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Fuel-efficient Mun Encounters


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Isn't the whole point of the suicide burn that it uses the Oberth efect most efficiently? Ie: burn as low in the grav well as possible.

Yes, that's correct.

I agree that skipping points 3 and 4 is the best way to go, however I don't understand why you can't just use the method I described.

For reasons described below:

If you have the smallest possible horizontal and vertical velocity (relative to the Mun) when you enter the Mun's SOI, isn't that the most efficient way to land?

Yes, if you actually don't have any munar relative velocity when you enter the Mun's SoI (there's the crux of the matter). In your plan, you don't meet that criterion.

If you're on the edge of the SOI, the best speed that you'd want to have is zero, so that you'll only have to cancel out the kinetic energy you get from falling to h = 0m

Agreed. However, the question is, how do you get to have that zero velocity? From your original post's suggestion:

- Start from lowest circular LKO

- Burn prograde at the right time so that your Kerbin Ap barely touches the Mun's SOI.

- Once inside the Mun's SOI, reduce your horizontal speed to zero (your vertical speed should be close to 0 m/s once inside Mun's SOI)

- Suicide burn to the surface

It's that "reduce your horizontal speed to zero" part that makes this way inefficient.

When you eject from Kerbin LKO, you put yourself into an elliptical orbit that has an apoapsis out by the Mun. By definition, this orbit does not match the Mun's. Your orbital velocity at apoapsis is going to be much lower than the Mun's. That means that you are going to have significant relative velocity to the Mun when you enter its SoI, there's no way around that.

So let's consider two possible approaches, A and B.

A is the plan you suggest, and involves these steps:

A1. You go for a Kerbin-eject trajectory that just grazes the Mun's SoI.

A2. You enter the Mun's SoI going nearly horizontally relative to the Mun, with a munar periapsis that is very high (right out by the SoI boundary), and at a high velocity relative to the Mun.

A3. You do an orbit-killing burn that reduces your velocity (relative to the Mun) to zero.

A4. You free-fall to the Mun.

A5. Suicide burn to the surface.

B is the plan I suggest, and involves these steps:

B1. You go for a Kerbin-eject trajectory that puts your munar periapsis surface-grazingly low. (Let's say you put the periapsis right at the surface).

B2. You arrive at periapsis going very fast and nearly horizontally.

B3. Suicide burn to the surface.

Let's look at what you have to do once you're in the Mun's SoI:

Plan A requires two burns, A3 + A5.

Plan B requires one burn, B3.

It is true that A5 < B3; my understanding is that this fact is what's causing you to prefer scheme A.

However, the key difference here is that A3 is a significant burn at high altitude. Plan B does all of its burn right down on the munar surface, which optimizes Oberth effect; plan A does a big chunk of it in the worst possible place, right up at the edge of the Mun's SoI.

So Plan B uses less dV than plan A, because A3 + A5 > B3.

Edited by Snark
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Actually there is a way that if you get in an orbit very similar to the Mun's, the game might cause your ship to capture without a burn. Apperently it is very rare, but it just happened to me around Vall.

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Isn't the whole point of the suicide burn that it uses the Oberth efect most efficiently? Ie: burn as low in the grav well as possible.

I agree that skipping points 3 and 4 is the best way to go, however I don't understand why you can't just use the method I described.

If you have the smallest possible horizontal and vertical velocity (relative to the Mun) when you enter the Mun's SOI, isn't that the most efficient way to land?

If you're on the edge of the SOI, the best speed that you'd want to have is zero, so that you'll only have to cancel out the kinetic energy you get from falling to h = 0m

Suicide burn is not primarily about Oberth effect, it's about minimizing gravity loss in your landing burn by minimizing the time gravity affects you in a suborbital trajectory. If it was about Oberth effect, you would want to enter the Mun SoI in a radial orbit!

Oberth effect is about maximizing the work of a burn by increasing the distance you apply the force over. Work is equivalent to kinetic energy if you burn parallel to the prograde direction. And distance is the integral of velocity WRT time.

While you use the some of the same physics equations to explain both, the emphasis is on slightly different parts. Oberth effect is about how velocity effects energy change from a force, suicide burn is about how greater time under consistant acceleration leads to greater velocity change.

Gravity turns OTOH are also about reducing gravity losses but also maximizing thrust efficiency. By burning prograde you maximize energy conversion of thrust (using the same equations we explain the Oberth effect with). You use gravity to change your velocity vector (via vector addition) and allow you to efficiently transition to horizontal flight. The turn is also meant to most quickly reach the point where gravity acceleration is maintaining your orbit so you spend less time (and thus energy) countering it.

That's why aerodynamically stable craft fly themselves in a gravity turn below 30km. The aerodynamic stability causes heading to converge to a prograde course! (Often better than SAS ever could) A useful atmospheric compromise is to have an atmospheric stage set a Ap at about 40-50km (after drag losses) while keeping a high AoA to the horizon before burnout. You stage it away and coast until the prograde vector is closer to the horizon before activating the next stage. You sacrifice some of the Oberth effect (because you let gravity reduce velocity magnitude) for reduced drag losses.

Oberth effect is simply an observation that increased velocity of the burn causes increased work. There are two aspects of velocity: magnitude which is highest at Pe and direction which is highest parallel to orbital trajectory. That's why radial and normal burns are horrid. Their velocity is only your vertical velocity component, which can be very low!

Edited by ajburges
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Suicide burn is not primarily about Oberth effect, it's about minimizing gravity loss in your landing burn by minimizing the time gravity affects you in a suborbital trajectory. If it was about Oberth effect, you would want to enter the Mun SoI in a radial orbit!

But... you DO want to enter Mun's SoI in a radial orbit, with a speed as close to zero as possible.

Radial orbit = straight line to the center of the Mun, right?

That's the best scenario you could find yourself in if you wanted to land on the Mun (and if you ignore how you got there in the first place). It's not the only way to do a suicide burn, sure.

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There was a thread that experimentally explored this a while back, it had some incorrect assumptions but it had interesting results. In summary, even while biasing the results to radial transfer, capture burn followed by gravity turn needed less dV (by a small amount, but it was biased towards radial transfer)

Couple issues with radial intercept of Mun...

A transfer trajectory to a radial orbit needs more dV then a transfer to prograde by a few dV. While only 5-10 dV it is more.

While a radial decent vs capture burn and gravity turn have similar energy needs, the radial decent fights gravity drag for all energy transfer. In contrast, a capture burn is a couple hundred dV without gravity drag. Since no craft have infinite TWR and few landers have ludicrous TWR that small amount of gravity drag is a tangeable loss.

Timing is another concern, the higher your TWR, the smaller the margin you have for correct timing. The further your timing is of, the more inefficient. Theoretical vs practical is always a pain.

High TWR landers also waste a lot of mass in engines. A capture and gravity turn has more flexible acceleration requirements, so you can choose a higher mass efficiency power plant and use less fuel.

Radial capture limits you to direct accent missions. Again, this means you need to take more mass with you. Enter the tyranny of the rocket equation and even more efficiency losses.

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For returning from a Mun orbit, simply burn retrograde when your vessel is exactly in between Kerbin and the Mun. In this way, you 'plummit' into Kerbin's atmosphere.

Burning retrograde whilst in Munar orbit will just send you back to the Mun surface. By definition, being in orbit around Mun means you are still in Mun's SOI.

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