IncongruousGoat

Sure, sounds good to me. In news of the solver, things are going well, although there are still one or two things to work out. In particular, the math seems to go squirrelly where Nervs are concerned. I should have it all working and with a proper release tomorrow.

Since the constraining equation is just the sum of all the variables, the gradient vector works out to <1,1,...,1>, since for each partial derivative one variable gets reduced to 1 via power rule, and the rest go to zero since they're being treated as constants. In other news, I've started work on a solver program using the equations I came up with. So far the math looks promising-I'm planning on using Newton's method to approximate a solution. Interestingly, the number of stages doesn't change the computational complexity of finding the optimum mass arrangement, given a certain set of motors. Of course, more stages changes the overall complexity, just because you have to check more possible motor arrangements, but that was to be expected. The real roadblock so far has been setting up the build environment-my computer isn't set up to build cross-platform C++ programs with UIs, so I've been spending the afternoon dealing with that. I'll release it on GitHub (and provide a link, of course) once it's working.

The challenge is done in Career mode, since facility upgrades aren't a mechanic in Science mode. And, yes, science points from contracts count, although grinding contracts for the science required sounds incredibly tedious.

Ah. Whoops. Messed up my terminology. I meant to say that it can't be solved for x1 algebraically. EDIT: There, I fixed it.

@Cunjo Carl Going back and reading what I wrote, I realize that my point about TWR was a bit... confusing. I was trying to point out that wet mass/dry mass ratio is consistent across the liquid fuel tanks (well, all the ones we care about), but that there is no consistent relationship between TWR and Isp in engines, and that the lack of such a ratio makes the math more difficult. I'm actually more looking for a solver program, although probably not a webapp, since I have absolutely no experience with web programming. Anyways, math. Based on @Abastro's work I started trying to work out the general case for n stages, given that we know what motors we're using for each stage (and only one type of motor per stage), and it would seem like there isn't an analytical solution. There's a numerical solution, one I could write a program to deal with, but not analytical solution. Oh, wait. Decouplers are a thing. Hm. Honestly, I don't think the mass of a decoupler is going to make too much of a difference in these calculations one way or the other.

Does anybody know how Red Dragon is supposed to generate power once it arrives at Mars? In transit it has the solar panels on the trunk, but once it lands is it going to deploy solar panels from some internal compartment? Is it going to carry an RTG? Is it going to run on batteries?

No. Mars Oasis was Musk's original plan. It fell apart when he tried to buy a refurbished Soviet ICBM, and realized it would be prohibitively expensive to do so. It was this that motivated him to found SpaceX and drastically decrease launch costs.

I've been thinking about this, and I had an idea. If you could get general equations using the same set of variables for vessel mass and vessel delta-V, given a certain number of stages, you could relatively easily use some calculus to find an analytical solution for the optimal staging setup given a certain constraining mass. The question then becomes working out a general-form equation for the delta-V of the full setup. If we're accounting for multiple engines, the Isp and TWR change from stage to stage, making it difficult to get a general equation, for an arbitrary number of stages, for an arbitrary number of engines per stage. Which leads me to my next thought. The best way to approach this would probably be to work out equations for a fixed number of stages (so a 1 stage equation, a 2 stage equation, etc.). Then, find the optimal engine/fuel tank ratio for each one of those. Whichever number of stages provides the most delta-V is the optimal one. The problem then becomes tying Isp to TWR in a reasonable way. We already know the mass ratio for the fuel tanks, but engines are a bit trickier. Optimally, there would be a consistent relationship between the two, but there really isn't. I plotted the relationship, with TWR on the x axis and Isp on the y axis here. I'm not considering the Twin Boar for now, for purposes of simplicity. As I see it, there's only one analytical solution to this: Giving the quantity of each engine its own variable. This would provide an analytical solution, but in the form of a system of seventeen (ish) equations. We can probably ignore the Thud, Ant, and Spider, but I hesitate to throw any other motors out the window, and I'm only ignoring those since their optimal use case is not as a transfer stage motor. Asparagus and drop tanks, you say? They'd probably require their own sets of equations. The more I think about this, the more I start to think that a solver is the way to go. Or, in other words, I've got an urge to do some math and am interested in helping with the general-case solution.

That makes more sense. For some reason I read "500 km SSO" as "500x500 km LEO", hence the mistaken assumption. That, and I thought that Moon Express's payload was a rover, and not (as @Streetwind pointed out) a tiny lander doing a propulsive hop. And I thought I did my research.

Wait, what? How is anybody going to get anything to the surface of the Moon using Electron? To get from LEO to the surface of the Moon, you need 3.1 km/s for the transfer outwards, and then another 2.7 km/s (ish) for the braking burn. Electron can only launch 150 kg to LEO. Let's say that the rover we're trying to deliver weighs 10 kg (which, mind you, is lighter than Sojourner, the lightest rover ever deployed). That gives us 140 kg for the transfer vehicle. Now, it's safe to say this transfer vehicle will be using storable propellants, putting the vacuum Isp around 300s. Given this, the transfer stage's dry mass would have to be around 10 kg for the math to check out, resulting in a 14:1 wet mass/dry mass ratio for the transfer stage. Which is ridiculous, considering the scale. Does anybody have any information on this? Because, as I see it, assuming my assumptions are reasonable, I don't see how it's possible to use Electron to complete the X prize.

Definitely scientist. I love planning big, complicated missions, running lots and lots of calculations, testing every piece until I can feel sure that it will work exactly as intended... and then flying the mission and watching it unfold, all according to the grand plan. The bigger and more ambitious the mission, the better. I also tend to gravitate towards lower mass designs, because moar boosters is rarely the best answer to a problem.

Gregmore... I am your evil mirror-world twin! No! No! That's not true! That's IMPOSSIBLE!

Aerobraking at Jool is impractical to the point of uselessness. The same can be said of Laythe, unless you've already captured in the Jool system. Gravity assists are the best bet for cheap captures.

First off, you should not need to do any mining whatsoever. The Jool system is 100% conquerable without mining. Now, to the estimates. Looking at some rough Hohmann transfer window numbers, I would ballpark 5,200 m/s (assuming you start and end at Vall), not including delta-V required to get to Jool and get back. Breaking that down, that's Vall->Laythe, 900 m/s , Laythe->Tylo, 1500 m/s , Tylo->Bop, 1300 m/s , Bop->Pol, 600 m/s , Pol->Vall, 900 m/s. As an aside, for getting to Jool, you should consider figuring out gravity assists. A Laythe or Tylo gravity assist can mean a free capture into the Jool system, which can save a couple thousand m/s. Using gravity assists to get there can save another thousand or so, but is both difficult and mind-numbingly tedious, so I don't recommend it if you're willing to just throw some more delta-V at the problem. For getting back, it's advisable to try and take advantage of the Oberth effect and eject straight from low orbit of some moon, to the tune of more delta-V savings. Hope these things helped. The Jool system is one tough cookie to take on all at once.

Kerbal Engineer Redux

False. I always take "good" care of Jeb. He really enjoys those multi-decade Mk1 capsule trips. The user below me skis.

Well, "best" is difficult to pin down, given the number of possible criteria. But, going on the metric of "most impressive mission undertaken", I present Wayfarer, the craft I used for my grand tour (one launch with one Kerbal, plant one flag on every body with a solid surface & return home): Sorry for the cluttered screenshot, but challenge submission viewers like seeing lots of numbers. If you want a boatload more pictures, the mission album is here: http://imgur.com/a/SFUuC

I'm not concerned about accommodating a longer tube. I'm concerned about making a longer tube. Fuel tanks aren't trivial to make, and they certainly aren't off-the-shelf.

It's not a question of doing the things themselves. Grid fins, landing legs, etc. are more economically efficient simply because you're only producing one launch vehicle. Running one rocket assembly line is hard enough. Running, say, 4 would be a nightmare. It would, to an extent, defeat the point of assembly line construction. And seeing as having a really good vertically integrated rocket assembly line is one of the things that makes SpaceX so price competitive, moving away from that model would be crippling. It's all about standardization. It's much easier to do one thing really well than 4 things really well.

I was more concerned with the way a shorter tank would affect the center of mass, given that changing the first stage length necessarily moves the second stage up or down, which is going to change the CoM, especially when the first stage is nearly empty. But, regardless of that, the real problem here is that you would have to re-build the assembly line in order to change the tank size. The manufacturing that goes into something like a rocket fuel/oxidizer tank turns out to be non-trivial to change. Making significant changes to the assembly line for every launch would be prohibitively expensive.

If only it were that easy. You can't actually just stretch or shrink a rocket like that, since changing the tank volume will change a whole bunch of other things, like the structural and aerodynamic load on the entire vehicle, the propellant distribution, the center of mass (and therefore your avionics programming), the amount of backfill helium needed, and probably some other stuff I'm not thinking of right now. Plus, you have to change your assembly line around, which is a lot of effort. It's simply easier to build a standard size rocket, and just not use all of its capacity for some (or, more realistically, most) launches.

7/10, for over-engineering and mods.

Pick up whatever book I happen to be reading and read some.

Well, if your craft weighs 300 tons, and you want to land on Vall, then you need a thrust-to-mass ratio of at least 3.5, for a TWR of 1.5 (and having it this low will mean an unpleasant and inefficient landing). So, that means you need to be producing at least 1050 kN of thrust with your engines. Since each NERV produces 60 kN, this means 18 engines. Well, not quite. See, 18 NERVs weigh 54t, which means we have to factor the weight of engines added into our calculations. Doing some simple algebra yields a figure of 22 engines. Honestly, I think you'd be better off using the closed-cycle rapiers. 66 tons of nuclear engine are going to do horrible things to your delta-V.

I'm of the opinion that the value of carbon is severely understated. Not only is it necessary for making all sorts of things (like silicone, which is good for sealants), but more importantly it's necessary if you want to expand the population in-situ at all, for the simple reason that the carbon atoms that will end up composing the new colonists need to come from somewhere, and shipping them from Earth sort of defeats the point, and is really expensive. Same for phosphorous and nitrogen, although not quite to the same extent.