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At first, I would say that if you burn straight from AP @80km would save you some 200 dV. But then I realized it won't. And the reason for that is that you would already have spent the same dV if you were circularizing.
That said, unless you are doing some grav assist, the cheapest maneuver you can do is from 80km LKO. Maybe 75km if you can cut it, but you know the difference between those is very small.
You can save a little time thought.
In a different scenario, if you were launching to minmus you can save some dV if you launch at the correct time of day, by launching at the correct angle already. That could save you some 200 dV, I guess.
It's wrong.
If both trajectories are perfectly executed, the closer to the body the burn is executed, the less DV you'll use, due to the Oberth effect, so you'll save some DV toward going stable LKO, and then doing the other burn.
Using mathematics, both trajectories will need the same DV, the difference will be about Oberth effect, which will be more important if you're pushing closer to Kerbin.
In theory, that will save you a few m/s as DV, though it will be very small (i guess less than 10 m/s DV), so the difference is not noticeable for a short travel to Mun, because trajectories won't be perfect and will lose more DV than you'll gain with Oberth effect.
I would be glad to hear your exaplaination about why a stable orbit will save you DV, because both trajectories will need the same DV (except for Oberth effect) when you calculate it.
PS : When doing the maneuver, both trajectories are quite the same to Mun, so don't bother with this question, as you won't even notice the difference. But a Kerbin-Duna travel will show a difference of about 200m/s DV, because the Oberth effect is much more important when you're close to Kerbin than far away from Kerbol.
Source : https://en.wikipedia.org/wiki/Oberth_effect
So, if you start your burn at 0m from KSC, you'll save some DV toward burning at 80km high. But the maneuver is much more tricky, except if you use some kind of autopilot (and even then, i doubt it can perfectly handle atmospheric flight without any variations).
https://www.youtube.com/watch?v=0dx7ScJSAwo
Further improvements are possible, obviously, if you really want to build up an enormous rocket.
That's the proper explaination, though the n°1 can be performed with a standard atmospheric ascent. In my opinion, n°1 is a standard ascent, and then you continue to burn above 70km to complete the trajectory to Mun, while n°2 is a standard ascent, then circularize, then burn from circular orbit to the Mun.
Both solutions will need the same amount of DV, except Oberth effect, which will be higher in n°1, so less DV needed in n°1.
If you don't realize a standard ascent in n°1, you'll lose a lot of DV into atmospheric flight, because you'll need very high thrust when you'll reach terminal velocity, and kinetic energy will be lost as heat. So, with the same standard ascent, 1 and 2 are very close to each other in DV requirement, n°1 is the most efficient but very hard to realize as you need to plan your burn from the ground, n°2 will require about 10m/s more DV but is much more easier to achieve, that's what most players will do.
n°3 is pointless if you're looking on DV requirements, as it will require much more DV than 1 and 2, BUT you'll shorten travel time. It's not efficient, and i doubt it's even possible without futuristic engines when talking about interplanetary.
Because when landed, the Oberth effect applies, since you're quite literally at the lowest point of your peri.
The idea is that from the start, you've flown perfectly. Any corrections result in a net loss and you're no more efficient or worse off. Practically speaking, a direct ascent is more efficient, you just won't realise this until the distances become extreme.
(Or you have really bad TWR, then you have no choice but to orbit)
A small error in inclination can result in a much bigger deviation at your destination. So you better correct it before you depart. Also, what do you mean by "direct ascent"? Afaik direct ascent was an early proposed mission mode in the Apollo program.
direct
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-oberth effect will be higher at 0m than 70km
-We're talking about perfect trajectories. You're right on one point, it will be much much much easier to reach a trajectory close to perfect when setting up the node maneuver from a circular orbit than from the ground, so in practise, it's probably the best to do for a Kerbin-Mun travel as the gain is very low. But a perfect trajectory from the ground will always be cheaper in DV requirements than a perfect maneuver from a circular orbit, the tiny difference is the Oberth effect.
Also you said "unless you can do all that on the fly", which is very hard, but possible. Again we're talking about perfect trajectories.
My conclusion :
From a mathematical point of view, the cheapest way to reach Mun, using both perfect trajectories and similar TWR (like Toastie Buns explained) is a single burn from the ground compared to circularizing the orbit.
From a pragmatic player point of view, the perfect trajectory from the ground will be so hard to set up, that you'll probably lose more DV in maneuver corrections than you gain from Oberth effect for such short travel.
But don't forget that if players may fail to set up the perfect trajectories, autopilots are much more precise and regular than any human will never be, some people are using them, some other don't, but if you're using an autopilot, corrections will be applied automatically, so you can correct trajectories on-the-fly. And in that case, direct trajectory will probably win by few m/s.
About Oberth effect, it's not noticeable for a Mun travel, but for Jool, there is almost 30% difference in DV requirements, so you'll notice it, even if you lost more DV by correcting more times on a single Kerbin burn than from Kerbol's orbit.
apollo was going to direct ascent *back to Earth* which would've meant landing the heat sheild on the Moon, instead of re-docking with it in Lunar orbit.
Again, I am talking from a mathematical simplified point of view, so the ship is a point, Kerbin a ball and kerbonauts are smart
OE is due to speed, not altitude. If you orbit, your speed is highest when your are at the lowest point. Thaths why you execute prograd/retrograde maneuvers at that point.
Terminal velocity is very useful in ascent, the optimal speed to ascent is the max speed you can reach under terminal velocity. Above terminal velocity, you can beat frictions using high thrust, though you'll reach very high energy losses.
To ascent, you have to beat gravity, which means reach the furthest away you can the faster you can (this is true for non-atmospheric bodies), but the energy loss will be multiplied above terminal velocity. So the optimal speed to ascent for a perfect aerodynamic body is the same as terminal velocity at this given altitude. As ships are never perfect shaped and suffer more energy loss, this optimal speed is lower than terminal velocity, depending on the shape.
You can test yourself easily, make 3 rockets with a given DV (lets say 1000m/s). Fly straight above until fuel is out, and notice apoapsis altitude. Try to stay at 50m/s for the first one, 250m/s for the second one and 500m/s for the last one, and check which one fly the highest, the second one will beat others easily.
That's also why you don't make rockets with 10.0 TWR from KSC, such rockets will reach high speeds but be very inefficient in DV.
Guide to understand terminal velocity/optimal ascent speed : http://www.alphasheep.co.za/2014/05/ksp-fuel-optimal-ascent.html