Should I build a refueling station at the edge of Kerbins SOI?

[kerbonaut101]

Ive been thinking that if I construct a large space station right on the edge of the Kerbins SOI (75,000,000m?) then I could use that as a refuelling station to regain the fuel lost from things such as orbital insertion, manoeuvres ect... has anyone dont anything similar to this?

[Jouni]

Refueling stations at high orbits can be useful, if you are going to Duna or Eve. The best place is probably the orbit of Minmus, as it's cheaper to go there than to a high orbit around Kerbin.

For the other planets, launches from low orbits are more fuel-efficient than launches from high orbits. Due to the Oberth effect, you need less delta-v to reach Jool from a 100 km orbit than from a 30000 km orbit.

Before 0.23.5, placing the refueling station to a 600 km orbit was a good choice. It allowed you to use 100000x time warp while waiting for a launch window, and reaching the other planets from there was essentially as efficient as from lower orbits. Now such concerns are less important, as you can also time warp at the tracking station.

Other useful altitudes were 160 km (less lag, as Kerbin is drawn with less detail than at lower orbits) and 80-120 km (easy to reach for SSTOs that may not have too much fuel reserves).

[mhoram]

I placed my refuelling station in a 300km orbit.

I had two reasons not to put it to a 75km orbit.

1. 75km is the standard orbit for my launches, so I might accidentially crash into it.

2. A rendezvous between ship and station via a Hohmann transfer need some time until the angle between both objects fit (this time can be reduced by adjusting the launch time, which I often do not care about). The time spent waiting decreases with the difference between the orbit altitudes.

[JedTech]

Ive been thinking that if I construct a large space station right on the edge of the Kerbins SOI (75,000,000m?) then I could use that as a refuelling station to regain the fuel lost from things such as orbital insertion, manoeuvres ect... has anyone dont anything similar to this?

I experimented a lot with higher refueling stations, but ultimately they are not great because it takes so long to orbit that you can't get to your desired ejection angle during a given transfer window.

[ScottyDoesKnow]

1. 75km is the standard orbit for my launches, so I might accidentially crash into it.

2. A rendezvous between ship and station via a Hohmann transfer need some time until the angle between both objects fit (this time can be reduced by adjusting the launch time, which I often do not care about). The time spent waiting decreases with the difference between the orbit altitudes.

For 1, this is pretty much impossible. Even if you're in the same point of your orbit as the station (around 100 meters out of a 4.2 million meter orbit) you'd also have to have matched planes exactly.

For 2, the easiest way I've found to rendezvous (in both effort and time) is to launch ahead of your target (doesn't need to be very precise). Then you just raise your apoapsis until you get a rendezvous one orbit later.

[Epthelyn]

If you're planning on using it primarily to refuel rockets launched from the ground into orbit then the higher the better. As Jouni pointed out, you lose the bonus from the Oberth effect but you're saving more than that if you're essentially beginning an interplanetary insertion burn from right on the edge of the SoI.

If you ever want to use it for incoming craft (e.g. a Kerbin - Duna shuttle) then something in the middle seems to work best; most initial, untrimmed, encounters usually end up somewhere a way below the edge of the SoI unless they're really marginal so it's nice to know that you'll be fairly close to refuelling without having to do much else. You don't want to be too low because of more slowing down (although it's made easier by aerobraking in the case of Kerbin) and potentially wanting to leave again.

In the end it's really up to what you want to save. I have most of my rendezvous-based infrastructure on the edge of Kerbin's SoI or at least between Mun and Minmus because I'd rather save on transfer dV to other planets; I'm more inclined to save as much as I can on long-distance journeys on the basis that even if I need another thousand or so dV in a launcher it requires far less time to fail a few launches than it does to get half way back from somewhere and find that that 200m/s I might have saved by doing X was lost because I did Y instead.

Some people would probably see this is a weird way of doing it because for some applications it makes it less useful, but it works. In my case the added benefit prior to .23.5 was being out the range of Kerbin's evil 'ocean-lag' in higher orbits, so I could enjoy the full sphere of camera angles without getting impatient with framerates.

[Starstrider42]

I experimented a lot with higher refueling stations, but ultimately they are not great because it takes so long to orbit that you can't get to your desired ejection angle during a given transfer window.

But that wouldn't be as much of a problem for lower orbits (say, Minmus, or between Mun and Minmus), right? You'd have an orbital period of only a few days, but the delta-V needed to escape Kerbin would still be 700-1000 m/s lower than in LKO...

(Please correct me if I'm wrong. I'm starting to make plans for a high Kerbin station, and I'd like to know if my assumptions are invalid).

[Epthelyn]

But that wouldn't be as much of a problem for lower orbits (say, Minmus, or between Mun and Minmus), right? You'd have an orbital period of only a few days, but the delta-V needed to escape Kerbin would still be 700-1000 m/s lower than in LKO...

(Please correct me if I'm wrong. I'm starting to make plans for a high Kerbin station, and I'd like to know if my assumptions are invalid).

The point is that if you wanted to burn exactly on a specific launch window then it's very difficult to do from a higher orbit; unless you miraculously launched at a time where your future orbits would be at a certain point at a particular time then it's unlikely to be practical.

However, you're right. Any dV lost from ignoring the exact time of a launch window will almost certainly be made up by starting in a very high orbit. In fact you can relatively quickly escape the SoI entirely and then begin the transfer in a much easier fashion, saving on the ejection angle difficulties; they only exist because if you don't leave Kerbin at the right angle you're going to go in completely the wrong direction.

[Claw]

Refueling station location seems to be a fairly person preference.

Personally, having refueling stations at Minmus or on the outer edge of the SOI aren't useful. I prefer at the Mun or less.

Having a station far away from Kerbin means you miss out on some Oberth effect. You can get around this by doing your initial burn toward Kerbin (essentially setting up an eliptical orbit), then doing the interplanetery burn at Kerbin PE. This has the advantage of refueling around 600-700 dV compared to leaving straight from LKO, but requires some trickery with Setting up the orbits.

- Minmus has the disadvantages of an inclined orbit and a long orbital period. The inclined orbit makes setting up interplanetery trips more annoying, and the long orbital period make transfer window timing difficult to control. You are at the mercy of Minmus' long orbit. You also miss out on Oberth from Kerbin unless you sling back toward it.

- The edge of Kerbin's SOI misses out on Oberth, but you would be able to refuel the 900-1000 dV it takes to get there. If you planned on slinging back to Kerbin for some Oberth, you are going to be at even more mercy of the very long orbit time.

- Mun orbit is nice because you can use Munar gravity to help capture incoming and outgoing craft, and the orbital period isn't so crazy long. You still have to do some orbital burn trickery that takes a bit of practice. It's not inclined and only has a difference of about 100-200 dV when compared to Minmus.

[Technical Ben]

Ive been thinking that if I construct a large space station right on the edge of the Kerbins SOI (75,000,000m?) then I could use that as a refuelling station to regain the fuel lost from things such as orbital insertion, manoeuvres ect... has anyone dont anything similar to this?

I do this, but docking can be difficult as it's hard to get so close at such great distances. So it can be handy, but is extra work. I have a fuelling station, or use tugs to refuel existing transports as they reach higher orbits, just before a departure.

Refueling stations at high orbits can be useful, if you are going to Duna or Eve. The best place is probably the orbit of Minmus, as it's cheaper to go there than to a high orbit around Kerbin.

For the other planets, launches from low orbits are more fuel-efficient than launches from high orbits. Due to the Oberth effect, you need less delta-v to reach Jool from a 100 km orbit than from a 30000 km orbit.

Before 0.23.5, placing the refueling station to a 600 km orbit was a good choice. It allowed you to use 100000x time warp while waiting for a launch window, and reaching the other planets from there was essentially as efficient as from lower orbits. Now such concerns are less important, as you can also time warp at the tracking station.

Other useful altitudes were 160 km (less lag, as Kerbin is drawn with less detail than at lower orbits) and 80-120 km (easy to reach for SSTOs that may not have too much fuel reserves).

Oh, so scratch that idea. I guess the only reason to do it then is "rule of kool".

[JedTech]

Basically if you want to gently nudge yourself into the suns SOI and then do your transfer burn in the suns SOI, then a higher orbit is a great starting point for a refuel station. But if you want to do a interplanetary transfer burn from kerbin SOI, then you should burn from a low orbit (I prefer 120k for higher warp speeds), this allows you to burn at an efficient ejection and phase angle while utilizing the oberth affect.

Edited April 6, 2014 by JedTech

[O-Doc]

I've thought long and hard about this and tried many approaches. I now think the best position for a refueling base is at KSO. Above KSC? I'd have to test to exact angle from KSC. With a KSO base you get.

1. Good launch windows which line up with info you have on the ground.

2. Most of your dV to get out of KSOI taken care of.

3. Opportunity to sling shot Mun on less time critical departures.

4. Ability to do longer burns more precisely.

This is where I'm going to put my new departure lounge anyway.

Edited April 6, 2014 by O-Doc

[Pds314]

I placed my refuelling station in a 300km orbit.

I had two reasons not to put it to a 75km orbit.

1. 75km is the standard orbit for my launches, so I might accidentially crash into it.

2. A rendezvous between ship and station via a Hohmann transfer need some time until the angle between both objects fit (this time can be reduced by adjusting the launch time, which I often do not care about). The time spent waiting decreases with the difference between the orbit altitudes.

Actually, the odds of crashing into it are extremely low, and the typical speeds will be easily low enough to dodge (<<100 m/s). Unless of course you are sending things up into the same orbit but retrograde.

The rendezvous thing makes sense.

[Starstrider42]

For the other planets, launches from low orbits are more fuel-efficient than launches from high orbits. Due to the Oberth effect, you need less delta-v to reach Jool from a 100 km orbit than from a 30000 km orbit.

What do you know, you were right: high parking orbits really are bad for your fuel economy.

Since I couldn't believe my intuition was wrong, I did some math. The image I'm linking is the burn delta-V (shaded contours) needed as a function of the height of a circular starting orbit around Kerbin (horizontal axis) and the desired delta-V relative to Kerbin's orbit around the sun (vertical axis). The red curve along the lower left is the height at which you burn the least fuel for a given interplanetary delta-V.

Bottom line: if you're headed for Eve or Duna, you want to burn from just inside the Mun's orbit. For any other destination, you want to be a lot lower. There go my station plans...

(Pardon the messy plot. I'm better at math than I am at pretty graphics.)

Edited April 7, 2014 by Starstrider42
log distance scale

[mhoram]

@Starstrider42

Great chart!

To see the optimal starting altitudes for high dV targets, a logarithmic horizontal axis could be more appropriate.

Do you mean by height the altitude above sealevel or radius of the orbit?

[Starstrider42]

@Starstrider42

Great chart!

To see the optimal starting altitudes for high dV targets, a logarithmic horizontal axis could be more appropriate.

Do you mean by height the altitude above sealevel or radius of the orbit?

Getting a working log plot in Mathematica is harder than you'd think. I think I've got everything consistent...

And yes, height is altitude above sea level.

[Eric S]

The trick to efficient transfers from high orbit is to drop your periapsis down to 75-100 km, then burn to the desired velocity at periapsis. You'll find that by doing this, you save about 500-600 delta-v post refueling compared to refueling in LKO. Think of it as doing most of your transfer burn, then refueling and finishing the burn on the next orbit (with some delta-v burned to match orbits with the Mun/Minmus/your refueling station).

I've never had a problem with hitting transfer windows from high orbits, as transfer windows tend to be several days wide with minimal delta-v differences. The timing can be tricky, but it's always possible unless you're going to Moho, those tend to be narrow (but frequent) windows. If you have problems hitting windows from Minmus (12 earth day orbit), try it from the Mun, you won't save as much delta-v, but the orbit is just over one and a half earth days.

[magnemoe]

What do you know, you were right: high parking orbits really are bad for your fuel economy.

Since I couldn't believe my intuition was wrong, I did some math. The image I'm linking is the burn delta-V (shaded contours) needed as a function of the height of a circular starting orbit around Kerbin (horizontal axis) and the desired delta-V relative to Kerbin's orbit around the sun (vertical axis). The red curve along the lower left is the height at which you burn the least fuel for a given interplanetary delta-V.

Bottom line: if you're headed for Eve or Duna, you want to burn from just inside the Mun's orbit. For any other destination, you want to be a lot lower. There go my station plans...

http://i.imgur.com/i2UWTXK.png

(Pardon the messy plot. I'm better at math than I am at pretty graphics.)

This came as an surprise to me, I put up an shipyard in Minmus orbit with the extraplanetary launchpad mod. launched a ship to Jool and it cost me 2500 m/s, I believed it would be 1500-1800 m/s not far more expensive, so moving the shipyard to Minmus was a mistake, far smarter to bring ore and fuel down to LKO.

[Starstrider42]

The trick to efficient transfers from high orbit is to drop your periapsis down to 75-100 km, then burn to the desired velocity at periapsis. You'll find that by doing this, you save about 500-600 delta-v post refueling compared to refueling in LKO. Think of it as doing most of your transfer burn, then refueling and finishing the burn on the next orbit (with some delta-v burned to match orbits with the Mun/Minmus/your refueling station).

I've never had a problem with hitting transfer windows from high orbits, as transfer windows tend to be several days wide with minimal delta-v differences. The timing can be tricky, but it's always possible unless you're going to Moho, those tend to be narrow (but frequent) windows. If you have problems hitting windows from Minmus (12 earth day orbit), try it from the Mun, you won't save as much delta-v, but the orbit is just over one and a half earth days.

Indeed. Interplanetary transfers to the inner solar system, at least, are a lot cheaper. I'll have to try this some time.

(Don't worry, I don't plan to spam you guys with these plots. This is the last one.)

Edited April 7, 2014 by Starstrider42
Stupid, stupid math error

[mhoram]

Indeed. You can do any interplanetary transfer for less than 750 m/s if you drop down from Minmus orbit to 80 km, or 1000 m/s from Mun orbit. I'll have to try this some time.

I am sorry, but I am not sure if I understand the intention of this graph correctly.

Lets assume X (horizontal axis) is the starting altitude above sea level and Y is the desired delta-V relative to Kerbin's orbit around the sun (vertical axis).

I believe there are two burns involved.

One from a X*X orbit to a 80km*X orbit within the SOI of Kerbin

A second one from a 80km*X orbit within the SOI of Kerbin to the target orbit that differs by Y from Kerbin's orbit around the sun.

I would find a graph interesting that sums up both burns, but your graph does not display that value (at Minmus starting altitude the needed dV would be larger than 900m/s for all target dV-values, because that is about the value needed to get into a 80km*Minmus orbit).

So does the graph only display the value of the second burn? If one assumes that the refuelling station is in a circular orbit, this value alone is however not so important.

I tried shortly to find a formula for the calculation of these interplanetary target dV values, but was not successfull. Can you point me to a documentation or paper.

[Starstrider42]

I would find a graph interesting that sums up both burns, but your graph does not display that value (at Minmus starting altitude the needed dV would be larger than 900m/s for all target dV-values, because that is about the value needed to get into a 80km*Minmus orbit).

This is plotting the sum of the two burns. 900 m/s is the delta-V needed to get from a 80 km orbit to a 80 km × 47000 km orbit. The delta-V needed to get between a 80 km × 47000 km orbit and a 47000 km circular orbit (which is what's relevant here) is 250 m/s.

Also, something I should have clarified: the second plot chooses the better of Eric's transfer and a simple prograde burn. The jog in the contours is the point where the two methods use the same amount of fuel.

EDIT: turns out I did make a math error: I assumed a periapsis of 80 km from Kerbin's center, not 80 km above the surface. New plot is up.

I tried shortly to find a formula for the calculation of these interplanetary target dV values, but was not successfull. Can you point me to a documentation or paper.

The main formulas I use for these calculations are that the speed at periapsis of an elliptical orbit is sqrt(μ/a) × sqrt((1+e)/(1-e)), while the speed at apoapsis is sqrt(μ/a) × sqrt((1-e)/(1+e)). μ is the gravitational parameter of the sun, a the semimajor axis, e the eccentricity. The rest is just taking the desired periapsis and apoapsis of a Hohmann transfer from the KSP Wiki, and subtracting Kerbin's orbital speed (also from the KSP Wiki).

Edited April 7, 2014 by Starstrider42

[mhoram]

This is plotting the sum of the two burns. 900 m/s is the delta-V needed to get from a 80 km orbit to a 80 km × 47000 km orbit. The delta-V needed to get between a 80 km × 47000 km orbit and a 47000 km circular orbit (which is what's relevant here) is 250 m/s.

My mistake - you are right.

The main formulas I use for these calculations are that the speed at periapsis of an elliptical orbit is sqrt(μ/a) × sqrt((1+e)/(1-e)), while the speed at apoapsis is sqrt(μ/a) × sqrt((1-e)/(1+e)). μ is the gravitational parameter of the sun, a the semimajor axis, e the eccentricity.

I am familiar with these formulas as far as no SOI-changes are involved, but the point I do not understand yet is the transition between Kerbin's SOI and Sun's SOI.

The rest is just taking the desired periapsis and apoapsis of a Hohmann transfer from the KSP Wiki, and subtracting Kerbin's orbital speed (also from the KSP Wiki).

As far as I understand it, a Hohmann transfer is only a valid approach, if no SOI changes are involved, but in this case there is a SOI-change between the burn at the 80km Kerbin periapsis and the arrival at the target planet. So in this case it is at best an approximation and I can not tell, how good this is.

Let's take an example as I understand the method according to your description: going from Kerbin to a circular orbit near Duna (values are very much rounded)

Please correct me, when I deviate from your calculations or make an error.

Kerbins Semimajor Axis: rK = 13599 Mm

Sun'S mu: 1.1723328×10¹⁸ m³/s²

Let's chose the target orbit around Duna

Target Semimajor Axis: rD = 20000 Mm (assumption of a circular orbit)

From here we can calculate:

Kerbins orbital velocity: 9285 m/s

Eccentricity of the transfer orbit: eT = (rD - rK) / (rD + rK) = 0.19

Semimajor of the transfer orbit: aT = 16800 Mm

Velocity at periapsis of the transfer orbit within Sun's SOI: = sqrt(μ/aT) × sqrt((1+eT)/(1-eT)) = 10130 m/s

Subtract Kerbins orbital velocity within Sun's SOI: 845 m/s

At this point I am stuck what to do with this velocity.

Edited April 7, 2014 by mhoram
corrected error in calculation

[Starstrider42]

Velocity at periapsis of the transfer orbit within Sun's SOI: = sqrt(μ/aT) × sqrt((1+eT)/(1-eT)) = 11259 m/s

Agree with you until this point -- using the same formula, and the same values for μ, aT, and eT, I get 10,130 m/s. I get the same answer as you if I put the 1/(1-e) term outside the square root, though.

I handle the SoI transition by assuming that the speed with which a ship leaves Kerbin's SoI is the speed at infinity of the hyperbolic orbit within the SoI. This is, as you pointed out, an approximation: the escape speed at the SoI boundary is 290 m/s, so the ship will leave Kerbin going slightly faster than my calculations assume. It would be easy to correct for this (just move the planets down to v_SOI = sqrt(v_inf^2 - (290 m/s)^2) in the above chart), but it wouldn't change much. I'm pretty sure my assumption that all the planets are coplanar introduces a much bigger error.

These charts were never intended to be a precise delta-V guide; I made them to see how the different rules of thumb people were quoting interacted, and which came out on top.

Edited April 7, 2014 by Starstrider42

[Othuyeg]

I love to have one in Mün orbit. It is easy to plan interplanetary operations and it is easy to refuel the station and the ships coming to it.

[mhoram]

Agree with you until this point -- using the same formula, and the same values for μ, aT, and eT, I get 10,130 m/s. I get the same answer as you if I put the 1/(1-e) term outside the square root, though.

Found this problem at the same time as you.

I handle the SoI transition by assuming that the speed with which a ship leaves Kerbin's SoI is the speed at infinity of the hyperbolic orbit within the SoI. This is, as you pointed out, an approximation: the escape speed at the SoI boundary is 290 m/s, so the ship will leave Kerbin going slightly faster than my calculations assume.

And at this point you assume that the velocity difference (between Kerbin and the transfer orbit periapsis) can be set equal to the escape speed at the SoI boundary.

From there it is quite easy to calculate the needed velocity at 80km periapsis within Kerbins SOI and calculate the difference to the 80 x altitude orbit.

Thanks for the explanation. Clever idea!

It would be easy to correct for this (just move the planets down by v_inf -> sqrt(v_inf^2 - (290 m/s)^2) in the above chart), but it wouldn't change much. I'm pretty sure my assumption that all the planets are coplanar introduces a much bigger error.

I also don't think this is much of a stretch.