I spent last night looking into this compelling suggestion. I wanted to find out if it could be done using a data logger at a typical r/c field so the first step was to figure out the value for Terminal Velocity (TV).

Turns out its pretty easy because theres no vortex drag in an unpowered vertical dive with a symmetrical airfoil. So at equilibrium of gravity and parasitic/form drag we get:

mg = F(drag) OR: mg = V^2 [rAC/2]

m = 10# airplane
g = gravity (32.2 ft/s^2)
r=air density (0.0705 #/ft^3 @ 90F and 500 ft asl)
A = frontal area of airplane (1.076 ft^2)
C = drag coefficient (I guessed 0.1 like a smooth sphere) Cessna 172 is 0.024 so I think this is conservative. Anybody know?

Solving for V and plugging the numbers I got 291 fps or 198 mph! Thats with a conservative drag coefficient! A Cd of .05 results in a TV of 412 fps or 281 mph!

Next I wanted to determine how high I would need to start the descent from zero initial velocity to arrive at TV of 291 fps. A simple assumption often done to solve this problem is to assume constant acceleration. Using the derivative form for acceleration a = dv/dt and velocity v = ds/dt results in the kinematic relation:

a ds = v dv , where ds is the change in distance we want and dv is the change in velocity that we now know.

Since a is just gravity (g) if things are assumed constant we get:

g ds = v dv

Solving the integral and evaluating up to a maximum of TV (291 fps) I got 1,315 feet! Yikes! Thats with no air resistance!

OK, in the real world we have air resistance so the equation for a really is:

a = g - F(drag) OR a = g - .0038V^2

I won't burden you with the kinematic solution but it winds up being a natural logarithmic function which is bad, really bad. Total height needed to achieve TV using air resistance is 5270 feet!

If you've ever tried to see how fast your car will go you'll appreciate whats going on here. The last 10 percent take 3 times as much distance as building the first 80% of the total. Thats why log functions are bad for us here.

One other interesting thing I discovered was while calculating the frontal area of the plane. It turns out the fuselage is only 9% of the total while the Duellist wing comprises 81% of the total!!! So if you want to go fast use a thin wing with a long chord and short wingspan - in other words a JET!

I did a run through with the engines removed and found I could lighten the plane by a couple of pounds. I couldn't save all the weight because I have to add ballast to the nose for balance. The TV changed to 175 mph but the logarithm is relentless with very little change to vertical height. I'm going to continue to work on this to see if I can start the dive at a high horizontal speed but that rules out my no-prop hopes.