Is it more fuel efficient to hop once or several times?

[Conbadicus]

Lets say I'm on the mun with a science lander and I want to go to another biome. Is it better to do one large hop or do skirt across the surface/do multiple small hops ?

[Snark]

Moving to Gameplay Questions.

One big hop is better than multiple little ones.  The distance you get from a hop goes with the square of the dV you use to launch^*, so it's mathematically advantageous to dole out the dV in big chunks rather than little ones.

* The simple "it goes with the square" relationship is strictly mathematically true for the simple case of approximating gravity as constant and the ground as a plane.  If you're doing really long-distance hops where you're moving a significant distance around the Mun's circumference, then the math gets a bit more complex, but the basic principle still holds.

[Conbadicus]

Thanks

[Nich]

Although optimal angle is not 45 degrees if you are approaching orbital velocity.  If you are covering 1/4 or 1/8th of the body you want to aim flatter.  Using the new kerbnet you should be able to find a nice area with 4-5 biomes within 20km of each other and in this case 45 degrees is the best angle.

[bewing]

While what snark said is true, it's landing that eats your fuel all up. In a long hop you land once. In 3 short hops you have to land 3 times.

[wumpus]

1 hour ago, bewing said:

While what snark said is true, it's landing that eats your fuel all up. In a long hop you land once. In 3 short hops you have to land 3 times.

Oddly enough, as distances grow longer it is more efficient even without landing (or landing with parachutes).  Sub-orbital hops require delta-v proportional to Sqrt(sin(theta)/1+sin(theta)).  So it takes roughly 90% of the delta-v needed to go a quarter way around the planet that it does to go half way.  I'd expect considerable savings on a single flight (with or without an atmosphere) for anything that you want a flatter profile than 45 degrees.

[Superfluous J]

6 hours ago, Nich said:

Although optimal angle is not 45 degrees if you are approaching orbital velocity.  If you are covering 1/4 or 1/8th of the body you want to aim flatter.  Using the new kerbnet you should be able to find a nice area with 4-5 biomes within 20km of each other and in this case 45 degrees is the best angle.

I don't remember if this is true or not, but I always aim for 45 degrees over the line between the two points that cuts through the planet, aiming up to miss terrain.

This of course only works for targets less than 90 degrees away

[Snark]

10 hours ago, bewing said:

While what snark said is true, it's landing that eats your fuel all up. In a long hop you land once. In 3 short hops you have to land 3 times.

Well, not quite.  Landing eats up half of your fuel, if done efficiently; it's the exact mirror image of taking off.  If the landing is done inefficiently, then yes, it would eat up more than taking off.  (Landing efficiently generally requires more skill / practice than taking off efficiently, since you have to time when to start the burn.)

A long hop, you take off once and land once.  The dV to land is equal to the dV to take off.

In three short hops, you take off three times and land three times.  Both the takeoffs and the landings eat up the fuel.

[FancyMouse]

1 hour ago, Snark said:

Landing eats up half of your fuel, if done efficiently; it's the exact mirror image of taking off.

(half the fuel is obviously wrong - I believe you meant half the delta V)

(I'm assuming single staged ship across the board, as I believe it's also your assumption)

Not exactly - because of the TWR increase between full and empty ship, it won't be the exact mirror image no matter what.  And therefore landing would be a tiny little bit more efficient if done perfectly.

The extreme example of this would be, suppose you spent 1400m/s for your takeoff+landing using Poodle, then your touchdown TWR could be 1.5x of your takeoff TWR. The delta-V equation here can derive back the wet/dry mass ratio, thus the TWR ratio, given the amount of dV spent.

Practically, though - for all moons of size up to Mun, TWR difference is usually within 1.2x and when flying manually you won't notice the difference, and assuming mirror image is a pretty good approximation for them. Not quite applicable for bigger things, though.

Edited January 4, 2017 by FancyMouse

[Snark]

13 minutes ago, FancyMouse said:

(half the fuel is obviously wrong - I believe you meant half the delta V)

Yes, that's what I meant, thanks for catching.  (Which, of course, means that landing uses less of your fuel than takeoff, since you're lighter then... even if improved TWR weren't taken into account.)

[Superfluous J]

I believe this could all be explained by the Oberth Effect. It's always most efficient to burn your fuel when you are moving the fastest. The moment you stop burning on the way up, any more fuel used to burn upwards will be less efficiently spent than fuel spent at that moment, including any fuel you spend after you landed and start hopping again.

[DrunkenKerbalnaut]

5 hours ago, 5thHorseman said:

I believe this could all be explained by the Oberth Effect. It's always most efficient to burn your fuel when you are moving the fastest. The moment you stop burning on the way up, any more fuel used to burn upwards will be less efficiently spent than fuel spent at that moment, including any fuel you spend after you landed and start hopping again.

Which is the exact argument it took for someone to get it through my thick skull  .

Higher TWR will achieve higher speeds quicker. In turn, higher initial velocity begets higher final velocity. And so TWR is your friend (in vacuum hops), because you spend less time getting faster... Or something like that . 

Thanks 5thHorseman, I needed a reminder.

[Sharpy]

Note in stock, without aids such as KER, on any body with considerable gravity, doing a perfect landing without a dozen reloads is about impossible. There are tricks like setting up a maneuver node at the surface, but you'll still be off by good 100 meters from optimum. And on Tylo 100 meters is a long way down. Or way too fast.

Even with KER executing a perfect suicide burn is a bit of challenge.

So, while in theory landing can cost you less than launch (by the dV value of durability of your landing legs; slam into the ground at 15m/s instead of touching down), in practice you'll waste considerably more fuel, unless you're really lucky - or use aid of mods.

[Nich]

On 1/3/2017 at 5:13 PM, 5thHorseman said:

I don't remember if this is true or not, but I always aim for 45 degrees over the line between the two points that cuts through the planet, aiming up to miss terrain.

This of course only works for targets less than 90 degrees away

Good use of averages Kind of sad I never realized that.