Why does the oberth effect work?

[Starman4308]

If I were sitting on an asteroid falling towards periapsis, then right at periapsis I pushed myself of of the asteroid, would I pick up kinetic energy greater than my strength in pushing off the asteroid?

Your kinetic energy relative to Earth's gravitational field would increase in a rather disproportionate fashion compared to the chemical energy you used pushing yourself off that asteroid. Your kinetic energy relative to what you pushed off of would be proportional to chemical energy spent*. The reason overall energy is conserved, even in Earth's reference frame, is that, despite giving yourself a huge kinetic energy boost, you also removed a lot of the asteroid's kinetic energy relative to Earth's gravitational field.

*And, with a rocket, you are pushing off of your propellant, which conveniently travels with you right up until you burn it.

I think I am fundamentally misunderstanding this somehow. Does the energy from the Oberth effect come from leaving mass behind at periapsis, that I carried towards periapsis?

Oberth comes out of the fact that kinetic energy is not linearly dependent on velocity: KE = 1/2*m*v^2. As such, a given change in velocity gives you much more KE when you are already traveling fast.

[GoSlash27]

Does more kinetic energy (with a given vessel mass) not mean more speed for that vessel?

More effecting in what way? Higher apoapsis compared to a burn at higher periapsis (less Oberth effect) - an apoapsis that would have required more fuel if the burn would have taken place at higher periapsis?

If more Oberth effect verse less Oberth effect does not save fuel (or gets you more speed for the same amount of fuel) then why use it at all?

Speed <> kinetic energy, but we often short-hand them as the same thing. For a fixed mass, they're comparable... but misleading since the relationship between them is not linear.

Delta- vee is delta- vee. That never changes based on your starting velocity. Likewise, thrust, burn times and fuel flow don't change depending on your starting velocity.

But delta- kinetic energy *does* change based on your starting velocity. Adding 1KM/sec to your velocity won't do as much to change your apoapsis at low speed as it will do at high speed.

Please bear with me if I'm rehashing something you're already familiar with, but I need to present this to illustrate how it works.

Kinetic energy is 1/2M*V^2. The kinetic energy after you do a burn is 1/2M*(v+D)^2. <-- "D" is your delta-vee.

We don't care about the mass or an exact value, so let's eliminate the stuff that doesn't change.

Kinetic energy is proportional to (v+d)^2.

Let's foil this out to look at what effect our burn is causing.

Ek is proportional to v^2+2vd+d^2

Our burn did not cause the initial change in velocity, we arbitrarily chose that. So we'll eliminate that.

2vd+d^2

^ This is the effect that your burn has on your total kinetic energy.

That "v" sitting in there is giving you a boost in your gain simply because you were going faster when you did it.

Why it matters is because doing your transfer burn at as high a velocity as possible can save you a huge amount of delta-vee (and hence fuel) over doing it at a low velocity. So much so, that the gain will even offset the loss in kinetic energy associated with climbing out of a gravity well.

It would seem that the most effective way to do a transfer is to climb out of the gravity well (about 1Km/sec) and refuel, then proceed on your way.

But in reality, that robs you of 2,300 m/sec you could've had during your burn had you refueled in LKO and burned from there. You still have 9,300 m/sec from your orbit around Kerbol, but you *had* 11,600 m/sec at the bottom of the gravity well.

Doing your burn from down there would've saved you 1,800 m/sec to get to the exact same kinetic energy, so even losing the 1,000 climbing out, you still come out ahead.

Even better, you could climb out and refuel, then dive back in and do your burn. That would add another 1KM/sec to your velocity at burn, which saves you even more.

It's counter-intuitive, but that's how it works. All because DV isn't linear to kinetic energy.

Best,

-Slashy

Edited November 13, 2014 by GoSlash27

[GoSlash27]

GregA,

We're talking about different concepts. Pushing off of an asteroid is force (newtons). Changing your velocity is delta v (m/sec). Kinetic energy is energy (Joules).

Pushing off of an asteriod at high speed vs. low speed won't increase the force with which you pushed, nor will it increase the speed you add by doing so. But it *will* add more kinetic energy than it would have done at low speed, and thus will more greatly affect your apoapsis.

Best,

-Slashy

[GoSlash27]

No. The Oberth effect doesn't change your dV in the slightest. It changes the kinetic energy you gain or lose from your change in velocity. The faster you are going, in the frame centered on the body you are orbiting, the more effecting your velocity change is.

andrewas,

Actually, it's cumulative for all the frames you're referencing. They don't have to affect you to count. You get a free 175 m/sec for launching East, plus 2,300 m/sec for LKO, plus 9,300 m/sec for Kerbin's orbit around Kerbol. All of this applies to a transfer to another planet. If you were transferring to another star system, you would also pick up the velocity of Kerbol around the galaxy.

Best,

-Slashy

Edited November 12, 2014 by GoSlash27

[LethalDose]

What i'm confused about is how it gets you a delta-v advantage when you have to spend delta-v to get up to that speed?

Magic. Gravity is magic and Oberth was a freaking wizard. But seriously, it was good question and the whole conversation is a good exploration of the issue. I especially liked your post on the first page:

The way I see it that works in my mind is that the higher kinetic energy you have at periapsis, the higher your apoapsis will be. Since kinetic energy grows with the square of velocity, the faster you are moving, the less change in velocity you need to get the same change in kinetic energy.

[GoSlash27]

Sorry for spamming, but I just thought of another way of explaining it that may be more intuitive.

You know how when you do a transfer from LKO to mun or minmus the apoapsis climbs very slowly at first, but towards the end of the burn it's rocketing upwards at a much faster rate? It's not due to you being close to Kerbin or anything like that. You could do the same thing on an interplanetary transfer and see the same effect; the apoapsis climbs slowly at first, but climbs much more rapidly towards the end.

So what causes that? You'd expect it to be linear. Halfway through the burn, you'd expect your apoapsis to be halfway to the target, but that's not how it works out.

This is the Oberth effect at work. As you accelerated, your kinetic energy (and thus your apoapsis) increased at an exponential rate. The first 100 m/sec didn't buy you much, but the last 100 m/sec made a radical change.

Harnessing the Oberth effect is making the same change in apoapsis for less DV by doing your burn while travelling at a higher speed.

Hope that makes sense,

-Slashy

[Red Iron Crown]

The Oberth Effect, at its simplest, is this: A change in the size of your orbit costs less delta-V when the burn is made at higher speed.

We look at delta-V maps and such and start to think that delta-V is what gets us places in KSP, and in a sense that's true. But more specifically, delta-V is what we spend to buy changes in our orbit's size, and the size of the orbit is determined by its energy. We change our velocity (i.e. expend delta-V) to add or subtract kinetic energy from our orbits, changing their size.

The secret is that each m/s of speed change is worth more kinetic energy if it is done at higher speed.

Delta-V is the currency we spend to buy a change in energy, and the Oberth Effect sometimes lets you buy at a discount. The reason for this is that kinetic energy is not proportional to speed but to the square of speed. Adding 10 m/s to a ship moving at 1000m/s adds much more kinetic energy than to the same ship moving at 100m/s. Here is a simple mathematical example showing the energy change in those two situations:

A 2-ton ship is in an eccentric orbit with a speed of 100m/s at apoapsis and 1000m/s at periapsis. It performs a 10m/s prograde burn, adding to its speed.

Kinetic energy is calculated as KE=0.5*m*v², where m is the mass and v is the speed. (We'll ignore the mass change from fuel spent for simplicity and because it's the difference in speed in which we're interested)

If the burn is performed at apoapsis:

Change in KE = KE(finish)-KE(start)

= 0.5*m*v(f)² - 0.5*m*v(s)²

= 0.5*2*(110)² - 0.5*2*(100)²

= 12,100 - 10,000

= 2,100 kJ (kilojoules, a metric unit of energy)

If the burn is performed at periapsis:

Change in KE = KE(finish)-KE(start)

= 0.5*m*v(f)² - o.5*m*v(s)²

= 0.5*2*(1010)² - 0.5*2*(1000)²

= 1,020,100 - 1,000,000

= 20,100 kJ

So, even though the ship spent exactly the same amount of fuel and changed speed by exactly the same amount, almost ten times as much energy was added when the burn was performed at higher speed. We got more "bang for our buck" with the burn, which manifests by changing the size of the orbit by a greater amount.

How to utilize the Oberth effect:

- At low periapsis is the best place to perform most burns because speed is higher.

- Use low parking orbits for ships intended to go to other bodies.

- When intercepting a body, set a low periapsis for your approach and do your capture burn there.

Clarifying some common misconceptions:

- The Oberth Effect does not increase the delta-V a ship has. This is solely determined by Tsiolkovsky's Rocket Equation, speed is not a factor. The Oberth effect lets you spend less dV to change an orbit's size.

- The Oberth Effect does not provide more speed for the same fuel spent. It provides the same speed change but more orbital energy for the same fuel spent.

- The Oberth Effect does not only work in the prograde direction. The Oberth Effect is symmetrical, subtracting energy from an orbit is also best done at high speed.

- The Oberth Effect does not need to be programmed into the simulation. It is entirely a consequence of the most basic kinetic energy equation.

- The Oberth Effect does not apply to inclination changes (normal +/- burns) or eccentricity changes (radial +/- burns). Those type of burns aren't trying to change the amount of energy an orbit has, but instead its direction. This is best done at the slowest point in the orbit (Ap).

- The Oberth Effect is not a gravity assist or slingshot. A gravity assist is using a celestial body's gravity and orbital speed to change the shape of an orbit, no propellant need be expended to complete the maneuver. The confusion arises because it is often efficient to combine a gravity assist with a burn that does take advantage of the Oberth effect, but the burn and the slingshot are two separate things.

- The Oberth Effect is not caused by gravity. It is not a gravitational effect, but gravity can create situations where it can be harnessed by increasing the speed of the ship.

Edited November 13, 2014 by Red Iron Crown
Reworded the misconceptions.

[KerbMav]

This may sound like an answer, but it is actually a longish question.

In short: Am I right or what?

Pilots of (especially sail-)planes turn kinetic energy (velocity) into potential energy (altitude) - ignoring losses due to drag here.

In an orbit the satellite does the same, its potential energy at AP becomes kinetic energy at PE, the value is the same.

The higher I am, the deeper I fall, the faster I am at my lowest point in orbit. The reverse is true too, the faster I am at my lowest point in orbit, the higher I can go before gravity has slowed me down and I start to fall.

When I add velocity at my PE, I will go up higher later at my AP.

As the relation between kinetic energy and velocity is different from the relation between potential energy and altitude, but the sum of kinetic energy and potential energy always stays the same, a change in velocity by 100m/s results in a different change in altitude depending on my velocity at the beginning of my burn.

Basically, the way I see it, Oberth is a very complicated way to justify the behaviour of orbiting objects, but has the advantage of giving an explanation coherent with fundamental laws of physics. (Which must be my most anti-science statement since a very long time!)

Another question regarding fuel efficiency:

Is the only way to exploit Oberth to save fuel by not launching into a high orbit - or do I even save fuel by lowering my PE first should I wish to raise my AP afterwards?

How to utilize the Oberth effect:

- At low periapsis is the best place to perform most burns because speed is higher.

- Use low parking orbits for ships intended to go to other bodies.

- When intercepting a body, set a low periapsis for your approach and do your capture burn there.

Some common misconceptions:

- The Oberth Effect increases the delta-V a ship has. This is solely determined by Tsiolkovsky's Rocket Equation, speed is not a factor. The Oberth effect lets you spend less dV to change an orbit's size.

- The Oberth Effect provides more speed for the same fuel spent. It provides the same speed change but more orbital energy for the same fuel spent.

- The Oberth Effect only works in the prograde direction. The Oberth Effect is symmetrical, subtracting energy from an orbit is also best done at high speed.

- The Oberth Effect needs to be programmed into the simulation. It is entirely a consequence of the most basic kinetic energy equation.

- The Oberth Effect applies to inclination changes (normal +/- burns) or eccentricity changes (radial +/- burns). Those type of burns aren't trying to change the amount of energy an orbit has, but instead its direction. This is best done at the slowest point in the orbit (Ap).

- The Oberth Effect is a gravity assist or slingshot. A gravity assist is using a celestial body's gravity and orbital speed to change the shape of an orbit, no propellant need be expended to complete the maneuver. The confusion arises because it is often efficient to combine a gravity assist with a burn that does take advantage of the Oberth effect, but the burn and the slingshot are two separate things.

- The Oberth Effect is caused by gravity. It is not a gravitational effect, but gravity can create situations where it can be harnessed by increasing the speed of the ship.

Good list, basically summing everything you really need to know about Oberth without fully understandig it.

But educationally it is better to give examples of misconceptions in the negative (does not, is not, etc.) form. We tend to remember wrong examples when they were phrased positively, because we learn what we read/hear repeatedly and reading a false statement (if only as an example) counts as a repetition.

Edited November 13, 2014 by KerbMav

[K^2]

Is the only way to exploit Oberth to save fuel by not launching into a high orbit - or do I even save fuel by lowering my PE first should I wish to raise my AP afterwards?

If you want to raise your AP, you should always burn at PE, but lowering PE intentionally just to raise AP is a waste of fuel.

Unless, of course, you have an opportunity to lower your PE for free using a flyby. Rosetta's Earth flyby, for example, was angular momentum trade, rather than energy trade. It lowered its PE and raised its AP without major energy change. If you have opportunity to do this, then yeah, Obereth effect will consequently make it easier to leave the system. But that's because you get free angular momentum.

This is something to keep in mind in general. When you adjust your orbit, you need to change your energy and your angular momentum. Obereth effect makes it most efficient to get energy low, but it's also the worst place to burn for angular momentum. This is part of the reason why Hohmann transfer is most efficient way to change orbits (barring inclination change). At lowest point, you get most of the energy change you need, and at highest point, you get most of the angular momentum change.

[Laie]

The reason the Oberth effect works is because orbital mechanics aren't velocity, but rather kinetic energy.

We all think of it in terms of "ÃŽâ€V" in m/sec, but in reality they're "ÃŽâ€Ek" in terms of joules.

Scrap the "kinetic", make that only "energy". Kinetic energy at periapsis becomes potential energy at apoapsis and vice versa.

Getting to (say) Jools means you have to increase the energy of your vessel so that it can reach the altitude of Jool.

If I were sitting on an asteroid falling towards periapsis, then right at periapsis I pushed myself of of the asteroid, would I pick up kinetic energy greater than my strength in pushing off the asteroid?

I think I am fundamentally misunderstanding this somehow. Does the energy from the Oberth effect come from leaving mass behind at periapsis, that I carried towards periapsis?

No and No.

The key is that a change in velocity is always linear (+1m/s is +1m/s and that's that), however, a change in kinetic energy is quadratic. If you accelerate from 2m/s to 3m/s, your energy increases 4->9; accelerate another +1m/s and it goes 9->16. Although you expend the same amount of work, you gain +5 energy in once case and +7 energy in the other.

If you jump off that asteroid, your (and the asteroids') change in velocity will always be the same, regardless of when and where you do it. Your change in energy, however, will depend on how fast you were going at the moment of your jump. And this only applies if you're jumping towards, or away from, the direction you're moving in.

[GoSlash27]

KerbMav,

Oberth effect is actually a way of explaining the disparity in kinetic energy that results from doing the same burn at different speeds. Other than that, yeah... that's pretty much it.

K^2,

The hohmann transfer is actually not the most efficient way to change orbits, that honor goes to the bi-elliptic transfer. The reason that it works is, indeed, the Oberth effect.

IRT the original question, yes, depending on the circumstances you can save some DV by dropping first, but it's easy to overdo it and wind up costing yourself more at the end. Generally not worth it for small changes, as the investment is more than the return.

Besides making transfer burns cheaper it also works in reverse, making captures cheaper. You should do capture/ circularization burns at periapsis to get the most delta Ek reduction for your delta v.

Best,

-Slashy

Edited November 13, 2014 by GoSlash27

[Red Iron Crown]

But educationally it is better to give examples of misconceptions in the negative (does not, is not, etc.) form. We tend to remember wrong examples when they were phrased positively, because we learn what we read/hear repeatedly and reading a false statement (if only as an example) counts as a repetition.

That's a good point, thanks for raising it. Fixed.

The hohmann transfer is actually not the most efficient way to change orbits, that honor goes to the bi-elliptic transfer. The reason that it works is, indeed, the Oberth effect.

Careful, Hohmann transfers are sometimes more efficient than bielliptic transfers, it depends on how much the SMA is being changed. Bielliptic transfers also have the penalty of taking a large amount of time for a relatively small efficiency gain, they're generally not worthwhile unless the delta-V budget is very tight.

[GoSlash27]

Careful, Hohmann transfers are sometimes more efficient than bielliptic transfers, it depends on how much the SMA is being changed. Bielliptic transfers also have the penalty of taking a large amount of time for a relatively small efficiency gain, they're generally not worthwhile unless the delta-V budget is very tight.

Agreed.

Best,

-Slashy

[K^2]

(Edit: Warning. Everything in this post is wrong.)

I've specifically stated,"barring inclination change". In a 2d circular transfer, Hohmann is most efficient. In 3d, you add a 3rd parameter, requiring a 3rd burn. Most general elliptic to elliptic transfer is a 4 parameter change, requiring 4 burns. All of this is because each constant of motion has its own optimization. (There are actually 6 constants, but the assumption is that we do not care about final time and anomaly.) Energy with Obereth effect being only one of these constant - optimization pairs. Angular momentum is another one that is easy to understand. From there, things get complicated.

Edit: Pardon me. That's 5 parameters/burns total for a most general 3d transfer. Anomaly is completely defined by the other orbital elements. It's only the time of periapsis that we don't care about. The reason it's 3 in circular to circular is because both argument of periapsis and longitude of ascending node become irrelevant. So bi-elliptic can get away with a 3-burn optimization. The most general problem is a 5-burn monstrocity, and I have no idea if a closed form expression for it even exists or if it has a name.

Edited November 14, 2014 by K^2

[Red Iron Crown]

In a 2d circular transfer, Hohmann is most efficient.

That is not always the case. If the ratio of the SMAs of the initial and final circular orbits is sufficiently large, a bielliptic transfer costs less dV even if they are already coplanar. There's a worked example on the Wiki page GoSlash27 linked.

[K^2]

What do you know? So it is. Well, there goes everything I believed in.

Thank you for correcting me.

[LostOblivion]

I understand the Oberth effect from a math standpoint with the conservation of momentum, but not intuitively. It is my intuitive understanding that the Oberth effect exists because gravity pulls you towards the primary body, and the faster you are able to get away from it, the less time you spend closer to it than you would otherwise, because gravity decreases with the square distance you are from the primary body. Slap me if my intuitive understanding is bollox! :-)

[-Velocity-]

It is my intuitive understanding that the Oberth effect exists because gravity pulls you towards the primary body, and the faster you are able to get away from it, the less time you spend closer to it than you would otherwise, because gravity decreases with the square distance you are from the primary body. Slap me if my intuitive understanding is bollox! :-)

That's correct.

[RainDreamer]

An old derelict post just got gravity assisted by an errant user and got thrown out of its graveyard orbit!

On topic, because the thing is already back and all, I always thought of the orbeth effect as this: If your craft is already moving at high speed, then the energy expended by the fuel goes more toward increasing the craft speed rather than propelling itself away from the nozzle. Kind of like rolling a ball downhill.

I am probably very wrong with this kind of thinking though. But it is how I intuitively imagine the effect in play.

[GoSlash27]

Old post, but clearly still useful

RainDreamer's intuitive understanding is closer to the mark than LostOblivion's.

LO,

Forget about gravity. It has no bearing on how the Oberth effect works.

Changing orbits is all about changing energy. We change our energy by adding or subtracting velocity, but the relationship between them is not linear. Doubling your velocity does not double your energy, it quadruples it.

Therefore it stands to reason that the faster you are going when you make a velocity change, the larger the resultant change in your energy.

Best,

-Slashy

[Bill Phil]

At higher altitudes you have more Potential Energy, at lower altitudes you have more kinetic energy. The Oberth effect takes advantage of that KE.

[-Velocity-]

Old post, but clearly still useful

RainDreamer's intuitive understanding is closer to the mark than LostOblivion's.

LO,

Forget about gravity. It has no bearing on how the Oberth effect works.

Changing orbits is all about changing energy. We change our energy by adding or subtracting velocity, but the relationship between them is not linear. Doubling your velocity does not double your energy, it quadruples it.

Therefore it stands to reason that the faster you are going when you make a velocity change, the larger the resultant change in your energy.

Best,

-Slashy

No Slashy, Lost Oblivion's interpretation is perfectly correct, and you are very off track when you say that gravity has no effect. Gravity is CENTRAL to the Olberth effect, because it's what defines your point of maximum efficiency- your closest approach to a gravitating body!

However your mathematical statements are correct, as they are essentially based the equivalent of Work = Force*Distance. The gravity of a body makes you move faster the closer you are to it, and so when you apply an amount of force with your engine, it is applied over a further distance due to the increased velocity, resulting in more energy (work) added.

Anyway, I personally find Lost Oblivion's interpretation to be the most intuitive, but you can keep your interpretation if it seems more intuitive to you; mathematically, they are equivalent.

[GoSlash27]

Velocity,

As much as I am *not* interested in arguing, I feel the need to correct this for clarity:

The Oberth effect is not dependent on gravity. It has nothing to do with being close to a point source or being far away from it. The reduction of gravitational attraction over distance doesn't factor into it. It doesn't matter whether you're in close proximity to a planet or in open space.

Adding velocity to a higher velocity imparts more kinetic energy than adding velocity to a lower velocity.

Now... as a practical matter, yes. We have our highest velocity at the periapsis of an orbit, which is why we choose to burn there. *BUT* that gravity has nothing to do with how or why the Oberth effect works. Burning at twice the velocity imparts 4 times the kinetic energy. This is true regardless of whether there's a planet nearby or not.

Best,

-Slashy

Edited February 19, 2015 by GoSlash27

[SuperFastJellyfish]

Adding velocity to a higher velocity imparts more kinetic energy than adding velocity to a lower velocity.

This is one of the most concise ways to put the Oberth effect into laymans terms I've ever read. +1

[-Velocity-]

Velocity,

As much as I am *not* interested in arguing, I feel the need to correct this for clarity:

The Oberth effect is not dependent on gravity. It has nothing to do with being close to a point source or being far away from it. The reduction of gravitational attraction over distance doesn't factor into it. It doesn't matter whether you're in close proximity to a planet or in open space.

Adding velocity to a higher velocity imparts more kinetic energy than adding velocity to a lower velocity.

Now... as a practical matter, yes. We have our highest velocity at the periapsis of an orbit, which is why we choose to burn there. *BUT* that gravity has nothing to do with how or why the Oberth effect works. Burning at twice the velocity imparts 4 times the kinetic energy. This is true regardless of whether there's a planet nearby or not.

Best,

-Slashy

No need to argue, and thank you for the correction. I was confused about what the term Oberth effect meant, and where it was supposed to apply. I thought the term was defined to apply ONLY around a gravitating body- in which case, the gravity determines the velocity (and how much kinetic energy you keep from the encounter- or your gravitational potential energy at your apoapsis- increases the faster you "run away" from the gravitating body, as Lost Oblivion said). However, I looked up the official definition and it looks like the Oberth effect is actually defined more generally, simply stating the obvious that you get a larger increase in energy per unit delta-V when you are moving faster (assuming your apply the delta-V in the direction of or against your motion)! And obviously, work = force*distance works in deep space, not just around a gravitating body

Edited February 20, 2015 by |Velocity|