Minimal Hohmann Transfer versus maximum Oberth Effect - What requires less delta-v?

[Fearless Son]

So traditionally when I do a Hohmann Transfer, I typically plan my maneuver to require the most minimum amount of delta-v possible to reach the sphere of influence of the other body. Say I was going from the low orbit of an inner body to one of its moons, I would circle the orbit searching for the spot where I can have the smallest prograde burn and still have an encounter with the other body.

But lately, I have been wondering, am I being penny-wise and pound-foolish with my delta-v? I was thinking that since the Oberth Effect means I get more "bang for my buck" at lower periapsis, would it be a better savings in overall delta-v to spend a little more accelerating to a closer approach, so that I could spend a lot less delta-v making my capture burn? Plan my Hohmann Transfer to take me as close to the outer body as I can get away with, then burn just above the other surface or atmosphere to achieve capture.

Edited August 16, 2015 by Fearless Son

[Mastikator]

Spending 5-10m/s dv to get a significantly closer approach could easily save you ~50-800m/s dv (depending on where you go etc) on capture. It usually easiest to do a mid-way adjustment, relatively cheap and you still have a lot of control.

Just be wary of going into atmospheres or crashing into mountains. Get as close as possible but not closer

[GoSlash27]

So traditionally when I do a Hohmann Transfer, I typically plan my maneuver to require the most minimum amount of delta-v possible to reach the sphere of influence of the other body. Say I was going from the low orbit of an inner body to one of its moons, I would circle the orbit searching for the spot where I can have the smallest prograde burn and still have an encounter with the other body.

But lately, I have been wondering, am I being penny-wise and pound-foolish with my delta-v? I was thinking that since the Oberth Effect means I get more "bang for my buck" at lower periapsis, would it be a better savings in overall delta-v to spend a little more accelerating to a closer approach, so that I could spend a lot less delta-v making my capture burn? Plan my Hohmann Transfer to take me as close to the outer body as I can get away with, then burn just above the other surface or atmosphere to achieve capture.

I can't say absolutely that the second approach is cheaper in all cases, but it's certainly the way I do it. I transfer directly to orbital height (or below if aerocapturing).

Best,

-Slashy

[Alshain]

I go for my target Periapsis as far away as I can manage. It's really easy for the Mun and Minmus, for those I burn in orbit of Kerbin and then don't usually burn again till it's time to capture.

The process is a little harder for other planets due to the difficulty in working with maneuver nodes at that great a distance, I usually make a small course correction once I get out into interplanetary space. However, even then it's a pretty great distance.

Another good practice is to put your periapsis in the middle of the moon on the maneuver node and then add a little radial burn to bring it back out. This will give you a little deeper arc and result in an even smaller capture burn. Generally speaking, you will save Delta V by burning more around Kerbin, than you do around your target.

- - - Updated - - -

By the way, increasing your prograde to find an intercept is not always the answer. Move the entire maneuver node around in your orbit, you can often get a lower periapsis with the same amount of fuel simply by starting your burn earlier or later.

Here is a step-by-step

1. Establish a parking orbit (assuming you don't want to bother with a direct burn from the ground, which is cheaper but harder).

2. Create a maneuver node and drag prograge till Ap just barely touches the Mun's orbit.

3. Grab the white circle and move the maneuver around in your orbit till you find an intercept.

4. Continue playing with the position of the maneuver till you get the Pe just inside the planet's surface. Adjust prograde/retrograde if you have to, but do it sparingly.

5. Pull on the Radial marker to bring the Pe up and out of the Mun.

If you do this right, your trajectory should look more like a "U" than a wide "V". Alternatively you can move the maneuver to get your target Pe and adjust it using Prograde/Retrograde but that will result in the "wide V" appearance and it will use more fuel for both the burn and the capture burn. (Radial burns are almost free if coupled with another maneuver)

Edited August 16, 2015 by Alshain

[Pecan]

i) The further from the target you can make adjustments, the better.

ii) The closer you approach a body the stronger its gravity will affect you.

iii) Hitting mountains is a 'bad thing' (unless they've been really naughty and deserve it)

So right from the start, aim for as low a Pe around the target as you can cope with without screaming.

This maximises the amount your flight-path will be deflected by the body and Oberth.

At Pe burn to lower your Ap to the comfortable altitude you actually want to settle into.

At Ap, circularise.

[Laie]

So right from the start, aim for as low a Pe around the target as you can cope with without screaming.[...]

At Pe burn to lower your Ap to the comfortable altitude you actually want to settle into.

At Ap, circularise.

(Buzz Sound) Wrong!

Someone, someday, explained that one should best brake at the altitude one wants to settle into. Said person claims to have done the maths... my limited experience with scansat probes confirms it: One should aim for the altitude where one wants to circularize. Do not brake at low PE then raise it.

That's somewhat academical as usually one wants to land. Triply so because other factors may also go into the equation, like having to adjust inclination at some point. So for myself, I have slightly adjusted that rule to "try to put the periapsis where you will need it later". Not lower, not higher, just there.

[Empiro]

(Buzz Sound) Wrong!

Someone, someday, explained that one should best brake at the altitude one wants to settle into. Said person claims to have done the maths... my limited experience with scansat probes confirms it: One should aim for the altitude where one wants to circularize. Do not brake at low PE then raise it.

That's somewhat academical as usually one wants to land. Triply so because other factors may also go into the equation, like having to adjust inclination at some point. So for myself, I have slightly adjusted that rule to "try to put the periapsis where you will need it later". Not lower, not higher, just there.

It actually depends on the altitude you want to settle at, your velocity when entering the SOI, and also the size of the body you're orbiting. If the desired orbit reasonably close to the body, you're entering fairly slowly, or if the body is small, then it's best to go directly to the desired altitude. Otherwise, you'll want to get as close as possible, get your AP to the desired altitude, and then circularize at AP.

For example, if you're in orbit at Minmus altitude around Kerbin, and you want to go to Jool, it's best to burn retrograde, lower your PE close to Kerbin, and then burn to Jool at PE, rather than burning directly to Jool. The reverse is also true: if you're coming from Jool and want to get to orbit at Minmus altitude (and you're not aerobraking), it's best to get close to Kerbin, lower your AP to Minmus altitude, and then circularize.

[GoSlash27]

It actually depends on the altitude you want to settle at, your velocity when entering the SOI, and also the size of the body you're orbiting. If the desired orbit reasonably close to the body, you're entering fairly slowly, or if the body is small, then it's best to go directly to the desired altitude. Otherwise, you'll want to get as close as possible, get your AP to the desired altitude, and then circularize at AP.

For example, if you're in orbit at Minmus altitude around Kerbin, and you want to go to Jool, it's best to burn retrograde, lower your PE close to Kerbin, and then burn to Jool at PE, rather than burning directly to Jool. The reverse is also true: if you're coming from Jool and want to get to orbit at Minmus altitude (and you're not aerobraking), it's best to get close to Kerbin, lower your AP to Minmus altitude, and then circularize.

^ This is my understanding as well. Think of it as a reverse bi-elliptic transfer.

In some cases you can save a few m/sec by intentionally undershooting and then circularizing at Ap. I personally don't bother doing it that way because the small savings (if any) generally aren't worth the hassle.

Best,

-Slashy

[Alshain]

It actually depends on the altitude you want to settle at, your velocity when entering the SOI, and also the size of the body you're orbiting. If the desired orbit reasonably close to the body, you're entering fairly slowly, or if the body is small, then it's best to go directly to the desired altitude. Otherwise, you'll want to get as close as possible, get your AP to the desired altitude, and then circularize at AP.

For example, if you're in orbit at Minmus altitude around Kerbin, and you want to go to Jool, it's best to burn retrograde, lower your PE close to Kerbin, and then burn to Jool at PE, rather than burning directly to Jool. The reverse is also true: if you're coming from Jool and want to get to orbit at Minmus altitude (and you're not aerobraking), it's best to get close to Kerbin, lower your AP to Minmus altitude, and then circularize.

This is correct, depending on what moon you are at. For example, orbiting Ike is not going to make a huge difference over Orbiting Duna because of Ike's proximity to Duna. It should be theoretically more efficient, but I guess the question is if it is really worth the effort for that small amount of fuel. That depends on how well you planned.

[Pecan]

(Buzz Sound) Wrong!

To be honest, I usually let MJ do the mundane things so I'd just put Pe at the required altitude too, most of the time.

That's different to what's efficient though - extreme cases make the extreme case (reductio ad absurdum); take a direct transfer from Kerbin to Moho, target orbit 750km for a Scansat satellite, as a fairly common/plausible example.

With a direct transfer to Moho, and Pe set to 750km, you're going to be tearing in with your flight-path hardly deflected by Moho's gravity. Needs a huge, long, injection burn to slow you down enough to capture (which is why Moho's considered hard-ish).

Set Pe to 7.5km, say, and your flight-path will be deflected by (IIRC and again it depends on the exact intercept) nearly 90-degrees before you do anything else. Yes, you're travelling relatively faster, because you have fallen that much closer, but the dV to close the orbit and capture is much less (quite apart from having more time in which to do it, since gravity-deflection is extending the time until your Moho escape - which is down to patched conics).

Because your Pe is already very low you get maximum Oberth when you burn to create and lower your Ap. Since the Ap is 100 times your Pe there is also a lot less work to do than if you were circularising low-down. Circularising low, then raising Ap and re-circularising is indeed a bad idea.

Now, with the point that you have not circularised low, you transfer to Ap and finally circularise. Two burns - the major braking manoeuvre being done with the maximum benefit or gravity-assist and Oberth. That plus minor circularisation burn is, I believe, much less than the capture unassisted by gravity.

TL;DR

Sooooo - if you want to do a direct transfer to Moho, and don't use Moho's gravity to the full, you are effectively doing a sun-relative Kerbin altitude to Moho altitude Hohmann transfer and both burns (lower Pe, circularise) are pretty big. Using Moho to gravity-brake you have less of a burn to do and maximum benefit of Oberth.

[Fearless Son]

(Buzz Sound) Wrong!

I would think that when combining the circulatization capture with an aerobreaking maneuver, you most definitely want to aim for a periapsis lower than you actually want to settle your orbit at, otherwise your orbit will simply degrade due to repeated atmospheric pass through. In theory, that should require less total delta-v expended due to the atmosphere giving you some "free" delta-v to slow down, before you spend a little more on the opposite side (where you want your final orbital height to be) to raise the periapsis out of the atmosphere.

[Stoney3K]

That's somewhat academical as usually one wants to land. Triply so because other factors may also go into the equation, like having to adjust inclination at some point. So for myself, I have slightly adjusted that rule to "try to put the periapsis where you will need it later". Not lower, not higher, just there.

If you plan your maneuvers right, you can even brake for landing directly without having to circularize an orbit. Usually that means shooting for a Pe that is just above the terrain, and brake with a full retrograde burn until you reach your desired landing spot.

A parking orbit may be more useful if you want to land on a very specific spot, instead of "anywhere that's solid", though. On Mun and Minmus, I usually aim for a 10-15km circular parking orbit and de-orbit from there.

[Fearless Son]

A parking orbit may be more useful if you want to land on a very specific spot, instead of "anywhere that's solid", though. On Mun and Minmus, I usually aim for a 10-15km circular parking orbit and de-orbit from there.

Yeah, now that biomes are a thing on every planet and ore concentrations vary across the surface, being able to land on a particular spot instead of just anywhere solid becomes much more important.

Heck, even landing on Kerbin benefits from that now if you want to maximize the recouperation of funds from any lander. The closer it is to KSC, the cheaper it is to recover.