Ah, yes, I was getting to that...
Truth be told, I have no idea whatsoever about landing gear on aircraft, so I snipped the landing gear off of Orbiter's STS, calculated their volume with MeshWizard, and then multiplied that with the density of a modern warship- 0.5 tons/m^3 (I know it sounds like an extremely odd example, but still...).
That's how I got to that figure. Maybe it had something to do with including the landing gear doors with the actual gear itself. :shifty:
Landing gear doors will probably need to be of a different material than the landing gear itself, especially considering that they will need to have a TPS on them.
One option you might consider would be assuming landing gear weight as a percentage of vehicle weight--
this page suggests that 3% or so of total vehicle weight is a good first-order estimate.
As a more specific look at the shuttle's gear, I'll use the following pictures for reference:
One thing you'll note is that a whole lot of the volume of the landing gear assembly is in the tires, which are mostly air, with some rubber holding the whole thing together. I'm not sure how thick the tires would be. There might be data out there on airplane tires for heavy aircraft that you could look into in order to figure out how dense that rubber is and how much of it is actually air.
From the first image, you can see that a lot of the structural components are fairly thin pieces--an I-beam of whatever they're made of is quite strong for its weight.
From the second image, you can see the cylinder in the middle (which probably makes up the second-biggest contribution to volume, after the tires) is a hydraulic system designed to cushion the impact of landing--there's probably a lot of hollow-ness there. Again, not sure what that looks like in cutaway or how much it masses, but there might be data out there somewhere for similar devices.
There also seems to be a whole book on the subject--
chapter 8 applies to landing gear weight, book starts
here, other chapters/appendices available by looking at the
index of that directory. Looks like it could be an interesting read...
I'm not sure how durable the gear would have to be... obviously it has to withstand a 60-70 ton craft landing at high speed, but I'm also concerned about the need to land in an emergency with propellant tanks full, which would require landing a nearly 400 ton craft. Either way, they still have to withstand the takeoff of a 400 ton craft.
It's fairly common for aircraft to need to land at a lighter weight than they took off at, which is why that A380 which experienced engine failure a couple months ago spent a few hours circling and dumping fuel. The shuttle also dumps fuel during an abort maneuver (RTLS I know for sure, haven't read as much about the others), so I think that's a perfectly reasonable thing to be able to do.
Consider also what
kinds of emergencies you're planning to handle. Presumably you'll have more than one engine onboard--Will your craft be able to fly on only one engine? Real multi-engine aircraft are capable of continuing flight with an engine missing. For your craft, if you had a single engine fail shortly after takeoff, what would you do? Seems to me that "fly in circles over/near the landing site and burn off fuel to reduce weight using the remaining engines" is a reasonable course of action, and then you don't really have to design the thing to handle a max-gross landing.
As for the extreme case "just took off, all engines failed," there's not really much use for a strong landing gear there, either--at that point you're probably looking at an off-airport landing (in the Hudson, maybe?) and in that case landing gear is either useless (for a water landing) or just used as additional padding (for a ground landing).