Delta V Economics

[Doodle]

Hi fellow Kerbonauts and Rocket-Kcientists. I got a question about Delta V usage.

Does it make a difference in Delta-V used if I bring something to a 75km/75k Kerbin Orbit and then start from there to the Mun/Minmus(or whatever else) or if I bring something to a 120k/120k Kerbin Orbit before traveling?

Or does it not matter at all as in "DeltaV to lowOrbit + DeltaV to transfer = DeltaV to highOrbit +DeltaV to transfer"

I think I read/heard somewhere that DeltaV changes at a higher speed are more efficient (dunno if it was about the Hoffmanstransger) So a lower Orbit where the ship has a higher space should be more efficient then a higher orbit where the ships have lower speed or?

A confused little Kerbal.

[Wjolcz]

The lower the orbit the more dV you save. But it shouldn't be an enormous difference between 75k and 120k, I think. You would save about 100m/s or so. Probably even less.

E: basically if you're thinking about going from 75x75km or 120x120km you better go from 75km. Setting Ap of 120km and circularizing orbit is just a waste of fuel.

Edited March 23, 2015 by Veeltch

[Wanderfound]

The lower you are in the gravity well (which implies moving faster to maintain an orbit), the more benefit you gain from the Oberth effect.

You're best off in fuel efficiency terms starting your interplanetary burn from the lowest orbit possible; the transfer burn from 100x100 requires less ÃŽâ€V than the transfer from 70x70, but that saving is outweighed by the cost of lifting the 75x75 to 100x100 in the first place.

There are still reasons for high orbits, though; especially with a low TWR ship, starting a transfer burn fom too low may send you back into the atmosphere where you start losing ÃŽâ€V to drag.

[Kerbart]

Would a trajectory that inserts you straight from launch into the Mun SOI bring some savings? I'd imagine that not having to raise your Kerbin periapsis from -600km to +75km would save you some 500^m/_s dV.

[Wanderfound]

Would a trajectory that inserts you straight from launch into the Mun SOI bring some savings? I'd imagine that not having to raise your Kerbin periapsis from -600km to +75km would save you some 500^m/_s dV.

I believe so, but get confirmation from someone with a better grasp of the physics. You still want to be launching "sideways" rather than up, though, in order to avoid losing too much to gravity drag.

There's also the option of launching into an elliptical orbit, with it positioned so that your transfer burn happens at periapsis. That's tricky to get right, though.

[Doodle]

Ok good to know that the smaller Orbit might be better. I soon have to send my first rockets to Eve and Duna (my first ever transpher Window should be open in the next 100 days) So I can start lifting all my probes to those Planets and their moons into low orbit already.

[impyre]

I'm reading the question as: "If I have a craft with a given dV, will it benefit from a higher or lower orbit." And the answer to that (as well as so many other good questions) is that it depends. Gravitational pull decreases with a square root function, so the further out you are the less you'll have to fight against gravity (but you get less benefit for each additional km of altitude). Furthermore, the way to really look at this is in the form of energy. The higher an object is, the more energy it will have. All orbits of the same period have the same total energy. A perfectly circular orbit maintains a constant balance between kinetic and potential energy, while a highly elliptical orbit trades potential energy for kinetic energy as it approaches periapse and trades that kinetic energy back to potential energy as it approaches apoapse. This having been said, the greater the orbital period the greater the stored energy... and the greater the stored energy, the less you need to add to get an escape trajectory. So if I'm interpreting your question correctly, higher is better. However, it does take fuel, time, and energy to get there... and as others have pointed out, if you're going to simply go for a transfer there's no need to circularize at 800km. Higher orbits will allow you to more easily take more fuel with you (and spend less getting escape) at the cost of additional launches and efficiency.

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http://ksp.olex.biz/ see this link for dV's and more.

Edited March 23, 2015 by impyre

[rkman]

The lower the orbit, the easier it is to have an ascent path close to horizontal, which greatly reduces gravity loss.

[impyre]

Not really. It takes less dV to obtain a trajectory with the same angles from higher altitude. If you don't believe me, you can try for yourself. Spend 1200 m/s at 70km x 70km orbit, (where orbital velocity is already something like 2300 m/s) and then spend the same dV at 500km x 500km and see what happens. "Gravity losses" are higher the lower you are (where the pull of gravity is stronger), and is also related to the amount of time spent in the gravity field (which will be lower if you start from higher up). In any case, you don't really lose energy to gravity once in orbit, you just trade one form of energy for another. Arguably the most efficient method (even though the question isn't really efficiency here) is take-off directly to munar flyby, and burn an oberth maneuver to get the proper escape.

[Kelderek]

Another way to think of it is like this: imagine you have a 75 km x 120 km elliptical orbit where the 75 km periapsis corresponds to the same location where you would do your transfer burn to the Mun (or wherever else you may be going). In that example, the 120 km apoapsis is already in the right direction, so the DV you used to go from 75x75 to 75x120 is not wasted. If you were to circularize at the 120 km apoapsis, then all the DV you spend to do that would be entirely wasted relative to your plan to eventually leave orbit because in that example you are burning on the opposite side of the orbit. So at a minimum you would be wasting the DV that it takes to go from 75x120 to 120x120, and at a maximum, if your transfer burn location does not match up with the 75 km periapsis, then you would waste even more DV than that by going to 120x120.

Keep in mind though that if your transfer burn is long enough (like several minutes with a low TWR like with an LV-N on a high mass vessel), then you might run the risk of re-entering the atmosphere if the altitude of your orbit is too low.

Also, if you plan to use any of the popular online transfer calculator tools to find phase angles, ejection angles, ejection burn times, etc., those tools are all expecting that you start from a circular parking orbit. I'm sure the math gets far more complicated if you try to do a direct launch into your transfer without making an orbit first.

[Captain H@dock]

You're best off in fuel efficiency terms starting your interplanetary burn from the lowest orbit possible; the transfer burn from 100x100 requires less ÃŽâ€V than the transfer from 70x70, but that saving is outweighed by the cost of lifting the 75x75 to 100x100 in the first place.

However, as a side question (if I may) would anyone know how important is the dV gain between starting from a very LKO and a higher one, assuming your tanks would be full anyway (by being able to re-fuel on the final orbit before transferring, which with an SSTO tanker plane is pretty much free)?

Edited March 23, 2015 by Captain H@dock

[impyre]

Here's a craft that burned 1301 m/s of dV from a 72km x 72km orbit.

And here's the exact same craft (with same dV) launched from 570km x 570km.

As you can see, both attain a straight escape trajectory equally well (the higher orbit escape is noticeably straighter though). And both attain about the same altitude for solar apoapse (though the higher orbit had a slight advantage). Had I used alex's calculator (which I linked above) I'd have noticed that the ejection angle is significantly closer to the desired angle for the higher orbit... In this test I burned both vessels at 150 degrees to prograde. Had I compensated in the ejection angle for the higher orbit, it would've attained an even greater altitude advantage over the lower launch. As I said before, launching from a higher orbit means that it takes less dV to get the desired escape trajectory (and thus the same craft will arrive with more fuel)... but this comes at the cost of additional fuel delivered after reaching the parking orbit (but if you're going to refuel anyway, might as well make it worthwhile right?) the only case in which this information is useless is if you intend to go directly from launch to interplanetary transfer with no refueling (which when combined with staging is indeed the most efficient, if cumbersome, method).

edit: can someone please explain how to use spoilers to me?

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That is because DeltaV to lowOrbit + DeltaV to transfer = DeltaV to highOrbit +DeltaV to transfer is not true, as mentionned above.

However, as a side question (if I may) would anyone know how important is the dV gain between starting from a very LKO and a higher one, assuming your tanks would be full anyway (by being able to re-fuel on the final orbit before transferring)?

The advantage isn't hugely significant, but it is noticeable. The difference between 70km circular and 550km circular (when going to duna) is about 200 m/s dV. Of course, the further you're going to be going, the more significant that advantage becomes. Bear in mind you can go much higher too... launching to duna from an orbit similar to minmus (say if you just barely escaped minmus) would only require 664m/s as opposed to the 1060m/s required from LKO. For those of us with refueling bases on minmus, this is a huge deal. One last thing I'll mention, 100m/s dV worth of fuel in a large interplanetary ship can translate to 2000m/s dV for landers and such (depending on relative sizes it could be more or less). This means that if you leave from a higher orbit, you extend your dV budget for landers significantly.

Edited March 23, 2015 by impyre

[Kerbart]

I believe so, but get confirmation from someone with a better grasp of the physics. You still want to be launching "sideways" rather than up, though, in order to avoid losing too much to gravity drag.

Well, yes, not "straight" as in "to the moon in a straight line", but straight as in "without bothering to set up a Kerbin orbit". Basically launch as usual, but instead of circularizing your orbit (raising the periapsis) raising the apoapsis for a Mun intercept instead.

[impyre]

Well, yes, not "straight" as in "to the moon in a straight line", but straight as in "without bothering to set up a Kerbin orbit". Basically launch as usual, but instead of circularizing your orbit (raising the periapsis) raising the apoapsis for a Mun intercept instead.

I'm not certain you'll save anything that way, it may even be more expensive in terms of dV. Think of it like a rendezvous; how much energy it takes to establish capture is directly tied to your velocity relative to the target. To establish capture around a body, you'll have to kill a chunk of that relative velocity (not necessarily all though). By raising periapse before doing transfer burn, you're ensuring that you arrive at apoapse with some horizontal velocity already. If you are approaching your encounter going the opposite way as the body you are intending to be captured by, you'll have to burn off quite a bit of velocity to establish orbit... that's why we approach heading the same way as the target in its orbit. It catches up because we are moving slower than it is... even in this case, relative velocity is still high enough that some must be burned off for capture. If you burn straight there without raising periapse, you'll have almost no velocity (so the target will be approaching at greater relative velocity). I'm not sure whether this increase in dV required to establish orbit is enough to offset the savings by not raising periapse before transferring, but it will be interesting to research.

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Or for that matter whether it's more efficient to establish orbit before landing...

[Red Iron Crown]

Not really. It takes less dV to obtain a trajectory with the same angles from higher altitude. If you don't believe me, you can try for yourself. Spend 1200 m/s at 70km x 70km orbit, (where orbital velocity is already something like 2300 m/s) and then spend the same dV at 500km x 500km and see what happens.

That's true, but you haven't considered the difference in obtaining the initial orbit. Spend the same dV from surface->parking orbit->final burn and the lower orbit will win every time.

[Captain H@dock]

I think he was interpreting the first post as in "considering the same ship at different orbit". Since LFO is pretty much free, I'd say refueling makes that interpretation relevant.

[Kryxal]

Given that he's considering a refuel in the parking orbit, I wouldn't go for the high OR the low orbit, I'd take an elliptical one. It's the best of both worlds really.

[Red Iron Crown]

I don't see mention of refueling in the OP, but if the fuel is being sent up from Kerbin then the low orbit is usually still better. Cheaper to get the fuel up there.

[Empiro]

In general, lower is better. It will cost you less total delta-V to go from Kerbin -> LKO -> Mun Transfer than to go from Kerbin -> HKO -> Mun Transfer. There were a couple of threads a while back that showed that the most efficient transfer is actually one where you do your entire burn at once while still inside the atmosphere (still performing a gravity turn and so forth). The savings aren't really that much though, and it's easier to just establish LKO first.

The savings really come into play when going interplanetary due to the Oberth Effect. If you're going to Jool, for example, it costs less Delta-V to go from LKO to Jool than to go from a circular orbit at the edge of Kerbin's SOI to Jool, even if you magically warp your ship from LKO to the high orbit for 0 cost.

[Kryxal]

Or not-so-magically ... it's a real consideration with Minmus refueling operations (Kethane/Karbonite mods). You're actually better off dropping your orbit first, I believe, but it's even better if you can establish that elliptical orbit (LKO plus over 900 delta-v for a cost of 200 delta-v or so, so long as the periapsis is in the right place).

[tsotha]

Would a trajectory that inserts you straight from launch into the Mun SOI bring some savings? I'd imagine that not having to raise your Kerbin periapsis from -600km to +75km would save you some 500^m/_s dV.

I don't see why. Intuitively I would think if you're burning horizontally just out of the atmosphere there's an instant in time where you could stop and be in a stable orbit. Which would imply you could start in that same stable orbit without loss of efficiency. As to the dV cost of raising your periapsis, well, you're already raising it to the Mun's orbit.

[rkman]

Not really. It takes less dV to obtain a trajectory with the same angles from higher altitude. If you don't believe me, you can try for yourself.

I was talking about getting up to altitude. And it is an argument primarily against direct ascent to the Mun.

Spend 1200 m/s at 70km x 70km orbit, (where orbital velocity is already something like 2300 m/s) and then spend the same dV at 500km x 500km and see what happens. "Gravity losses" are higher the lower you are

Gravity loss is negligible anyway as long as the trajectory is close to horizontal. Another upshot of starting transfer burn at low altitude is increased Oberth effect.

[Red Iron Crown]

Or not-so-magically ... it's a real consideration with Minmus refueling operations (Kethane/Karbonite mods). You're actually better off dropping your orbit first, I believe, but it's even better if you can establish that elliptical orbit (LKO plus over 900 delta-v for a cost of 200 delta-v or so, so long as the periapsis is in the right place).

I'm fairly sure it will be better to bring the fuel to the ship in LKO rather than bringing the ship to the fuel in orbit around one of the moons, especially as the fuel from the moons will be "free" while the fuel needed to transfer the ship to the moon has to be bought on Kerbin.

I remember someone (Yasmy, I think) ran the numbers for interplanetary transfers starting from orbit around the Mun or Minmus, it was not always worthwhile to drop to a low Kerbin periapsis before ejecting. I should try to dig up the post. Found it, leaving from the Mun to go to Eve or Duna gains no efficiency by dropping to a low Kerbin periapsis.

Edited March 24, 2015 by Red Iron Crown

[TheXRuler]

Not really. It takes less dV to obtain a trajectory with the same angles from higher altitude. *snip*.

This is true, those are some quite good observations however there are some problems with your explanation.

When you burn while deeper in the gravity whell you will be faster, this means your ship (and also your fuel) has more energy (the kinetic energy from your orbital velocity is what makes this difference). Now when you burn the fuel you will get more energy from burning the fuel, due to the fuel containing more energy. This is the oberth effect.

The thing is while you need less dV to change your orbit from a high circular orbit, it takes more fuel to get this amount of dVthan when you are lower down and going faster.

Gravity losses are what you get when you are fighting gravity, eg. at the beginning of every rocket launch you are using your engines to counteract gravity's pull on your ship. Say the gravitational acceleration is 9.81 m/s² (g on earth) then you are loosing 9.81 m/s² of the dV you are producing. This is why it is, to a certain point, better to go sideways while launching since your lateral velocity will counteract gravity without the aforementioned gravity losses, also the thrust applied in lateral direction is free of gravity losses and adds only to your orbital velocity. This is of course disregarding drag losses.

Thirdly, the most efficient way to go to mun would be a launch with a gravity turn, then, insted of circularizing you would do your munar injection burn. Get a really low periapsis and do a nice, safe, and efficient grazing trajectory. Shortly before you reach periapsis you start a retrograde burn and maintain a grazing trajectory while slowing down. By doing this you maintain a high lateral velocity for the longest possible time, again reducing gravity losses to an absolute minimum.

Edited March 24, 2015 by TheXRuler

[Starhawk]

Intuitively I would think if you're burning horizontally just out of the atmosphere there's an instant in time where you could stop and be in a stable orbit.

That's what I had been thinking. Then, I realized that this is not the case. The most efficient IP transfer trajectory from launch will leave your periapsis inside Kerbin. You save the delta-v of working on your periapsis at all, this way.

Happy landings!