Delta-V

[LethalDose]

Are you sure? Don't we get more acceleration per unit of thrust, the faster we go?

Aphobius is correct, the amount of acceleration you get per unit fuel is not speed dependent. As you burn, fuel, though, your vessel's mass will decrease, which in turn will increase acceleration per unit fuel expended. This is not Oberth effect, though.

Oberth effect is you gain more energy per unit of fuel expended (or really, dV expended) at high speeds versus low speeds. This can be clarified looking at the equation for kinetic energy:

KE = 1/2 mV²

and the equation for KE at the end of the burn:

KE = 1/2 m(V + dV)²

The amount of energy gained by expending a set amount of dV is smaller if your V is low (i.e. your vessel is moving slowly) than the amount of energy you gain when V is higher(i.e. your vessel is moving fast). The difference in the amount of energy gained is due to the squaring term. The kinetic energy is, in a way, related to whether or not you will have an closed orbit (staying around a body) or an open (escape) orbit.

[This is really simplified, but hope it helps see the difference between increased acceleration at high speeds (doesn't happen) and increased energy at high speeds (does happen)]

Edited April 29, 2014 by LethalDose

[rkman]

Oberth effect: "when travelling at high speed... higher ...final speed (for the) the same impulse" http://en.wikipedia.org/wiki/Oberth_effect

Oberth effect is you gain more energy per unit of fuel expended (or really, dV expended) at high speeds versus low speeds.

What does that "more energy" do? Does it result in more speed? For the same amount of fuel burned in the same amount of time as we might have at lower speed? Does it increase the thrust of the engines?

Edited April 30, 2014 by rkman

[LethalDose]

Well, I know my definition of ISP was not entirely correct as I didn't do much technical reading on it, I just checked the KSP wiki which linked me to the wiki and I gave a rough definition based on what that said.

What it boils down to, if I understand correctly, is that higher ISP means the engine is more efficient. This doesn't mean it has higher thrust, it just gives you more ÃŽâ€v for amount of fuel used. A different engine might have more thrust and therefore accelerate faster, but uses more fuel to do so. This is the important part when mission planning, because if you can do longer burns, you want the more efficient engine, but for shorter burns you might want more thrust instead.

Of course vehicle weight matters, that's where TWR comes in.

And now I've lost my train of thought.

You're nailing it, though.

TWR is related to acceleration, and high TWR allows you to spend dV rapidly and make short burns. It's also important for getting off of planetary surfaces since you're burning, in part, in opposition to against gravity.

ISP is related to efficiency, in other words, how much dV the fuel gives you.

Even more briefly:

ISP -> how much dV you have to spend.

TWR -> how fast you can spend the dV you have.

[Red Iron Crown]

We don't get more thrust from the Oberth effect, but we do get more energy change.

Reaction engines that carry their reaction mass with them (rockets, ions, etc) have a peculiar property: They always produce the same accelerative force for the same fuel flow rate, regardless of speed when operating in orbit. This has the consequence that they produce the same amount of acceleration no matter what the speed, assuming equal masses. So we can calculate how much change in velocity, delta-V, the fuel/engine/ship combination has, via the rocket equation I posted earlier. Most other types of engines produce constant power for the same fuel flow rate, which means that at higher speeds they accelerate more slowly. This is why we don't measure the delta-V of cars, boats and airplanes, the cases we're more used to.

Because the delta-V remains the same for the rocket at any speed, you can see that 1 m/s of dV accelerates the rocket by 1 m/s whether its starting speed is 10 m/s or 1000 m/s. The tricky thing is, kinetic energy is proportional to the square of speed. Adding 1 m/s to 1000 m/s adds more kinetic energy than adding 1 m/s to 10 m/s, quite a bit more, as it turns out. So even though our speed changed by the same amount, the burn at higher speed creates a bigger change in the orbit's energy than the same burn at lower speed. This bigger orbital energy change results in not more speed, but a bigger change in the orbit's shape.

This is important, because changing the orbital energy is what really gets us to our destinations. Think of delta V as the currency we spend to change our orbital energy. The Oberth effect allows us to buy at a discount.

It should be mentioned that the Oberth effect only applies when we wish to change our orbit's energy, via a prograde or retrograde burn. When we're changing the inclination or eccentricity of the orbit without changing its energy, it is far more efficient to burn when the speed is slower.

Edit: Who let all these ninjas get in?

[Baythan]

So, based on these definitions and descriptions of the Oberth effect.. the best(well, most efficient) time to change orbit shape(increase/decrease Ap or Pe) is at Periapsis because at the BOTTOM of the orbit, you are travelling faster.

In other words you can raise or lower Ap more per ÃŽâ€v spent at Pe than you can raise or lower Pe while at Ap.

[rkman]

I don't get it. Does "more energy" of the Oberth effect not result in 'more speed gain in the same amount of time at the same amount of thrust' (at higher speed vs lower speed)?

And how is more speed gain in the same amount of time not more acceleration?.

Edited April 30, 2014 by rkman
rephrased

[Red Iron Crown]

I don't get it. Does "more energy" of the Oberth effect not result in 'more speed gain in the same amount of time at the same amount of thrust' (at higher speed vs lower speed)?

And how is more speed gain in the same amount of time not more acceleration?.

Don't feel bad for not getting it, it's pretty counterintuitive at first.

You don't gain more speed change, you gain more energy change. A prograde or retrograde burn of 10m/s changes your speed by 10m/s no matter what speed you start at, the acceleration remains exactly the same. But the amount of energy added for a prograde burn and subtracted for a retrograde burn is much more when the burn starts at a higher speed. This greater energy change manifests itself not as more speed, but as a greater change in the orbit's size.

[LethalDose]

So, based on these definitions and descriptions of the Oberth effect.. the best(well, most efficient) time to change orbit shape(increase/decrease Ap or Pe) is at Periapsis because at the BOTTOM of the orbit, you are travelling faster.

In other words you can raise or lower Ap more per ÃŽâ€v spent at Pe than you can raise or lower Pe while at Ap.

Bingo.

Edit: Who let all these ninjas get in?

We were here the whole time, bro.

Oberth effect: "when travelling at high speed... higher ...final speed (for the) the same impulse" http://en.wikipedia.org/wiki/Oberth_effect

What does that "more energy" do? Does it result in more speed? For the same amount of fuel burned in the same amount of time as we might have at lower speed? Does it increase the thrust of the engines?

I can't find that line in the wiki you linked. Maybe because it's so cut up, but... /shrug

The "more energy" causes escape from the parent body. I'm gonna explain how it goes in my head. If you're worried about getting more confused, you may not want to think about this too hard, or even read it.

Elliptical orbits have negative specific orbital energy (Yeah, negative energy is wierd, but its what the equations say). Hyperbolic and parabolic orbits have positive and 0 energy, respectively. To achieve escape from a body around which a vessel is orbiting (and, therefore, the vessel has negative energy), the vessel must add energy into it's orbit until it's energy is at least zero. An efficient way to add energy to the orbit is to burn at periapsis (e.g., exploit the oberth effect). Therefore, burning at periapsis to exploit the Oberth effect is an efficient way to achieve an escape orbit.

... uh, any questions?

The bad news is that you can't really understand the Oberth Effect without discussing orbital specific energy. The good news is that you don't have to understand the Oberth effect to benefit from it. Basically, If you're orbiting high above a high gravity body, it's usually more efficient to drop down close to the body to make your escape burn from said body. 'Cause it works.

Edited April 30, 2014 by LethalDose

[Red Iron Crown]

I don't know why you would think specific orbital energy can be negative. No matter the shape, at any point the craft has altitude (positive potential energy) and speed (positive kinetic energy). Add them together and you have orbital energy, divide that by the ship's mass and you have specific orbital energy.

[LethalDose]

I don't know why you would think specific orbital energy can be negative. No matter the shape, at any point the craft has altitude (positive potential energy) and speed (positive kinetic energy). Add them together and you have orbital energy, divide that by the ship's mass and you have specific orbital energy.

Yep, like I said, it's weird. I'd guide you to this wiki page.

Specifically, "Equation forms for different orbits":

energy of an elliptical orbit is given by the equation e = -mu/2a

mu's always positive, a's always positive, the specific orbital energy is negative.

This is, honest to Odin, the point where I don't get it, but this is 100% consistent across all the sources I've looked at.

Edit:

Further down in the same article, it explicitly states the ISS has a specific orbital energy of -29.6 MJ.

Edited April 30, 2014 by LethalDose
ISS evidence

[UmbralRaptor]

I don't know why you would think specific orbital energy can be negative. No matter the shape, at any point the craft has altitude (positive potential energy) and speed (positive kinetic energy). Add them together and you have orbital energy, divide that by the ship's mass and you have specific orbital energy.

Generally as calculated, 0 potential energy is at infinite distance from the parent body, so something in orbit will have negative potential energy.

energy of an elliptical orbit is given by the equation e = -mu/2a

Ditto hyperbolic orbits, though a goes negative for bookkeeping reasons. Also for both, E = v²/2 - µ/r. Which hopefully makes the tradeoff between kinetic and potential a bit clearer. Edited April 30, 2014 by UmbralRaptor
tyop

[Baythan]

Basically, If you're orbiting high above a high gravity body, it's usually more efficient to drop down close to the body to make your escape burn from said body. 'Cause it works.

In the end, this is what I would do anyway for one simple reason. If I'm in an elliptical orbit with a high Ap and a low Pe and I just want to escape the SOI, I'd burn at Pe because the Ap is already closer to escape and therefore requires less ÃŽâ€v to move it to escape altitude.

Of course, if you are in an orbit where escaping in that direction is BAD, say, because that is the direction the body is travelling and escaping is only going to be temporary, then you have to burn elsewhere anyway.

So in the end, is there any specific situation where NOT burning at Pe would SEEM like a good idea but in fact be a bad idea? I've heard one or two people mention making use of the Oberth effect in KSP, but still haven't figured out any reason why this is something we wouldn't be doing as a matter of course already if we've learned how to fly efficiently without ever having heard the term or it's definition.

In other words, what's the point? Aren't we already using this information without actually knowing it in these terms?

[Red Iron Crown]

Yep, like I said, it's weird. I'd guide you to this wiki page.

Specifically, "Equation forms for different orbits":

energy of an elliptical orbit is given by the equation e = -mu/2a

mu's always positive, a's always positive, the specific orbital energy is negative.

This is, honest to Odin, the point where I don't get it, but this is 100% consistent across all the sources I've looked at.

Edit:

Further down in the same article, it explicitly states the ISS has a specific orbital energy of -29.6 MJ.

Thanks for showing me this. Just when I think I've got a reasonable layman's grasp of orbital mechanics you throw me a curveball like this.

It's really counterintuitive, and it's not really clear to me why this is the convention. Negative potential energy seems nonsensical to me.

[blizzy78]

Perhaps this can help: http://farside.ph.utexas.edu/teaching/336k/Newtonhtml/node42.html

(Please note that the actual math is beyond me right now.)

We conclude that elliptical orbits (e<1) have negative total energies, whereas parabolic orbits (e=1) have zero total energies, and hyperbolic orbits (e>1) have positive total energies. This makes sense, since in a conservative system in which the potential energy at infinity is set to zero we expect bounded orbits to have negative total energies, and unbounded orbits to have positive total energies. Thus, elliptical orbits, which are clearly bounded, should indeed have negative total energies, whereas hyperbolic orbits, which are clearly unbounded, should indeed have positive total energies.

[LethalDose]

<Words>

In other words, what's the point? Aren't we already using this information without actually knowing it in these terms?

The point is that if you are high above a planetary body in a roughly circular orbit and want to escape, you can burn retrograde and drastically drop your periapsis (which decreases your orbital energy), and then burn for escape at your new lower periapsis.

This strategy will typically provide you with a substantial dV savings due to the oberth effect.

[rkman]

"when travelling at high speed... higher ...final speed (for the) the same impulse" http://en.wikipedia.org/wiki/Oberth_effect

I can't find that line in the wiki you linked. Maybe because it's so cut up, but... /shrug

"when travelling at high speed" is simply the condition under which the Oberth effect applies (is stronger):

"In astronautics, the Oberth effect is where the use of a rocket engine when travelling at high speed generates more useful energy than one at low speed."

Which "can (does?) result in a higher change in kinetic energy and final speed than the same impulse applied farther from the body for the same initial orbit"

This greater energy change manifests itself not as more speed, but as a greater change in the orbit's size.

So there seems to be disagreement as to the Oberth effect resulting in greater energy change and more speed, vs greater energy change and not more speed.

Next up: measurements. In ksp I can't measure kinetic energy directly but i can measure speed.

Would it be a valid comparison if the initial orbits have the same Ap, but different Pe? If not that, then how should a valid comparison between "less Oberth effect" and "more Oberth effect" (for one and the same vessel and burn time) be made?

In the mean time i submit this Scott Manley video where he demonstrates fuel saving due to Oberth effect: shorter burn time (less fuel spent) to increase velocity to escape velocity. Which means that if burn time would have been the same, more speed would have been gained.

Edited April 30, 2014 by rkman

[Red Iron Crown]

So there seems to be disagreement as to the Oberth effect results in greater energy change and more speed, vs greater energy change and not more speed.

The wiki article is definitely worded in a bit of a confusing manner.

Next up: measurements. In ksp I can't measure kinetic energy directly but i can measure speed.

Would it be a valid comparison if the initial orbits have the same Ap, but different Pe? If not that, then how should a valid comparison between "less Oberth effect" and "more Oberth effect" (for one and the same vessel and burn time) be made?

You can measure specific orbital energy by looking at the semi-major axis of the orbit. Some mods calculate this for you (KER, MechJeb off the top of my head) but it's simple arithmetic if you don't use mods:

SMA = ApoapsisAltitude + PeriapsisAltitude + KerbinDiameter

Set yourself up in an eccentric orbit, the more eccentric the greater the effect will be. Calculate SMA. Quicksave. Set up a burn at periapsis that doesn't make your orbit escape and note the dV spent. Complete burn and calculate SMA. Quickload and set up a burn for the same amount of dV at apoapsis. Complete the burn and calculate SMA again, and you'll find that the SMA change from the periapsis burn was greater than the SMA change from the apoapsis burn.

[Aphobius]

"when travelling at high speed" is simply the condition under which the Oberth effect applies (is stronger):

"In astronautics, the Oberth effect is where the use of a rocket engine when travelling at high speed generates more useful energy than one at low speed."

Resulting in "...a higher change in kinetic energy and final speed than the same impulse applied farther from the body for the same initial orbit"

So there seems to be disagreement as to the Oberth effect results in greater energy change and more speed, vs greater energy change and not more speed.

Next up: measurements. In ksp I can't measure kinetic energy directly but i can measure speed.

Would it be a valid comparison if the initial orbits have the same Ap, but different Pe? If not that, then how should a valid comparison between "less Oberth effect" and "more Oberth effect" (for one and the same vessel and burn time) be made?

First of all, it would be a good idea to learn at least the Newton's laws of motion and law of universal gravitation, before trying to understand orbital mechanics effects.

But to solve that great dilemma that you have. If you are near (in low orbit) a planet and you have 10000m/s delta-v available. If you make a 2000m/s prograde burn and after a few hours you realize that wasn't enough for what you want to achieve and you actually have to burn all the fuel, so you make another 8000m/s prograde burn. In that few hours you've got away from the planet slowly (starting from 2000m/s) and gravitation slowed you down, maybe you even lost all that 2000m/s and your speed is now 0m/s and after the 8000m/s burn your speed is going to be ... 8000m/s.

But if you burn all the 10000m/s from the beginning, while you are in low orbit. You'll get away from the planet much faster, so you'll spend less time near the planet (where the gravity is higher) so the gravitation of the planet is not going to slow you down too much, you might lose like 100m/s, so your final speed is going to be 9900m/s instead of 8000m/s.

So with the same amount of delta-v (10000m/s) in the first case your final speed is 8000m/s and in the second case it's 9900m/s.

This is not an accurate explanation, but it explains the Oberth effect pretty well to people with poor physics education.

EDIT: The Oberth effect is not about the general idea of this effect, the Oberth effect is about the equations that help you to calculate this things exactly. The idea is pretty simple if you have very little common sense, the hard part was finding the equations to calculate this thing exactly, not understanding the idea.

EDIT 2: I omit the initial speed on purpose, to make the explanation simpler. But I have to add this, this is the interesting part about the Oberth effect, that gravitational slowing down affects not only the speed that you've got from the burn, but also the speed that you initially had. So let's assume in my example above you had 2000m/s initial speed when you were in low orbit. In the first case you, after the 2000m/s burn, your speed is going to be 4000m/s and after a few hours let's say it dropped to 500m/s, if burn the other 8000m/s that you still have, you'll have 8500m/s.

But in the second case, if you burn 10000m/s from low orbit, after the burn your speed is going to be 12000m/s, but since you go so fast and you spend so little time near the planet (where gravitational acceleration is very high), after the same amount of hours from the first case, your speed can be 11800m/s. So with 10000m/s burn, you've got a speed of 11800m/s (considering you are so far away, the planet is not going to slow you down anymore), because you've carried with you a part of the initial speed that you had in low orbit.

The values are random and exaggerated but the general "patterns" are correct.

Edited April 30, 2014 by Aphobius

[LethalDose]

So there seems to be disagreement as to the Oberth effect resulting in greater energy change and more speed, vs greater energy change and not more speed.

I don't think there's disagreement. Everything you listed above deals with energy. dV is dV. It's constant, meaning the amount of dV you get for burning a set amount of fuel is not dependent on velocity or position. The amount of energy or work that dV can do, however, is dependent on those factors (velocity, location)

It looks like this is the source of your confusion:

Which "can (does?) result in a higher change in kinetic energy and final speed than the same impulse applied farther from the body for the same initial orbit"

The context of that quote is really about maximizing KE, which, as the equation shows, is best done by increasing velocity, since the V term is squared and you get more out of it when starting from a higher speed. For any given elliptical (0 < eccentricity < 1) orbit, the equations for just velocity and a set amount of dV would look like this:

V_{final, ap} = V_{initial, ap} + dV

V_{final, pe} = V_{initial, pe} + dV

dV is constant (I assure you), so this can be rewritten as

V_{final, ap} - V_{initial, ap} = V_{final, pe} - V_{initial, pe} = dV

And since V_{initial, pe} > V_{initial, ap}, then V_{final, pe} > V_{final, ap}

So I believe this is what that line in the wiki is saying: By expending your dV at periapsis (where velocity is highest intially), you attain the highest total velocity for that amount of dV, and therefore the highest KE for that amount of dV.

RE: Measuring orbital energy, you simply don't need to. As I've said before, specific orbital energy (of which KE is only a part) is needed to understand the Oberth effect, but not use it effectively. The Oberth effect will be most pronounced with a lower Pe, which it sounds like you already knew.

[rkman]

The Oberth effect will be most pronounced with a lower Pe, which it sounds like you already knew.

No question there. My issue (confusion) is with statements saying that the Oberth effect results in 'greater energy but not greater speed'.

kinetic energy = 1/2mass*v²

There obviously is a relation between speed and energy. Velocity increases as kinetic energy increases (just not at the same rate).

So i don't see how it can be true that 'more Oberth effect' results in greater energy gain but not greater velocity (speed) gain:

You don't gain more speed change, you gain more energy change. ...This greater energy change manifests itself not as more speed, but as a greater change in the orbit's size.

versus

...you attain the highest total velocity for that amount of dV, and therefore the highest KE for that amount of dV

It started with me saying that 'more Oberth effect' results in more acceleration for a given burn time with a given vessel. To me that's just a different way of saying "more speed gain for a given burn" - which indeed seems to be what the Oberth effect results in.

The fact that it can also be formulated in terms of kinetic energy does not mean there is not greater velocity gain.

Edited April 30, 2014 by rkman

[Red Iron Crown]

That was a bit of a simplification. More precisely: The Oberth effect doesn't result in more speed change at the point of the burn, so it doesn't increase the amount of dV available (a common misconception). It can result in a higher peak speed in the orbit, as that is a component in the specific orbital energy and it is a greater energy change that results from the Oberth effect. I think I may have confused you by trying to distill it down to the most basic points, sorry.

[rkman]

That was a bit of a simplification. More precisely: The Oberth effect doesn't result in more speed change at the point of the burn,

Thanks for the clarification Iron Crown.

I did some testing, which confirms your latter point.

vessel mass ~7

TWR 0.75

Ap 12.12Mm

Pe 400km vs Pe 70km, delta-v spent 65m/s at Pe (~10sec burn).

Speed-after-burn is simply initial speed + delta-v spent.

As expected end Ap is considerably different (37.7Mm vs 64.7Mm), which i would attribute exclusively to differences in initial velocity due to differences in Pe, if i would not know about the Oberth effect.

All in all i do not understand the Oberth effect any better than before (though i do know how to use it), but i do have a better notion of what it is that i don't understand about it. Not that i could tell you right now, i need to think about it. Thanks to all for their efforts trying to explain it.

[Red Iron Crown]

maccollo posted an interesting example of the Oberth effect in action in the big thread we had about Oberth a few months ago (which coincidentally got bumped just yesterday). He does a capture burn around a moon with an eccentric orbit as the result. If he does the capture at the desired apoapsis altitude it costs much more dV than if he does the burn at the desired periapsis altitude, even though the resultant orbit is the same in both cases.

This also demonstrates that the Oberth effect works for retrograde burns, too. Another common misconception is that it only works for prograde burns.

[eypandabear]

Hey guys, longtime lurker making an account here to contribute to this discussion.

I believe there are two things in particular that confuse many people about the Oberth effect:

1. The Oberth effect, like many things in physics, can be understood and explained in multiple equivalent ways.
   
2. The Oberth effect is often confounded with gravity assists, which also tend to exploit the Oberth effect.
   

I am not going to say anything here that hasn't been said before by others in this thread, I am just trying to distill the facts to help

those who still struggle understand this concept.

The important thing to see is that the Oberth effect is just the astronautical term for something that, on the face of it,

has nothing to do with orbital mechanics. For any particle with mass m and velocity v, the non-relativistic kinetic energy can be

given as E = (1/2) m v^2. As the particle is accelerated, the kinetic energy increases at a rate of dE/dv = mv = p, which is the

momentum of the particle.

Accelerating your car from 100 km/h to 120 km/h takes 22% more energy than from 80 to 100. The same is true for rockets.

From a kinematic point of view, this is everything you need to know to understand the Oberth effect. Note that this has nothing to do with

orbital mechanics, gravitational drag or what have you.

Another way to look at it is that energy is a force F applied along a distance s. For a fixed burn time t and force (thrust) F, the distance

s along which the force is applied is longer if the craft moves faster, which increases the energy. This is the exact same physical effect, just

explained differently.

Hermann Oberth famously recognised that this simple kinematic fact had implications for rocket-propelled spaceships (sci-fi in his day), hence the name.

A spacecraft in an elliptical orbit moves fastest at periapsis, which means that the same delta-v applied at periapsis results in a

higher increase in kinetic energy than if the burn had been performed at any other point. Kinetic energy at one point in the orbit corresponds to potential energy, i.e. altitude, at the opposite

side, hence why burning at periapsis increases your apoapsis. This is also true vice versa, i.e. burning at apoapsis increases your periapsis. However, the potential energy increase in the first case

is higher - this, in a nutshell, is the Oberth effect.

At a more "microscopic" level, the higher kinetic energy can be described by the rocket exhaust obtaining less of the total energy, leaving more to the rocket. But this

isn't necessary to understand the Oberth effect. All you need to know is that rocket engines apply velocity-independent thrust to the spacecraft.

[Red Iron Crown]

^^ That is an excellent first post, welcome aboard! I hope you lurk less and post more.