A simple experiment to help you visualize the Oberth effect.

[xcorps]

I was having a conversation earlier today with a fellow who was trying to figure out how to use the Oberth Effect in KSP.

The Oberth effect isn't something that you use, it's something that happens if you perform a burn in an elliptical orbit at Perigee. While I was trying to explain it to him, I suddenly figured out how to show it to him in game.

If you are having trouble with the concept, follow these simple steps and never worry about Mr. Oberth again because it's more natural than you think.

1) Launch a craft capable of obtaining a circular 150k orbit, inclination as close to zero as possible, ellipse as close to zero as possible.

2) Make a circular orbit and draw out a maneuver node where the new AP touches the orbital plane of the Mun. Drag your node around, and you will see that the new AP always crosses the plane of the orbit of the Mun.

Now to demonstrate Oberth.

1) Launch the same craft, make an orbit with an AP of 150k but a PE of only 75k.

2) Create a maneuver node at PE that will cross the orbital plane of the Mun. Note the altitude of AP.

3) Drag the node to AP. Now, your AP is well away from the orbital plane of the Mun.

This is because at PE your velocity is quite a bit higher than your velocity at AP. By burning at PE, you give yourself a discount on the fuel needed to obtain your desired velocity.

That is the Oberth Effect at work. It's not something you can manipulate, it's basic physics. All you can do is take advantage of it.

Edited June 30, 2014 by xcorps

[imax]

If only this post had some pictures =)

[Vindelle_Sunveam]

I agree with imax. your article will be easier to grasp for the newbies if you add pictures. Can you make an addendum that explains how it impacts inerplanetary travel ? It is the part that confuses me

[NecroBones]

If only this post had some pictures =)

Or better yet, a video!

Maybe I'll make one like that at some point, if no one else does.

[Specialist290]

Or better yet, a video!

Maybe I'll make one like that at some point, if no one else does.

I'd find such a thing to be quite handy, myself. Keep me posted if you do!

[arsmith]

Here you go:

Edited July 4, 2014 by arsmith
Evidently I can't figure out imgur tags

[NecroBones]

I'd find such a thing to be quite handy, myself. Keep me posted if you do!

It just so happens I threw this together tonight:

EDIT: Video replaced with version 2, on the next page of the thread...

Edited July 5, 2014 by NecroBones

[blizzy78]

It just so happens I threw this together tonight:

I wish you had explained it such that it's not the altitude that is relevant, but the actual velocity your vessel is currently having. Of course that velocity is higher the lower your altitude is.

[Red Iron Crown]

The Oberth effect isn't something that you use, it's something that happens if you perform a burn in an elliptical orbit at Perigee. While I was trying to explain it to him, I suddenly figured out how to show it to him in game.

This isn't precisely correct, though it gets the general gist. The Oberth effect happens in circular orbits just as well as elliptical ones (though it's easiest to demonstrate in an eliptical orbit). The burn does not necessarily have to happen at periapsis, though the Oberth effect will be maximized there. Any point away from apoapsis will have increased Oberth effect compared to completing the burn at apoapsis.

I wish you had explained it such that it's not the altitude that is relevant, but the actual velocity your vessel is currently having. Of course that velocity is higher the lower your altitude is.

This. You'll get more benefit from the Oberth effect from a 100km orbit around Kerbin than from a 20km orbit around the Mun.

[NecroBones]

I wish you had explained it such that it's not the altitude that is relevant, but the actual velocity your vessel is currently having. Of course that velocity is higher the lower your altitude is.

I thought I did. I went through lots of trimming in the wording, so maybe I cut too much of that out. I can rework it. I have a new copy rendering.

Edited July 4, 2014 by NecroBones

[NecroBones]

OK, version 2, making a better point about the velocity:

[frog]

Thanks for the insight, xcorps and necrobones!

I did a little experimenting to see how much efficiency can be won by making use of the Oberth effect. It was done in two parts. These experiments were done manually and without the help of MechJeb, so values aren't perfect but clear enough.

First, I made a circular orbit at 180km around Kerbin. From any point in this orbit, it took appx 790m/s of delta-V to reach the elevation of the Mun. I then shrunk the orbit to an elliptical with the apoapsis at 180km and the periapsis at 70km--this burn cost appx 82m/s. In this new orbit, burning prograde at the periapsis to reach Mun elevation required appx 778m/s of delta-V, while burning from the apoapsis now cost 870m/s.

Then, I made a circular orbit at 10Mkm. To reach Minmus elevation from here, it cost 159m/s of delta-V. Shrinking my orbit again to an elliptical with the periapsis at 70km required 377m/s. From the new periapsis, burning to Minmus took 74m/s.

What we see is: the Oberth effect is NOT effective enough to warrant shrinking an orbit. If you've already spent the delta-V to make an orbit, trying to increase your speed by shrinking your periapsis is very inefficient.

Secondly, I applied this to escape trajectories, to see if shrinking your orbit would have a different result. However, the results were similar. In a circular 10Mkm orbit, escape was reached with 191.6m/s of delta-V. After shrinking the periapsis to 70km (as above--377m/s), the escape delta-V rung in at 84.4m/s, in total over twice the fuel cost.

Ultimately, it seems the Oberth effect is only useful if you don't have to change your orbit to make use of it. I suppose that means: the lowest possible orbit after launch is the best one. Might this also indicate the if your initial orbit is elliptical, depending on the ejection angle it might be more efficient to burn from a non-apsis rather than first circularizing the orbit?

Does anyone see any holes in my methods or in my conclusions, or have any evidence that shows the Oberth effect being more efficient?

PS Hello Kerbal forums!

[NecroBones]

Those are some good experimental observations. Though, it's worth noting that the Oberth Effect is always present. It's just a matter of whether you can maximize its benefit or not, based on what velocity you currently have when you do your burn.

But yes, usually you won't want to burn opposite to what your end-goal is (such as shrinking your periapsis, only to transfer to a higher orbit), simply because you are countering some of your existing velocity.

There is a maneuver that's similar to this though, which is called a Bi-elliptic transfer. This involves raising your apoapsis first, well outside of your current or destination orbit, and it requires the semi-major axis (the "radius" of the longer axis of the ellipse) to change by more than a factor of about 12 in order for it to save you any energy. The wikipedia page for this explains it pretty well.

There are other times though, where choosing your periapsis prior to the maneuver is quite possible. For instance, if you've transferred to another planet's SOI, just as you enter that SOI, you can use the "normal" and "radial" handles on a maneuver to control the inclination and periapsis of your approach, which could save you a lot of energy over making those corrections later, as well as set yourself up for additional maneuvers at your nearest approach.

And of course, when leaving Kerbin, this can be an incentive to use a low-altitude parking orbit prior to your escape burn, or at least have the parking orbit's periapsis at a low altitude on the appropriate side of the planet for your escape.

Edited July 5, 2014 by NecroBones

[Red Iron Crown]

What we see is: the Oberth effect is NOT effective enough to warrant shrinking an orbit. If you've already spent the delta-V to make an orbit, trying to increase your speed by shrinking your periapsis is very inefficient.

...

Does anyone see any holes in my methods or in my conclusions, or have any evidence that shows the Oberth effect being more efficient?

First, whether it's worthwhile enough depends on how much you need to change your orbit. To reach the Mun, Minmus, or to hit escape velocity, I agree that it's generally not worth it. But if you're attempting a large transfer to say, Jool, Eeloo or Moho, the difference becomes a good bit larger making it more worthwhile.

Second, it's better not to burn retrograde to lower your periapsis to harness the Oberth effect. As Necrobones mentioned, that would be burning away speed that you'll have to add later. What you can do is burn to change the eccentricity of your orbit (i.e. a burn with a large radial component). This will drop your periapsis without changing your current speed; that way the dV you spend for this first orbital change doesn't work against you when you go to burn prograde at periapsis.

Third, kudos to you for experimenting and sharing your results, that's a great first post. Welcome to the forums!

[mhoram]

First, whether it's worthwhile enough depends on how much you need to change your orbit. To reach the Mun, Minmus, or to hit escape velocity, I agree that it's generally not worth it. But if you're attempting a large transfer to say, Jool, Eeloo or Moho, the difference becomes a good bit larger making it more worthwhile.

Second, it's better not to burn retrograde to lower your periapsis to harness the Oberth effect. As Necrobones mentioned, that would be burning away speed that you'll have to add later. What you can do is burn to change the eccentricity of your orbit (i.e. a burn with a large radial component). This will drop your periapsis without changing your current speed; that way the dV you spend for this first orbital change doesn't work against you when you go to burn prograde at periapsis.

A while back there was a discussion about the efficiency of a two-burn strategy for leaving Kerbins SOI from a circular orbit.

Such a "first burn retrograde, then burn prograde at Periapsis" approach can be more efficient than a single burn method.

Have a look at this chart and the discussion for details.

Decreasing Periapsis by a radial burn is an interesting idea ... never thought about that.

However I believe that setting up this burn in a way that the Apoapsis points in the right direction is a difficult task - counterexamples welcome.

[AlexinTokyo]

I think one of the best explanations/demonstrations I've seen for the Oberth effect involved fixed ÃŽâ€v burns at different altitude periapsides above an object on a hyperbolic orbit. I can't remember where I saw it, though (it may not even have been KSP related.

I think it could be duplicated by setting the periapsis to differing heights on SOI entry around a body (Tylo might be a good choice in KSP), and then showing the differing results of burning for 500 m/s (or whatever) at those different altitudes/velocities.

It becomes clear very soon that it costs much less ÃŽâ€v to capture/circularise at a lower periapsis (i.e. greater velocity) than at a higher one.

[Red Iron Crown]

A while back there was a discussion about the efficiency of a two-burn strategy for leaving Kerbins SOI from a circular orbit.

Such a "first burn retrograde, then burn prograde at Periapsis" approach can be more efficient than a single burn method.

Have a look at this chart and the discussion for details.

Perhaps I overgeneralized there, a two burn strategy using a retrograde burn to lower periapsis can definitely save dV overall. Though I find the savings to be minimal unless you're burning for a target further than Eve or Duna.

Decreasing Periapsis by a radial burn is an interesting idea ... never thought about that.

However I believe that setting up this burn in a way that the Apoapsis points in the right direction is a difficult task - counterexamples welcome.

It doesn't have to be perfectly aligned, i.e. periapsis at exactly the right angle to prograde for the maneuver (though that would be the ideal case). As long as the transfer burn happens in the lower part of the orbit it will still harness Oberth. The eccentricity change is generally more costly in dV than a retrograde burn to lower periapsis; this cost is offset by the higher speed at periapsis, meaning a lower dV expenditure for the transfer burn itself.