Vector

You've got me beat. It's only been 7 years since anticipation for GTA V (for PC) began.

It is possible to calculate. Let's see.. I had another screen shot which I left out of the album because it wasn't very interesting, but it is relevant here: This shows that at launch there was 6480 fuel and 39600 oxidizer. 37932 oxidizer was delivered After landing, I had 973 fuel and 1032 oxidizer remaining. So I spent 6480 - 973 = 5507 fuel and 39600 - 37932 - 1032 = 636 oxidizer. The cost of fuel is 5184/6480 per unit The cost of oxidizer is 1425/7920 per unit The cost of spent fuel is 5507*5184/6480 = $4406 The cost of spent oxidizer is 636*1425/7920 = $114 The cost of delivered oxidizer is 37932*1425/7920 = $6825 The cost of spent and delivered fuel together agrees (within rounding) to the quoted total net cost of $11,348. Now, if you were to deliver a balanced mixture of fuel + oxidizer instead of pure oxidizer, how much would you get? Well, the mass of delivered oxidizer is 37932 units times 39.6 / 7920 tons per unit = 190 tons. One orange tank has 14.4 tons of fuel and 17.6 tons of oxidizer for a total of 32 tons of fuel + oxidizer. A 190 ton payload of fuel+oxidizer excluding the tanks would therefore deliver 190/32 = 5.94 orange tanks worth. This would be 2880 * 5.94 = 17,107 units of fuel and 3520 * 5.94 = 20,909 oxidizer. This balanced payload would be very slightly higher in terms of units of fuel+oxidizer at 38,016 (instead of 37,932). But since fuel is so much more expensive than oxidizer, the cost of the balanced payload would be much higher, at 17107*5184/6480 = $13,686 for the fuel and 20909*1425/7920 = $3762 for the oxidizer. The payload would cost $17,448 instead of $6825. The total cost of payload plus fuel spent would then be 17448 + 4406 + 114 = $21,968, which is nearly twice what I spent for the cheaper payload. The score with the balanced payload would then be about 38,016*38,016/21,968 = 65,787 points. This indirectly suggests that if DundraL had delivered an equivalent mass of pure oxidizer, then his score would have been even higher than mine.

Finally finished docking delivery of oxidizer and full recovery, like I had talked about. I had to use MechJeb for the landing predictions, because without it, I can't even hit the continent. I used only the landing prediction and flew the entire mission manually. I also used MechJeb's 'prevent overheats' because I have a horrible tendency to overheat nuclear engines since there is no warning in map view. Craft cost: 517,374 Recovered: 506,026 Net cost: 11,348 Delivered oxidizer: 37,932 Score: 37932*37932/11348 = 126,792 Powered landing with jets is tricky. I knew it would be hard but I underestimated how difficult it would be. I crashed many times before I got a successful landing. If anyone is interested, here is the craft file. Bigger is definitely possible, but it is already a bit sluggish, so going bigger would be just more unpleasant to fly.

Jet power to orbit with very little rocket boost is definitely possible without wings, although I don't believe it's feasible without air-hogging. If TWR is greater than 1 you can adjust your attitude to fly level, no wings required. At low speed you will be mostly vertical, and at high speed you aim mostly horizontal. But don't take my word for it, I'm working on a demonstration.

I've also been working on something else, more in the spirit of the challenge, but still exploiting the rules... One observation: rules say fuel to orbit, not fuel tank to orbit, so if you were to dock, unload the fuel, and return the tank, you might save some cost in a plausible refueling scenario. Second observation: oxidizer is cheaper than fuel, but scored equally, so if you deliver mostly oxidizer, you can get the same fuel + oxidizer at lower cost. Both of these mostly only matter when using a spaceplane that burns very little fuel and recovers all the parts. I've got an airhogged jet that can deliver approximately 3500 fuel + oxidizer (almost all oxidizer) to orbit, for a net cost of about 1450, but I haven't got the whole thing together yet including docking and recovery. The cost of the jet is almost 400k, but it's all recoverable except for the fuel spent and the fuel delivered. If it works, it would score in the ballpark of 7000 or so, and if I strapped 5 together it might even exceed the score of my Whackjob imitation. I'm not sure if I will finish it, but I thought it was an interesting idea...

Craft file: https://dl.dropboxusercontent.com/u/25339567/KSP%20Craft%20Files/Big%2052b.craft Cost is 8029533, nothing is recovered so that is the total cost. Fuel + oxidizer is 218435 + 266976 = 485411 Score is 485411 / (8029533 / 485411) = 29,344.6

If one orange tank is too small, decide on some fixed size, maybe four orange tanks or ten S3-14400 or whatever you think is the right size, and score based on lowest cost to get it to orbit. Then you will have an efficiency challenge and not a size... no wait, efficiency... no wait... actually size challenge.

Your formula is essentially quadratic in payload and linear in cost, so bigger will win even if it's less efficient cost-wise. The penalty for inefficiency is relatively minor as long as you can get the biggest payload possible into orbit, so it's more of a size challenge than an efficiency challenge. A while ago I made this rocket, trying simply to get as big as possible. Thread has link to craft file. It has fuel + oxidizer of 485411, and loading in the current version shows a cost of 8029533. According to your calculation this has a score of 29344.

I'm planning on setting up a 2-stage staging system so that both stages make it to orbit (SSTO essentially) and then the first stage has its own parachutes and control system so it can be recovered. But yeah asparagus is going to have a lot of non-recoverable parts and going to be very expensive.

So I kept trying, and I was able to actually reach Eve this time, spending only 873 m/s. The radial approach turned out to be a bad idea. The problem with radial is that there is no way to control the phase of the Mun at intercept time. Moving radially (same SMA but different eccentricity) predetermines the location of the intersection between the orbits of the ship and Kerbin and if the Mun is not in the right phase, there's not much you can do. Moving prograde or retrograde (resonant orbit), there are a range of available locations, so minor adjustments to the orbital period will shift the phase of the Mun and can put it wherever is best for a gravity assist. High level summary of the mission: 1. Mun flyby, try to get Kerbin Ap + Pe = 22,800,000m so orbital period matches Mun's orbital period. 2. One month later, another Mun flyby, this time leaving Kerbin prograde and shooting for nearest resonance, which happens to be 6:7. Use future Ap+Pe to guide fine tuning of second Mun flyby. 3. 7 years (and 6 orbits) later, Mun flyby, boosting speed and apoapsis for 4:3 resonance 4. 4 years (and 3 orbits) later, another Mun flyby, boosting speed but turning a bit radial inward instead of pure prograde, to retain 4:3 resonance with higher eccentricity. (Not enough boost to reach 3:2 resonance) 5. 4 years (and 3 orbits) later, another Mun + Kerbin flyby drastically changing orbit to mostly retrograde velocity, lowering periapsis to Eve. 6. Small burn to get Eve intercept 6 orbits in the future Also, I have a script which makes it easy to grab snapshots of the quicksaves along the way, so if you're interested in detailed quantification and the maneuvers, you can download them from here. I've included a quicksave for each of the screen shots in the image album.

Yes. You clearly have a good grasp of the mechanics, and there are probably additional ways to take advantage of the Mun that I haven't thought of. The simple cases are good for establishing the principles, even if unrealistic, and then from there the actual maneuvers can be understood and executed. As for Earth/Venus fly-bys, this is true but not really the same thing. It is already well-established in KSP that Kerbin-Eve-Kerbin can give you a big boost, but using multiple Mun fly-bys is not common. Conventional wisdom seems to be that Munar gravity assists are not worthwhile for going interplanetary.

In pictures, to clarify, suppose you leave Kerbin prograde: And suppose your velocity relative to Kerbin is insufficient to reach Duna or Eve. To recap the single-body limitation, if you return to Kerbin and sling-shot around Kerbin, you will have exactly the same velocity relative to Kerbin, and you will be still unable to reach Duna or Eve. The best you can do is to be perfectly prograde or perfectly retrograde and you can't get beyond that. No matter how many Kerbin fly-bys you do, you will have the same relative velocity relative to Kerbin. You can try an Oberth burn but you can't gravity slingshot yourself anywhere. With an extremely small deep-space maneuver, you can aim for the Mun and for a moment ignoring the relatively low mass of the Mun, you could sling shot around the Mun like this: Now you have retrograde velocity relative to Kerbin that is greater than the prograde velocity you had before. Specifically it's equal to your previous velocity plus twice the velocity of the Mun relative to Kerbin. Then on your next Kerbin intercept you can aim for this: and you can again leave Kerbin with more prograde velocity than you had retrograde velocity before. And you could continue this without limit. In reality, the mass of the Mun is too low for it to work like this, and prograde/retrograde velocity means lengthy waits for intercepts. What I've been aiming for, but so far unable to pull off is something like this: where most of the velocity is radial so the orbital period is the same as Kerbin, but you still get a small boost once each year. By fine-tuning the fly-by, it should be possible to precisely control the amount of prograde/retrograde velocity and thereby precisely control the orbital period to line up the intercept the following year. In principle it should be possible to get a small boost every year for several consecutive years with only tiny correction burns. Then the easy part would be to ultimately swing the accumulated radial velocity into prograde or retrograde and go to Eve or wherever.

I agree with that as long as you are only ever interacting with one body. With multiple slingshots you can get assists that would have been available if the body had higher mass (or smaller diameter), but you can't get more than that. When you interact with multiple bodies it's not true because you can take advantage of the relative motion of the bodies. When you leave Kerbin's SOI and intercept a year later, you are interacting with multiple bodies, so the single-body upper limit doesn't apply. You could theoretically get unlimited velocity off of Kerbin and the Mun, for the same reason you can get unlimited velocity off of Kerbin and Eve. But you must leave Kerbin's SOI to do so, or else you are subject to the single-body limitation you mentioned.

So I tried again to see how efficiently I could get to Eve from LKO, and I encountered a few things. First, the radial ejection idea is something that should work in principle but I was unable to pull it off because I kept having trouble lining up the ejection as Kerbin kept moving around the Sun. Eventually I gave up and just ejected in whichever direction, but even if I had been able to eject radially, I would have needed to tweak the final Mun flyby to set up a Kerbin encounter 1 year in the future. Unfortunately, when you're in Kerbin's SOI, you can't set it as a target, nor can you get "Closest Approach" indicators one year in the future. You have to compute the orbital period using the periapsis and apoapsis. In the past I hadn't ever tried to actually eject radially and I had gone for a resonance to minimize deep-space correction. For this test run I did not ejected radially and I also made an error in the calculation for orbital period, and I had to wait 7 years AND burn 42 m/s to get another Kerbin encounter. Awful on both counts. I was able to get another Mun flyby, and lower my solar periapsis down to Eve's orbit, but as a proof of concept I had not taken care to eject near AN/DN (too focused on trying to leave radially), so I was actually still quite far from Eve. Ideally one would time the ejection properly and this wouldn't be a problem. All told, I spent 911 m/s from LKO, and 42 of that was due to a blunder, so I think 870 to 880 m/s could be very realistic if all is done well. This is also assuming that you are willing to possibly wait a while to get an encounter with Eve. The final flyby that gets your orbit to intersect with Eve's orbit will allow you some "leverage" to get an Eve enounter, but you won't have much room to move so you might have to aim for an encounter several years out.

I know it's heresy to speak of using gravity assists from the Mun to go interplanetary, but it can save a couple hundred m/s delta-V. The trick is making multiple passes by the Mun. As many people have observed, a gravity assist from the Mun can get you out of Kerbin's SOI but not anywhere interesting, and burns in interplanetary space are horrendously inefficient. But if you intercept Kerbin a year later and make a second pass at the Mun (and a third), you can build up energy and eventually reach Eve. And once you reach Eve, with skill you can gravity-assist yourself anywhere. I haven't perfected the technique, but it does work. You can get to Eve for not much more than the cost of getting to Mun. I'm finding that it works best to leave Kerbin neither prograde nor retrograde but radially, to keep the same orbital period as Kerbin for the second intercept. Once in interplanetary space it is possible with extremely small adjustments to tweak the phase of the Mun at the second intercept, so it is in the proper position for a boost. It is a bit time consuming, but for those of you adept at gravity-assists, it's very doable.