To Hofmann or bi-elliptical.

[Chocki]

I was reading up on diffrent orbital maneuvers when I saw bi- elliptical. Basically, it is rasing your Ap to a point higher then your target orbit at Pe. Then burning at new Ap to raise Pe to target orbit, and then burning (retrograde) to lower your Ap to target orbit. At times, this is more efficient then a direct Hofmann transfer (when the ratio of final semi major axis to initial semi major axis is 11.94 or greater according to wiki). The reason it is more efficient is because of the Oberth effect (rockets function better the faster they are moving).

So, I wanted to apply this to some basic things in game. Like setting an orbit close to the mun for escape or mun encounter. According to wiki Mun has a semi major axis (SMA from now on) of 12,000,000. Assuming an initial parking orbit of 85,000 after launch the ratio would be (11,000,000 / 85,000) 129.41. Meaning, that a bi-elliptical orbit change would be better (save delta v) assuming you don't go crazy with your first Ap change burn.

After some more napkin math. Int SMA / Fin SMA > 11.94 flop the equation around to Int SMA /11.94 > Fin SMA should give us the change in altitude for when bi- elliptical can possibly become more efficient. Starting from an initial orbit of 85,000, calculates to 7118.92. Again, assuming you don't go crazy with that first Ap kick. In my example, I would guess a 12,000,000 Ap would be fine.

Now, I am no math, or orbital flight master. I would still need to figure out what a Hoffmann transfer would cost, then figure out the total cost of the bi- elliptical (3 burns) then compare.

I want to assume that my math for when bi- elliptical can possibly become better then Hoffmann is incorrect. 7119m just seems so small, but delta v isn't figured. Is my math or theory on this incorrect? I still haven't been able to do delta v calculations (not sure of the formula or its factors, and I'm sure mass will be a major portion which I currently don't have access to realistic test numbers). But please, pick it apart.

[RoboRay]

It's Hohmann, by the way.

Somebody did the math a couple of months ago, and there's no destination from Kerbin that is more efficient to use a bi-elliptic transfer to reach. The forum-monster ate that thread, unfortunately, and I don't remember the specifics of the work.

Edited May 8, 2013 by RoboRay

[Tw1]

Btw, It's hohman.

I wouldn't use a bi-elliptical transfer to get to Mun, as it's simpler just to do a holman like transfer orbit, then burn retro to do a capture. But I've found it can save some delta v when slowing down from a hyperbolic orbit, by leaving it really eccentric, then acting like it's a bi-elliptical.

Only useful when delta v is really tight.

Or, if you're changing inclination, this can be cheaper.

Edit: RoboRay beat me to it. I believe the term is being ninja'd?

Edited May 8, 2013 by Tw1

[Spatzimaus]

A bi-elliptic (not bi-elliptical) transfer is more efficient in those few situations where the SMA ratio is very large, as you noted. The problem is, how often does that happen? The only SOI that isn't extremely limited in size is the sun's, and since you'll be starting at Kerbin there's nothing more than 12 times its distance to go to. If you're going from LKO to, say, Minmus, then maybe you could do a bi-elliptic to get there with less energy, but the bi-elliptic requires a burn at a point outside the orbit of the thing you want to intersect, and you can't go far beyond Minmus before leaving Kerbin's sphere of influence (at which point its gravitational pull becomes zero, meaning a bi-elliptic wouldn't work at all). A burn to Mun is a bit more manageable, but you'd still be pretty limited in where you placed your outer burn.

And your math is wrong. Semi-major axis is a RADIUS, not an ALTITUDE. There's no "85km SMA" orbit around Kerbin, because the planet's radius is 600km; the orbit you refer to has an SMA of 685km. If you're trying to get to Mun (SMA 12000km), you see that it's less than an 18:1 ratio, so you're not far above the break-even point of the bi-elliptic.

The other problem is that a bi-elliptic is just not as easy to do in KSP, because of timing. A Hohmann (not Hoffmann, not Hofmann) transfer has the big advantage that you can initiate it at any point on your circular orbit and immediately see whether you'll intersect your target. So if the timing isn't right for your transfer, just hit time acceleration until you're a bit further around the orbit. I've had times where I went five or six orbits before the transfer lined up correctly. But with KSP, that sort of acceleration takes little effort, so it's not a problem. A bi-elliptic transfer has a severe timing limitation; you're not circularizing at the outer orbit, so you have to immediately thrust at apogee and hope that the new perigee intersects the object you want. Chances are it won't, which means you'd need to rotate or expand the first burn, which means adjusting the second burn again. Lather, rinse, repeat.

And in most cases, the amount of delta-V you save is small, on the order of a few percent. This isn't usually worth the headaches, because in KSP we can't design things precisely enough. In the real world you can make a design have JUST enough fuel to get to its destination, so it really helps to save a little bit, but in KSP we've only got a small assortment of fuel tank sizes and we can't be as precise on our steering, so we'll generally overbuild. Heck, on my first Minmus landing, I had enough spare fuel to land on Mun on the way back, because the design I was using was intended to go to Duna; doing a more complex orbital insertion just wouldn't have made much of a difference.

[SmallChange]

BTW, It's Hurfman.

[iRommel]

the hoffman maneuver is an attempt to has more cheeseburgers.

[itsme86]

I looked it up, it's Hulkman.

[ComradeGoat]

Bi-elliptic is something I only ever use when I want to make a massive orbital plane change. Beyond that, there doesn't seem much use in the game.

[Chocki]

You guys are worse then reddit. Hohmann is autocorrected to Hofmann on my phone, deal with it. Bi-elliptic isn't considered a word according to old Android systems.

I figured that converting to KSP measurements and physics would kill any benefit gained. So, in reality (game wise) any type of bi-ellpictic transfer just isn't woth it, either by timing or the small savings in delta v.

[lazarus1024]

Exactly, it is pretty much just useful for large plane changes. Otherwise wayyyyy to fiddly to use and rare instances it saves much in the way of dV for the effort.

For plane changes it can save a huge amount of dV though, especially if you were already in an eliptical orbit to begin with. Two good uses for it then are when you want to initally map a planet or moon, especially if it has a low rate of rotation. Then when you enter the SOI you just make sure you leave a high AP when deccelerating for capture. Then change plane at the AP point for fun and profit. Map away.

[allmappedout]

Pretty sure it's He-man....You save Delta-V by the power of greyskull.

[maltesh]

Quick Desmos Graph showing the difference in delta-V when transferring from a circular orbit around the sun to a circular orbit destination using a Hohmann Transfer (Green Curve) and an infinite-distance bi-elliptic transfer (Orange curve). Vertical lines and bands show the semimajor axes of the various worlds in the Kerbin system, as well as the periapsis and apoapsis ranges for worlds whose orbital eccentricities > 0.1

Click the image to visit the Desmos Graph. Horizonta axis is in millions of kilometers of distance from the center of the sun, vertical axis is km/s of delta-V.

As the graph shows, given the above simplifying assumptions, the bi-elliptic beats the Hohmann if your circular-orbit destination has a radius of less than about 1.14 million kilometers, or greater than about 163 million kilometers.

[RoboRay]

You guys are worse then reddit. Hohmann is autocorrected to Hofmann on my phone, deal with it. Bi-elliptic isn't considered a word according to old Android systems.

You were politely corrected. Bitching at the people who are helping you only hurts you in the long-run.

Good luck, from now on.

[Spatzimaus]

You were politely corrected. Bitching at the people who are helping you only hurts you in the long-run.

That, and the complaining about the corrections just made it worse. Calling it a Hofmann transfer might not be correct, but you can explain that you couldn't remember the exact name and just got it wrong. We've all done that from time to time, given how esoteric a lot of the discussions can get. But blaming Android's vocabulary and auto-correct is a different story; if it was constantly changing the name to something you KNEW to be wrong, then you should have turned off the auto-correct before posting. Standard dictionaries simply aren't good for technical discussions, which tend to be loaded with proper names, and "bi-elliptic" is a word no matter what Android tells you (and "bi-elliptical" is not).

But yeah, if you're going to complain when people correct the mistakes you made repeatedly, you're not going to get much help on these boards. People here tend to be very precise with their feedback, when they're not just posting cool looking screenshots.

[Chocki]

I wasn't bitching about the actual responses. The repeated correction of an already pointed out spelling error, no matter the possible cause is what I was referring to. The responses I got that where more then "I think it's xxx" I am very greatful for, espically maltesh's.

[Wavelength]

BTW, It's Hurfman.

Im totally gonna name one of my kerbals that. :3

[numerobis]

A bielliptic transfer from LKO to Mun is just barely a savings, but it is a savings. Packled's min deltaV challenge proved that much.

[magnemoe]

Bi-elliptic is something I only ever use when I want to make a massive orbital plane change. Beyond that, there doesn't seem much use in the game.

Yes, typical use is like then I landed on Moho north pole while the mothership was in equator orbit. Raise AP high where your orbit intercept, burn to align them and burn to circulate at PE, a bit more complicated as I wanted to match up with the mothership

[PakledHostage]

A bielliptic transfer from LKO to Mun is just barely a savings, but it is a savings. Packled's min deltaV challenge proved that much.

Stochasty's method also involved Munar gravitational assist to minimise delta-V required to reach the Mun from LKO. Too bad that and so many other good threads were lost...

[Iansoreta]

Bi-elliptic is something I only ever use when I want to make a massive orbital plane change. Beyond that, there doesn't seem much use in the game.

For me, it's more different for me than yours. I already knew Bi-elliptic Transfer, but I haven't use it yet since I keep changing the versions of KSP. I heard that it is more fuel efficient if I use that type of maneuver. Let us thumbs up if we persuade ourselves to do it for the first time.

[Nao]

http://forum.kerbalspaceprogram.com/showthread.php/4374-KSP-Orbit-Mechanic-1-2a-Optimize-Your-Orbits

^ This might be of help here, there are several charts that show the braking points for Hurfmann to bi-elliptic transfer, as well as possibility to calculate the difference of the two methods in KSP environment.

It's interesting how difference between the two methods can be quite small, especially when counting aerocaptures. It's possible to save a lot of time with minimal fuel cost doing bi-elliptical transfer instead waiting for proper launch windows.

It's a real shame it's a discontinued project , i still use it from time to time to plan more complicated missions.