oberth effect

[Geschosskopf]

I ask the knowledgeable to clear up some points that have been bugging me for a while concerning Oberth....

It seems to me there's no point in even thinking about the Oberth Effect because it's not going to change what you'd be doing anyway just from an orbital maneuvering standpoint. Oberth about fuel-efficiency: you get more delta-V per unit of fuel burned the faster you're going at the time. You're going fastest at Pe so that's the most fuel-efficient place to burn. But you're going to burn at Pe anyway because that's where you need the least delta-V, however efficiently you're burning fuel to make it, to change your Ap. Thus, even if Oberth didn't exist, you'd still be burning at Pe to get the desired Ap (or escape trajectory). This will still require the same amount of delta-V, but because there's Oberth, you get a bonus in fuel efficiency so this delta-V doesn't require as much fuel as it would otherwise. IOW, Oberth is just a side-effect of what you'd be doing anyway, so isn't in itself a stand-alone thing you need to plan for. Is this correct?

Also, it seems to me that Oberth only comes into play at all when you're not in a circular obit. If you're in a circular orbit, you're going the same speed all the way around so have the same burn efficiency due to Oberth at all points on the circle. This implies that Oberth has no bearing at all on doing transfer burns from parking orbits, except that starting in a lower orbit with a higher speed would be a bit more fuel-efficient that starting in a higher orbit with a lower speed. However, assuming your ship got into its parking orbit starting from the ground on that planet, wouldn't you have already reaped the benefit of the lower altitude during launch? The delta-V for the actual transfer burn is less from the higher orbit because you've already done part of the burn to get into the higher orbit in the first place. But in any case, no need to worry about Oberth because its presence or absence isn't going to change how you do the burn once you're in the parking orbit. Is that correct?

[Red Iron Crown]

Also, it seems to me that Oberth only comes into play at all when you're not in a circular obit. If you're in a circular orbit, you're going the same speed all the way around so have the same burn efficiency due to Oberth at all points on the circle. This implies that Oberth has no bearing at all on doing transfer burns from parking orbits, except that starting in a lower orbit with a higher speed would be a bit more fuel-efficient that starting in a higher orbit with a lower speed. However, assuming your ship got into its parking orbit starting from the ground on that planet, wouldn't you have already reaped the benefit of the lower altitude during launch? The delta-V for the actual transfer burn is less from the higher orbit because you've already done part of the burn to get into the higher orbit in the first place. But in any case, no need to worry about Oberth because its presence or absence isn't going to change how you do the burn once you're in the parking orbit. Is that correct?

It should be made clear that Oberth effect is related to speed, not altitude. Once in orbit, the two are closely related, but it matters for a launch when there is low altitude combined with low speed so there is little Oberth effect.

If you are in a circular orbit your periapsis and apoapsis are so close that the difference between them speed wise is negligible or actually zero, so it doesn't really matter where in the orbit you make the burn; Oberth will be about the same at all points in an orbit.

WRT lower parking orbits versus higher ones, lower is better. To get from a lower orbit to a higher one requires raising the apoapsis at some point on the lower orbit, and you're right in thinking this part would be identical to starting a transfer burn from the lower orbit. However, the circularization burn and remaining part of the transfer burn would be done in the higher orbit where the Oberth effect would be smaller.

It is generally best to do a transfer burn all at once from the lowest possible parking orbit.

[Rhomphaia]

This implies that Oberth has no bearing at all on doing transfer burns from parking orbits, except that starting in a lower orbit with a higher speed would be a bit more fuel-efficient that starting in a higher orbit with a lower speed. However, assuming your ship got into its parking orbit starting from the ground on that planet, wouldn't you have already reaped the benefit of the lower altitude during launch? The delta-V for the actual transfer burn is less from the higher orbit because you've already done part of the burn to get into the higher orbit in the first place. But in any case, no need to worry about Oberth because its presence or absence isn't going to change how you do the burn once you're in the parking orbit. Is that correct?

Not really no. for a large enough burn the Oberth effect will still apply. Take a transfer to Jool plotted with http://alexmoon.github.io/ksp/

for the window on day 169, starting from a 100km orbit you need 1,992m/s for your ejection burn

Start from a 1000km orbit you need 2,013m/s for the ejection burn, plus you would have spent more to get into that orbit in the first place. even if you were refuelling in the parking orbit before departure, the higher orbit wouldn't save you anything.

It is kind of an extreme example, since the Kerbal solar system is so small it is a lot less important than it would be in ours.

[bernierm]

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.

[AlexisBV]

Oberth about fuel-efficiency: you get more delta-V per unit of fuel burned the faster you're going at the time.

No. You always get the same delta-V per unit of fuel. You get more kinetic energy if you're already going fast.

[AlexisBV]

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.

I don't know what kind of car you drive, but I disagree with your point. Your engine has to work a lot harder to increase your speed if you're already going fast.

Just a reminder:

kinetic energy = mass/2 * speed^2

For example,

1000kg vehicle, 0 to 10m/s: 50kJ difference in kinetic E

1000kg vehicle, 30 to 40m/s: 350kJ difference in kinetic E (7 times more, even though it's the same deltaV).

Ventis' graph above illustrates this quite well.

Of course, cars suffer even more in that respect because of tire friction and aerodynamic drag, so the engine has to work even harder at high speed. Have a look at specs for really high performance cars. A 1000hp car might make 400km/h, while a 800hp car will make 380km/h (ballpark figures from vague memories of a Top Gear episode). But that 200hp difference can get you from zero to 200km/hr quite easily (hell, my first car only had 60hp and I pushed it to 190km/h )

Edited February 24, 2014 by AlexisBV

[Red Iron Crown]

Ugh, a car analogy and a bad one at that. Cars become harder to accelerate the faster they are going, due to greater aerodynamic and mechanical friction losses. And they aren't propelled by shedding mass, so Oberth wouldn't apply anyway.

[wasmic]

The easiest way to explain Oberth that I have come across (actually, I'm not sure whether it's correct), is that when you fall down into a gravity well, you pick up speed. If you accelerate while in the bottom of the well, you'll move out of the well faster than you went in, and you'll lose less energy on the way out than you gained on the way in.

[Roastduck]

Nope, the Oberth effect still applies to retrograde burns (although I'm not 100% sure how or why!)

Basically, to reach a specific orbit, you need a specific velocity. delta-V is just the difference between CURRENT and TARGET velocity. to reach a higher orbit, you need a higher velocity, and burning at Pe will mean burning at your highest CURRENT velocity, and thus the difference will be smaller (lower delta-v, and less fuel burned as a result).

If you want to lower your orbit, your TARGET velocity will be lower than your CURRENT. And since you begin to decelerate after you pass Pe, it is more efficient to burn retrograde at Pe to drop your Ap to the target altitude, then coast the rest of the way and circularize at Ap.

[Kryxal]

The easiest way to explain Oberth that I have come across (actually, I'm not sure whether it's correct), is that when you fall down into a gravity well, you pick up speed. If you accelerate while in the bottom of the well, you'll move out of the well faster than you went in, and you'll lose less energy on the way out than you gained on the way in.

And it took that long for somebody to use the "common" sense explanation (which is, admittedly, more obvious when you consider a powered assist or slingshot) ... though the math is certainly important. Mostly, you can just use it and know it works without worrying too much about WHY it works, just remember it's not the be-all and end-all of things. If things line up right to catch a slingshot while sacrificing a bit of Oberth assistance, you may be better off.

[Red Iron Crown]

Except that it doesn't actually explain the Oberth effect, and introduces the idea that you gain energy on the way down and lose it on the way up, which is incorrect.

[AlexisBV]

Ugh, a car analogy and a bad one at that. Cars become harder to accelerate the faster they are going, due to greater aerodynamic and mechanical friction losses. And they aren't propelled by shedding mass, so Oberth wouldn't apply anyway.

I mentioned those losses already, and they are indeed the reason cars have a limited maximum speed. However, the analogy is still valid in that for a given same excess available power beyond aero and friction losses, you get more instantaneous acceleration if you're slow.

Oh, and (non-electric) cars are propelled by shedding mass, just not as directly as rockets but either way, the relation between kinetic energy, speed and dV doesn't depend on the method of propulsion.

Edited February 24, 2014 by AlexisBV
Grammar

[Geschosskopf]

If you are in a circular orbit your periapsis and apoapsis are so close that the difference between them speed wise is negligible or actually zero, so it doesn't really matter where in the orbit you make the burn; Oberth will be about the same at all points in an orbit.

WRT lower parking orbits versus higher ones, lower is better. To get from a lower orbit to a higher one requires raising the apoapsis at some point on the lower orbit, and you're right in thinking this part would be identical to starting a transfer burn from the lower orbit. However, the circularization burn and remaining part of the transfer burn would be done in the higher orbit where the Oberth effect would be smaller.

It is generally best to do a transfer burn all at once from the lowest possible parking orbit.

Thanks for clearing this up.

Not really no. for a large enough burn the Oberth effect will still apply.

OK, thanks.

No. You always get the same delta-V per unit of fuel. You get more kinetic energy if you're already going fast.

I have to disagree with you here. Even ignoring Oberth, you certainly do not always get the same amount of delta-V per unit of fuel. Delta-V is just another word for acceleration (change in velocity) and acceleration = F/m. For a given engine, full throttle F and Isp are both constant but m decreases as fuel burns. Thus, throughout the burn, the instantaneous acceleration you're getting increases as the mass decreases (IOW, TWR increases), and each increment of the burn consumes the same amount of fuel due to the constant Isp. Thus, you more acceleration per unit of fuel as the burn continues, which is the same as saying more delta-V per unit of fuel. This happens all by itself even before considering Oberth.

Also, Kinetic Energy Ek = 1/2 * m * v^2. As fuel burns, m decreases so Ek decreases from that cause. Thus, any net increase in Ek has to be due to a velocity increase. Increasing velocity = changing velocity = delta-V = acceleration. And as outlined above, acceleration increases during a burn, resulting in more delta-V per unit of fuel.

So now Oberth is adding Ek to the ship on top of this weight-loss process. Adding Ek means increasing velocity, which means accelerating the ship, which means delta-V. That is, what Oberth is doing is adding a bit more acceleration to what the engines are already providing. Thus, you're getting a higher amount of delta-V out of the burn without having to burn more fuel to get it, so again, more delta-V per unit of fuel. That's why I'm saying Oberth is a fuel-efficiency thing.

======================

But anyway, apart from doing transfer burns in the lowest orbits possible, is there any reason at all to ever worry about the Oberth Effect? You're not going to change where you do your burns because of it. Placement of maneuver nodes is dictated by vector addition: starting vector plus burn vector = desired vector. If Oberth saves you some fuel in the process, great, but you're still going to place the node in that position regardless.

Or am I missing something?

[WhiteKnuckle]

But anyway, apart from doing transfer burns in the lowest orbits possible, is there any reason at all to ever worry about the Oberth Effect? You're not going to change where you do your burns because of it. Placement of maneuver nodes is dictated by vector addition: starting vector plus burn vector = desired vector. If Oberth saves you some fuel in the process, great, but you're still going to place the node in that position regardless.

Or am I missing something?

Capture burns?

[AlexisBV]

I have to disagree with you here. Even ignoring Oberth, you certainly do not always get the same amount of delta-V per unit of fuel. Delta-V is just another word for acceleration (change in velocity) and acceleration = F/m. For a given engine, full throttle F and Isp are both constant but m decreases as fuel burns. Thus, throughout the burn, the instantaneous acceleration you're getting increases as the mass decreases (IOW, TWR increases), and each increment of the burn consumes the same amount of fuel due to the constant Isp. Thus, you more acceleration per unit of fuel as the burn continues, which is the same as saying more delta-V per unit of fuel.

Methinks we're mixing up the context here. I agree that you get more dV per unit of fuel for a light vehicle vs. a heavy vehicle. But that was not what I was referring to. If you look at my post including the quote, you'll see that I said that you get the same dV per unit of fuel for slow vehicle vs. a fast one.

[AlexisBV]

Capture burns?

And slingshots.

[Geschosskopf]

Capture burns?

But you're going to do a capture burn at Pe anyway because that's where you get the best leverage to create an Ap.

Methinks we're mixing up the context here. I agree that you get more dV per unit of fuel for a light vehicle vs. a heavy vehicle. But that was not what I was referring to. If you look at my post including the quote, you'll see that I said that you get the same dV per unit of fuel for slow vehicle vs. a fast one.

And that's what I disagree with. The whole thing about Oberth is that the faster you go, the more benefit you get. But what is the nature of this benefit and how do you measure it? 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.

[Bobnova]

Faster in reference to what?

I feel like this discussion is missing something, namely that even in a perfectly circular orbit around Earth (Kerbin, whatever) your speed relative to galactic rest is changing. You're going around something that is going around something that is going around something that is going around something. If you're orbiting the moon, add another something.

So, which rest frame are we comparing our velocity to here?

[Geschosskopf]

Faster in reference to what? ... So, which rest frame are we comparing our velocity to here?

Well, Oberth happens when you burn and all burns take place in something's SOI, where the speedometer measures relative to that central body. So I'd assume that's the frame of reference.

[lumpman2]

Imagine that you are trying to stack the biggest tower possible (of any material you like). If you start with a larger tower, adding the same amount of material causes the tower to be higher than if you started with a shorter one.

For example, if you were adding 4 ft of material to the tower, it's better to start with 5 ft rather than 1 ft because then you have a larger tower in the end.

When you are orbiting closer to the planet, you move faster. (You have to assume that you are in an elliptical orbit, otherwise the difference in velocity in negligible or nonexistant.) When you're farther away, you orbit slower. So, let's say that you're going 2000 m/s at periapsis, and 200m/s at apoapsis. Now you want to reach 3000 m/s. The amount of delta-v that you need to burn at your Pe is only 1000 m/s, but at your Ap it's now 2800 m/s. Therefore, you save more delta-v when you orbit closer to the planet while you burn because you have a higher velocity then. Of course, you could also be in a higher/lower circular orbit and have different velocities in those two orbits - the Oberth effect also manifests itself here. So it's usually better to be orbiting at 70-100 km where you're going about 2.3 km/s instead of 2 Mm where you're going about 1 km/s.

[Bobnova]

All these calculations are Real Life calculations though, there isn't a single SOI for real life. They may or may not have anything meaningful to do with KSP.

The "Oberth Effect" in KSP was specifically programmed in, so unlike real life there really is a definitive answer to both what exactly the calculation is and what your speed is.

Taking an orbit around Gilly and an orbit around Phobos as KSP and Real Life examples, your orbital velocity around the parent body is going to be rather lower than that body's velocity around its parent body.

In KSP it's simple, the Oberth effect happens because the Devs made it happen, in the way the Devs made it happen.

Why it happens in real life? That's something different, and that's where my question on what reference frame all these calculations are using comes from.

[sal_vager]

Actually I don't think the KSP oberth effect is programmed, KSP uses patched conics for all orbits and this takes your velocity into account, and oberth effects are part of that.

It worked for Apollo

[Kryxal]

Actually, in a sense, the Oberth effect WAS programmed in ... gravity was programmed, orbital mechanical are an effect of that, and the Oberth effect is a direct result of that.

Really, there are two ways of looking at things, the math side of things and conceptually. The math side of things has been gone over pretty well, the conceptual side seems a bit rougher. If it makes it any clearer, think of it like pushing a sphere up a hill with no friction. You're better off giving a great big push at the bottom than pushing steadily all the way up - in delta-v terms anyway.

[Jouni]

In KSP it's simple, the Oberth effect happens because the Devs made it happen, in the way the Devs made it happen.

Why it happens in real life? That's something different, and that's where my question on what reference frame all these calculations are using comes from.

The whole point of Oberth effect is that reference frame doesn't matter. For the same burn, you get the same delta-v, no matter which reference frame you happen to use. In some reference frames, you get more kinetic energy from the burn than the chemical energy of the fuel you burned. This used to confuse people, but Oberth explained it.

The Oberth effect becomes relevant to spaceflight, if we fix the reference frame to some nearby body with nontrivial gravity. When you move away from that body, some of your kinetic energy (relative to that body) is transformed into potential energy (relative to that body). The faster you move, the less this loss of kinetic energy affects your velocity (relative to that body). So if you want to move to a higher orbit or escape the gravity of a planet, you need less delta-v, if you do the burn when you are moving fast relative to that body.

[SSSPutnik]

The Oberth-effect ist really quite simple.

And it is not some esoteric effect... it is just maths.

It all depends on how a rocket engine works. You throw exhaust out and actio vs. reactio, the rocket moves forward.

Lets make it simple. Lets say, the exhaust fumes masses as much as the rocket and the rocket is standing still.

If the exhaust leaves the rocket with a certain force, half of that force is in the exhaust and half is in the rocket. Both move away from each other with the same speed. Both have then the same kinetic energy.

If the rocket is moving, then still exhaust and rocket move away from each other and the same speed (if both have the same weight).

BUT since the rocket was moving, the exhaust has less kinetic energy, because it is has the force minus the speed the rocket had before burn.

And the rocket has the burn force PLUS the speed. So the rocket has more kinetic energy than the exhaust.

This goes so far that the exhaust can be moving forward AFTER the burn, if the exhaust velocity is smaller than the velocity of the rocket.

Lets say, exhaust velocity is 5000 m/s. But the rocket before the burn is moving at 10.000 m/s.

I understand that perfectly, but what happens if you burn retrograde... People say you still get Oberth but I think no because then the exhaust has an even higher velocity.