Optimal gravity-assisted grand tour (AKA Voyager like mission) challenge

[adammada]

Goal of this challenge is to discover best path for flyby mission of Kerbol System.

Rules:

1. You have to use ship provided in this post.

2. You can only use fly-help mods like Kerbal Alarm Clock, Protractor, MechJeb etc. You can strap them to provided ship.

3. No cheats.

4. You have to launch your ship before 10-th year (time displayed in Tracking Center).

5. There is hard limit of 30 years of flight time. What happens later is not taken into score.

Score:

- 10 points for flyby of planet (means entering its SOI), excluding Kerbin. Moons are ignored. Counts only once for planet.

- 20 points bonus for flyby of all planets

- 20 points for ending in Kerbol escape trajectory

- -1 point for every full year of flight (counts mission time)

- In case of draw, who has more remaining fuel - wins.

Because goal of this challenge is to provide best mission plan, you are required to document your fligh, so others can recreate it.

Craft: http://kerbalspaceprogram.com/voyagerchallengecraft/

TIP:

Read here metaphor's advices:

http://forum.kerbalspaceprogram.com/showthread.php/37340-One-Engine-to-Rule-Them-All!?p=476805&viewfull=1#post476805

http://forum.kerbalspaceprogram.com/showthread.php/37340-One-Engine-to-Rule-Them-All%21?p=476018&viewfull=1#post476018

Edited June 27, 2013 by adammada

[duncan1297]

Did you attempt the challenge?

[adammada]

Yes. I tried to go from Kerbin to EVE on first transfer window (day 138), then from EVE tried to flyby to Moho, but no luck. This gives me 10 points .

[Mr Shifty]

This sounds pretty interesting. Does the craft require any mods? How much delta-V do we have? I will attempt tonight or tomorrow.

[adammada]

No mods required. About 7500 delta-V.

[Eric S]

It does sound interesting, but the time limit bothers me, though I can see why it's there.

[Mr Shifty]

Progress: so far I've done Eve->Moho->Eve->Duna (+ bonus Ike) and now I'm scheduled for intercept with Kerbin at around the 6 1/2 year point. I still have about 524 m/s of fuel left to try to get to the outer planets. (And now that I know a few more tricks, I could do much better with fuel if I tried again.) Will post screenshots when complete, but my current score would be 27. (I've got 3 more years of flight time before Kerbin intercept.)

[adammada]

Another try. I looked at this page: http://alexmoon.github.io/ksp/

And found good delta-v window from Eve to Moho at 187 day. So i looked when i could go from Kerbin to Eve, to get there at 187 day. And it was:

Kerbin -> Eve

Departure

Year 1, day 128 at 13:59:54

Arrival

Year 1, day 187 at 10:09:03

Time of flight

58 days 20:09:09

Phase angle

-74.43°

Ejection angle

85° to retrograde

Ejection inclination

-12.33°

Ejection delta-v

1,329 m/s

Transfer periapsis

9,226 Mm

Transfer apoapsis

13,713 Mm

Transfer inclination

1.82°

Transfer angle

250°

Insertion inclination

N/A

Insertion delta-v

N/A

Total delta-v

1,329 m/s

Eve->Moho

Departure

Year 1, day 186 at 1:47:08

Arrival

Year 1, day 206 at 7:37:17

Time of flight

20 days 5:50:09

Phase angle

-171.51°

Ejection angle

141° to retrograde

Ejection delta-v

1,578 m/s

Transfer periapsis

5,577 Mm

Transfer apoapsis

9,625 Mm

Transfer angle

133°

Plane change time

Year 1, day 192 at 17:19:42

Angle to intercept

100.99°

Plane change angle

0.02°

Plane change delta-v

3 m/s

Insertion inclination

N/A

Insertion delta-v

N/A

Total delta-v

1,581 m/s

So i went to Eve, then straight from Eve to Moho (and because of gravity assist i used less about 800 m/s, so even counting non optimal Kerbin-Eve transfer it was profit). Now i ended on big-inclination orbit, which crosses Eve orbit and 700 delta-v left. Can't see good options to get back to Eve, even after few full oribits.

I think that next time i will try to intercept Moho when i can do it without inclination change.

Current score: 20 points (Eve + Moho, less than year of flight).

Edited June 28, 2013 by adammada

[Mr Shifty]

Alright, here's my entry. I managed to get Kerbin intercept at the 6 year point, and probably could have eked out a Dres intercept, but the time it took would have negated any point gain and I would have had about zero fuel left at that point, so I'll finish after getting Duna.

I count:

Eve: 10 points

Moho: 10 points

Duna: 10 points

Ike: 0 points

3 years, 28 days of transit: -3 points

Total: 27 points

Fuel Remaining: 524 m/s

I have MechJeb's delta-V stat window up in most of these shots so you can see fuel progress, and Kerbal Alarm Clock shows absolute game time. (I launched to Eve on day 1.)

Javascript is disabled. View full album

[Mr Shifty]

Here are the reasons this is tough, and some tips:

1) The only thing a planet can do (without thrust) is bend your orbit. If it bends your orbit toward its own prograde this will add to your heliocentric velocity; if it bends it toward retrograde, this will subtract from your heliocentric velocity.

2) The most a gravity assist can add to your velocity is 2x the planet's heliocentric speed, but this only occurs if you approach the planet directly from its retrograde or prograde, and are going slow enough (and/or get close enough) to bend your orbit 180 degrees around the planet.

3) Since your vessel's orbit around the sun is counterclockwise, like all the planets, it is impossible to approach a planet's orbit at an angle greater than 90 degrees to its prograde. This means that the most help you can get from any planet in the prograde direction is 1x the planet's speed. Effectively, it is easier to use gravity assists to descend toward the sun than to ascend away from it because everything is orbiting the same direction. One way to think about this is: if I throw a baseball directly at a train coming toward me, its velocity change when it hits the train is going to be large, but if I throw a baseball in the same direction that a train is travelling, and the train hits it from behind, the velocity change will be smaller. In the Kerbin solar system, all the trains are travelling in the same direction.

4) So, a fuel efficient solution would be to ascend to Eeloo or Jool and then use gravity assists to descend from there. The problem with this strategy is the time constraint on the challenge. Orbits take so long out there that if you wait 2-3 orbits for an intercept point, you'll zero out your score for intercept in the first place.

[metaphor]

3) Since your vessel's orbit around the sun is counterclockwise, like all the planets, it is impossible to approach a planet's orbit at an angle greater than 90 degrees to its prograde. This means that the most help you can get from any planet in the prograde direction is 1x the planet's speed. Effectively, it is easier to use gravity assists to descend toward the sun than to ascend away from it because everything is orbiting the same direction. One way to think about this is: if I throw a baseball directly at a train coming toward me, its velocity change when it hits the train is going to be large, but if I throw a baseball in the same direction that a train is travelling, and the train hits it from behind, the velocity change will be smaller. In the Kerbin solar system, all the trains are travelling in the same direction.

All directions might be counterclockwise around the Sun, but that's not always your speed relative to the planet you're using for your gravity assist. It's not very obvious what direction you will come in to the planet's SoI. If you go to a superior planet, for example from Kerbin to Duna on a Hohmann transfer, when you reach Duna you will be going slower than it, so from Duna's point of view you will be coming at it in the retrograde direction. So if you can turn that around and leave Duna's SoI in the prograde direction, you will have gained a lot of energy in your orbit.

It's like throwing a baseball at 40 mph in the same direction as a train going 70 mph. That baseball is still traveling at 30 mph toward the train from the perspective of the train. If it bounces off the front of the train at 30 mph, it will then be going at 100 mph relative to you. Your baseball analogy for an inferior planet is somewhat inaccurate, because both the baseball and the train are almost always going in the same direction, unless your ship is in a retrograde orbit. Going to an inferior planet is more like throwing the baseball at 100 mph at the back of a train going 70 mph. After hitting the train, the ball will bounce off at 30 mph backwards with respect to the train, or 40 mph forwards from your point of view.

So in general it's just as easy to get gravity assists to raise your orbit as it is to get gravity assists to lower your orbit. For example, if you go from planet A orbiting at 1 AU to planet B orbiting at 1.2 AU, you can get a gravity assist from planet B to kick you out to an orbit with an apoapsis of around 1.4 AU. But this is also dependent on the mass of the planet. The lower your periapsis is, the more bending the planet's gravity can do, but you can't get your periapsis below the surface/atmosphere of the planet. So there's a limit to how much energy you can get from a gravity assist, especially if you're coming in fast. Jool, Eve, and Kerbin in general can all provide significant gravity assists, the other planets can't do as much. (This is also why most real robotic probes to the outer planets use gravity assists from Venus and Earth, but not from Mars.) But if you come in at 20 km/s, even going really close to Kerbin or Eve is not going to bend your trajectory any significant amount.

[Mr Shifty]

It's not very obvious what direction you will come in to the planet's SoI. If you go to a superior planet, for example from Kerbin to Duna on a Hohmann transfer, when you reach Duna you will be going slower than it, so from Duna's point of view you will be coming at it in the retrograde direction.

OK, this makes sense, given that the planet is travelling faster than the vessel, but see below.

It's like throwing a baseball at 40 mph in the same direction as a train going 70 mph. That baseball is still traveling at 30 mph toward the train from the perspective of the train. If it bounces off the front of the train at 30 mph, it will then be going at 100 mph relative to you.

But if you're facing the train and throw the ball as it approaches, it will be going 110 mph relative to the train. If it bounces off the front of the train at 110 mph relative to the train, it will now be going 180 mph relative to me: speed of object + 2 * speed of assistant => 40 mph + 2*70 mph = 180 mph, which is your max for a 40 mph ball and a 70 mph train.

Going to an inferior planet is more like throwing the baseball at 100 mph at the back of a train going 70 mph. After hitting the train, the ball will bounce off at 30 mph backwards with respect to the train, or 40 mph forwards from your point of view.

OK, I start to see what you're saying here. Everyone is travelling counterclockwise, so you can never get close to an optimal boost, but your speed relative to the assistant planet can be either retrograde or prograde to the planet's orbit and for non-Hohmann transfers, it's a combination of your relative speed and relative angle that determine which one it is. (For Hohmann transfers, you get a boost from higher planets and a buck from lower ones.)

I did find this paper, which has a very nice formula (formula (3)) for calculating the change in angle you'll get from a gravity assist given your initial relative velocity and periapsis. I was trying to figure out if I could design a calculator for gravity assists in KSP, but I don't think it would end up being very useful.

[PakledHostage]

@adamada: I think this is a great challenge! Like Mr Shifty, I like to do some degree of pre-planning of my mission trajectories rather than just winging it. I don't have a lot of time for that right now, but I hope that nobody minds if I necrobump this challenge in 3-4 months.

Also, it is interesting to point out that the gravitational assist that Voyager 2 received from Neptune actually slowed it down. Not enough to prevent it from escaping the solar system, but it was slowed by more than a kilometre per second due to the encounter.

[adammada]

In another try i decided to go straight to Moho, when he is in ecliptic (co i would have two eve-orbit intersects). 1500 m/s delta-v. It was successfull, but i couldng get to Eve, cause its orbit is inclined. After inclination change to cross Eve orbit in one place, i still couldnt hit it, event with 10 orbits. Time for more scientific approach i think.

[sal_vager]

Adammada, your challenge has been chosen for this month's Featured Thread, and good luck to all who participate

[TheMontgomery]

Hmm... I'm already scheming up a craft for this, I'm excited to give it a shot.

[farthen]

This is a really great challenge. I tried it but failed miserably at my approach from Eve to Moho. It's really difficult to plan the trajectories correctly. Even more so as you basically want to plan out all of your encounters from the beginning on, especially because of the Oberth-Effect.

[Patupi]

I got a Duna, then Eve flyby, then came up short on a Dres insertion, mainly due to the angle. Had to swoop round Kerbol a couple of times to get the Eve intercept without wasting fuel. Total time (till I found I'd missed Dres) 424 days.

I'm going to give this another go, perhaps oscilating from inner to outer planets, doing flybys on PE and AP alternately? Have to think how efficient that would be

Edited July 22, 2013 by Patupi