# oberth effect

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"Given that you are going to travel a parabolic orbit around the Sun that has an escape velocity of 200 km/s at periapsis, you have an initial velocity of 3.2 km/s, and you wish to exit the Oberth Maneuver with a final velocity of 50 km/s, calculate the required ÃŽâ€v burn at periapsis.

Vesc = 200 km/s = 200,000 m/s. Vh = 3.2 km/s = 3200 m/s.Vf = 50 km/s = 50,000 m/s.

ÃŽâ€v = sqrt(Vf2 + Vesc2) - sqrt(Vh2 + Vesc2)

ÃŽâ€v = sqrt(50,0002 + 200,0002) - sqrt(32002 + 200,0002)

ÃŽâ€v = sqrt(2,500,000,000 + 40,000,000,000) - sqrt(10,240,000 + 40,000,000,000)

ÃŽâ€v = sqrt(42,500,000,000) - sqrt(40,010,240,000)

ÃŽâ€v = 206,000 - 200,000

ÃŽâ€v = 6,000 m/s = 6 km/s

So by burning 6 km/s of ÃŽâ€v, you get an actual ÃŽâ€v increase of 46.8 km/s. That's 40.8 km/s for free. Sweet!"

See... You do get bonus speed... The increased energy is increased kinetic energy...

I think I see where the issue is now ... you appear to be saying that using 1000 m/s of delta-v changes your speed more than 1000 m/s. It doesn't do so at the moment (or interval) of application. The Oberth effect does, however, allow that 1000 m/s of delta-v to have a considerably greater effect on your speed at a later point of the orbital track, such as (as above) comparing entering a body's SoI and leaving it after that application of delta-v. The burn is still 1000 m/s, but as your PE tends back to 0 (remembering that it's 0 at infinity and negative in the gravity well) your KE gain was such that you picked up more than 1000 m/s AT A DISTANCE.

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Your car example isn't actually an illustration of the Oberth effect, it's just a conservation of momentum problem, and you don't get any extra speed when traveling faster. I'm gonna tweak your numbers a bit so I don't have to type as many things into my calculator.

Mocknizzle, your math doesn't even seem correct...

Firing a 1kg object backwards at 400ms generates 80000 J of energy, this is enough to push the 1000kg car an extra 12.5ms = 37.5ms...

kE = 80000 = (0.5 x 1) * (400^2)

or for 400-25...

kE = 70312.5 = (0.5 x 1) * (375^2)

v= SQRT(2kE/m)

Jouni seems to be right there as well...

Edited by SSSPutnik
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I mean, you can do the algebra and type the numbers into a calculator yourself if it makes you feel any better, you'll get the same result.

Jouni and I are applying the same concept to the problem (conservation of momentum) and are arriving at the same conclusion:

Regardless of the initial velocity v0, the velocity of the car changes by v1, the velocity of the bullet by v2

He (she?) is just keeping track of the kinetic energies, while I took the simple route and only kept track of the momentums.

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I suggest you read it as well

As explained in that article, our spaceship is coming in on a hyperbolic interplanetary trajectory. As we enter the SOI of the body we're Oberth-ing around, we have some hyperbolic excess velocity Vh1 beyond escape velocity (this is what makes the trajectory hyperbolic). As we hit our periapse, we burn X m/s worth of fuel, increasing our speed at periapse by X. We then zoom away from the planet, now on an even more hyperbolic trajectory, with even more excess velocity than we gained at periapse, such that Vh2 > Vh1 + X.

I can't stress this enough: The Oberth effect doesn't magically give you more speed at periapsis than the conservation of momentum dictates. The effects are felt afterwards, in the form of an increased semi-major axis for elliptical orbits and an increased hyperbolic velocity for hyperbolic orbits.

Edited by MockKnizzle
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I get that, but how can you reach that increased semi major axis distance without a speed increase? Let's say you complete the orbit, (on a closed orbit). You're coming back to periapsis again, the speed is higher based on this new orbit. The author also states you get a 'free' deltaV increase. deltaV = velocity change.

Edited by SSSPutnik
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I get that, but how can you reach that increased semi major axis distance without a speed increase? Let's say you complete the orbit, (on a closed orbit). You're coming back to periapsis again, the speed is higher based on this new orbit. The author also states you get a 'free' deltaV increase. deltaV = velocity change.

I think you guys are talking past each other.

Mock is saying the increase in velocity at that point in the orbit corresponds exactly with the delta V expended.

When you come back to that point an orbit later you velocity will be exactly what you came in with+the amount you accelerated. The increase in velocity only happens as you fall away from the planet.

Dammit I'm so bad at explaining things when I'm intoxicated:confused:

The effects are felt afterwards, in the form of an increased semi-major axis for elliptical orbits and an increased hyperbolic velocity for hyperbolic orbits.

In elliptical orbits there is also a kind of increase in speed. At any given altitude the velocity difference will be greater than the amount accelerated at periapsis.

An example of this would be a lunar transfer. By going just a tiny tiny bit faster at periaps, the transfer time is cut from a week to about 3 days.

On a somewhat related note, this is why you want to encounter Moho at perihelion if you want to get captured.

Edited by maccollo
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I get that, but how can you reach that increased semi major axis distance without a speed increase? Let's say you complete the orbit, (on a closed orbit). You're coming back to periapsis again, the speed is higher based on this new orbit. The author also states you get a 'free' deltaV increase. deltaV = velocity change.

He said there was no magical free speed increase. You get the speed increase you pay for.

What he's saying is, if you burn 500 dV at periapsis, you add 500 m/s (let's pretend it's like a maneuver node and you add it instantaneously) to your speed. If you burn 500 dV at apoapsis, you ALSO add 500 m/s to your speed.

However, by burning at periapsis you add more TOTAL ENERGY to your orbit than if you burned at apoapsis, and that TOTAL ENERGY equates to a faster speed when you leave the object's SOI.

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Simple SIMPLE explain:

Your orbit depends not on speed, but on energy.

Speed on top of current high speed "makes" more energy than the same speed on little starting speed.

So. Oberth says that if you move fast already, same rocket will change energy more, thus change orbit more.

in space, easiest way to get "free" "speed" for this effect, if to be orbiting close to a heavy body. Planet is good, big planet better. sun best!

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A couple of things I'd like to clarify as I've been thinking about the Oberth effect and its consequences.

The Oberth effect isn't some isolated phenomenon that needs to be separately programmed into KSP. It is a consequence of kinetic energy being proportional to the square of speed in Newtonian physics. You cannot have Newtonian physics without also having the Oberth effect. So the Oberth effect must be in KSP, since its physics model is Newtonian.

From the rocket equation it can be seen that the only factors that affect dV are starting mass, ending mass, and Isp. If none of those factors change, then dV cannot change. So it should be obvious that speed has no effect on the amount of delta-V for a given craft, i.e. the Oberth effect cannot add or subtract any delta-V.

Similarly, delta-V is a measurement of potential acceleration. If a craft increases its speed by 10m/s at a given point in its orbit, it necessarily has spent exactly 10m/s of dV to gain that speed. It doesn't matter at what altitude or speed this occurs, a 10m/s dV burn will always add 10m/s of speed. So the Oberth effect cannot increase the amount of speed gained by spending a given amount of dV.

So, if the Oberth effect doesn't increase the amount of dV or get more acceleration from dV what is its advantage?

Energy.

The orbital energy of a craft is the sum of its potential energy (from altitude) and its kinetic energy (speed). If no dV is spent, this sum is constant at all points in the orbit. Kinetic energy is converted into potential energy and back again as the craft moves through its orbit. To change orbits, energy must be added (or subtracted) to the orbital energy. This is done by spending delta-V. But remember, delta-V is not a measure of energy, but of potential acceleration. It is this distinction that makes the Oberth effect possible.

1 m/s of dV always results in 1 m/s change in velocity, but not all m/s are equal in terms of energy. Because kinetic energy is proportional to the square of speed, the faster you are going the more energy is added by each m/s of speed gained. The speed gained is the same but the energy gained is greater. So, if we look at the kinetic energy change for a 1-ton craft spending 1m/s of dV to accelerate by 1 m/s at different initial speeds using the formula Ek = 1/2mv2 we get the following (I have assumed no mass change from the burn to keep the math simple):

0m/s -> 1 m/s = 0.5KJ energy added

10m/s -> 11m/s = 10.5KJ energy added

100m/s -> 101m/s = 100.5KJ energy added

Each of these burns consumes exactly the same amount of dV, but the amount of kinetic energy added to the orbital energy is vastly different. This is the heart of the Oberth effect: dV spent at high speed changes orbital energy by more than spending dV at low speed.

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MarvinKitFox, you are wrong I'm afraid. The mass of the object is only relevant as far as orbital speed matters. If you did a burn at 10ms 10m above the sun you would get very little Oberth boost.

SOI is irrelevant too. There are no soi in real life.

I'm willing to take the orbital total energy argument under advisement, but I don't see how, 10 seconds after burn the energy mysteriously starts to bleed into velocity. An orbit has a set velocity based on energy for every point of its orbit.

One thing I really don't get is why Oberth doesn't just say, warm or cool the mass of the ship a few degrees depending on energy gain since a lot of physics processes express themselves into waste heat or cooling.

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SOI is irrelevant too. There are no soi in real life.

Your velocity only makes sense relative to some other object. There's not speed without reference frame. So if it is about your orbital velocity about Earth, you use Earth as reference.

I'm willing to take the orbital total energy argument under advisement, but I don't see how, 10 seconds after burn the energy mysteriously starts to bleed into velocity. An orbit has a set velocity based on energy for every point of its orbit.

As you burn, the chemical energy stored in your fuel is bleeding into your velocity. Immediately.

As you travel along the orbit, your energy transfers between your potential energy (measured by distance from the body you orbit) and your kinetic energy (measured in your velocity).

One thing I really don't get is why Oberth doesn't just say, warm or cool the mass of the ship a few degrees depending on energy gain since a lot of physics processes express themselves into waste heat or cooling.

Neither potential nor kinetic energy have anything to do with temperature. In Newtonian physics, at least. Unless you crash into something, in which case in real world all your kinetic energy transfers to temperature almost immediately.

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MarvinKitFox, you are wrong I'm afraid. The mass of the object is only relevant as far as orbital speed matters. If you did a burn at 10ms 10m above the sun you would get very little Oberth boost.

SOI is irrelevant too. There are no soi in real life.

Actually, I think you're both right. Oberth effect is only related to speed as you say. As MarvinKitFox implies, it is easier to get to a higher speed when orbiting a more massive body than a smaller one.

I'm willing to take the orbital total energy argument under advisement, but I don't see how, 10 seconds after burn the energy mysteriously starts to bleed into velocity. An orbit has a set velocity based on energy for every point of its orbit.

Remember that orbital energy is the sum of potential and kinetic energy, and as the craft moves through its orbit it exchanges kinetic energy for potential energy as it rises and slows to apoapsis, then exchanges potential energy for kinetic energy as it falls and gains speed. The orbital energy remains the same, but the distribution between kinetic and potential changes. So if you add a given amount of energy to an orbit, it will change the speed only at the point the burn was made but will change speed and altitude at every other point.

One thing I really don't get is why Oberth doesn't just say, warm or cool the mass of the ship a few degrees depending on energy gain since a lot of physics processes express themselves into waste heat or cooling.

Because there is no energy gain in the total system. Oberth doesn't add any energy to the system, it just allows more energy to be exchanged between ship and exhaust for a given burn.

Let's say that a 10m/s dV burn will increase a craft's kinetic energy by 1000KJ if done at periapsis and 100KJ if done at apoapsis.

If done at periapsis, the craft gains 1000KJ of kinetic energy and the exhaust loses 1000KJ of kinetic energy, no net change in the kinetic energy of craft + exhaust.

If done at periapsis, the craft gains 100KJ of kinetic energy and the exhaust loses 100KJ of kinetic energy, no net change in the kinetic energy of craft + exhaust.

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How you can write that and not see that Oberth reduces dV requirements is beyond me. Changing the amount of fuel spent is changing the amount of dV spent.
So it should be obvious that speed has no effect on the amount of delta-V for a given craft, i.e. the Oberth effect cannot add or subtract any delta-V.

So does Oberth reduce dV requirements, or does is not have the ability to change dV requirements?

This is why I've been harping on "dV is not a physical quantity" - your craft does not "have delta-v" any more than your car "has miles." Your craft has fuel, which it can use to change it's velocity, just as your car has fuel which it can use to travel some distance. The point I've been trying to make - and which we now seem to agree upon based on your more recent post - is that delta-V is analogous to the distance to your destination; Oberth can not decrease your delta-V requirement any more than driving a more fuel efficient car can make your destination closer.

What it can do, though, is have the same effect as burning the fuel more efficiently. You still need the same delta-V to get where you're going, but you just need less fuel to get there.

=Smidge=

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So does Oberth reduce dV requirements, or does is not have the ability to change dV requirements?

When you are transferring e.g. to Jool, you use less dv if you do the whole transfer burn in Kerbin LKO than if you burn in LKO to just escape Kerbin SOI and then plot another maneuver to meet Jool from Sun orbit.

So yes, Oberth effect changes dv required to do certain maneuvers or transfers.

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So does Oberth reduce dV requirements, or does is not have the ability to change dV requirements?

This is why I've been harping on "dV is not a physical quantity" - your craft does not "have delta-v" any more than your car "has miles." Your craft has fuel, which it can use to change it's velocity, just as your car has fuel which it can use to travel some distance. The point I've been trying to make - and which we now seem to agree upon based on your more recent post - is that delta-V is analogous to the distance to your destination; Oberth can not decrease your delta-V requirement any more than driving a more fuel efficient car can make your destination closer.

What it can do, though, is have the same effect as burning the fuel more efficiently. You still need the same delta-V to get where you're going, but you just need less fuel to get there.

=Smidge=

Oberth can reduce the dV requirements to change orbital energy by some specified amount, it cannot change the amount of dV a given craft has. The two statements are not contradictory.

Changing the orbital energy is what really gets us to our destinations. dV is the currency we spend to make those orbital energy changes. Sometimes we can get more change in orbital energy from a given amount of dV because of Oberth.

Delta-V is a physical quantity. It is derived from starting mass, ending mass, and Isp, which are all physical quantities. Your craft "has delta-V" just as surely as it has fuel in its tanks, because delta-V is an expression of how much that fuel can change the craft's velocity. It is a fuel gauge that is corrected for vessel mass and engine efficiency. Oberth does not allow you to get more dV for the same amount of fuel. Otherwise dV calculators for craft would be useless, because delta-V would vary depending on the craft's situation.

Edited by Red Iron Crown
New page so I added quote.
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So does Oberth reduce dV requirements, or does is not have the ability to change dV requirements?

This is why I've been harping on "dV is not a physical quantity" - your craft does not "have delta-v" any more than your car "has miles." Your craft has fuel, which it can use to change it's velocity, just as your car has fuel which it can use to travel some distance. The point I've been trying to make - and which we now seem to agree upon based on your more recent post - is that delta-V is analogous to the distance to your destination; Oberth can not decrease your delta-V requirement any more than driving a more fuel efficient car can make your destination closer.

What it can do, though, is have the same effect as burning the fuel more efficiently. You still need the same delta-V to get where you're going, but you just need less fuel to get there.

=Smidge=

Except in the cases people are discussing, DeltaV is not analogous to the distance to your destination, it is analogus to the range of your car.

The diference with cars is that the same car can have a widely different range from a full tank of gas depending on how it is driven.

With a rocket however, the amount it can change its velocity with a full tank of gas is the same.

In a road trip there will not always be a straight road between the start and the destination, there may be several different possible routes.

Understanding the Oberth effect is about choosing the most efficient route to your destination.

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Sorry for this very long and wordy post, but you obviously put a lot of time and thought into yours and I felt I should do the same. If you see where I've made an error or obvious misstep, please point it out. It is entirely possible that I don't understand this as well as I think I do.

I appreciate your hard work. But I think a lot of our differences are because we're talking past each other. The term "delat-V" means different things in different contexts and I think we're using it different ways. To try to clear this up, I'll use the following terminology from now on:

• DVR: Delta-V Required for the planned maneuver. This number is the immutable amount of velocity change necessary for the planned maneuver, as shown by the maneuver node system in the game. This is immutable because it's totally vector addition. At the point where you place the maneuver node, your ship will have a certain velocity vector. The burn at the maneuver node is another vector, DVR. DVR adds to the ship's starting vector to sum up to the vector the ship will have in its new orbit after the burn. Thus, DVR is analogous to the physical straight-line distance between 2 points.
• DVC: Delta-V Capacity of the ship, based on its mass, engine, and fuel alone, ignoring Oberth. DVC is consumed during burns. IOW, DVC is the available delta-V number reported by MechJeb and KER. For purposes of this discussion, however, DVC is not applicable because we will assume we always have enough fuel in the tank for the planned maneuver. I mention it only make sure nobody think's I'm talking about it here.
• DVA: Delta-V Applied. The amount of velocity change applied to the ship in the course of making a burn. During the burn, DVA < DVR. At the end of the burn, DVA = DVR. If Oberth really has any effect in the game, it supplies some of DVA because it can't have any effect on DVR. Thus, we also have:
• DVE: Delta-V from the Engine. This is the portion of DVA due solely to the engine burning fuel without considering Oberth. DVE happens over time throughout the burn and is a function solely of the engine's thrust compared to the sihp's mass and how that changes due to the engine's fuel consumption.
• DVO: Delta-V from Oberth Effect. This is the portion of DVA due solely to the Oberth Effect, taking into account the ship's velocity and how that changes throughout the burn.

There is no other way for Oberth to have an effect. Oberth only happens during burns so must be part of DVA. It can't change DVR because that's fixed by situational geometry. Therefore, the net result of Oberth, if it has any in the game, can only be to reduce the fraction of DVA supplied by DVE.

You can say that Oberth is defined in terms of energy, not velocity. However, a change in velocity (whether speed, direction, or both) is the primary measurable effect of changing Ek. You can't measure energy directly, you can only calculate it. If you can't measure an effect, then you can't calculate energy because all the terms in an energy calculation are the measurable effects you can see. Such as Ek = 1/2 * m * v^2. Thus, even though Oberth is defined in terms of energy, in the physical, measurable world, he shows up as velocity (and by implication, acceleration and thus thrust).

Therefore, DVA = DVE + DVO.

If there is no Oberth effect in the game, then DVO = 0 and DVA = DVE. If this is true, at the end of the burn, DVA = DVR = DVE.

However, if Oberth is in the game, then DVO > 0 so DVE < DVA. If this is true, then at the end of the burn, you still have DVA = DVR, so this means DVE < DVR.

This is perhaps amenable to in-game measurement to determine of Oberth is in the game and, if so, how much good he does us. But DVE < DVA means any good he does us is in terms of saving fuel and nothing else.

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I appreciate your hard work. But I think a lot of our differences are because we're talking past each other. The term "delat-V" means different things in different contexts and I think we're using it different ways. To try to clear this up, I'll use the following terminology from now on:

• DVR: Delta-V Required for the planned maneuver. This number is the immutable amount of velocity change necessary for the planned maneuver, as shown by the maneuver node system in the game. This is immutable because it's totally vector addition. At the point where you place the maneuver node, your ship will have a certain velocity vector. The burn at the maneuver node is another vector, DVR. DVR adds to the ship's starting vector to sum up to the vector the ship will have in its new orbit after the burn. Thus, DVR is analogous to the physical straight-line distance between 2 points.
• DVC: Delta-V Capacity of the ship, based on its mass, engine, and fuel alone, ignoring Oberth. DVC is consumed during burns. IOW, DVC is the available delta-V number reported by MechJeb and KER. For purposes of this discussion, however, DVC is not applicable because we will assume we always have enough fuel in the tank for the planned maneuver. I mention it only make sure nobody think's I'm talking about it here.
• DVA: Delta-V Applied. The amount of velocity change applied to the ship in the course of making a burn. During the burn, DVA < DVR. At the end of the burn, DVA = DVR. If Oberth really has any effect in the game, it supplies some of DVA because it can't have any effect on DVR. Thus, we also have:
• DVE: Delta-V from the Engine. This is the portion of DVA due solely to the engine burning fuel without considering Oberth. DVE happens over time throughout the burn and is a function solely of the engine's thrust compared to the sihp's mass and how that changes due to the engine's fuel consumption.
• DVO: Delta-V from Oberth Effect. This is the portion of DVA due solely to the Oberth Effect, taking into account the ship's velocity and how that changes throughout the burn.

There is no other way for Oberth to have an effect. Oberth only happens during burns so must be part of DVA. It can't change DVR because that's fixed by situational geometry. Therefore, the net result of Oberth, if it has any in the game, can only be to reduce the fraction of DVA supplied by DVE.

You can say that Oberth is defined in terms of energy, not velocity. However, a change in velocity (whether speed, direction, or both) is the primary measurable effect of changing Ek. You can't measure energy directly, you can only calculate it. If you can't measure an effect, then you can't calculate energy because all the terms in an energy calculation are the measurable effects you can see. Such as Ek = 1/2 * m * v^2. Thus, even though Oberth is defined in terms of energy, in the physical, measurable world, he shows up as velocity (and by implication, acceleration and thus thrust).

Therefore, DVA = DVE + DVO.

If there is no Oberth effect in the game, then DVO = 0 and DVA = DVE. If this is true, at the end of the burn, DVA = DVR = DVE.

However, if Oberth is in the game, then DVO > 0 so DVE < DVA. If this is true, then at the end of the burn, you still have DVA = DVR, so this means DVE < DVR.

This is perhaps amenable to in-game measurement to determine of Oberth is in the game and, if so, how much good he does us. But DVE < DVA means any good he does us is in terms of saving fuel and nothing else.

You are still thinking of the Oberth effect as something magical that appears.

DVA, DVE and DVO are all the same thing. Once again I refer to this post

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DVA, DVE and DVO are all the same thing. Once again I refer to this post

With all due respect, you are entirely mistaken.

If "DVA, DVE and DVO are all the same thing", then there is no Oberth effect at all. Also, the post to which you refer has nothing at all to do with Oberth. It is merely vector addition. You are comparing the DVRs to get from Orbit A to Orbit B directly vs. Orbit A to intermediate Orbit C to Orbit B. The numbers you cite are the immutable constants implicit in the situations you describe. Nothing more or less.

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With all due respect, you are entirely mistaken.

The numbers you cite are the immutable constants implicit in the situations you describe. Nothing more or less.

Which is exactly what the Oberth effect is.

It just that the early rocket scientists did not fully understand those immutable constants. Oberth did.

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I appreciate your hard work. But I think a lot of our differences are because we're talking past each other. The term "delat-V" means different things in different contexts and I think we're using it different ways. To try to clear this up, I'll use the following terminology from now on:

That's a good idea, it is important to distinguish between delta-V of a craft and delta-V required for a maneuver.

DVC: Delta-V Capacity of the ship, based on its mass, engine, and fuel alone, ignoring Oberth. DVC is consumed during burns. IOW, DVC is the available delta-V number reported by MechJeb and KER. For purposes of this discussion, however, DVC is not applicable because we will assume we always have enough fuel in the tank for the planned maneuver. I mention it only make sure nobody think's I'm talking about it here.

It is also important to note that nothing other than changing the craft's starting mass, ending mass, or Isp can change DVC as it is derived from those numbers.

DVA: Delta-V Applied. The amount of velocity change applied to the ship in the course of making a burn. During the burn, DVA < DVR. At the end of the burn, DVA = DVR. If Oberth really has any effect in the game, it supplies some of DVA because it can't have any effect on DVR. Thus, we also have:

DVE: Delta-V from the Engine. This is the portion of DVA due solely to the engine burning fuel without considering Oberth. DVE happens over time throughout the burn and is a function solely of the engine's thrust compared to the sihp's mass and how that changes due to the engine's fuel consumption.

DVA will always equal DVE, because...

DVO: Delta-V from Oberth Effect. This is the portion of DVA due solely to the Oberth Effect, taking into account the ship's velocity and how that changes throughout the burn.

...this isn't a thing. The Oberth effect does not change the amount of speed gained (or lost) from a given burn. A burn that produces 10m/s of DVE will accelerate the craft by exactly 10m/s, no matter what its speed is when the burn is made.

DVR: Delta-V Required for the planned maneuver. This number is the immutable amount of velocity change necessary for the planned maneuver, as shown by the maneuver node system in the game. This is immutable because it's totally vector addition. At the point where you place the maneuver node, your ship will have a certain velocity vector. The burn at the maneuver node is another vector, DVR. DVR adds to the ship's starting vector to sum up to the vector the ship will have in its new orbit after the burn. Thus, DVR is analogous to the physical straight-line distance between 2 points.

Here's where I think you're running into trouble. When you set a maneuver node and it calculates the effect of that burn, it takes Oberth into account because it is an inherent characteristic of Newtonian physics. It knows what your speed will be at the node, thus it can accurately calculate how much kinetic energy will be added by the burn.

Oberth, in its simplest form is: dV expended at higher speeds adds more energy than the same dV added at lower speed.

In the case of your maneuver node, the speed is known so Oberth is accounted for. No differences are possible because the speed at that point is fixed until we expend our dV.

To really see Oberth's effect, take an elliptical orbit, burn some amount of dV at Ap and calculate the orbital energy afterwards, then revert to before the burn. Burn the same dV at Pe and calculate the orbital energy, it will quickly become apparent that the burn at Pe gained you more orbital energy. I'm at work now, so I can't perform the experiment, give me a few hours and I'll whip up something and share the results.

There is no other way for Oberth to have an effect. Oberth only happens during burns so must be part of DVA. It can't change DVR because that's fixed by situational geometry. Therefore, the net result of Oberth, if it has any in the game, can only be to reduce the fraction of DVA supplied by DVE.

Oberth is in the game, it has to be. It's not some mystical effect that needs to be coded separately, it is the observation that, because speed and kinetic energy are not linearly related, expending dV at higher speeds gains more kinetic energy. It is a consequence of the most basic kinetic energy calculation, without which a game like KSP would not be possible.

You can say that Oberth is defined in terms of energy, not velocity. However, a change in velocity (whether speed, direction, or both) is the primary measurable effect of changing Ek. You can't measure energy directly, you can only calculate it. If you can't measure an effect, then you can't calculate energy because all the terms in an energy calculation are the measurable effects you can see. Such as Ek = 1/2 * m * v^2. Thus, even though Oberth is defined in terms of energy, in the physical, measurable world, he shows up as velocity (and by implication, acceleration and thus thrust).

OK, I'll measure the effect, using an example I posted earlier:

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.

Burning 100m/s of dV will always result in a 100m/s change in speed (assuming a prograde burn), so the speed changes by 100m/s in both cases.

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

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

= 1/2mvf2-1/2mvi2

= 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)

= 1/2mvf2-1/2mvi2

= 1/2*900*2002 - 1/2*1000*1002

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

= 13,000,000 J

I have measured the change in speed from 100m/s of dV spent, it is 100m/s. I calculate the change in kinetic energy, it is larger when the craft is going faster. Oberth.

Therefore, DVA = DVE + DVO.

If there is no Oberth effect in the game, then DVO = 0 and DVA = DVE. If this is true, at the end of the burn, DVA = DVR = DVE.

However, if Oberth is in the game, then DVO > 0 so DVE < DVA. If this is true, then at the end of the burn, you still have DVA = DVR, so this means DVE < DVR.

This is perhaps amenable to in-game measurement to determine of Oberth is in the game and, if so, how much good he does us. But DVE < DVA means any good he does us is in terms of saving fuel and nothing else.

All of this is based on the flawed assumption that Oberth somehow adds dV, which it doesn't. It adds more kinetic energy per unit of dV spent.

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Except in the cases people are discussing, DeltaV is not analogous to the distance to your destination, it is analogus to the range of your car.

Which is one reason why this discussion has managed to hit 15 pages. It's somewhat wrongheaded and easily causes confusion.

The diference with cars is that the same car can have a widely different range from a full tank of gas depending on how it is driven.

With a rocket however, the amount it can change its velocity with a full tank of gas is the same.

Exhibit A. If that were true, there would be no consequence of the Oberth effect because the total amount your craft can accelerate would be constant regardless of circumstance. However, your engine is more effective at higher speeds - meaning that if you start at a higher velocity your fuel is worth more delta-V. It's NOT the same.

This confusion goes away when you stop thinking of delta-V as a number that MechJeb throws at you as if it were a physical metric of your craft. Delta-V is not an intrinsic property of your craft just as the miles you can drive is not an intrinsic property of a car. It's a potential that is subject to change based on conditions... one of which being how fast you're already going.

=Smidge=

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Oberth doesn't reduce the dV required for a very specific maneuver, such as "raise the apoapsis of a 100km circular orbit to 1000km". It reduces the dV requirement for larger goals, such as "get from the surface of Kerbin to Duna's SOI". The first case is too specific, by defining the starting orbit we've defined the starting orbital energy, and thus the speed at which the burn will be made, which defines the Oberth effect! The second case gives us the flexibility to choose the speed at which we make our burn and harness the Oberth effect fully.

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Which is exactly what the Oberth effect is.

It just that the early rocket scientists did not fully understand those immutable constants. Oberth did.

No, that's not at all what the Oberth effect is.

DVR is totally a function of the geometry of the situation. It's analogous to the distance between 2 points on land. It has nothing at all to do with the ship. Oberth is an expression of how a ship becomes more fuel-efficient the faster it's going.

It's confusing because the velocity of the ship at the time of the burn is the central factor in both vector addition and Oberth. The greater a ship's velocity vector is towards the desired direction, the less of a burn vector it needs to make the change. Hence, DVR is lower. And it also happens that the faster the ship is going, the more fuel Oberth saves you. But the 2 are not the same at all and are based on totally different things.

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