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# What causes the tiny inefficiency across a porkchop transfer map?

## Question

You can see that there's an efficient transfer but in the middle of it is a little sliver of inefficient transfer. I'm just rather curious what actually is causing that?

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Posted (edited)

You will see this anytime the initial body and final body are not 100% coplanar. It's due to a couple things.

1. The porkchop plot assumes a single ejection burn, and a single capture burn, with no corrections.
2. A perfect Hohmann transfer involves you reaching the target body at 180 around the sun from where you left.
3. AN and DN will always be 180 degrees apart from each other.

Thus, if you did not leave exactly at the AN/DN with the target planet, directly hitting the target planet exactly 180 degrees around your orbit involves making the departure point one of the AN/DN.  This requires an extreme normal/antinormal burn to do, essentially rotating your orbit 90 degrees

Alternately, you just burn prograde to eject, and then do a small correction burn at the AN/DN.  It's just that the chart can't capture this, due to the lack of considering correction burns.

Edited by Lt_Duckweed
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On 8/21/2022 at 4:57 PM, Frostiken said:

You can see that there's an efficient transfer but in the middle of it is a little sliver of inefficient transfer. I'm just rather curious what actually is causing that?

@Lt_Duckweed has the right idea.  I will offer one correction and say that the best place to make the mid-course correction is not at the node, since the node being in the wrong place is the root of the problem, but I'll get to that.  If you take a look at the Alex Moon launch planner, just using the default Kerbin-Duna ballistic transfer, you'll see a sliver of inefficiency cutting across the plot.  Switch the transfer type to 'Mid-Course Plane Change', and you'll see that the inefficiency goes away.

When two orbits are not coplanar (which is the case for most orbits, even in KSP), then the mathematical solution for their intersection is a line, called the line of nodes, that joins the ascending and descending nodes.  If you depart your origin at that node, then you can move efficiently in your original orbital plane and encounter your target, because when you reach it, the target will also be in your original orbital plane; you'll end up in an inclined orbit about the target, but you'll at least encounter it.  If you depart from somewhere that isn't the node, then you need an orbital solution that will intercept the target.  For intercepts that are relatively close to the nodes, you can get the encounter with only a slight amount of inclination, but anything that is more than a few degrees of true anomaly away will require a transfer that is a polar orbit of the sun--at least if you want to get the encounter with a single transfer burn.

Adding a mid-course correction provides a much cheaper solution, because the midpoint of the transfer is an efficient point to change your node relative to the target.  The cheapest place to change the node is as far away from the node as possible.  For a (nearly) Hohmann transfer, that's at only one point (since you generally only use half of the Hohmann orbit), so the solution isn't difficult to calculate.  However, some porkchop plotters don't bother with that solution because, for one thing, the solution that doesn't involve mid-course corrections is usually going to be cheaper anyway, and for another, if you're advanced enough in KSP to use a porkchop plot, then you're probably advanced enough to know about mid-course corrections, too.

If you want to see more evidence of this effect, then you can play with the Alex Moon planner and try transfers between destinations with high relative inclinations, such as Kerbin-Eeloo and Kerbin-Dres (or, for an extreme and dramatic example of this, try Dres-Eeloo).  Look at the ballistic (single-burn) transfer, and then re-plot using the same general settings but with a mid-course correction.

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depends. that plot is for what transfer?

I've seen a lot such artifacts fro transfers to dres and eeloo, so I guess it has to do with inclination and eccentricity. but aside from that, I really have no idea.

do notice it is mostly a mathematical artifact. you can make a transfer in that line of inefficiency, at the cost maybe of a small correction manuever. but that plot does not account for that.

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Okay thanks everyone for the responses. I'm not sure I totally get it though, but that porkchop planner did help by illustrating more extreme examples. Basically, that sliver is where it wants to do a polar dive over the sun, because of the inclination difference? I kind of feel like I need an MS Paint illustration of why this is the problem, and why for that very magical sliver of transit, a standard transfer is impossible...

So if Mechjeb can't account for mid-course plane changes, what can? Should you just use the standard Mechjeb transfer planner, or is there something better? If you're using the Mechjeb system is it actually less efficient than it ever could be with mid-course correction? And what's the best point for correction?

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On 8/29/2022 at 8:37 PM, Frostiken said:

I kind of feel like I need an MS Paint illustration of why this is the problem, and why for that very magical sliver of transit, a standard transfer is impossible...

That's not quite it.  The transfer isn't impossible; it's just extremely inefficient to use a one-burn transfer when you're on that sliver.

Part of the issue is that there's no single solution to the problem of how to get from your origin to your destination.  There are literally infinite paths to take.  The porkchop plot exists as a tool to help you choose from a group of solutions that offer some value or benefit over other possible choices, but it's important to remember that choices in that range  are all trade-offs of one another.  One set of solutions covers fast transfers, which take less time in transit.  Another might cover immediate transfers, which let you leave right away.  Another set covers efficient transfers in terms of delta-V expended.  There are valid use cases for all of these:  a fast transfer may be the best option when you have a life support mod to consider.  An immediate transfer may be needed for a rescue mission.  An efficient transfer is good for when you have limited delta-V or want to save it for some other part of the mission.

However, when setting up the plot, there are still a few assumptions that the planner has to make.  One of them is whether you want a ballistic transfer (that is, one burn at the beginning that gets the encounter), but sometimes that's not the best one in terms of your delta-V budget.  Sometimes, a mid-course correction is cheaper, for the same reason that sometimes, it makes more sense to raise your apoapsis before making a drastic inclination change.

Generally, the best place to do that is as far from the line of nodes as you can get on that leg of the orbit--i.e., the mid-course correction--but if we've already established that this is a ballistic, or single-burn transfer, then that's not an option.  The only burn that you can use to make the encounter is the initial interplanetary ejection burn.

In most cases, you can add a bit of inclination (and possibly a bit of radial, too) to get a satisfactory encounter, but in extreme cases, the only solution to encounter a planet that will be a few billion kilometres to your origin plane's celestial north when you get there is one that arrives from the celestial north itself.  This doesn't necessarily mean a totally polar orbit, but a burn that has you ejecting at 30° inclination when you don't need to do so is going to be inefficient no matter how you arrange it.

On 8/29/2022 at 8:37 PM, Frostiken said:

So if Mechjeb can't account for mid-course plane changes, what can? Should you just use the standard Mechjeb transfer planner, or is there something better? If you're using the Mechjeb system is it actually less efficient than it ever could be with mid-course correction? And what's the best point for correction?

Well, you can, to begin.  If you want the very best in terms of efficiency, then I'd suggest using a transfer calculator (e.g. the Alex Moon planner or the mod that incorporates it into the game) and using the information from it to set up the burn.  But that's not strictly necessary; you can get very good corrections on your own.  The best place for a mid-course correction is a point 90° of true anomaly away from your encounter with the destination--or, rather, I should say from the point where you would like to encounter your destination, since you won't encounter it without the correction.

I should also point out that the ballistic transfer is sometimes the better choice.  MechJeb's advanced transfer calculator is very good.  It automatically offers the best available ballistic choice, and that is usually negligibly different from the one with a course correction.   Let's not forget that that sliver of inefficiency doesn't matter much unless the transfer that you want falls on it.  If--if--it does, then sometimes, you're close enough in inclination that a mid-course correction is more expensive than simply working with the inclination difference ... or, of course, picking a different transfer.  The option that works best also depends a lot on your mission:  even when the delta-V difference is slight, different trajectory choices will affect your orbital insertion when you arrive at your destination, and possibly cost you more in terms of local manoeuvres if you're looking for a specific inclination on arrival.  An example of where this is relevant would be when you're transferring to Jool:  arriving in an inclined orbit over Jool in itself doesn't mean much, but if you want to visit the moons, then you'll probably want to arrive with an inclination close to matching theirs.  Of course, changing your arrival characteristics so that you get favourable encounters requires a mid-course correction anyway, so you may be stuck with that.

If you want to try your hand at figuring this for yourself, then I strongly recommend perusing Rocket and Space Technology and getting a feel for some of the mathematical relationships involved here.  The link will send you partway down the page; there's a subsection titled Non-coplanar Trajectories that touches on some of your questions.  Also, it has diagrams!

Good luck, and should you have any further questions, please don't hesitate to ask.

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20 hours ago, Zhetaan said:

That's not quite it.  The transfer isn't impossible; it's just extremely inefficient to use a one-burn transfer when you're on that sliver.

Part of the issue is that there's no single solution to the problem of how to get from your origin to your destination.  There are literally infinite paths to take.  The porkchop plot exists as a tool to help you choose from a group of solutions that offer some value or benefit over other possible choices, but it's important to remember that choices in that range  are all trade-offs of one another.  One set of solutions covers fast transfers, which take less time in transit.  Another might cover immediate transfers, which let you leave right away.  Another set covers efficient transfers in terms of delta-V expended.  There are valid use cases for all of these:  a fast transfer may be the best option when you have a life support mod to consider.  An immediate transfer may be needed for a rescue mission.  An efficient transfer is good for when you have limited delta-V or want to save it for some other part of the mission.

However, when setting up the plot, there are still a few assumptions that the planner has to make.  One of them is whether you want a ballistic transfer (that is, one burn at the beginning that gets the encounter), but sometimes that's not the best one in terms of your delta-V budget.  Sometimes, a mid-course correction is cheaper, for the same reason that sometimes, it makes more sense to raise your apoapsis before making a drastic inclination change.

Generally, the best place to do that is as far from the line of nodes as you can get on that leg of the orbit--i.e., the mid-course correction--but if we've already established that this is a ballistic, or single-burn transfer, then that's not an option.  The only burn that you can use to make the encounter is the initial interplanetary ejection burn.

In most cases, you can add a bit of inclination (and possibly a bit of radial, too) to get a satisfactory encounter, but in extreme cases, the only solution to encounter a planet that will be a few billion kilometres to your origin plane's celestial north when you get there is one that arrives from the celestial north itself.  This doesn't necessarily mean a totally polar orbit, but a burn that has you ejecting at 30° inclination when you don't need to do so is going to be inefficient no matter how you arrange it.

Well, you can, to begin.  If you want the very best in terms of efficiency, then I'd suggest using a transfer calculator (e.g. the Alex Moon planner or the mod that incorporates it into the game) and using the information from it to set up the burn.  But that's not strictly necessary; you can get very good corrections on your own.  The best place for a mid-course correction is a point 90° of true anomaly away from your encounter with the destination--or, rather, I should say from the point where you would like to encounter your destination, since you won't encounter it without the correction.

I should also point out that the ballistic transfer is sometimes the better choice.  MechJeb's advanced transfer calculator is very good.  It automatically offers the best available ballistic choice, and that is usually negligibly different from the one with a course correction.   Let's not forget that that sliver of inefficiency doesn't matter much unless the transfer that you want falls on it.  If--if--it does, then sometimes, you're close enough in inclination that a mid-course correction is more expensive than simply working with the inclination difference ... or, of course, picking a different transfer.  The option that works best also depends a lot on your mission:  even when the delta-V difference is slight, different trajectory choices will affect your orbital insertion when you arrive at your destination, and possibly cost you more in terms of local manoeuvres if you're looking for a specific inclination on arrival.  An example of where this is relevant would be when you're transferring to Jool:  arriving in an inclined orbit over Jool in itself doesn't mean much, but if you want to visit the moons, then you'll probably want to arrive with an inclination close to matching theirs.  Of course, changing your arrival characteristics so that you get favourable encounters requires a mid-course correction anyway, so you may be stuck with that.

If you want to try your hand at figuring this for yourself, then I strongly recommend perusing Rocket and Space Technology and getting a feel for some of the mathematical relationships involved here.  The link will send you partway down the page; there's a subsection titled Non-coplanar Trajectories that touches on some of your questions.  Also, it has diagrams!

Good luck, and should you have any further questions, please don't hesitate to ask.

Son of a B, that's brilliant, that actually made everything make sense.

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