Orbital altitude and transfers between bodies - Differences in delta-v efficiency

[Ohls]

Is there any difference in total delta-v usage depending on what starting orbital altitude you choose on Kerbin?

For example. I always try to land a orbit around 100km before taking of to other bodies. I also typically keep my refueling stations at this altitude. But is it more efficient to hit 200km, 300km, 1000km before taking of to other bodies? Obviously you will spend more delta-v to achieve that orbit but will you save that when leaving Kerbin?

[DeepOdyssey]

It's not, because of oberth effect.

[Ohls]

It's not as in it doesn't matter what orbital altitude you choose, or it's not as in it's more efficient to start out with a low orbit?

[R0cketC0der]

It will take less delta-V if you get into the lowest possible orbit.

[Epthelyn]

It's more efficient to start off a transfer at a lower altitude because of the, previously mentioned, Oberth effect. The faster you're moving, the more energy the fuel has when you burn it: http://en.wikipedia.org/wiki/Oberth_effect

Basically if you're going from Kerbin to Duna, it'll cost you considerably less dV to transfer from a 100km x 100km orbit around Kerbin than it would from, say, a 1000km x 1000km orbit.

[Jouni]

For single-launch ships, interplanetary launches from low orbits always require less delta-v than from higher orbits. If you build a modular ship and refuel it before the launch, higher orbits may be better, depending on the target planet.

All this assumes that the ship has a reasonably high TWR, allowing it to complete the transfer burn in 5 minutes or less. With low TWR, interplanetary launches from low orbits can be very inaccurate, requiring you to do significant course corrections on the way. In such cases, it may be preferable to start from a higher orbit with a longer orbital period.

[Kryxal]

The other option is multiple burns, but even so you'll probably want a BIT higher orbit, and you'll only be able to safely add about 800 m/s of delta-v before you risk getting caught up on the Mun.

[Eric S]

If you're looking at strictly the amount of delta-v to go from your parking orbit to the planet, then there's a peak efficiency orbit that tends to be fairly high up. For example, for Duna, the orbit is somewhere around 9000-9100 km. This orbit gets lower as you need a higher ejection velocity. For Jool, the orbit is in the 380-390 km range.

However, if you're looking for total delta-v from launch, then the lower the better for the most part, as the amount of delta-v you'll save over launching from a low (80-100km) orbit is generally less than it will take to transfer to and circularize in the higher orbit.

This is basically because of the Oberth effect. The actual reason that the Oberth effect exists is because delta-v is delta-v regardless of your velocity, but the amount of kinetic energy is based on the square of your velocity, so 1 m/s of velocity means more kinetic energy the faster you go. This is important because escaping a planetary SoI is basically trading kinetic energy for potential energy, so the cheaper you come by the kinetic energy, the less delta-v is required to achieve escape.

If your mind doesn't wrap around that description easily, there's another way to think of it. The faster you leave a planet's SoI, the less time the gravity of that SoI has to slow you down, allowing you to keep more of your base velocity. So, if you find the exact velocity it takes to escape an SoI from a low orbit, then add 1 m/s on top of that, you'll escape the SoI with more than 1 m/s left over. The lower in the gravity well you start, the stronger this effect, so the higher the magnification.

This is also one of the resons why if you want to change your apoapsis, it's most efficient to do so from your periapsis.

[MarvinKitFox]

Being at a higher orbit makes the planning and execution of interplanetary transfers easier, as the slower orbital speed allows a better approximation of "instantaneous burn" that most calcs assume.

However, in terms of pure delta-v, you will benefit more from starting at as low an orbit as possible.

More precisely, starting at as high an orbital speed as possible, so as to get maximum benefit from Oberth effect "amplifying" the efficiency of your maneuver.

for example: Achieving kerbin escape velocity needs:

from 100km LKO: about 920 d-v

from 1000km circular orbit: about 600d-v.

But to get to the 1000km orbit from 100km, you already burned 730 m/s, so you total usage is 1330m/s.

Or how about this for a nice shiny example. You want to go to Jool.

From 100km LKO: deltav needed = 1893m/s.

From 1000km LKO: deltav needed = 1895m/s. (plus the 730 you spent getting there)

No, really! Try it!

Even thought you already "invested" 730m/s to get to 1000km, you actually have to spend *more* to get to Jool orbit from there

Of course, if you are smart, you would realise that 70km is better than 100.

Same scenario, from 70km LKO, needs 1891 m/s d-v to get to Jool orbit. Plus you save the ~45m/s needed to swim up to the 100km mark.

((Personally, I tend to do my interplanetary burns from ~150km, as my engine choices tend to give me TWR of .15 or less. This means loooong burns on interplanetary transfers. Burning a long time before the node, when skimming the atmosphere, means ramming the atmosphere. Bad idea! About 150km gives me enough leeway to play with early burns without dipping too low during the burn))

Edited June 29, 2014 by MarvinKitFox

[mhoram]

There are differences in total delta-v usage.

Starstrider42 made some calculations about this question.

See http://forum.kerbalspaceprogram.com/threads/75542?p=1072850&viewfull=1#post1072850

Further on in that thread the idea of

1) drop Periapsis to 75km

2) rise Apoapsis to escape SOI

was discussed. As it turned out this method can be more efficient.

[Ohls]

Wow, you guys are amazing. Thanks everyone for taking the time to answer my fairly simple question with some fairly fleshed out answers!

[Pecan]

All else being equal when you enter a body's SOI you know you'll leave it with the same velocity - speeding up as you drop to periapsis and (unless you crash!) slowing down again as you climb back to escape. In a similar way if you start a transfer from a high orbit - near the edge of the current SOI - you know you'll only need a small extra push to reach escape velocity. The least-fuel burn would be maximising speed by falling from an apoapsis at the edge of the current SOI to a periapsis as low as possible above the current planet, thus needing least extra push in the first place and taking maximum advantage of Oberth (as has been mentioned). Whether it's worth it or not is a different matter.