IMHO, mostly from making EX motors up to O, and lots of sims, the price is closer to 2K if you do the work yourself. It shouldn't take all that much of a rocket to get to just that altitude from a place like Black rock. However, it needs to be the RIGHT rocket!
Getting the experience to get there is probably at least 10K and a few years. I could be underestimating that part!
One can theoretically make a 75mm motor on totally custom hardware that could get there, if the rest of the rocket can take a high mach flight at fairly low altitude. It does get a little easier as you go a little larger, say, 88mm. Burn duration is your friend. I wouldn't go larger than 114mm for that altitude. So that would be your potential motor diameter range. I'm assuming EX motor here with high Density ISP propellant. I'm not aware of commercial motors that really fit the flight profile. N5800 for instance would be better if it didn't hit as hard, and had a few more grains.
Of course you COULD go larger than 114mm, but then instead of a modest motor in the O range you'll need a P. Your price and logistics will go up tremendously. So will the necessary size of your team.
It's not really all that hard to design a motor that could potentially boost a rocket to double your goal or more. The problem is getting it to survive Mach 4. So the engineering that you might want to think about is how to get it to your goal plus at least a 10% margin (wind cocking allowance) as slowly as you can. Then it is more likely to survive.
An even more modest two stage can solve the stagnation temperature and aero load problems, at the cost of complexity yielding additional failure modes. How much rocket do you need to light at 20Kft to get to 60Kft on a somewhat tilted flight due to a 40 knot wind at altitude? Not much. Then figure out how to get that small rocket to 20Kft while fairly vertical and successfully light it. (just an example) A two stage alleviates the need for a tower so you can use a conventional rail with less overall drag penalty. The parts are much smaller to transport, helping the logistics.
But until you can get to the point where you can engineer a few solutions, it is hard to do the price vs probability of success tradeoff. Just figure out the sorts of things you'll need to be good at, and start learning them!
Gerald
