Hello, this is Mark from Helios. Sorry for the delay, I've been really busy with the electrical systems of the X2 prototype. But now I'm waiting for a power unit to ship from China, so I figured I'd take a moment to catch up with you guys.
Let's see... so many questions. As far as engines, the prototypes and the P500 all use common brushless electric engines. I have 2 I'm eyeballing for the P500, one is more expensive and peaks at about 11kW, and the other is really cheap and peaks at 6kW. Both are 90+% efficient including the propeller. Which one I get will probably depend on whether we ever end up getting funding assistance, or if I'm paying for this myself...
20% would be very optimistic for the solar panels, sadly. At STP (Standard Temperature and Pressure) the panels I used on the first prototype were only about 8% efficient. However, at 25,000 feet the super cold air increases energy production by about 30%. So that helps. As you say, if you aren't planning on 24/7 flight you can use more power than the panels actually provide. The real limiting factor is the power system. More on the math behind the speeds will be below. It gets pretty dry and I don't want to put you to sleep before I answer all your questions :)
You mentioned using hot air or heating the lifting gas, which is a pretty cool idea and I could definitely see that working in a combustion engine design. I know the Graff and Hindenburg both had ventilation systems coming off their engines that worked well. However, in an electrical world heating isn't a luxury we can afford. It takes too much power, and the engines are so efficient they don't product much excess heat. I have been toying with the idea of putting the engine controllers in a position where air could blow across them into the pilot area, to heat the hands of the pilot. The controllers get fairly warm during constant use. But it definitely wouldn't be enough to heat the envelope.
You asked about materials. The X1 envelope was made with laminated nylon, because its light and easy to work with. However the X2 is meant to be a high fidelity prototype, so I'm using alot of the same materials I will use on the P500. It has a seperate outer envelope and inner envelope. The outer is made with Dacron, the same material used in aircraft and sailboat sails. Its not quite as strong as nylon, however it has better endurance in weather and sunlight. The inner envelope of the X2 was made with laminated nylon, and the P500 will be a thicker ripstop nylon/PU mix. I got some sample materials from Lamcotec, and they had a strong and lightweight nylon/PU that I liked. In the X1, X2, and P500 the gondola is made with fiberglass composites, mixed with sheet styrene and even some styrofoam in the X1.
Ok, now the math part. Got your caffeine ready? So, the formula for the velocity of a basic aerodynamic shape is:
Power = 0.5 * AirDensity * Velocity^3 * CrossSection * DragCoefficient
Where Power is the power required in watts, AirDensity is the kg/m3, Velocity^3 is the velocity in meters per second cubed (that cubed is a real kicker). CrossSection is the cross section against the flow of air in square meters, and DragCoefficient is a number that basically represents how aerodynamic the shape is. In my tests with the X1, the DragCoefficient was between 0.03 and 0.05. I went with the conservative number of 0.05.
AirDensity is 0.56 kg/m3 at 25,000 feet, and the cross section of the P500 is 90 m2. (All the units have to be metric for the equation to work)
The maximum power output of the P500 depends on how many power units are installed. For this example I'll assume they put in 50 power units, which can deliver about 6kW sustained.
6000=0.5*0.56*V^3*90*0.05
Simplified, that gives
4761.9 = V^3
So then V must be about 17. Now, thats in meters per second. To get MPH, we can multiply 2.24. So, it can go a maximum sustained speed of 38 MPH. It can keep going for about an hour and a half before the batteries are exhausted.
For a 24/7 sustained speed, we look at the power of the panels, which is 2700W at 25,000 feet. Averaged over a 24 hour period we can assume you will get about 1/3 of that because of the changing angle of the sun throughout the day (remember, no clouds at 25,000 feet). So our power we are working with is 877 watts. The battery chargers are about 91% efficient and the engines+propellers are about 90% efficient. So we really have about 718W around the clock. Plug that back into the equation above and we get about 18 MPH. Not very fast, to be sure. But then you fly into the jet stream for another 95 MPH added to your speed, and you can coast along at 113 MPH. Only flying east, of course. That's something that would be more beneficial to a cargo ship flying to China and back perhaps. Because you just keep flying east the whole time.
Still, I could see this being popular with the general aviation crowd. Basically you fly to the local lake or whatever, float around on the water while the solar panels charge back up, then fly home.