I took a look at your balloon proposal. In order to go higher it would essentially need to be lighter / generate more lift than the extra components subtract from it in weight. I started looking into some of the math involved and I wasn’t able to clearly see whether you could get enough additional lift.
I think one way of thinking about it is “lift per unit of helium / hydrogen”. Adding heat essentially increases the efficiency of a given quantity of lift gas in lift production, but max height will be dictated by bursting diameter, which will be a function of internal gage pressure. At max altitude, you are essentially trading weight from lift gas with weight of your heater and recirculation system. If the mass of gas you save by heating it is greater than the mass added by the heater and recirculation system, you get more lift, which means you can pull a bit of gas out (pre-launch) and postpone bursting ever so much longer, and thereby go higher.
A 3S 3000mAh LiPo at 30C will theoretically max at 90 amps at ~11V, or about 1kW, and weighs some 8 oz or so, I think. The heater you’re proposing pulls 1.5kW. So you’ll need a pretty heavy LiPo just to power the heater.
The amount of gas in a balloon at launch … for an 8ft dia. balloon is about 270 cubic feet, at STP (unpressurized) is some 3lbs of helium according to these online calculators, so maybe you could get it hot enough to save a pound of gas? (How hot would it need to be? 100°F? 150? Is it a polytropic process, making the math that much harder?) Whether or not you could save that would depend on so many factors, though, and I’m personally concerned with what the heat loss will be at altitude; it’ll be hotter than atmospheric if you heat it, but it needs to be way hotter (delta-T of some 100°F or better, I’m guessing) to get the necessary efficiency to offset the additional weight, and I’d have to do the math / research, but I feel like a thin layer of latex will not be great at preventing heat loss.
A lot of smaller concerns I remember. With a closed hydrogen-only system, you technically can’t start a fire no matter how hot the heater gets (must have oxygen, period), so unless there’s a good chance of accidentally letting it get oxygen I wouldn’t be concerned about that aspect of overheating. I’m not particularly concerned about a fan; added weight for a function I’d hope I could fulfill with convection, and fancy ductwork or something if I had to do something to cool the heater. I want to see what a 1500W heater looks like; I did stuff with resistance wire (NiCr) a while ago and I’d expect 1500W-worth to be quite a lot of wire (i.e. kinda heavy). I would not add any extra weight I didn’t absolutely have to, so no valves, no sideways jet valves, absolutely nothing fancy at all, unless I had a compelling case it’d make it more efficient.
Basically, for a variety of reasons I think your proposed balloon would be too heavy and inefficient (in heating the gas and keeping it hot) to actually achieve a higher altitude as intended, and I don’t think it has any practical use outside of achieving a higher altitude that a normal balloon couldn’t fulfill more simply. (Keep in mind I don’t actually have much experience with weather balloons, so I could be totally off-base.)
I think if you had a better (i.e., higher power to weight ratio with a reasonable energy to weight ratio) power source than a LiPo, it might become more realistic. I’d say some kind of fuel (gasoline, kerosene), but then you need oxygen from somewhere, making the system more complex, maybe intractably so. At that point, it’s pretty much a regular hot air balloon anyway.
It’s a very interesting math / physics problem, though. I came up with a differential equation for balloon lift; I’m guessing it’ll have to be numerically solved, and I will also need stress-strain for the balloon material, which I’m having trouble finding. Given enough development, I might be able to simulate the flights, which would remove a lot of the difficulty, the same way OpenRocket makes rocket design relatively simple.
The forces that matter most are gravity, buoyancy / gas pressure (same thing), and drag. Wind is not very relevant unless it’s going to cause a balloon material failure; I’m not trying to predict anything besides altitude at this point, so I don’t care much about moving sideways. Balloon material restorative force is relevant in a lot of the internal dynamics that have implications on the growth of the balloon, as well as the heat stuff (the balloon growing actually makes the thermodynamics a bitch of a problem for me).
When you set up Newton’s Law, you get acceleration is dependent on the square of velocity (drag) multiplied by a few things which are altitude dependent (density, drag coefficient (also depends on velocity), cross sectional area (which depends on pressure differential primarily, which will depend on altitude and lift gas temperature / density)). The lift will depend on balloon diameter (only, I think), which will depend on altitude and lift gas state (which I need to relate to altitude or velocity somehow if I can). Thus it all becomes a differential equation with the dependent variable of altitude and independent variable of time, but it’s very nonlinear, and unless a lot of simplifications can be made or accidentally have one of those nonlinear DEs that have solutions, it will have to be solved numerically.
There’s some simpler analyses on the internet that make a lot of assumptions, and a few altitude vs. time plots. They all suggest that assuming a constant lift rate is reasonable, since as drag reduces due to lower density, the balloon grows in frontal area to essentially balance it out again, keeping lift rate essentially constant, and the data shows straight(ish) lines that suggest it’s a reasonable assumption. So for the time being a super-detailed analysis is likely unnecessary … unless you start heating it up, then things get weird (unless there’s some simplifications I haven’t seen). Anyway, I think that for the upcoming mission, I won’t have to do really hard math, but for your balloon it might be useful.
I need to stop.
ANYWAY, so that’s a lot of my thoughts regarding your balloon proposal. I hope I’m not coming off too poorly or too critical; FWIW the way I see it is if you have good answers for most questions / criticism, you’re probably on a good track, and if you don’t, it’s probably better to learn it’s not tractable and abandon such “dead-horse” tracks before you burn 100 hours and $2,000 on something you can’t get to work.
It’ll probably fly, but I don’t think it’ll be better than modern designs without a bunch of consideration.
Just though of one other thing: hot latex might have different material properties (i.e. a different burst point). Something to consider.
Ok, stopping now.
