  I don't feel like letting go without a fight. (6 day burn, I suppose that mod allows warp during burn?) It takes about 2.5 hours to run a test at eloo (the sailboat I just tested had something like 25 gigantors, generating 4 per sec at "peak angle", so well less than 1/ps for each fully exposed gigantor at eloo.) Still, I'm a pretty clever lab rat, there's a couple things I haven't tried yet.

Still, I don't hold out any hope that this would scale to 1500 tons, and not in a form that would carry you beyond duna anyway. Meanwhile, a challenge is a challenge, how big can the xenon systems scale? and what does it do to counter the lack of sun at eloo in a not horrible fashion?  I don't really do kerballed missions, I fly into things too much, but it might be fun to setup a much smaller group of probes , dropping them off would still be quite a trick, even more so, because I do not fly with the least amount of elegance, the fuel would be monumental.  (my "super probe" could probably visit 4 maybe 5 planets, but not land anything, and not much science on board)

The peak power point for the xenon engines seems to be a 3 thruster system, at least for deep space. (the only configuration that can yield 1.8m/s with long range in the dark.)

Anyway, I guess I'm off to play with fuel cells for the moment, thanks for the tip on fusilages, I'll be playing with the nervs next.

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