oberth effect

[SSSPutnik]

My attempt, from an everyday point of view:

Say you're driving in a car and want to go 10 km/hr faster. If you're already going 50 km/hr, you just barely have to tap the gas pedal to get to 60; you're increasing your speed by not even 10%. However, if you're only going 10 km/hr, you've got to push that pedal a lot harder to get the same additional 10 km/hr; you're doubling your speed.

It's intuitive in a car, you just know that's the way it works. It's easier to make the car go faster when it's already going fast.

Now, for a spacecraft, it is moving fastest when it is nearest the body it's orbiting. As you've undoubtedly seen yourself, as you move further from a body, your orbital speed drops. So the best place to add more speed (m/s) is when you're closest to the body you're orbiting.

Sorry that's not the Oberth effect... And an electric car doesn't lose enough mass.

The Oberth effect comes into being because you are dumping mass from your ship that is left with less energy than when it was inside your ship.

Edited February 25, 2014 by SSSPutnik

[Red Iron Crown]

You say this benefit is increasing the ship's Ek, so I explained how this can only be measured in terms of more delta-V per unit of fuel burned. Burning the fuel by itself gives you X delta-V, Oberth adds some more delta-V without burning additional fuel because increasing Ek means increasing, and thus "delta-ing", velocity. So, you get more delta-V for a given amount of fuel burned if you're going faster than slower. If this ain't true, then Oberth has no measurable benefit.

Oberth doesn't gain you any dV, it just lets you use your dV more efficiently.

An example:

A 1-ton craft is in an eccentric orbit with an orbital velocity of 1000m/s at periapsis and 100m/s at apoapsis. There is enough fuel to complete a 100m/s dV burn.

If the burn is done at periapsis, the kinetic energy change is as follows:

delta-Ek = Ek(final)-Ek(initial)

= 1/2mv_f²-1/2mv_i²

= 1/2*1000*1100² - 1/2*1000*1000²

= 605,000,000 - 500,000,000

= 105,000,000

If the burn is done at apoapsis, the kinetic energy change is as follows:

delta-Ek = Ek(final)-Ek(initial)

= 1/2mv_f²-1/2mv_i²

= 1/2*1000*200² - 1/2*1000*100²

= 20,000,000 - 5,000,000

= 15,000,000 J

So you can see, that even though the same delta V was expended, the change in kinetic energy is an order of magnitude larger when burning at periapsis due to the Oberth effect.

Edited February 25, 2014 by Red Iron Crown
Carelessly had apoapsis and periapsis reversed.

[SSSPutnik]

Red Iron Crown. Can you complete the above but for a 100ms retrograde burn?

[Red Iron Crown]

Red Iron Crown. Can you complete the above but for a 100ms retrograde burn?

Sure.

A 1-ton craft is in an eccentric orbit with an orbital velocity of 1000m/s at periapsis and 100m/s at apoapsis. There is enough fuel to complete a 100m/s dV burn.

If the burn is done at periapsis, the kinetic energy change is as follows:

delta-Ek = Ek(final)-Ek(initial)

= 1/2mv_f²-1/2mv_i²

= 1/2*1000*900² - 1/2*1000*1000²

= 405,000,000 - 500,000,000

= -95,000,000 J

If the burn is done at apoapsis, the kinetic energy change is as follows:

delta-Ek = Ek(final)-Ek(initial)

= 1/2mv_f²-1/2mv_i²

= 1/2*1000*0² - 1/2*1000*100²

= 0 - 5,000,000

= -5,000,000 J

So you can see, that even though the same delta V was expended, the change in kinetic energy is an order of magnitude larger when burning at periapsis due to the Oberth effect.

[Red Iron Crown]

As a thought experiment, imagine the following:

Two identical ships are docked together, with one facing prograde and the other facing retrograde. An explosive charge is placed between them and detonated at periapsis thrusting the ships apart with equal force in the prograde and retrograde directions, with each ship's kinetic energy changing by the same amount. Each ship perceives the other as fuel it has expended to change its velocity. The ship headed in the prograde direction, you will admit, gains extra kinetic energy due to the Oberth effect. Due to conservation of energy, the ship headed in the retrograde direction must have lost exactly the same amount of energy as the ship going prograde gained, so it must have experienced the Oberth effect as well.

The Oberth effect is symmetrical. The exhaust of the ship gains or loses exactly the same amount of "extra" energy as the ship itself.

[SSSPutnik]

Thanks... The exploding ship explanation is really good (and very Kerbal to boot!).

Awesome... So in summary...

Burning retrograde, your exhaust gains kE, you lose it and slow even more.

Burning prograde, your exhaust loses kE, you gain it, speeding up.

Edited February 25, 2014 by SSSPutnik

[Bobnova]

Sure.

A 1-ton craft is in an eccentric orbit with an orbital velocity of 1000m/s at periapsis and 100m/s at apoapsis. There is enough fuel to complete a 100m/s dV burn.

If the burn is done at periapsis, the kinetic energy change is as follows:

delta-Ek = Ek(final)-Ek(initial)

= 1/2mv_f²-1/2mv_i²

= 1/2*1000*900² - 1/2*1000*1000²

= 405,000,000 - 500,000,000

= -95,000,000 J

If the burn is done at apoapsis, the kinetic energy change is as follows:

delta-Ek = Ek(final)-Ek(initial)

= 1/2mv_f²-1/2mv_i²

= 1/2*1000*0² - 1/2*1000*100²

= 0 - 5,000,000

= -5,000,000 J

So you can see, that even though the same delta V was expended, the change in kinetic energy is an order of magnitude larger when burning at periapsis due to the Oberth effect.

This is interesting to me. The prograde one is too, but it makes more sense.

I feel like this equation is ignoring that if you raise your AP or PE speed you're going to have a serious effect on the other one, too. To use KSP as an example if you burn to 0m/s in Kerbin orbit, your PE is going to be in the atmosphere (or the ground, if we use an airless body) and a hell of a lot faster than 1000m/s. Using 0 is problematic (to my mind anyway) due to multiplying by it. I guess computing orbital energy after smashing into a planet is sort of silly on my part though. Seems like the PE would still have a higher velocity even if you didn't drop it all the way into the planet though. (It ignores the change in mass due to fuel too I think, but I'm willing to ignore that. Maybe it's a solar sail)

Time for me to launch something into Kerbin orbit and start running the numbers I guess.

I really appreciate you taking the time to lay the equation out in a simple enough way for me to understand!

EDIT:

And for narrowing it down to Kinetic energy. That's important.

Edited February 25, 2014 by Bobnova

[Vanamonde]

I now feel less stupid for being unable to comprehend the Oberth effect, because it seems no one else does, either.

Somebody correct me if I'm wrong, please, but gravity has nothing to do with it. To make up completely silly numbers to make for a clear example, suppose one rocket is going 100m/s while another identical rocket is sitting still. Then they both burn the same amount of fuel through the same engines, and the formerly-stationary rocket is now going 10m/s. Wouldn't Oberth mean that the already-moving ship is now going something like 111m/s? Doesn't it somehow get more out of the same burn because it was already moving?

[maccollo]

To make up completely silly numbers to make for a clear example, suppose one rocket is going 100m/s while another identical rocket is sitting still. Then they both burn the same amount of fuel through the same engines, and the formerly-stationary rocket is now going 10m/s. Wouldn't Oberth mean that the already-moving ship is now going something like 111m/s? Doesn't it somehow get more out of the same burn because it was already moving?

No. The one that was moving at 100 m/s will now move at 110 m/s.

The relative velocities will remain unchanged. However, the rocket that was moving initially gained much more kinetic energy, because the difference between (10^2)/2 and 0 is much less than the difference between (100^2)/2 and (110^2)/2

[Red Iron Crown]

Thanks... The exploding ship explanation is really good (and very Kerbal to boot!).

Awesome... So in summary...

Burning retrograde, your exhaust gains kE, you lose it and slow even more.

Burning prograde, your exhaust loses kE, you gain it, speeding up.

That wording really shows how Oberth is win-win. The only loser is your exhaust!

[Vanamonde]

relative velocities will remain unchanged. However, the rocket that was moving initially gained much more kinetic energy

Okay, now I understand even less. If the increased kinetic energy isn't reflected by a speed boost, what benefit is there to it?

[Red Iron Crown]

This is interesting to me. The prograde one is too, but it makes more sense.

I feel like this equation is ignoring that if you raise your AP or PE speed you're going to have a serious effect on the other one, too. To use KSP as an example if you burn to 0m/s in Kerbin orbit, your PE is going to be in the atmosphere (or the ground, if we use an airless body) and a hell of a lot faster than 1000m/s. Using 0 is problematic (to my mind anyway) due to multiplying by it. I guess computing orbital energy after smashing into a planet is sort of silly on my part though. Seems like the PE would still have a higher velocity even if you didn't drop it all the way into the planet though. (It ignores the change in mass due to fuel too I think, but I'm willing to ignore that. Maybe it's a solar sail)

Ooops, you're right about the mass used, how embarrassing. Let me rerun the numbers:

A 1-ton craft is in an eccentric orbit with an orbital velocity of 1000m/s at periapsis and 100m/s at apoapsis. There is enough fuel to complete a 100m/s dV burn. The fuel to complete the burn masses 0.1 tons.

Prograde example:

If the burn is done at periapsis, the kinetic energy change is as follows:

delta-Ek = Ek(final)-Ek(initial)

= 1/2mv_f²-1/2mv_i²

= 1/2*900*1100² - 1/2*1000*1000²

= 544,500,000 - 500,000,000

= 44,500,000

If the burn is done at apoapsis, the kinetic energy change is as follows:

delta-Ek = Ek(final)-Ek(initial)

= 1/2mv_f²-1/2mv_i²

= 1/2*900*200² - 1/2*1000*100²

= 18,000,000 - 5,000,000

= 13,000,000 J

Retrograde example:

If the burn is done at periapsis, the kinetic energy change is as follows:

delta-Ek = Ek(final)-Ek(initial)

= 1/2mv_f²-1/2mv_i²

= 1/2*900*900² - 1/2*1000*1000²

= 364,500,000 - 500,000,000

= -135,500,000 J

If the burn is done at apoapsis, the kinetic energy change is as follows:

delta-Ek = Ek(final)-Ek(initial)

= 1/2mv_f²-1/2mv_i²

= 1/2*900*0² - 1/2*1000*100²

= 0 - 5,000,000

= -5,000,000 J

Sorry for the wall of math, I should have done it right the first time.

[maccollo]

Okay, now I understand even less. If the increased kinetic energy isn't reflected by a speed boost, what benefit is there to it?

In pretty much every orbital equation the velocity factor is squared. It's energy that matters. So even if you can't change how much delta V you have at your disposal you can influence how much of an effect that change will have by burning at the right points.

This is where gravity comes in, because while it isn't directly relevant to the oberth effect it determines your velocity at any given point in an orbit.

If you come in for a munar injection burn, doing that burn just above the surface as opposed to way out you can get captured into the same orbit for much less delta V, because you move faster closer to the planet.

Edited February 25, 2014 by maccollo

[Poynting]

The wiki also says its used to increase speeds during flybys...

Yes its called a powered flyby and takes advantage of your increased speed close to the planet.

Approach planet slowly -> gravity accelerates you by amount X as you slowly fall towards the planet -> Increase speed with a burn at apoapsis -> Gravity has less time to slow you down on exit so you escape with some of the velocity you gained falling towards the planet.

(This can be used on stationary planets unlike the slingshot effect which requires the planet to be orbiting another body)

[Red Iron Crown]

The important thing to remember is that when completing a burn and expending dV, it's not the velocity change we're interested in per se, it's the change in the orbit's total energy.

At any point in an orbit, the orbital energy is constant. It is the sum of the potential energy (energy stored as altitude above the gravity well) and kinetic energy (the energy stored as velocity). This sum doesn't change as long as no dV is expended. Much of the potential energy is converted to kinetic energy as the craft falls from apoapsis to periapsis, then that kinetic energy converts back to potential energy as the craft climbs to apoapsis.

When we spend dV in the prograde or retrograde direction, we are adding or subtracting kinetic energy to the orbit. Burning prograde increases total orbital energy, burning retrograde decreases it.

The Oberth effect allows us to get more kinetic energy change from the same amount dV spent, and it is the kinetic energy change that is important. Think of dV as the currency spent to buy a change in kinetic energy. The Oberth effect allows you to buy at a discount.

[Padishar]

(This can be used on stationary planets unlike the slingshot effect which requires the planet to be orbiting another body)

<understatement>

Stationary planets aren't actually very common, you know...

</understatement>

[Red Iron Crown]

Okay, now I understand even less. If the increased kinetic energy isn't reflected by a speed boost, what benefit is there to it?

It's confusing because you're taking gravity out of consideration, which removes the potential energy of altitude. The increased kinetic energy will be converted into greater potential energy (i.e. greater altitude) at the other end of the orbit.

[SSSPutnik]

I think my explanation was simplest...

[SSSPutnik]

Yes its called a powered flyby and takes advantage of your increased speed close to the planet.

Approach planet slowly -> gravity accelerates you by amount X as you slowly fall towards the planet -> Increase speed with a burn at apoapsis -> Gravity has less time to slow you down on exit so you escape with some of the velocity you gained falling towards the planet.

(This can be used on stationary planets unlike the slingshot effect which requires the planet to be orbiting another body)

Sorry that's not the Oberth effect.

[maccollo]

Sorry that's not the Oberth effect.

A powered flyby/gravity assist is very much utilizing the oberth effect.

You take potential energy, turn it into kinetic energy by diving deep into the gravity well and burn when the kinetic energy is the highest.

Edited February 25, 2014 by maccollo

[SSSPutnik]

The description of the physics is wrong though. A gravity assist is also something different again, it doesn't even require dV expenditure.

Oberth is a boost you get based on kinetic energy.

As you fall you speed up, gaining kinetic energy, your fuel in your tanks also gains it.

If you thrust, preferably at periapsis, (highest speed) you are throwing exhaust mass backwards, because its slower relative to your ship the exhaust loses kinetic energy. Your ship gains kinetic energy to balance this.

This gives you an increase in speed greater than just the pure thrust of the engine.

Burning retrograde, your exhaust moves even faster, (ship speed + exhaust speed), hence it works then too as your ship has to lose kinetic energy to compensate.

Edited February 25, 2014 by SSSPutnik

[Kasuha]

A gravity assist is also something different again, it doesn't even require dV expenditure.

That's true, but if you do burn near the periapsis, you are utilizing Oberth effect.

[maccollo]

The description of the physics is wrong though. A gravity assist is also something different again, it doesn't even require dV expenditure.

Powered is the operative word.

*edit

You are correct tho. The description wasn't technically correct, but I wanted to avoid people getting confused into thinking that powered flybys have nothing to do with the oberth effect at all.

Edited February 25, 2014 by maccollo

[xcorps]

So here's my question:

Why wouldn't you want an elliptical orbit to transfer to a satellite in the same SOI of Kerbin? Getting an elliptical is easier than climbing to altitude then burning for circular then burning incline then burning for Hohmann transfer isn't it?

[Red Iron Crown]

I take it you mean burn until your apoapsis is at the altitude at which the satellite orbits? In effect a single direct burn from launchpad to transfer?

A few reasons I can think of:

- It's far more difficult to time correctly.

- Much of a direct burn would be in the atmosphere with drag losses.

- Your capture burn will be much more delta-V, spent where your velocity is much lower and hence less efficient.

- Inclination burns do not benefit from Oberth, in fact they are best done at apoapsis if possible.