Algorithm for Making Interplanetary Transfers (almost) as Easy as Getting to The Mun!

[arkie87]

KSP Community,

One thing that intermediate KSP players notice is the relative increase in difficulty/annoyance that comes with going interplanetary. As a new player, I had a lot of fun going to the Mun/Minimus since the available tools/information made the algorithm to get there simple: get into orbit, place a maneuver node randomly on your orbit, drag apoapsis to intersect the Mun’s orbit, and then adjust the location of the node until you get a good encounter.

In contrast, going interplanetary is more complicated, and either requires knowledge of phase-angles/calculations of launch windows (or plugins to provide/calculate this information), or requires trial and error setting up maneuver nodes, time warping (preferably in high orbit so you can use 100,000x), and repeating. For me, manually calculating launch windows is out of the question (requiring that would be liked requiring players to calculate CoT, CoL, or CoMâ€â€it is just out of the question). So, either the stock game must give the players the tools necessary to calculate launch windows, or an algorithm must exist that makes it possible without iteration/trial and error.

That said, I think I found an easy algorithm that makes getting to any planet (almost) as easy as getting to the Mun or Minimus: first get into orbit, then, set up a maneuver node (if you are going closer to the Kerbol, then place on dayside; otherwise, place on night side) drag out your apoapsis until you just leave Kerbin's SOI, and execute maneuver. You are now orbiting Kerbol in a very similar orbit to that of Kerbin (with a slight eccentricity). This situation is analogous to being in orbit around Kerbin and trying to get to the Mun/Minimus, and the same algorithm can be used from here on i.e. place a maneuver node somewhere on your orbit, drag your apoapsis until it intersects the planet of interest, and then move the maneuver node around the orbit until you get an encounter. Thus, getting to any planet is just like getting to the Mun/Minimus, albeit with one extra stepâ€â€first escaping Kerbin’s SOI.

I am aware, however, that there is one disadvantage to this methodâ€â€that is it less efficient than a transfer at optimum transfer window, since some deltaV is wasted in creating the eccentric orbit around Kerbol and additional losses from lack of fully using Oberth effect. However, the loss in efficiency/deltaV becomes less significant for planets farther from Kerbin since the amount of deltaV wasted creating the eccentricity is negligible compared to the transfer burn. In addition, the wasted deltaV also scales with offset from ideal launch window (thus, if phase angle is known to be approximately correct, this algorithm could be used anyway with minimum wated deltaV). Regardless, I think for new/lazy players, this algorithm is good enough.

What do you guys think? Is this obvious and/or a stupid idea or was it helpful?

[LethalDose]

What do you guys think? Is this obvious and/or a stupid idea or was it helpful?

No, it's a reasonable idea that accomplishes it's goal: Making transfers to other planets easier.

You've also hit the nail on the head with the method's rather sizable short-coming:

I am aware, however, that there is one disadvantage to this methodâ€â€that is it less efficient than a transfer at optimum transfer window, since some deltaV is wasted in creating the eccentric orbit around Kerbol and additional losses from lack of fully using Oberth effect. However, the loss in efficiency/deltaV becomes less significant for planets farther from Kerbin since the amount of deltaV wasted creating the eccentricity is negligible compared to the transfer burn. In addition, the wasted deltaV also scales with offset from ideal launch window (thus, if phase angle is known to be approximately correct, this algorithm could be used anyway with minimum wated deltaV). Regardless, I think for new/lazy players, this algorithm is good enough.

Burning transfers from Kerbolar orbits instead of LKO is much less efficient, and basically all the dV maps used rely on the latter method.

I also believe that you are mistaken about the the transfers losing less efficiency heading to distant planets. More distant planets require more dV. Expending that dV in LKO leads to faster ejections from Kerbin, which means less loss of velocity due to gravity drag. Hence, the efficiency of travel to more distant planets will be more greatly affected than to travel to closer destinations.

I'm really not sure it's a new idea, but I can't say I've seen it previously posted on the forums. Thanks for sharing.

[worir4]

I remember i used to do this when i didn't know about phase angles. I suppose it is a good method if you don't want to wait for a launch window!

[metl]

Except you still end up waiting. Regardless of which method used, you still have to wait for the proper intersect. That being said, this is about the only way for most players to do it unless they spend time looking it all up and/ or installing a mod to do it for them. My first trip to Duna was done this way. After warping at max warp for over a year, I finally decided I had to find a better way. I hope the needed information gets added to the tracking stations eventually that would give you a rough window to launch for the best intercept. For now, I use protractor (although somehow I always still need more Dv then the charts say.)

[arkie87]

I also believe that you are mistaken about the the transfers losing less efficiency heading to distant planets. More distant planets require more dV. Expending that dV in LKO leads to faster ejections from Kerbin, which means less loss of velocity due to gravity drag. Hence, the efficiency of travel to more distant planets will be more greatly affected than to travel to closer destinations.

Thanks for the reply.

I think the Oberth effect will be more "efficiently" utilized for farther planets when burning from LKO.

However, the relative fraction of extra deltaV to first escape Kerbin SOI from LKO compared to the total deltaV required from LKO to Jool (let's say) is less than from LKO to Duna, since more energy is needed to get apoapsis all the way out to Jook than to Duna.

Basically, it takes energy to increase the apoapsis, and if the eccentricity is small compared to the total needed change in apoapsis (w.r.t. Kerbol), the wasted deltaV will become a smaller fraction of total needed deltaV.

[arkie87]

Except you still end up waiting. Regardless of which method used, you still have to wait for the proper intersect. That being said, this is about the only way for most players to do it unless they spend time looking it all up and/ or installing a mod to do it for them. My first trip to Duna was done this way. After warping at max warp for over a year, I finally decided I had to find a better way. I hope the needed information gets added to the tracking stations eventually that would give you a rough window to launch for the best intercept. For now, I use protractor (although somehow I always still need more Dv then the charts say.)

True, you still have to wait, but the difference is (1) you can time warp at full speed since you are interplanetary and (2) this method is non-iterative... i.e. you dont have to park yourself in a high orbit around Kerbin, attempt a transfer, see that you need to warp a bit more, warp a bit more, and then try again and again until you get a decent encounter with small wasted deltaV-- instead, you can slide the maneuver node around to find the best transfer burn since you are already orbitting kerbol.

Hmm.... That got me thinking: perhaps the maneuver node tool should allow you to select the reference body i.e. Kerbin (or whatever body you are orbiting) or its parent i.e. Kerbol. For the case of the Mun, you can select the Mun, Kerbin, or Kerbol etc... this would make transfers much easier!@!@!@!

[merendel]

Your describing an inefficient version of a technique 5th horseman uses sometimes. do what your talking about for seting up the nodes but dont actualy burn them. first one that just bairly escapes kerbin and then set a second node along the predicted kerbol orbit that you slide around to get a connection to your target. Now deleate your first node and the second will snap back to kerbin orbit, this node is your launch window timer. You wont actualy fly this node but it will give you a very good indication of when you should setup a burn that will take you to your destination. Once that manuver node gets down to a few hours away deleate it and setup a standard transfer burn to reach the apropreate orbit for you target. Your now launching at a near optimum time and can take full advantage of oberth.

Heres a video where he shows the technique as he gives instructions.

[Concentric]

There was a "How do you plan your interplanetary trajectories" thread a little while back that brought up a method that instantly replaced my previous method of tangents (which isn't bad for a minimal-complexity, reasonable dV solution - though I don't think it's been comprehensively tested) that I had seen in another thread. Basically, by making a maneuver node that just escapes Kerbin in the right direction around Kerbol, you can then place a subsequent maneuver node in the plotted Kerbol orbit. You can move this and adjust it until you have an encounter, then delete the first maneuver node. The timing on this node will give a launch window, and you can timewarp at the tracking station at maximum until it is close. It's one of the reasons I put up a set of "flight-planner" probes in the career mode I was running at the time - I could get a series of launch windows lined up.

Basically, it's all the benefits of the method you've outlined above with none of the downsides. I'll try to find and credit the person who brought it up...

As for the method of tangents, it's similar to the old "Burn at Munrise" thing - if you're heading in the same direction around a central body, you're roughly at/just after launch window when the tangent to the orbit of the lower body from the lower body's location in the direction of motion intersects the higher body's location.

Edit: Ninja'd. Yeah, it was probably 5thHorseman. That seems familiar, I'll go check.

Edit2: Here is 5thHorseman's post in the interplanetary planning thread where he brought up the method. However, he credits it to an unknown person.

Edited November 10, 2014 by Concentric

[turkwinif]

-snip-

You sir, have given me an idea. It (kindof) combines the KSP Interplanetary Calculator and maneuver nodes. What if we make a maneuver node, target a planet, and then the maneuver node automatically visually represents, with a dotted line, the ejection angle and time until burn (time until burn being the transfer window time). With that, we'd have a little bit more info on when to burn, but still have to pull the apoapsis-marker on the node to simulate a burn. Plus, the target maneuver node wouldn't account for inclination differences and eccentricity.

This may be better described with pictures

[GoSlash27]

arkie,

Some helpful info on this technique:

http://forum.kerbalspaceprogram.com/threads/80857-A-Delta-V-Map-for-simple-flight-paths

Of particular interest is the comparison between both profiles in terms of DV.

A trip to Duna would cost 1,060 m/sec overall with this method (a 17% increase) while a trip to Eeloo costs an additional 3,190 m/sec (40%). And this understates the disparity quite a bit since most people do their transfer from orbit rather than the pad. Simple flight paths are definitely more costly for more distant missions.

IMO KSP really needs a built- in function to plan for transfer windows.

Best,

-Slashy

[arkie87]

Your describing an inefficient version of a technique 5th horseman uses sometimes. do what your talking about for seting up the nodes but dont actualy burn them. first one that just bairly escapes kerbin and then set a second node along the predicted kerbol orbit that you slide around to get a connection to your target. Now deleate your first node and the second will snap back to kerbin orbit, this node is your launch window timer. You wont actualy fly this node but it will give you a very good indication of when you should setup a burn that will take you to your destination. Once that manuver node gets down to a few hours away deleate it and setup a standard transfer burn to reach the apropreate orbit for you target. Your now launching at a near optimum time and can take full advantage of oberth.

Heres a video where he shows the technique as he gives instructions.

Interesting. Thanks for posting. It's a good (better) method, but requires setting up a lot of fragile maneuver nodes, and provides no easy way to time accelerate to this node (without switching back to tracking station).

Perhaps allowing you to control the reference body of your orbital trajectory would obviate the need to set up the first maneuver node (see above).

[GoSlash27]

*snip*

You, Sir, have given me an idea!

Suppose you launch a simple satellite to a point just outside Kerbin's SoI but in the same orbit. Using that, you could do the standard maneuver node thing and it would tell you when the transfer window would be. You could actually launch the mission from the pad with that info and do a little correction burn.

Best,

-Slashy

[metl]

Finding the Dv is good info, but there is still the terrible problem of figuring out where to set up the transfer without using all guesswork (unless you study orbital mechanics or have a phase angle mod.) I hadn't thought of it before, but like previously suggested, maybe there could be an "interplanetary flgiht" button that would give you a rough maneuver node, but could be fine-tuned for maximum efficiency. Hell, even incorporate it into the difficulty settings.

[maltesh]

Thanks for the reply.

I think the Oberth effect will be more "efficiently" utilized for farther planets when burning from LKO.

However, the relative fraction of extra deltaV to first escape Kerbin SOI from LKO compared to the total deltaV required from LKO to Jool (let's say) is less than from LKO to Duna, since more energy is needed to get apoapsis all the way out to Jook than to Duna.

Basically, it takes energy to increase the apoapsis, and if the eccentricity is small compared to the total needed change in apoapsis (w.r.t. Kerbol), the wasted deltaV will become a smaller fraction of total needed deltaV.

I wound up putting together a Desmos graph a couple years ago about this.

This graph shows the difference in delta-V when departing Kerbin to various destinations. The x-axis is the sun-centered semi-major axis of your destination in millions of kilometers, and the y-axis displays required delta-v in km/s. v_lko [Green Curve] is the delta-V required to burn from a circular orbit around Kerbin at an altitude of 100km directly into an hohmann trajectory for the destination, and v_2step [Red Curve] is the delta-v required to burn from that same 100km orbit to just escape Kerbin, and once outside its SOI, burn to a hohmann trajectory. The various vertical lines mark the semimajor axis of several of the bodies orbiting the sun, with the blue vertical line being the orbit of Kerbin.

The original graph, with its formulae, is here: https://www.desmos.com/calculator/0gebxscf2t

For any of the worlds in the Kerbin system the two-step method of burn-to-escape-Kerbin-then-burn-to-transfer in solar orbit, is always a significant wastage of delta-V over burning from LKO, and that fraction tends to get larger, the further your destination is from Kerbin, the larger that fraction becomes. For the interplanetary transfer, you're spending about 80% extra when going for Eve or Duna, about 90% extra when going to Eeloo, and about 95% extra when going to Moho by using the two-step method.

[arkie87]

arkie,

Some helpful info on this technique:

http://forum.kerbalspaceprogram.com/threads/80857-A-Delta-V-Map-for-simple-flight-paths

Of particular interest is the comparison between both profiles in terms of DV.

A trip to Duna would cost 1,060 m/sec overall with this method (a 17% increase) while a trip to Eeloo costs an additional 3,190 m/sec (40%). And this understates the disparity quite a bit since most people do their transfer from orbit rather than the pad. Simple flight paths are definitely more costly for more distant missions.

IMO KSP really needs a built- in function to plan for transfer windows.

Best,

-Slashy

I dont see how that table makes any sense. The difference between "simple flightpath" and "advanced flightpath" cannot be larger than the amount of fuel wasted to get out Kerbin's SOI i.e. approximately 1 km/s...

#AmIWrong?

I agree though that KSP needs better tools for (finding optimal) transfers. I'd prefer a tool that makes it relatively easy to find/tweak rather than information of launch window/optimum angles.

[Random Tank]

Yeah, this technique does make it easier, but it will confuse people when they see the dV charts, as they are doing it a much less fuel efficient way... I never did that technique, my first IP transfer (to Eve, bite me for not going to Duna) I did from LKO... I just wish there was more information and tools in-game to help newbies to do this...

[merendel]

Interesting. Thanks for posting. It's a good (better) method, but requires setting up a lot of fragile maneuver nodes, and provides no easy way to time accelerate to this node (without switching back to tracking station).

Perhaps allowing you to control the reference body of your orbital trajectory would obviate the need to set up the first maneuver node (see above).

Only 1 more node than what you are discribeing in your OP and 2 of them are not ment to be burnt, only for determining timeing. Not sure I'd call them fragile nodes. I do admit timewarp is an issue unless you use a mod like kerbal alarm clock but the technique is somewhat redundant as that mod can calculate launch windows for you.

On your second point I think a quick and dirty solution would be alow us to set maneuver nodes for the planets in the tracking center. You obviously couldnt fly a node set for kerbin to reach jool for example but you could set the node on kerbins orbit and drag it till it would intercept jool and then timewarp from there till the window approaches and then switch to your ship to setup the actual manuver from there.

W

[arkie87]

I wound up putting together a Desmos graph a couple years ago about this.

https://s3.amazonaws.com/grapher/exports/014pcud2cb.png

This graph shows the difference in delta-V when departing Kerbin to various destinations. The x-axis is the sun-centered semi-major axis of your destination in millions of kilometers, and the y-axis displays required delta-v in km/s. v_lko [Green Curve] is the delta-V required to burn from a circular orbit around Kerbin at an altitude of 100km directly into an hohmann trajectory for the destination, and v_2step [Red Curve] is the delta-v required to burn from that same 100km orbit to just escape Kerbin, and once outside its SOI, burn to a hohmann trajectory. The various vertical lines mark the semimajor axis of several of the bodies orbiting the sun, with the blue vertical line being the orbit of Kerbin.

The original graph, with its formulae, is here: https://www.desmos.com/calculator/0gebxscf2t

For any of the worlds in the Kerbin system the two-step method of burn-to-escape-Kerbin-then-burn-to-transfer in solar orbit, is always a significant wastage of delta-V over burning from LKO, and that fraction tends to get larger, the further your destination is from Kerbin, the larger that fraction becomes. For the interplanetary transfer, you're spending about 80% extra when going for Eve or Duna, about 90% extra when going to Eeloo, and about 95% extra when going to Moho by using the two-step method.

How is that possible. To get from LKO to outside Kerbin SOI takes roughly 1 km/s. Even if all this energy is wasted, the difference between the two approaches shouldnt be more than 1 km/s?

That's like saying that it takes more energy to get from LKO to Jool than it does if you were in Kerbin's orbit around Kerbol, but on the opposite side of Kerbol (i.e. not in Kerbin's SOI)...

If im wrong, can someone explain why...

[Concentric]

Of course, if you really can't wait in LKO, there's always the Exley Maneuver. Burn your escape and make the resulting orbit eccentric to the point that it meets the target orbit's orbital height, correct inclination on the way out, then set a maneuver node at the meeting point. Using only prograde/retrograde (preferably bringing the orbit closer to the target orbit) and adding orbits, get an encounter nearby within a few orbits after the node. Unfortunately, there'll be a lot more timewarping in Kerbol orbit, but I believe the dV budget is closer to the Hohmann transfer than to the method outlined in the first post. If you bring the orbit close to the target orbit, you'll even be coming in with lower relative speed, which can be handy if you have low thrust, e.g. ion probe to Moho.

Edit: And I believe Hop has something to say about patched conics, v_inf and the effects on delta-v requirements.

Edited November 10, 2014 by Concentric

[arkie87]

Not sure I'd call them fragile nodes.

They are fragile in the sense that if you click the node, it will reset, at least according to 5thHorsemen. Regardless, i think everyone agrees a built in tool would be ideal.

[GoSlash27]

How is that possible. To get from LKO to outside Kerbin SOI takes roughly 1 km/s. Even if all this energy is wasted, the difference between the two approaches shouldnt be more than 1 km/s?

That's like saying that it takes more energy to get from LKO to Jool than it does if you were in Kerbin's orbit around Kerbol, but on the opposite side of Kerbol (i.e. not in Kerbin's SOI)...

If im wrong, can someone explain why...

It's because of the Oberth effect. Your engines make more useful energy when travelling at a high velocity than a low velocity, so they waste less DV on a transfer burn from low orbit than high orbit.

Counter- intuitive, but true. Rest assured, the graphs are correct.

Best,

-Slashy

Edited November 10, 2014 by GoSlash27

[arkie87]

Of course, if you really can't wait in LKO, there's always the Exley Maneuver. Burn your escape and make the resulting orbit eccentric to the point that it meets the target orbit's orbital height, correct inclination on the way out, then set a maneuver node at the meeting point. Using only prograde/retrograde (preferably bringing the orbit closer to the target orbit) and adding orbits, get an encounter nearby within a few orbits after the node. Unfortunately, there'll be a lot more timewarping in Kerbol orbit, but I believe the dV budget is closer to the Hohmann transfer than to the method outlined in the first post. If you bring the orbit close to the target orbit, you'll even be coming in with lower relative speed, which can be handy if you have low thrust, e.g. ion probe to Moho.

Yes, i think i discovered this one too, but sometimes deltaV requirement is very large if the angles do not work out. It's very useful if you are afraid of aerobreaking though :-P

[maltesh]

How is that possible. To get from LKO to outside Kerbin SOI takes roughly 1 km/s. Even if all this energy is wasted, the difference between the two approaches shouldnt be more than 1 km/s?

That's like saying that it takes more energy to get from LKO to Jool than it does if you were in Kerbin's orbit around Kerbol, but on the opposite side of Kerbol (i.e. not in Kerbin's SOI)...

If im wrong, can someone explain why...

Because delta-V isn't Specific Orbital Energy. Specific Orbital Energy is the sum of your per-unit-mass Kinetic Energy (proprotional to the /square/ of your velocity) and your per-unit-mass Gravitational Potential Energy. How much Specific Orbital Energy you get out of expending a quantity of delta-v depends on where and how you do it. And it's your specific orbital energy that determines exactly how fast you wind up moving at any point in your orbit.

And yes, if you just burn to just escape Kerbin, you wind up at rest (or almost at rest) relative to Kerbin as you cross the SOI. The more velocity you put on at LKO, the larger the fraction of that velocity you still have when you cross the SOI boundary. Which is why burning in LKO is so helpful, especially for distant destinations

[arkie87]

It's because of the Oberth effect. Your engines make more useful energy when travelling at a high velocity than a low velocity, so they waste less DV on a transfer burn from low orbit than high orbit.

Counter- intuitive, but true. Rest assured, the graphs are correct.

Best,

-Slashy

I understand what Oberth effect is. But i still maintain that these charts make no sense:

Consider a spacecraft in the same orbit as kerbin but on opposite side of Kerbol such that it isnt in Kerbin SOI. It would take X deltaV to get from there to Jool.

That value is roughly equivalent to the amount of deltaV required for a spaceship that just barely left Kerbin SOI to get to Jool (maybe larger, since eccentricity might be aiming the right direction so some of the deltaV wont be wasted).

Thus, the maximum wasted energy is the ~1 km/s wasted deltaV needed to just barely get out of Kerbin SOI. The oberth effect allows you to double count your transfer burn and Kerbin SOI burn...

Can anyone explain why this is wrong without a generic "oberth effect rah rah rah"?

[maltesh]

I understand what Oberth effect is. But i still maintain that these charts make no sense:

Consider a spacecraft in the same orbit as kerbin but on opposite side of Kerbol such that it isnt in Kerbin SOI. It would take X deltaV to get from there to Jool.

That value is roughly equivalent to the amount of deltaV required for a spaceship that just barely left Kerbin SOI to get to Jool (maybe larger, since eccentricity might be aiming the right direction so some of the deltaV wont be wasted).

Thus, the maximum wasted energy is the ~1 km/s wasted deltaV needed to just barely get out of Kerbin SOI. The oberth effect allows you to double count your transfer burn and Kerbin SOI burn...

Can anyone explain why this is wrong without a generic "oberth effect rah rah rah"?

Basically, you're confusing Delta-V and Specific Orbital Energy. They're not the same thing, nor do they scale linearly with each other.

But honestly, if you don't want to go through the equations of it, you've presumably got access to Kerbal Space Program. You can pop a spacecraft into LKO, and put some maneuver nodes down, and take the measurements yourself.