Polar Orbits -- why does a larger orbit = less fuel needed?

[JoeSchmuckatelli]

Waaaay back when I ran across a tutorial / wiki page that explained why shifting from an equilateral to polar orbit was best done with a larger orbit.  I've been searching in vain for that information since returning to KSP.

 

Best I've come up with is this:  https://wiki.kerbalspaceprogram.com/wiki/Tutorial:_Advanced_Orbiting  -- and it confirms that a larger orbit is easier to 'turn' than a lower one... but why?

Trying to wrap my Covid-Isolated brain around this... thanks for any help!

[Superfluous J]

When you're higher up (and especially when you're at the top of an elliptical orbit) you are moving slower.

To turn your orbit, you need to basically come to a complete stop, and then do that same burn at a 90 degree angle. Actually it's 2 of that (not 2 funds, I'm using that as a square root symbol) because you can do it all in one burn and cut the diagonal. In total, it costs about 1.4 times your orbital speed to shift your direction 90 degrees.

If you're in LKO, you're going 2300 or so m/s so it would cost you about 3250 m/s to turn your orbit 90 degrees.

If you're up at the height of an ellipse well past Minmus' orbit, you may only be going 10-20m/s, so your turn will only cost 15-30m/s or so to turn.

It costs about 950m/s to get that elliptical orbit, and 950m/s to go back down, so instead of burning 3250m/s to shift your orbit 90 degrees you "only" have to burn 950+30+950=1930m/s. That's a savings of 1320m/s.

[JoeSchmuckatelli]

2 hours ago, Superfluous J said:

When you're higher up (and especially when you're at the top of an elliptical orbit) you are moving slower.

To turn your orbit, you need to basically come to a complete stop, and then do that same burn at a 90 degree angle. Actually it's 2 of that (not 2 funds, I'm using that as a square root symbol) because you can do it all in one burn and cut the diagonal. In total, it costs about 1.4 times your orbital speed to shift your direction 90 degrees.

If you're in LKO, you're going 2300 or so m/s so it would cost you about 3250 m/s to turn your orbit 90 degrees.

If you're up at the height of an ellipse well past Minmus' orbit, you may only be going 10-20m/s, so your turn will only cost 15-30m/s or so to turn.

It costs about 950m/s to get that elliptical orbit, and 950m/s to go back down, so instead of burning 3250m/s to shift your orbit 90 degrees you "only" have to burn 950+30+950=1930m/s. That's a savings of 1320m/s.

This is one of those "to go faster, you need to slow down" brain twisters... but now that you describe basically stopping and starting a whole new orbit - eyes widening!

 

…man have I wasted liquid propellant!

[Superfluous J]

By the way, if you launch north instead of east from the launchpad it only costs about 250 more m/s to do the gravity turn to orbit. THAT is the best way to go polar.

[AHHans]

9 hours ago, JoeSchmuckatelli said:

This is one of those "to go faster, you need to slow down" brain twisters... but now that you describe basically stopping and starting a whole new orbit - eyes widening!

Well, to quote Randall Munroe (with pictures linked from his site):

Space isn't like this:

It is like this:

And once you got going it's hard to change direction.

9 hours ago, JoeSchmuckatelli said:

…man have I wasted liquid propellant!

Welcome to the club! I believe most of us have at some point.

[JoeSchmuckatelli]

PLoS One for the Randal Munroe citation!

EDIT: @Superfluous J  -- I'm trying to do a polar survey of the Mun 'on the cheap'... I had a previous mission where I launched a lander & scanner combo... but arrived with only enough gas to land.  So the survey orbiter got dumped into an equatorial orbit.  Now I'm sending a small probe with small gas can attached to try to remedy the situation.

Only... just now, I realized that I probably could have done both if I had only known how to do a polar burn correctly!

 

Oh... and a "Refinement Question" -- I noticed that when I start my burns (or plan them) that my perapsis goes way out - including flipping to the apoapsis.  Should I try to compensate for that using a retrograde burn?  Or just accept it, finalize the burn at the new apoapsis and then drop back into the target altitude / distance?  Messing around trying to keep perapsis at a given level works, but significantly increases burn time... is that, then a 'wash' or a 'waste'?

 

Edited May 16, 2020 by JoeSchmuckatelli

[AHHans]

1 hour ago, JoeSchmuckatelli said:

Oh... and a "Refinement Question" -- I noticed that when I start my burns (or plan them) that my perapsis goes way out - including flipping to the apoapsis.

You mean when you plan - i.e. set up a maneuver node - a plane-change burn? Or when you try to do a plane change by locking to radial in/out and firing the engine? Yes, that's part of the "come to a  stop" part of a plane change maneuver.

Think about it. When you e.g. want to do a plane change by 90 deg (and could do it all in one short burst of dV), how fast would you keep going in your original direction?

1 hour ago, JoeSchmuckatelli said:

Messing around trying to keep perapsis at a given level works, but significantly increases burn time... is that, then a 'wash' or a 'waste'?

What exactly do you mean with the "messing around" part? In general -a @Superfluous J already wrote - it is more efficient to combine two burns in different directions into one combined burn.

[JoeSchmuckatelli]

OMG I totally missed that - he did say "cut the diagonal" 

Rueful chuckle 

 

Thanks

[Klapaucius]

21 hours ago, Superfluous J said:

By the way, if you launch north instead of east from the launchpad it only costs about 250 more m/s to do the gravity turn to orbit. THAT is the best way to go polar.

Added to that, if you have the DLC and launch into polar orbit from Woomerang, you will get a little savings in not having to overcome so much of the orbital velocity of Kerbin (not to mention you start out at a higher altitude)--though I have no idea if those savings add up to much.

EDIT: Just reread your later posts. It is quite easy to just enter directly into a polar orbit around the Mun rather than changing when you get there.  Simply set up your encounter such that you are bit above (or below) the orbital plane when you arrive.  I do this all the time (mostly unintentionally because I was sloppy on launch and my nodes are a bit off, but the point is you can do it )

Edited May 17, 2020 by Klapaucius

[archiebald]

A long time ago, for reasons of newbiness I ended up putting my new shiny Mun station into a retrograde orbit and realized it would cost a huge fuel bill to turn prograde so for  awhile I left it as it was.  I then found a nice article on simple orbital mechanics and plane changes which made me realize the solution was simply to raise my apoapsis as high as possible, burn prograde (very little d/v required), then circularize back at periapsis.

I can't remember the figures now but it was about 1/3 of what a direct turnabout would have cost.  Also a fun learning exercise.

[AHHans]

6 hours ago, archiebald said:

A long time ago, for reasons of newbiness ...

Well, for me it wasn't a station, but a contract satellite that I put into orbit the wrong way around. And I did "waste" the fuel by burning radial for a looong time. ("Wasting" because I wasn't going to do anything else with that fuel anyhow.)

[JoeSchmuckatelli]

13 hours ago, archiebald said:

A long time ago, for reasons of newbiness I ended up putting my new shiny Mun station into a retrograde orbit and realized it would cost a huge fuel bill to turn prograde so for  awhile I left it as it was.  I then found a nice article on simple orbital mechanics and plane changes which made me realize the solution was simply to raise my apoapsis as high as possible, burn prograde (very little d/v required), then circularize back at periapsis.

I can't remember the figures now but it was about 1/3 of what a direct turnabout would have cost.  Also a fun learning exercise.

This game, more than any other, makes me laugh, ruefully, at myself quite frequently.  Years ago, I was really good at (or rather understood) how to do efficient burns.  Coming back to the game, I find I've forgotten soooo much - and have to keep relearning it.

Case in point: the 'Cut the corner' thing**

I used to pride myself on 'sippy' gravity turn launches - where you just lean the rocket over and let gravity help you get to orbit efficiently -- leaving you with plenty of fuel for the destination burns.  Instead of remembering how to do that, in my current career I've been guilty of the whole "Launch straight up, turn 90" thing more often than not.  … well, perhaps not so much on my launches - but they've certainly been less efficient than they should / could be!

It's my landings that I've been 'knuckle-dragging-Neanderthal-style' flying.  Suicide burns because I've gotten lazy at the terminal end / forgotten how to do them correctly.  And everywhere I look, whether its shifting orbits or landing or whatever, there's a more efficient way of doing things that I've either forgotten or never learned.

Frankly, this is one of the reasons I'm having so much fun with KSP atm.  Being cooped up with my Quaran-Teens, I'm having to relearn how to play KSP almost from scratch.  Thankfully, there's a good community of folks willing to answer questions that have been asked and asked and asked!

 

 

**@Superfluous J reminded me of this above (and @AHHans reminded me that I was reminded about it after I blatantly missed it the first reading - thanks again!).