Minimum thrust to weight ratio.........
 

.....to do the full stunt pattern in style...?

The Old Timers would say that a competitive FOX .35 Stunrt Plane should be 40 ounces or less.
I've never flown competitive stunt and never questioned that rule of thumb...until recently I plugged the numbers into a static thrust calculator and found that a 10 x 6 APC spinning at 9500 rpm produces 41 ounces ..!
Now back in the day they didn't have APC props but they had some wooden props that I believe would have been pretty close.
So....it looks like having a 1 to 1 ratio is a good place to start when you do most of your flying over concrete and asphalt.
What sort of ratios are the modern day competitors working with...?

Combatpigg offers good advice. You will need the equivalent of 3D power for stunt, so if electric powered you are looking at 150 watts per pound. 1 to 1 power is a good estimate.

What I'm really curious about are the ratios that the top flyers use
What triggered this curiosity was recently looking through APCs prop catalog.
Whenever they list a prop with a decimal point in the diameter number you can bet it's a competition / specialty prop.
When I saw they sell a 11.5 x 4 ....my guess was that it was for CL stunt. [well maybe RC 3D too)
By just plugging in a random rpm number to go along with that prop [let's say 14000 rpm]...the result is 10 pounds of thrust...!
The resulting speed would be 55 mph...which gives this hypothetical plane a 5 second per lap pace...so I don't think this WAG is too far off.

I think 14,000 rpm is a bit high for stunt. 10,000 rpm is closer to what I look for before launch, sometimes even less, 9500 for my Fox 35 mounted on a Bi Slob. I normally launch at a very rich 2 cycle or even richer 4 cycle.

The stunt pattern requires climb capability similar to RC 3D flying, therefore, brute horsepower is NOT what I look for in a control line engine. Torque is what you need to turn long, low pitched, climb propellers. Consistency is second which often means awesome fuel draw from smallish venturis. Much different power profile than RC.

I think all the "Top flyers" are going electric now. The low pitch props are the normal to slow them down when heading down hill and keep the engine in it's power band.

Yeah a FOX .35 with a 10 x 6 is designed for 9500 to 10,000 rpm...
but 14,000 with a 4 pitched prop ought to be doable with most any piped schuernle ported engine and would give 5 second range laps ..which I believe is what the Top Pilots shoot for.
In this case I understand that the pipe is supposed to act as a rpm limiter to keep the model from speeding up on the down hill side of the manuevers.

By the time the Electric Flyers install an audio system to make the plane sound like it has an engine...isn't it too heavy by then...?
LOL.
I've seen the electric planes in action and they are impressive..especially with their programmable "accelerometers" to keep the models speed constant.