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How much dV do you lose with a higher LKO really?


dire
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So I noticed last week that I only needed something like 200 delta-V to get from a keosynchronous orbit at 2800 km to Munar orbit. And it got me thinking.

I know for interplanetary transfers Oberth effect is a big thing, but what's the real difference between a 100km orbit and a 1000 km orbit in terms of Oberth effect?

Also, for transfers within the Kerbin-Mun-Minmus system, I know in theory you're losing a bit of dV going from a Hohman transfer to a round orbit, and then from that round orbit to another Hohman transfer -- you should be losing roughly as much dV as you're spending to circularize, unless your first Hohman transfer was pointing in the wrong direction (at which point it's a wash). Is this intuitive answer anywhere near correct?

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On ‎8‎/‎20‎/‎2016 at 6:38 PM, dire said:

I know for interplanetary transfers Oberth effect is a big thing, but what's the real difference between a 100km orbit and a 1000 km orbit in terms of Oberth effect?

Let's take a look at some sample numbers by considering a flight to Duna.  In an orbit of 100 km, orbital velocity is 2246 m/s and escape velocity is 3177 m/s.  Therefore, from an orbit of 100 km, we must increase our velocity 3177 - 2246 = 931 m/s just to escape Kerbin gravity.  However, if we accelerate to exactly escape velocity we'll have no velocity left over after escaping.  For a typical Hohmann transfer to Duna, we must be traveling about 900 m/s relative to Kerbin after escaping the Kerbin's gravity.  This left over velocity is called hyperbolic excess velocity.  Burning from an altitude of 100 km, we find that we must increase our velocity to 3302 m/s in order to have a hyperbolic excess velocity of 900 m/s (math provided on request).  Therefore we must increase our velocity by 3302 - 3177 = 125 m/s above and beyond escape velocity, or we must provide a total Δv of 3302 - 2246 = 1056 m/s.  We see that we obtain 900 m/s in hyperbolic excess velocity for only a 125 m/s expenditure in Δv.  That's the Oberth effect at work.

Now let's look at the numbers for an ejection from an orbit of 1000 km.  Here orbital velocity is 1486 m/s, escape velocity is 2101 m/s, and, in order to produce a hyperbolic excess velocity of 900 m/s, we must attain a velocity of 2286 m/s.  Therefore, just to escape we must provide a Δv of 2101 - 1486 = 615 m/s, and, to produce the extra 900 m/s, we must provide additional Δv of 2286 - 2101 = 185 m/s.  The total ejection Δv is 2286 - 1486 = 800 m/s.

So we see that takes less Δv to eject from a 1000 km orbit (800 m/s) than it does to eject from a 100 km orbit (1056 m/s).  This is because we are higher up in the gravity well where it takes to less Δv to escape (615 m/s vs. 931 m/s).  However, when we look at how much Δv is takes to produce the 900 m/s hyperbolic excess velocity, we see that it is less from the 100 km orbit than the 1000 km orbit (125 m/s vs. 185 m/s).  This is because the Oberth effect is greater closer to the planet where the orbital velocity is higher. 

Therefore, the answer to your question is, for a hyperbolic excess velocity of 900 m/s (approximately that for a transfer to Duna), the difference in Oberth effect between a 100 km orbit and a 1000 km orbit is about 60 m/s.  Of course you can see that that's not the total story.

As we increase our orbital altitude, the Δv required to reach escape velocity decreases, and the Δv required to produce the hyperbolic excess velocity increases.  If we were to plot total Δv versus altitude, we would see that the Δv initially decreases with increasing altitude, reaches a minimum, and then starts to increase with increasing altitude.  The altitude at which the minimum occurs is called the gate orbit.  The height of the gate orbit is different for every transfer because the hyperbolic excess velocity is different for every transfer.

Of course, if you start out in a low orbit, you would never want to transfer to a higher orbit to perform the ejection.  This is because it takes more Δv to raise the orbit than what you can potentially save on the ejection burn.  In the example above, it takes 730 m/s to go from a 100 km orbit to a 1000 km orbit, while you save only 256 m/s on the ejection burn.  If you are launching into a temporary parking orbit from which you plan to perform an ejection burn, it is almost always best in terms of Δv to make your parking orbit as low as possible.  The only possible exception that I can think of is if you have a really long ejection burn, then there might be some benefit to launching into a higher and slower orbit.
 

Edited by OhioBob
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It should be noted that gate orbits only consider the dV to perform the ejection, not the dV to arrive into the parking orbit in the first place (OhioBob mentions this in his linked thread, it's an important point that shouldn't be missed). In most (all?) cases the total dV from pad to a complete ejection will be minimized by ejecting from as low an orbit as possible.

Gate orbits can make a lot of sense for stuff that gets fueled once in orbit, but for a simple launch-parking orbit-ejection mission LKO is cheaper.

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33 minutes ago, dire said:

I know for interplanetary transfers Oberth effect is a big thing, but what's the real difference between a 100km orbit and a 1000 km orbit in terms of Oberth effect?

There's no one size fits all answer to that question; the situation is more complicated than you might think.  For every transfer there is an ideal orbit, called the gate orbit, from which the dV is minimum.  Below is a thread from last year in which discussed this topic.  You might find it interesting.

 

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On 8/20/2016 at 5:38 PM, dire said:

I know for interplanetary transfers Oberth effect is a big thing, but what's the real difference between a 100km orbit and a 1000 km orbit in terms of Oberth effect?

Well, that varies with the type of engine.  In real life, the Oberth effect depends not only on the velocity of the ship, but on the mass flow rate of the burned fuel.  Thus, it does a lot more good for low-ISP engines than for high-ISP engines.  IOW, it helps chemical rockets a lot, thermal nuclear engines somewhat, but has no real benefit for ion engines.  But that's real life.  KSP factors in the Oberth effect on burns automatically and completely under the hood, so I have no idea if it takes this into account or not.

That said, however, there's more going on with using a higher parking orbit than a low one.  For instance, the higher you are, the longer your orbital period, so the less likely you are to reach your ejection burn node at the optimal time for the cheapest transfer.  Depending on how high you are, you might miss the best transfer window by days to a week, which increases the cost of the burn over what it could have been if you'd been lower and thus left at a more optimal time.  Plus, of course, the higher you are, the less Oberth.

Because of these inefficiencies, the only real reason to use a high parking orbit is if your rocket has a very low TWR so your transfer burn will be very long.  When you're down at 80-100km or so, you should never burn more than about 5 minutes at once.  Otherwise you lose a lot of efficiency due to cosine loss.  But the bigger your orbital radius, the longer burn you can do with acceptable cosine loss.  And if you have such a low TWR to want to do this, then you probably have way more dV than you really need, so you don't really care about the loss of efficiency from non-optimal departure times and lack of Oberth effect.

 

3 hours ago, Red Iron Crown said:

It should be noted that gate orbits only consider the dV to perform the ejection, not the dV to arrive into the parking orbit in the first place (OhioBob mentions this in his linked thread, it's an important point that shouldn't be missed). In most (all?) cases the total dV from pad to a complete ejection will be minimized by ejecting from as low an orbit as possible.

This.

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Things to remember:

- your orbital speed is proportional (as 1/square root) to orbital radius, not altitude. Kerbin radius is 600KM, so orbital speed at 70km orbit (at radius 670km) is only 15% better than one at 300km (radius 900). Difference between 70 and 90km is entirely negligible. Trying to squeeze the last few km of altitude for the burn isn't entirely worth it.

- transfers within system aren't really indicative of transfers outside the system. It may be very cheap to transfer from KEO to Mun, because the absolute difference in velocity is pretty small. When going to Duna though, what you're doing in LKO is applying lots and lots of delta-V outside Kerbin SOI.

Eh, just to make things clearer, let's try the Launch Window Planner. Optimal transfer to Duna from 80km and from KEO ( 2863km). No capture burn, mid-course plane change, we're interested only in ejection delta-V.

1,043 m/s for 80km LKO.

628 for KEO.

1099 to reach KEO from LKO, so 1727 to get to Duna *through* KEO.

684m/s lost only because you went through an intermediate, higher orbit.

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Example #1

A rocket has an initial mass of 10,000 kg.  Its engine produces a thrust of 100,000 N with a specific impulse of 350 s.  When operating, the engine’s mass flow rate is,

ṁ = 100000 / (350 * 9.80665) = 29.135 kg/s

The rocket is traveling in gravity free space at an initial velocity of 1000 m/s.  We burn the engine for 10 seconds, resulting in a final mass of,

mf = 10000 – 29.135 * 10 = 9708.65 kg

The change in velocity is,

Δv = 350 * 9.80665 * LN( 10000 / 9708.65) = 101.5 m/s

The final velocity is,

vf = 1000 + 101.5 = 1101.5 m/s

And the spacecraft’s change in kinetic energy is,

ΔEk = 0.5 * 9708.65 * 1101.5² – 0.5 * 10000 * 1000² = 889,763,445 joules


Example #2

A rocket has an initial mass of 10,000 kg.  Its engine produces a thrust of 100,000 N with a specific impulse of 350 s.  When operating, the engine’s mass flow rate is,

ṁ = 100000 / (350 * 9.80665) = 29.135 kg/s

The rocket is traveling in gravity free space at an initial velocity of 2000 m/s.  We burn the engine for 10 seconds, resulting in a final mass of,

mf = 10000 – 29.135 * 10 = 9708.65 kg

The change in velocity is,

Δv = 350 * 9.80665 * LN( 10000 / 9708.65) = 101.5 m/s

The final velocity is,

vf = 2000 + 101.5 = 2101.5 m/s

And the spacecraft’s change in kinetic energy is,

ΔEk = 0.5 * 9708.65 * 2101.5² – 0.5 * 10000 * 2000² = 1,438,166,420 joules

 
@Geschosskopf,

As you may have noticed, everything in these two examples is exactly the same except for the initial velocity of the rocket.  The thrust is the same, the specific impulse is the same, the mass flow rate is the same, and the burn duration is the same.  As you can see, the second example results in a much greater increase in kinetic energy than the first example. I didn’t require any “additional code” or perform any mathematical shenanigans to artificially add energy to the rocket.  There is no extra thrust involved.  I’m just performing straightforward calculations like we do in this forum all the time.

If you think there is something missing from these calculations, what is it?  What additional code would you add?  If my method doesn’t take into account the Oberth effect, then why is the change in kinetic energy greater in the second example than in the first?

 

Edited by OhioBob
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13 minutes ago, Geschosskopf said:

 In real life, the Oberth effect depends not only on the velocity of the ship, but on the mass flow rate of the burned fuel.

That's not a factor at all, the efficiency of the engine doesn't change how Oberth works (both in real life and KSP). All that is required for Oberth is kinetic energy increasing with the square of speed and thrust not changing with speed; both of these criteria are pass/fail.

17 minutes ago, Geschosskopf said:

Because of these inefficiencies, the only real reason to use a high parking orbit is if your rocket has a very low TWR so your transfer burn will be very long.  When you're down at 80-100km or so, you should never burn more than about 5 minutes at once.  Otherwise you lose a lot of efficiency due to cosine loss.  But the bigger your orbital radius, the longer burn you can do with acceptable cosine loss.  And if you have such a low TWR to want to do this, then you probably have way more dV than you really need, so you don't really care about the loss of efficiency from non-optimal departure times and lack of Oberth effect.

This is good practical advice, assuming one doesn't want to split up the burn (and even then the final part of the ejection may be so long it's not worthwhile).

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You stated that it only took 200 to get from Keosynchronous to Mun, but you didn't ask specifically how much more THAT took from, say, the surface of Kerbin. That's actually answered with many of the common dV maps including this one.

Assuming you launched, got into LKO of 80km, then got into Keosynchonous orbit from there, it would have cost you 3400+1115 m/s. I don't know the savings to Keosynchronous directly from launch but I'd be surprised if it was more than 100 m/s. Probably closer to 50 or less. Let's say it's 50 and anybody want to calculate/test it I'll happily edit this.

Launch to LKO to Mun is 3400+930 or 4330. Your launch to KSO to Mun would have been (3400+1065)+200 or 4665. So how much more efficient is 100km over KSO, to transfer to Mun? 335 m/s more efficient.

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6 minutes ago, Red Iron Crown said:

That's not a factor at all, the efficiency of the engine doesn't change how Oberth works (both in real life and KSP). All that is required for Oberth is kinetic energy increasing with the square of speed and thrust not changing with speed; both of these criteria are pass/fail.

You might want to re-read the Wikipedia page on Oberth effect.  It specifically says Overth has very little effect on ion engines.  The energy gained by the ship is at the expense of the kinetic energy of the exhaust.  Ion engines don't have much kinetic energy in their exhaust to start with (it has hardly any mass and not a whole lot of velocity), so there's not a lot to be gained from it. This compares with tons of LFO moving at high supersonic speeds coming out the back of a chemical rocket.  So yes, rocket ISP does have a lot to do with it.  Also, ion ships don't accelerate very rapidly, and Oberth also depends on ship speed.  Because ion ships spend a lot more time at lower speeds throughout the burn, they don't get as much benefit as a ship with a higher TWR.

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Re: Ion vs Chemical (i.e. Oberth & Fuel Flow)

At the end of the day, isn't this just a mater of how much impulse you can add to a craft at periapsis so you can maximize the Oberth effect? It doesn't directly matter what type of engine is used, just how much acceleration (thrust) it can provide. You can have an Ion engine, but if the craft is light enough, the acceleration is sufficient to take full advantage of Oberth. On the other hand, you can have the most powerful engine available, but if the craft is so heavy that acceleration is minimal, Oberth is not gonna help much. (Granted, there is lightening of the load as the fuel is burned, so you get better Oberth efficiency when you're near empty. However, I'm ignoring those details for now.) Seems like an argument over semantics and related details rather than the actual point at hand.

Optimal use of Oberth in the ideal, perfect scenario is being able to applied instantaneous acceleration. (This eliminates cosine losses.) Of course, the real world isn't that easy. Suffice to say to get nice Oberth benefits, your craft's burn time should be minimized as much as possible. Otherwise, try to ensure it's a small fraction of your orbital period (or orbital angular change: a "short" burn that takes up something like 45 degrees of an orbit may not be that good) or divide the burn into several burns.

Someone please correct me if I made any mistakes. I'm also learning bits and pieces of orbital mechanics as I mess with KSP and rocket science in general.

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44 minutes ago, Geschosskopf said:

  Ion engines don't have much kinetic energy in their exhaust to start with (it has hardly any mass and not a whole lot of velocity), so there's not a lot to be gained from it. This compares with tons of LFO moving at high supersonic speeds coming out the back of a chemical rocket.  So yes, rocket ISP does have a lot to do with it.

Ion engines have very high exhaust velocities, that's why they're so efficient. Chemical rockets have around the 4km/s exhaust velocity while Ions have 25-50km/s.

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1 hour ago, Geschosskopf said:

You might want to re-read the Wikipedia page on Oberth effect.  It specifically says Overth has very little effect on ion engines.  The energy gained by the ship is at the expense of the kinetic energy of the exhaust.  Ion engines don't have much kinetic energy in their exhaust to start with (it has hardly any mass and not a whole lot of velocity), so there's not a lot to be gained from it. This compares with tons of LFO moving at high supersonic speeds coming out the back of a chemical rocket.  So yes, rocket ISP does have a lot to do with it.  Also, ion ships don't accelerate very rapidly, and Oberth also depends on ship speed.  Because ion ships spend a lot more time at lower speeds throughout the burn, they don't get as much benefit as a ship with a higher TWR.

I see no mention of ion engines in the Wiki article. Ion engines have tremendous kinetic energy in their exhaust, because it is moving so fast (speed being a squared term in the kinetic energy equation, it more than makes up for the smaller exhaust mass).

But that's moot, because the mass or speed of the exhaust doesn't change Oberth's greater energy gains for the same amount of speed change. It works even if the mass of the ship doesn't change (if the EMDrive worked as advertised it would benefit from Oberth). It's all about the kinetic energy change of the vessel, and how adding to it when the vessel's kinetic energy is high is easier. A simple mathematical example of ships without changing mass is in the spoiler below.
 

Spoiler

 

Take a 2 ton ship in an orbit that has a speed of 1000m/s at periapsis and 100m/s at apoapsis. The ship completes a burn of 100m/s, either at Ap or Pe. Which changes energy more?

Apoapsis:

Eki = 0.5*m*v2
Eki = 0.5*2*1002
Eki = 10,000 kJ

Ekf = 0.5*m*v2
Ekf = 0.5*2*2002
Ekf = 40,000 kJ

ΔEk = Ekf - Eki
ΔEk = 40,000 - 10,000
ΔEk = 30,000 kJ

Periapsis

Eki = 0.5*m*v2
Eki = 0.5*2*10002
Eki = 1,000,000 kJ

Ekf = 0.5*m*v2
Ekf = 0.5*2*11002
Ekf = 1,210,000 kJ

ΔEk = Ekf - Eki
ΔEk = 1,210,000 - 1,000,000
ΔEk = 210,000 kJ

So even though speed changed by exactly the same amount in both case, the burn at periapsis added seven times as much energy to the vessel as the burn at apoapsis.

 

The above example doesn't consider mass lost during the burn, but we can do that too. In that case, the specific kinetic energy must be examined (i.e. kinetic energy per unit mass), because specific energy is what determines the size of the orbit. The specific orbital energy is the critical measure, which is the sum of specific kinetic energy and specific potential energy. The trajectory's semi-major axis is proportional to specific orbital energy. Let's look at two ships with differing engine efficiencies:

 

Spoiler

 

Take two 2 ton ships in an orbit that has a speed of 1000m/s at periapsis and 100m/s at apoapsis. Each ship completes a burn of 100m/s, either at Ap or Pe. One ships has relatively efficient engines and burns 0.5t of propellant to complete the burn, the other has relatively inefficient engines and burns 1.5t of propellant to do the same. Which changes specific energy more?

Efficient ship:

Apoapsis:

Eki = 0.5*m*v2
Eki = 0.5*2*1002
Eki = 10,000 kJ

Eski = Eki / mi
Eski = 10,000 / 2
Eski= 5,000 kJ/t

Ekf = 0.5*m*v2
Ekf = 0.5*1.5*2002
Ekf = 30,000 kJ

Eskf = Ekf / mf
Eskf = 30,000 / 1.5
Eskf = 20,000 kJ/t

ΔEsk = Eskf - Eski
ΔEsk = 20,000 - 5,000
ΔEsk = 15,000 kJ/t

Periapsis

Eki = 0.5*m*v2
Eki = 0.5*2*10002
Eki = 100,000 kJ

Eski = Eki / mi
Eski = 100,000 / 2
Eski= 50,000 kJ/t

Ekf = 0.5*m*v2
Ekf = 0.5*1.5*11002
Ekf = 907,500 kJ

Eskf = Ekf / mf
Eskf = 907,500 / 1.5
Eskf = 605,000 kJ/t

ΔEsk = Eskf - Eski
ΔEsk = 605,000 - 100,000
ΔEsk = 505,000 kJ/t

Inefficient Ship

Apoapsis:

Eki = 0.5*m*v2
Eki = 0.5*2*1002
Eki = 10,000 kJ

Eski = Eki / mi
Eski = 10,000 / 2
Eski= 5,000 kJ/t

Ekf = 0.5*m*v2
Ekf = 0.5*0.5*2002
Ekf = 10,000 kJ

Eskf = Ekf / mf
Eskf = 10,000 / 0.5
Eskf = 20,000 kJ/t

ΔEsk = Eskf - Eski
ΔEsk = 20,000 - 5,000
ΔEsk = 15,000 kJ/t

Periapsis

Eki = 0.5*m*v2
Eki = 0.5*2*10002
Eki = 100,000 kJ

Eski = Eki / mi
Eski = 100,000 / 2
Eski= 50,000 kJ/t

Ekf = 0.5*m*v2
Ekf = 0.5*0.5*11002
Ekf = 302,500 kJ

Eskf = Ekf / mf
Eskf = 302,500 / 0.5
Eskf = 605,000 kJ/t

ΔEsk = Eskf - Eski
ΔEsk = 605,000 - 100,000
ΔEsk = 505,000 kJ/t

 

The greater specific energy change from burning at high speed is the same, even though one craft has 3x the Isp of the other. The masses simply cancel out.

So it doesn't matter how efficient the ship's engines are, the benefit from Oberth is equal for all vessels changing speed by the same amount.

 

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45 minutes ago, Reactordrone said:

Ion engines have very high exhaust velocities, that's why they're so efficient

Sure, high exhaust velocities, but so little exhaust mass that it adds up to not much energy released in any period of time.  That's why the thrust is so low.  Instead of giving the rocket a swift kick in the pants, ion engines just fondle its buns.  Ion engines run on a few kW, chemical rockets release many MWs..

 

34 minutes ago, Red Iron Crown said:

So it doesn't matter how efficient the ship's engines are, the benefit from Oberth is equal for all vessels changing speed by the same amount.

It matters because the energy gained by the ship comes at the expense of the exhaust's energy, and there's not much of that to be had.  In addition, low thrust, high ISP means a long, long burn, so less of the burn takes place close to the planet.  Fuel efficiency may not be a term in the equations for the Oberth effect, but it necessarily impacts how the effect plays out.

And BTW, here's the part about Oberth and ion engines from the wiki article:

Quote

The Oberth effect is strongest at a point in orbit known as the periapse, where the gravitational potential is lowest, and the speed is highest. This is because firing a rocket engine at high speed causes a greater change in kinetic energy than when fired at lower speed. Because the vehicle remains near periapse only for a short time, for the Oberth maneuver to be most effective, the vehicle must be able to generate as much impulse as possible in as short a time as possible. Thus, the Oberth effect is much more useful for high thrust rockets like liquid-propellant rockets, and less useful for low-thrust reaction engines such as ion drives, which take a long time to gain speed.

 

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1 minute ago, Geschosskopf said:

It matters because the energy gained by the ship comes at the expense of the exhaust's energy, and there's not much of that to be had.  In addition, low thrust, high ISP means a long, long burn, so less of the burn takes place close to the planet.  Fuel efficiency may not be a term in the equations for the Oberth effect, but it necessarily impacts how the effect plays out.

In a manner of speaking I guess that's true. The ability to effectively harness Oberth is entirely related to TWR, engine efficiency is not a factor (or is at best an incidental one in that high efficiency generally, but not always, implies low TWR). Low TWR vessels have a more difficult time taking advantage of Oberth because they can't add speed fast enough in a single burn at Pe, eventually culminating in periapsis kicking for intermediate TWRs and spiral ejections IRL. A low-TWR low-Isp engine would suffer the same difficulties. Mass flow rate and Isp do not enter into it directly.

1 minute ago, Geschosskopf said:

And BTW, here's the part about Oberth and ion engines from the wiki article:

Thanks, don't know how I missed it. It's not contradicting what I've said: mass flow and Isp aren't important, it's just that ion craft IRL don't have the TWR to effectively harness Oberth like chemical rockets do (this is a big difference between IRL and KSP, where ions have much, much higher thrust).

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55 minutes ago, Geschosskopf said:

Sure, high exhaust velocities, but so little exhaust mass that it adds up to not much energy released in any period of time.  That's why the thrust is so low.  Instead of giving the rocket a swift kick in the pants, ion engines just fondle its buns.  Ion engines run on a few kW, chemical rockets release many MWs..

 

It matters because the energy gained by the ship comes at the expense of the exhaust's energy, and there's not much of that to be had.  In addition, low thrust, high ISP means a long, long burn, so less of the burn takes place close to the planet.  Fuel efficiency may not be a term in the equations for the Oberth effect, but it necessarily impacts how the effect plays out.

And BTW, here's the part about Oberth and ion engines from the wiki article:

 

Take a Mainsail powered rocket, add fuel tanks on top until you get 800m/s dv
Get that up to a 71km x 71km orbit
Make the manuever node of 800m/s prograde
Note the new Ap height

Take an Ion powered sat, add fuel and stuff until you get 800m/s dv
Get that up to a 71km x 71km orbit
Make the manuever node of 800m/s prograde
Wait until the node points less than 10 degrees from horizon...and burn only while the node points less than 10 degrees from horizon.
Note the new Ap height

Both Ap height are nearly the same(Ion should be worth about 7m/s less). This is because is because of cosine losses. Cos(10')=0.98, that is the amount of dv you are gaining in the direction that you actually desire...if we could minimize that angle we would have the equivalent of an instant burn(almost like the mainsail)

But thats Periapsis kicks, what about Oberth? Oberth is not programmed into the game and calculated under the hood. It is an effect that derives from the nature of the law of gravitation being inverse squared to distance. As long as gravity is calculated accurately, Oberth will just seamlessly join the show, never specifically being invited even...it does not know the ISP stats of any engine, it does not know the TWR of any craft, it doesn't even know how much cosine losses you had.

All Oberth is concerned with, is your change in prograde speed at periapsis

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38 minutes ago, Red Iron Crown said:

It's not contradicting what I've said: mass flow and Isp aren't important, it's just that ion craft IRL don't have the TWR to effectively harness Oberth like chemical rockets do (this is a big difference between IRL and KSP, where ions have much, much higher thrust).

But here's the thing....  Why do ion engines have such low thrust?  It's because they don't have much exhaust energy.  No matter how fast individual ions are moving, there's still only a few kW pushing them.  And because the extra velocity the rocket gets from Oberth comes from robbing energy from the exhaust, there's not much there for the rocket to steal.

This is why I say mass flow rate matters, albeit indirectly.  With a chemical rocket, you're moving tons of fuel in a short time.  With an ion engine, you're only moving a few drops of xenon in that same time.  Moving mass requires energy.  The more mass you move, and the faster you move it, the more energy you have in the exhaust, Thus, higher mass flow rate is a rough indicator of exhaust energy, at least when comparing chemical rockets to ion engines.

3 minutes ago, Blaarkies said:

Oberth is not programmed into the game and calculated under the hood. It is an effect that derives from the nature of the law of gravitation being inverse squared to distance.

In real life, that would be true, because it's a natural effect.  But it's not true in KSP because KSP doesn't obey conservation of mass.  The rocket's mass decreases as fuel is consumed, but that mass simply disappears from the game instead of lingering on as a trail of exhaust gases.  Therefore, KSP has to calculate the Oberth effect and add it into the game under the hood.  Squad has said so on more than one occasion.

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22 minutes ago, Geschosskopf said:

In real life, that would be true, because it's a natural effect.  But it's not true in KSP because KSP doesn't obey conservation of mass.  The rocket's mass decreases as fuel is consumed, but that mass simply disappears from the game instead of lingering on as a trail of exhaust gases.  Therefore, KSP has to calculate the Oberth effect and add it into the game under the hood.  Squad has said so on more than one occasion.

No it doesn't. I have written a tiny Autohotkey app that simulates gravity...by moving the mouse cursor around on screen:blush: 
Anyway I definitely did not add any function called oberthEffect(ISP, TWR)...but the cursor still obeyed the Oberth effect when I pressed the accelerate key at low altitude vs high altitude

All it needs is an accurate simulation of gravity. Mine used something similar to numerical analysis - run free body diagram forces and effects at very short time intervals.

So i am unsure what exactly SQUAD "added" to the code for the Oberth effect, as it works realisticaly by default

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4 minutes ago, Blaarkies said:

No it doesn't. I have written a tiny Autohotkey app that simulates gravity...by moving the mouse cursor around on screen:blush: 
Anyway I definitely did not add any function called oberthEffect(ISP, TWR)...but the cursor still obeyed the Oberth effect when I pressed the accelerate key at low altitude vs high altitude

All it needs an accurate simulation of gravity. Mine used something similar to numerical analysis - run free body diagrams forces and effects at very short time intervals.

I believe you are making a mistake here.  The net result of the Oberth effect is that the rocket gains more energy per unit of fuel burned when travelling faster than it does burning the same amount of fuel when travelling slower.  This "extra" energy cannot, of course, be created from nothing, and it does not come from gravity.  Gravity's only effect is to make the ship go faster the closer it is to the planet, but that's not where the Oberth effect actually comes from, it's just an enabler.  The "extra" energy gained by the rocket comes from a decrease in the energy of the exhaust stream.  The total energy of the (rocket + exhaust stream) remains the same due to conservation--it's only how the energy is divided between them that changes.

Therefore, to actually have a naturally occurring Oberth effect like in real life, you must have an exhaust stream to be the source of the "extra" energy.  But neither KSP nor your program have exhaust streams.  So unless you add an algorithm to calculate what the Oberth effect should be and apply it, you have no Oberth effect.

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5 hours ago, Geschosskopf said:

I believe you are making a mistake here.  The net result of the Oberth effect is that the rocket gains more energy per unit of fuel burned when travelling faster than it does burning the same amount of fuel when travelling slower.  This "extra" energy cannot, of course, be created from nothing, and it does not come from gravity.  Gravity's only effect is to make the ship go faster the closer it is to the planet, but that's not where the Oberth effect actually comes from, it's just an enabler.  The "extra" energy gained by the rocket comes from a decrease in the energy of the exhaust stream.  The total energy of the (rocket + exhaust stream) remains the same due to conservation--it's only how the energy is divided between them that changes.

Therefore, to actually have a naturally occurring Oberth effect like in real life, you must have an exhaust stream to be the source of the "extra" energy.  But neither KSP nor your program have exhaust streams.  So unless you add an algorithm to calculate what the Oberth effect should be and apply it, you have no Oberth effect.

So you are implying that i am lying about the Oberth effect in my little app? Not very nice of you then...
I have a very clear Oberth effect in app, but no code to actually "apply" it...it just happens. So i would really like if you can explain how Oberth is applied to my app accurately without me adding any code to take into account this effect.

Yes gravity does not feed any energy to the craft, definitely not what I implied but sorry if it could be misread that way. So, if we are in a highly elliptical orbit(very almost escaping SOI) and we increase speed 10m/s in the prograde direction(at Pe) we will exit the SOI with much more than 10m/s...this is known. Now let us redo this part using:
- SRB
- Mainsail
- Ion engine
...what you are implying, is that the 10m/s SRB/Mainsail will escape the SOI with a higher final velocity than the 10m/s Ion engine?
Think about this one for a moment. Does the fuel type, exhaust velocity, TWR or even the existence of the exhaust trail even matter? If the spacecraft was magically accelerated in the same circumstances as the other engines...would it have a different velocity at SOI escape?

Well Sir, let us settle this argument like the true scientists we are. Provide us with a reproducible experiment that proves your hypothesis.

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2 hours ago, Geschosskopf said:

So unless you add an algorithm to calculate what the Oberth effect should be and apply it, you have no Oberth effect.

I disagree with this statement.

The Oberth effect comes simply from accelerating at different velocities.

Take these two cases for a ship with a total mass of 1000kg before the acceleration phase, 900kg after the acceleration phase and a total (instant) acceleration of 100m/s:

1. A ship travels at 1000 m/s before the burn

The kinetic energy before the burn is: E = 1/2 m*v^2 = 1/2 * 1000 kg * (1000 m/s)^2 = 500 MJ (MJ in the sense of Megajoule and not Mechjeb)
The kinetic energy after the burn is: E = 1/2 m*v^2 = 1/2 * 900 kg * (1100 m/s)^2 = 544.5 MJ
It gained 44.5 MJ energy from the 100 m/s acceleration

2. A ship travels at 10 m/s before the burn

The kinetic energy before the burn is: E = 1/2 m*v^2 = 1/2 * 1000 kg * (10 m/s)^2 = 50 kJ
The kinetic energy after the burn is: E = 1/2 m*v^2 = 1/2 * 900 kg * (110 m/s)^2 =  5.445 MJ
It gained 5.395 MJ energy from the 100 m/s acceleration.

So in the first case the energy gain is much higher than in the second case. There is no need to apply any Oberth-Function.

Edited by mhoram
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5 hours ago, Geschosskopf said:

But here's the thing....  Why do ion engines have such low thrust?  It's because they don't have much exhaust energy.  No matter how fast individual ions are moving, there's still only a few kW pushing them.  And because the extra velocity the rocket gets from Oberth comes from robbing energy from the exhaust, there's not much there for the rocket to steal.

This is why I say mass flow rate matters, albeit indirectly.  With a chemical rocket, you're moving tons of fuel in a short time.  With an ion engine, you're only moving a few drops of xenon in that same time.  Moving mass requires energy.  The more mass you move, and the faster you move it, the more energy you have in the exhaust, Thus, higher mass flow rate is a rough indicator of exhaust energy, at least when comparing chemical rockets to ion engines.

As I said earlier, a vessel doesn't need to shed mass to experience the Oberth Effect, it just needs thrust to be the same at all speeds. The energy going into the exhaust is just how conservation of momentum works, it's not what causes the effect, per se. The exhaust stream is "necessary" in the sense that the only way we know how to make the same thrust regardless of speed is with a reaction engine carrying all its mass with it, but if some other propulsion were discovered that could do so without reaction mass then it would gain just as much from Oberth.

Ions and chemical engines experience exactly the same Oberth effect for a given amount and rate of velocity change. It's just that IRL ions have such a low TWR that they can't match the rate of velocity change of most chemical rockets.

5 hours ago, Geschosskopf said:

In real life, that would be true, because it's a natural effect.  But it's not true in KSP because KSP doesn't obey conservation of mass.  The rocket's mass decreases as fuel is consumed, but that mass simply disappears from the game instead of lingering on as a trail of exhaust gases.  Therefore, KSP has to calculate the Oberth effect and add it into the game under the hood.  Squad has said so on more than one occasion.

The Oberth Effect is a bit misnamed, it's not a separate effect but more of an observation of how the then-new rocket engines functioned in vacuum. All that is needed is for kinetic energy to be related to the square of speed, and for thrust to remain constant at any speed. The first is handled by Ek = 0.5*m*v2, which is one of the very first things added to any physics engine. The second seems obvious for rockets in vacuum. There's no separate calculation done by KSP for Oberth, it's entirely a consequence of constant thrust engines and the most basic Newtonian physics.

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8 hours ago, Geschosskopf said:

 The energy gained by the ship is at the expense of the kinetic energy of the exhaust.

Impulse is impulse, whether it comes from little mass at high ISP or the other way round.

Kinetic energy is "half mass times velocity squared". The Oberth effect is due to the "squared" -- adding speed to speed is linear, the energy gained is not.

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7 hours ago, Blaarkies said:

So you are implying that i am lying about the Oberth effect in my little app? Not very nice of you then...

No, I'm saying you do not understand how Oberth works so did not design your program to take it into account properly.  This is an honest mistake, not a deliberate deception.

 

7 hours ago, Blaarkies said:

...what you are implying, is that the 10m/s SRB/Mainsail will escape the SOI with a higher final velocity than the 10m/s Ion engine?

No, I am not saying that at all.  You are mistakenly thinking the Oberth Effect is adding energy for free in violation of conservation, so are expecting Oberth to produce higher Aps/velocites when ships with different engines expend the SAME AMOUNT OF dV.  This is not at all how Oberth works.  Ships with the same initial velocity that generate the same amount of dV will naturally have the same final velocity.  That's a no-brainer.  But that has nothing to do with the Oberth Effect.

The Oberth Effect is, at the bottom line, essentially an Isp buff.  Which is also a no-brainer because it's a trick used to increase rocket efficiency.  The faster a ship is moving when it burns, the less fuel it consumes to achieve a given amount of dV.   IOW, by using Oberth, a ship gets more dV out of its fuel supply, so can do more maneuvers further down the road.

Think of it like this:  You have 2 identical ships:  same engine, same amount of fuel, same mass.  They are out in intergalactic space where gravity is so weak you can ignore it.  The only difference between them is that they are moving at different velocities relative to some arbitrary point.  Both execute burns of the same arbitrary amount of dV.  So both have increased their velocity by the same amount.  However, the one that was going faster to start with will have more fuel remaining afterwards.

THAT is the Oberth Effect.  It has nothing to do with gravity.  We just use gravity an an enabler, to give our ship a higher initial velocity when it does a burn, so that it consumes less fuel during that burn.   It consumes less fuel because the faster it's moving to start with, the more energy it steals from its exhaust stream.

That is why your premise that the Oberth effect naturally arises from gravity alone is completely wrong.  And that is why you need more code to take the Oberth effect into account.

 

6 hours ago, mhoram said:

So in the first case the energy gain is much higher than in the second case. There is no need to apply any Oberth-Function.

Close, but you're still missing something.  If your math was all there was to it, then there would be no Oberth Effect at all.  You're just doing classical Newtonian dynamics, which is what everybody thought would happen until Herr Oberth noticed his namesake effect.  That's why we talk about Oberth today.  If the Oberth Effect could be explained by your math, then it wouldn't be a thing.  Thus, you do need an extra term in your equations.

As I said above, the Oberth Effect best thought of as Isp buff.  The faster a ship is going, the less fuel it needs to generate a given amount of dV.  In your math, you have the ships burning the same amount of fuel (same mass change).  You are assuming that this same amount of fuel produces 100m/s dV in both.  That is not the case.  The ship that was going faster to start with would either have achieved more dV for that same amount of fuel, or would have consumed less fuel for that same 100m/s of dV than the slower ship.  That is the Oberth Effect in action, which is why it has its own set of equations which you need to factor in on top of your classical Newtonian dynamics.

 

2 hours ago, Red Iron Crown said:

The Oberth Effect is a bit misnamed, it's not a separate effect but more of an observation of how the then-new rocket engines functioned in vacuum. All that is needed is for kinetic energy to be related to the square of speed, and for thrust to remain constant at any speed. The first is handled by Ek = 0.5*m*v2, which is one of the very first things added to any physics engine. The second seems obvious for rockets in vacuum. There's no separate calculation done by KSP for Oberth, it's entirely a consequence of constant thrust engines and the most basic Newtonian physics.

I see where you're coming from but still disagree.  Just as you can look at the Oberth Effect as an Isp buff with constant thrust, you can also think of it as a thrust buff with constant Isp.  Either way, you end up with the dV you wanted costing less fuel.  If the Isp (IOW, rate of fuel consumption) is the same, then the only way to burn less fuel for a given amount of dV is to have more thrust, so you achieve that dV in less time.

The way rocket engines behave in a vacuum was not foreseen by classical Newtonian dynamics.  Those would have an even split of the the energy/momentum of the exhaust stream and the rocket.  Equal and opposite reactions and all that.  But what really happens is, the faster the rocket is going, the more the division of the energy/momentum is biased towards the rocket.  Thus, the rocket gains more energy faster than basic Newtonian dynamics would predict, and so achieves a desired amount of dV in less time for less fuel, and thus is more efficient than expected.  Now, this bias towards the faster rocket can all be explained by Newtonian physics happening inside the engine, but it is not obvious or expected from applying Newton's laws of motion to just the rocket itself, as if it were a Newtonian billiard ball.

This non-obviousness is why I said the rocket is "stealing" energy from the exhaust stream.  If you look at the rocket simply as a Newtonian billiard ball, then the "extra" energy gained by the rocket appears to be "stolen".  But in actuality, due to the dynamics of the exhaust stream, it's just allocated differently.  Which is why I don't agree that some futuristic reactionless drive would still benefit from Oberth.  The less exhaust you have or, probably better, the less energy density the exhaust has, the less benefit you get from Oberth.  So if you have no exhaust at all, then you'd probably have no Oberth Effect, either.  But of course if you do have a reactionless drive, you could care less about fuel efficiency because you're not burning fuel, so Oberth wouldn't matter to you anyway.  Oberth is, after all, totally about saving fuel.

 

2 hours ago, Laie said:

Impulse is impulse, whether it comes from little mass at high ISP or the other way round.

Kinetic energy is "half mass times velocity squared". The Oberth effect is due to the "squared" -- adding speed to speed is linear, the energy gained is not.

Again, you're missing the point.  Oberth is about fuel efficiency, nothing more or less.  It's not about what speed you end up with, it's about how much fuel it cost you to get to that speed.

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25 minutes ago, Geschosskopf said:

I see where you're coming from but still disagree.  Just as you can look at the Oberth Effect as an Isp buff with constant thrust, you can also think of it as a thrust buff with constant Isp.  Either way, you end up with the dV you wanted costing less fuel.  If the Isp (IOW, rate of fuel consumption) is the same, then the only way to burn less fuel for a given amount of dV is to have more thrust, so you achieve that dV in less time.

No no no! You do NOT get more dV from the same fuel with Oberth. You get MORE energy from the SAME dV/fuel. Thrust and Isp don't enter into it. There's no "thrust buff" or "Isp buff" at all.

Quote

The way rocket engines behave in a vacuum was not foreseen by classical Newtonian dynamics.  Those would have an even split of the the energy/momentum of the exhaust stream and the rocket.  Equal and opposite reactions and all that.  But what really happens is, the faster the rocket is going, the more the division of the energy/momentum is biased towards the rocket.  Thus, the rocket gains more energy faster than basic Newtonian dynamics would predict, and so achieves a desired amount of dV in less time for less fuel, and thus is more efficient than expected.  Now, this bias towards the faster rocket can all be explained by Newtonian physics happening inside the engine, but it is not obvious or expected from applying Newton's laws of motion to just the rocket itself, as if it were a Newtonian billiard ball.

This is nonsense. The Oberth Effect is a classical newtonian effect, as explained and mathematically demonstrated above. I don't know how to put this more clearly:

The Oberth Effect is entirely a consequence of Ek = 0.5*m*v2 and constant thrust engines, not a separate phenomenon.

The reason it was a surprising observation from Oberth is because engines that don't change thrust with speed are extremely rare on Earth, to the point of non-existence. Most Earth-bound engines are constant power, which means they add speed at a lower rate as speed increases.

Quote

Again, you're missing the point.  Oberth is about fuel efficiency, nothing more or less.  It's not about what speed you end up with, it's about how much fuel it cost you to get to that speed.

It is about fuel efficiency, but not in the way you are describing. The amount of dV for a given amount of fuel in a vessel is given by the rocket equation, and that doesn't change with the vessel's speed. The vessel's speed therefore will not change the amount of speed change delivered by a given amount of fuel, that is fixed. What does change, however, is the amount of energy gained by a given speed change (and in turn fuel expenditure).

 

Edit: Found it, I wrote a little thing about Oberth and misconceptions around it, here: 

 

Edited by Red Iron Crown
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13 minutes ago, Geschosskopf said:

Close, but you're still missing something.  If your math was all there was to it, then there would be no Oberth Effect at all.  You're just doing classical Newtonian dynamics, which is what everybody thought would happen until Herr Oberth noticed his namesake effect.  That's why we talk about Oberth today.  If the Oberth Effect could be explained by your math, then it wouldn't be a thing.  Thus, you do need an extra term in your equations.

As I said above, the Oberth Effect best thought of as Isp buff.  The faster a ship is going, the less fuel it needs to generate a given amount of dV.  In your math, you have the ships burning the same amount of fuel (same mass change).  You are assuming that this same amount of fuel produces 100m/s dV in both.  That is not the case.  The ship that was going faster to start with would either have achieved more dV for that same amount of fuel, or would have consumed less fuel for that same 100m/s of dV than the slower ship.  That is the Oberth Effect in action, which is why it has its own set of equations which you need to factor in on top of your classical Newtonian dynamics.

If I am missing something, then please tell me what it is and provide the terms missing in my equations.
Calling the Oberth Effect an Isp buff is not how I understand the Wikipedia page: "The gain in efficiency is explained by the Oberth effect, which is that the use of a rocket at high speed generates greater mechanical energy."

And no: A ship, that has 100m/s vacuum Detla-V left, has exactly 100m/s left, no matter if it is moving at 10m/s or at 1000m/s in vacuum. Try the following: Bring a ship into a highly elliptical orbit - according to your agumentation the remaining-Delta-V (MJ/KER) readout of the ship should change depending on the velocity of the ship - that is something, I have never witnessed.

Please consider the possibility that it is you, who does not yet understand the Oberth effect.

RIC explained it way better than I was able to:

4 hours ago, Red Iron Crown said:

The Oberth Effect is a bit misnamed, it's not a separate effect but more of an observation of how the then-new rocket engines functioned in vacuum.

The Oberth effect is an observation of a fact and not an effect by itself. This observation is, that a vessel with a higher base velocity gains more kinetic energy from the same amount of Delta-V than a vessel with a lower base velocity. And the formula and numerical examples I gave, show exactly this fact.

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