How to design a near vertical take off airplane, conceptually?
Say I have an airplane, similar to a Zenith 701. Say that it has a stall speed of 50 mph and a wing area of 60 sq ft, and it weighs 500lbs.
Now I want to make it land at 20 mph with full power and my tail volume is sufficient to keep the nose up at 30 deg. I also have slats and flaps to ensure my wing stalls above 30 deg AOA.
Say my max HP is 100. I understand, as a general rule for GA aircraft, thrust is 4x100hp=400lbs. Vertical thrust would be 400 lbs x sin 30 deg x 65% prop efficiency for a prop in climb, giving me a vertical thrust component of 400 x .6 x 65% = 160lbs vertical thrust.
Now, I only need to produce 500-160=340 lbs of lift from my wings. So I increase my wing size so that I can fly at 20mph with a lift of 340 lbs.
Is this correct, at least conceptually?