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EndOfTheEarth

Oberth vs Apoapsis burn to LKO

Question

I've been spending some time messing with launch tactics in my efforts to get heavier payloads to Low-Kerbin Orbit, and while I have a system that works, I don't know if it's any more efficient than the old system I used.

In the old system, I would burn vertical 'til 12,500m, then start my turn, then burn until my Ap was at the desired altitude, then wait until I had reached Apoapsis to conduct my circulization burn.

After watching mechjeb ships do circulation burns, I decided to try something new:

I still do everything through the turn at 12,500m and burn until I have my desired apoapsis, but then I start burning on the 90 while still in atmosphere, and even below the horizon if the Apoapsis is getting too high. Using this, I can get a nicely circular orbit without having to wait until Apoapsis for my circularization burn.

Now, my gut is telling me that Oberth should mean that this is more efficient, since my burn is occurring at a lower altitude, but the fact that I'm burning in-atmosphere means that it should be less efficient due to drag. I don't have the tools or equipment to measure this, so can anyone tell me if one technique is mathematically proven to be more fuel-efficient than the other?

EDIT (from later post):

I'm not sure if my idea is getting clearly across. I already know about the gravity turn in relation to atmospheric pressure. What I want to know is if a n earlier below-horizon burn is better than waiting until Apoapsis to do the same burn.

Figure A:

TKnwStz.jpg

The old technique is on the left. The new technique is on the right.

Edited by EndOfTheEarth
for clarity.

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Just find a program that can give you your final mass or remaining delta-V at the end of each method. Just make two trips to the exact same final orbit. Both of these stats should give you a general idea of which was more efficient.

Mechjeb and Engineer both do this just fine.

I usually consider my remaining delta-V a kind of "high score" to beat each time I get an SSTO into orbit.

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I usually start turning to around 45 degrees at 10 km and I level off towards the horizon as soon as my Apoapsis reaches around 50km.

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Scott Manley did a video on this, and I found it helpful to me, as I was never sure when the proper time to turn over was:

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Everyone finds different methods work with their designs. The general rule is don't waste too much fuel till you're above about 20km-30km, so aim for and stay at about 200m/s or so till then. Then floor it and start your gravity turn when it suits you. I personally start my turn around the 25km/30km mark.

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Personally I'm a fan of tipping as soon as you're not jettisoning stuff that'll collide into the rocket. On a SSTO, I'm tilting before I clear the tower, but only by a degree or two; the trick is a much gentler turn than MechJeb typically provides. :P

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Mechjeb 2.0 has a nice recorder feature thar you can use to record spent delta-v which makes it easy to check different ascent profiles.

But generally I don't think this approach is better than the cruise to ap and burn. Yes you will get better effieciency due to the oberth effect but that delta-v will be wasted by changing your orbit instead adding energy to it since you're burning away from the prograde vector. This is also known as steering losses which is explained in Scott Manleys video.

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Everyone finds different methods work with their designs. The general rule is don't waste too much fuel till you're above about 20km-30km, so aim for and stay at about 200m/s or so till then. Then floor it and start your gravity turn when it suits you. I personally start my turn around the 25km/30km mark.

You don't need to stay slow until you reach 25/30km. Above 10km, terminal velocity races upward far faster than you can hope to accelerate. You're actually wasting fuel to gravity losses if you don't go full throttle above 10km.

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You don't need to stay slow until you reach 25/30km. Above 10km, terminal velocity races upward far faster than you can hope to accelerate. You're actually wasting fuel to gravity losses if you don't go full throttle above 10km.

Depends on your TWR - if you have a high TWR (above 3 or 4), keeping up with terminal velocity will mean a lot of drag in that 10-20 km stretch, but you don't really need to punch it that much. I believe the Goddard problem only strictly applies if you're going for max altitude, rather than orbital insertion. Waiting until 25 km to even start the gravity turn is probably too late for most rockets though.

Above 45 km there's not much drag left since the atmosphere's so thin, so Oberth beats drag - I usually aim for a horizontal flight path around 50-55 km, and my circularization burn ends up much smaller.

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The differently shaded blue areas on the altitude display are there for a reason - use them.

Basically Kerbin's atmosphere can be divided into three major sections, just as illustrated by the different shades of blue on the altitude display. The brightest is under 10000m - where terminal velocity is a major factor and vertical ascent is optimal. The medium blue area (statosphere?) is between 10 and about 30 thousand meters, note that this is where reentry effects become active at orbital velocity, drag is considerably reduced in this region and you can open up the throttle and slightly lead the prograde reticule as you gravity turn. The dark blue area is of very limited drag, this is where you finish your turn and get your horizontal velocity up to orbital.

Engineer redux shows all sorts of useful info, though not the gravity, drag and steering losses that MechJeb gives; I use the surface info panel for stuff like terminal velocity and force of drag for the early part of ascent and the orbit panel later to watch my apoapsis. Terminal velocity is 200 m/s at about 7000 m and as mentioned rockets up after ten thousand (stratosphere), a TWR of around two certainly cant keep up with it after that, so you might as well maximize thrust at this point for most rockets. Drag drops to negligible numbers once you are out of the stratosphere, so you might as well tip over and concentrate on horizontal velocity in the dark blue regime.

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You should be past 15,000 km before vt begins to out-race your rocket. If you are seeing that happen at 10km, your rocket isn't quite powerful enough. Shoot for lift-off TWR of about 170%. You should reach vt about 40 seconds in, and your first stage should run out of fuel about 95 seconds in. This puts you about 17km up, 500m/s, and with vt racing ahead. Good place to fire the second stage.

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Those are some way too specific numbers K^2. All designs are different. Minimum-mass designs can easily end up with significantly lower TWR of 1.5 or less. A rocket SSTO on the other hand can have its TWR change dramatically through the flight.

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Now, my gut is telling me that Oberth should mean that this is more efficient, since my burn is occurring at a lower altitude, but the fact that I'm burning in-atmosphere means that it should be less efficient due to drag. I don't have the tools or equipment to measure this, so can anyone tell me if one technique is mathematically proven to be more fuel-efficient than the other?

If you're burning continuously to get to LKO, particularly if you're burning below the horizon, then you're expending extra fuel. Of course there will be a balance where this approach beats a too steep launch, but if you're burning downward at any point in the launch, then you're canceling out delta-v that you spent in order to get up to that altitude in the first place. With a clean gravity turn you should be able to hit a reasonable LKO apoapsis at 90% or more of the velocity you need in order to circularize at that altitude, and most of the time I make it into space with a periapsis. If that's not the case, then you should try making your turn earlier or more abruptly (which will also reduce your gravity drag.)

Again, the exact balance between the two approaches depends entirely on the specifics of the launch, but generally speaking it's better to coast along a fairly flat trajectory rather than burning up too much early and then burning down to correct it later.

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you have to burn at apoapsis anyway: the question is, how fast you're travelling at the time you reach AP.

I consider ok anything more than 1500 m/s: more than 1800 m/s, I'm doing a fine job as a pilot.

this depends on your ascent profile: for me, it's a typical gravity turn at 10 km and 45°, and then gradually tilting down as I pass the 20km and 30km marks.

but more than the altitude per se, or the atmosphere indicator thingy at the top of the screen, what matters most is the air pressure - and you'll have to bring something like a barometer to see that.

those dark and light blue stripes are not a very good reference.

Kerbin's atmosphere ends at ~69km, but as someone mentioned, the "worst" part is up till 44-45km: as you reach that altitude, you should already be thrusting at 90°.

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Those are some way too specific numbers K^2. All designs are different. Minimum-mass designs can easily end up with significantly lower TWR of 1.5 or less. A rocket SSTO on the other hand can have its TWR change dramatically through the flight.

Because drag is proportional to mass, and because drag coefficients are pretty uniform, you can actually optimize the whole thing. The numbers I quote are within a few percent of optimal.

And yes, I take into account changes in TWR due to fuel consumption. These are going to vary a little with the choice of engine, but for the first stage, the difference isn't huge. You still end up within a few percent of these values. Naturally, SSTO will be different. You are forced into sub-optimal regime by requirement that you reach orbital speed with single stage.

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Sub-optimal? That hurts!

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Anyway, my TWR off the pad is somewhere around 2:1 (don't recall exactly). I do have to throttle back a few notches to stay below terminal velocity down low, but once I'm above 10km I can't hope to keep up with it even with the throttles wide open and TWR at something crazy like 7 or 8:1.

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Because drag is proportional to mass, and because drag coefficients are pretty uniform, you can actually optimize the whole thing. The numbers I quote are within a few percent of optimal.

Optimal for what objective function? You can't possibly be trying to say that every single goal has the same solution here. Sure most parts in KSP have the same drag/mass ratio, but rockets differ hugely in payload, staging, engine types (solids or nuclear engines will throw off your numbers more than a little), etc. Define a task before declaring a universal answer.

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I assume optimal in that for much of an SSTO's ascent you have more engine than you need, and are throttling down. 2STO designs are much weirder -- you throttle down in the latter part of the first stage, then go to (and stay at) max after staging.

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I'm not sure if my idea is getting clearly across. I already know about the gravity turn in relation to atmospheric pressure. What I want to know is if a n earlier below-horizon burn is better than waiting until Apoapsis to do the same burn.

Figure A:

TKnwStz.jpg

The old technique is on the left. The new technique is on the right.

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I'm not sure if my idea is getting clearly across. I already know about the gravity turn in relation to atmospheric pressure. What I want to know is if a n earlier below-horizon burn is better than waiting until Apoapsis to do the same burn.

Figure A:

TKnwStz.jpg

The old technique is on the left. The new technique is on the right.

The more efficient way would be to keep your initial Ap from rising so high and mange your throttle and pitch so that you keep your Ap just ahead of you, rising into a circular orbit at the desired altitude without needing to incur significant losses from off-axis thrust or needing a large antiradial component to hold your Ap down. Some pitch adjustments are liable to be required, though. I don't think I've ever managed a single-burn-to-orbit without dipping the nose below the horizon a little, but it wasn't much and I didn't need to keep it there for long.

I've only done it a couple of times, though, and one of those was unplanned (my orbital insertion stage failed, but I managed to creep into orbit on the interplanetary transfer engines. I then needed a tanker to come up and refuel before the mission could continue).

Edited by RoboRay

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The end result of the two burns you've pictured would be different. As Jason said, burning downward is a loss, but I think it's essentially the same as any other steering loss, 1 minus the cosine of the steering angle. And a burn anywhere other than 80km can't put you into an 80km circular orbit, period.

But assuming the periapsis in the "old technique" before the final burn is negative or very low, your gravity turn should have flattened out at a lower altitude. Then you would have burnt more during the gravity turn than you did with the "old technique," but the savings in the final burn will more than make up the difference. To think of it in a different way, you don't need to bring your apoapsis all the way up to its final height until after you've gotten to orbital speed.

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As far as I understand it, due to the nature of vector addition, any thrust off your velocity direction is inherently less efficient. And the Oberth effect doesn't help you at all because it works through higher orbital velocity at the periapsis. And you haven't achieved orbital velocity yet during your ascent.

.

The most efficient way is always to apply thrust exactly in the direction of your prograde, so if you want to circularize efficiently, you should till apoapsis where your prograde is horizontal.

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Optimal for what objective function?

Fuel/Payload. Is there another objective function?

EndOfTheEarth, if you are not burning prograde, you are wasting fuel. When you are burning downwards while still rising to apoapsis, you are wasting a LOT of fuel. Any optimal ascent to orbit will include a fast burn at the apoapsis. The only question is how much rotation you should do while you are raising the apoapsis. In vacuum, the answer is easy. You do the exact reverse of a suicide burn. With atmosphere, it's a much harder problem.

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Pad mass is common over in challenges (otherwise how do you count solids on an even footing?). Cost, eventually. And with the discrete nature of components here, you have to set a specific payload to have a well-defined optimal design. Combinations of engines, fuel, and staging that work best to get a 10 ton payload into orbit won't necessarily be the same as for a 20 ton payload. And you have to consider whether your payload has any engines of its own, if you can use those during the ascent, etc.

Edited by tavert

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