Burn efficiency question: Follow the ball or not?

[tfabris]

Let's say I'm doing a burn using a maneuver marker. It's a simple prograde burn, in other words, the only direction I need to burn is prograde. This means that, as I approach the maneuver point, the prograde indicator on my nav ball and the maneuver marker on my nav ball will slowly converge. When I reach the maneuver point, my prograde indicator and the maneuver marker indicator on my nav ball will be on top of each other. After passing the maneuver point, the two indicators will slowly diverge again.

Let's say for example that my burn is scheduled to be 2 minutes long.

I know that standard procedure says that I should aim at the maneuver marker on my nav ball early, and burn in a straight line for an even amount of time on either side of the maneuver point. For instance, in the case of the two-minute burn, I should burn starting at T minus one minute and finish burning at T plus one minute. This, according to what I've gleaned from reading other threads, will get me the most accurate positioning for my calculated destination.

But what if, instead of aiming at the maneuver marker, I aimed at the prograde marker on my nav ball? And kept turning my ship to follow it? Would this result in a more efficient use of fuel, thus allowing me to shorten the overall length of the burn slightly? Or would that be mathematically identical to the straight line burn?

[Sirrobert]

Normally it would probably not matter to much, but if you make some form of mistake, the node will adjust. If you say miss the burn, or get nudged to the side, you can burn directly at the node, and you will still end up with your projected flight path

[tavert]

Pointing prograde gives you the largest speed increase for a given burn. But if you burn prograde for an entire maneuver, your final orbit will differ from what the prediction said, since the prediction was assuming an impulsive (infinite thrust, zero duration) burn. Following the blue marker for a roughly centered burn should make your actual final orbit closer to the prediction.

For short burns it rarely makes all that much difference. For longer burns, this prograde vs fixed direction steering error is one contribution to inefficiency, along with the loss of Oberth effect since you aren't performing all of a burn at the lowest possible altitude. Both of these effects can be reduced by splitting the burn up into multiple shorter periapsis kicks.

[numerobis]

It is more efficient to burn straight than to burn in an arc. For short burns, the difference is miniscule.

[LameLefty]

This is an interesting question. What I've always done (and admittedly I could be doing it wrong - I'm not huge on long-distance interplanetary travel), is start my burn a little under half the burn duration ahead of time, while pointing dead at the maneuver marker, and burn until the residual velocity is as close to 0 as I can reasonably get it, tweaking course the whole time to keep the marker centered. In other words, for a 2 minute burn, aim and the marker and start at about T - 60 seconds, burning until T + 60.

I would like to hear what some of the more experienced interplanetary navigation experts have to say.

[tfabris]

Okay, Tavert and Numerobis are directly contradicting each other:

Pointing prograde gives you the largest speed increase for a given burn.

It is more efficient to burn straight than to burn in an arc.

Who's right? This is the core of my question.

[Kasuha]

By maneuver, you're adding certain impulse in certain direction. If you want to get to the place where you pointed your maneuver, you should follow the maneuver marker. By following the prograde marker you're making more efficient burn but you're diverging from your maneuver.

[tfabris]

Right, I know that by pointing away from the marker I'm diverging from the programmed maneuver. My main question was about the efficiency of the burn and the amount of fuel needed for a given delta v.

So you're on the same side as Tavert, saying that following the prograde arc will give me a more efficient fuel usage?

[Mr Shifty]

along with the loss of Oberth effect since you aren't performing all of a burn at the lowest possible altitude.

Long prograde burns start with the ship pointed radially somewhat toward the planet and thus have the effect of lowering your periapsis during the first 40% or so of the burn (until your speed is high enough that it overcomes the altitude loss due to the radial burn.) I wonder how much this effect compensates for burning at higher altitude for the second half of the burn.

Example (and these numbers are approximate):

If I've got a starting TWR of about 0.33 and a 2500 m/s burn to do, it takes about 10 minutes to do the full burn (because my TWR increases as propellant is expelled.) If I start at 100km, by the time I'm 4 minutes into the burn, my periapsis is down to about 80km, and when the burn is finished, I'm at about 400 km. More than 50% of the burn takes place lower than my initial altitude.

[numerobis]

Okay, Tavert and Numerobis are directly contradicting each other:

Who's right? This is the core of my question.

I am, of course.

I'm actually not 100% certain; I'd have to do the math exactly. Burning prograde increases orbital energy the most, but you don't really care about that -- you just want to increase the apoapsis. Burning prograde *exactly at periapsis* does exactly what you want.

What tavert and I definitely agree on is that the most efficient will be to cut the burn up into short segments so that the difference in each segment between a rotating prograde burn and a direct burn is insignificant.

[Kasuha]

That depends on what you're trying to achieve. If you just want to raise your apoapsis then yes. But the difference is negligible I believe.

[Mr Shifty]

What tavert and I definitely agree on is that the most efficient will be to cut the burn up into short segments so that the difference in each segment between a rotating prograde burn and a direct burn is insignificant.

Orbit pumping can, however, be ineffective in KSP because of patched conics. Eeloo, for instance, takes about 2000 m/s for your ejection burn from LKO. But, it only takes about 900 m/s to get to the edge of Kerbin's SOI, so you could still have a long burn ahead of you on that last orbit. Plus, it becomes very difficult to time your burns to coincide with interplanetary transfer windows.

[The_Rocketeer]

A really good question, and I can't say I know the answer for certain.

My hunch is that burning toward the maneuver vector is more efficient, mainly because the slight reduction of altitude prior to node would increase the Oberth effect. Since Kerbal physics aren't the most accurate recreation of RL physics, honestly the best way to find out is probably to try both.

[tfabris]

Burning prograde increases orbital energy the most, but you don't really care about that

Actually, that's exactly the question I was asking, it was in fact the very thing I cared about.

[The_Rocketeer]

Actually, that's exactly the question I was asking, it was in fact the very thing I cared about.

It might be the question you were asking - and in which case there's your answer - but perhaps it's not the question you SHOULD be asking. Burning prograde will store more of the energy you apply by keeping you in a circular orbit, with only gravity to affect your trajectory. However to intercept a moon, you don't need a circular orbit. An eliptical one will use a little more fuel to change your trajectory to climb much more steeply, but you'll save that much and more when you fall into the moon's gravity and get dragged along with it, meaning you don't need anything near as much orbital velocity to stay at that altitude once you get there.

[Mr Shifty]

Burning prograde increases orbital energy the most

This is trivially true, but it's not necessarily useful information. It matters very much where in your orbit you burn prograde and how fast you're already going. In some circumstances it's more efficient overall to shape your orbit by burning in a non-prograde direction. Sort of in the same way that it's often faster to travel the hypotenuse of a triangle than to traverse the two sides, even if you're absolute speed is slower.

[tfabris]

Agreed that *where* you burn is the most important thing, because there are places in your orbit that are more efficient than others for certain kinds of desired destinations. That's good general advice for navigation. But that's not the question I asked. Also agreed that staying pointed at the maneuver marker is the only way to ensure that you actually reach your calculated destination. Again, not the question I asked.

My question was: *All other things being equal*, which is the more fuel-efficient burn for a given delta-v? Follow the ball or stay in a straight line?

I think that your original answer, Mr. Shifty, was the one that got closest to the heart of the question: If you stay pointed at the maneuver marker in a straight line, then you're doing part of your burn pointing slightly down at the planet and thus decreasing altitude slightly and thus increasing the Oberth effect slightly for that portion of the burn. The question becomes, is that then offset by the portion of the burn that occurs pointing slightly away from the planet and thus decreasing the Oberth effect slightly? And overall, are those effects, in the end, mathematically identical to what I would have done if I'd turned my nose and stayed pointing prograde the whole time?

[Crush]

along with the loss of Oberth effect since you aren't performing all of a burn at the lowest possible altitude.

7/10 KSP players greatly overestimate the Oberth effect (of the other three, two haven't heard of it yet, one has actually understood it).

[Mr Shifty]

And overall, are those effects, in the end, mathematically identical to what I would have done if I'd turned my nose and stayed pointing prograde the whole time?

Pretty sure that the answer to this is no. I'm fairly certain that if you burn prograde for a 10 minute burn, you'll end up with a lower apoapsis (and lower eccentricity) than if you burn in a straight line toward the average "prograde" for the burn. Should be pretty trivial to test this with KSP: set up a prograde maneuver node point toward it and (using an external timer) start burning 5 minutes before the node, continue for 10 minutes. Note the result. Quickload and repeat, pointing prograde the whole time. (Use MechJeb's Smart ASS to stay pointed in the right direction.)

[tfabris]

I asked the forum so that I wouldn't have to test it myself. :-)

PS: I'm not using MechJeb, just running stock Kerbal.

[tfabris]

By the way, from what I hear you saying, I think you're saying that staying pointed prograde will result in a slightly more circular orbit, and that staying in a straight line will result in a slightly more elliptical orbit (with a higher apogee overall). Interesting. So the question isn't just which is more energy efficient, but, for a given amount of energy spent, what does that energy get spent towards?

[The_Rocketeer]

My question was: *All other things being equal*, which is the more fuel-efficient burn for a given delta-v? Follow the ball or stay in a straight line?

All other things being equal, your prograde and maneuver vectors would be in the same place. Being in a gravity field will always have a practical effect on the efficiencies of reaching a given point.

As for "a given delta-v", burning prograde will not result in the same delta-v as burning linear toward your maneuvre vector, as you will be applying force in a radial-out direction as well as toward your maneuver vector. Later you would have to break off from your prograde vector for a correction burn to expend 'exactly the same delta-v'.

Edited October 22, 2013 by The_Rocketeer

[Kasuha]

This whole discussion took longer than it would take you to do the test.

[tfabris]

I can poke at a forum during the day in between my other tasks, but I can't play Kerbal during the day. :-)

[phunk]

I would think that if you're turning during the burn, a portion of the thrust at the beginning and end of the burn will be in opposite directions, wasting fuel. Burning in a single direction should be most efficient.

ETA: But then again, if you burn at prograde at opposite sites of an orbit, you're burning in opposites directions and it certainly doesn't cancel out, so I'm probably wrong.

Edited October 22, 2013 by phunk