Diamard,

Couple of points. Stability might not be what you think it is... The aerotreks CoG is probably around the guys backside... the engine is slung down the back, there's little significant weight up top and its stability is like a parachute, with most of the weight COG suspended under the point of lift. Slinging the lift elements in the middle will move the point of lift and cog together and you've got a stability issue. Note CoG, centre of lift and centre of effort are different things. Thats for a stable two plane solution, if you're going to move and fly and transition in three planes then you get complicated and start looking at centre of areas and aerodynamics. Bottom line is you need to work out the controls because lifting off the ground probbly isn't the biggest challenge, controlling it will be. You've got the choice of multiple thrust elements and speed controls, pitch controls like a helicopter or another control/thrust solution entirely.. The helicopter rotor head is proven and controlable and you could put a gyro stabiliser on it...

For Prop Math there's a potentially huge amount of area to cover but look at Momentum disk theory and Blade element theory. Both together will cover most of what you want to do. Be prepared that most introductory propeller math calculates thrust from a given lift provided by the prop - but doesn't calculate the lift...

Prop math also ignores 3d fluid effects, tip effects and inlet and exhaust factors. until it gets complicated most of the theory assumes the blade works like a wing which isn't true, there's a pressure on the underside as a result of prop slippage, the prop acting like a fan rather than a wing, which is more prevelant when the vehicle is slow or stationary.. Ducted fans are attractive because they remove the tip losses from the air spilling over the tip and so can be more efficient in certain circumstances, like Jet turbines. The same theory produced the tip fences you see on modern airliners. For Ducted fans to gain any benefit the tip has to be VERY close to the duct, the tip and the blade generally can be much broader.

If I really had to contemplate propellors strapped anywhere close i'd use a ducted fan and LOTS of kevlar .

For ducted fan ideas look at the hovercraft guys....

Andrew