Warning: Some bullshit calculations in the following text, not only assumptions but heavy guesswork/random stuff
It's a matter of balance between lift off speed and acceleration to reach this speed:
- Higher mass means less acceleration for the same force and possibly higher stall speed if wings are same
- Acceleration time to a speed beyond stall speed dictates take-off run and distance
- For higher acceleration more force is needed
Propeller efficiency, increasing drag and wheel friction complicates the issue but let's keep things simple, I directly take engine HP -> force so could be all wrong from now on....
Same stuff could have been described with wing loading (W/S) and T/W ratio terms too...
Take off distance = square of speed/2 * acceleration (from Aerodynamics For Naval Aviators book, let's see if we can work with it)
d= V^2/2a
So if we keep stall speed same with scaled up wings for heavier TB3,
Assuming lift off speed is 50 knots, 25.7 meters/sec for both TB2 and TB3 (which is propably not but the ratios may hold and give us some idea)
For TB2, 300 meters observed for takeoff run from youtube videos
300m=25.7*25.7/2*a
300m= 660/2*a
a=1.1 m/s^2 (acceleration)
TB2= 650 kgs
TB3= 1200kgs
Now if we use the same engine and propeller on TB3, and let's say the mass is still 1.85 times of TB2. New acceleration will be 0.594 m/s^2 from F=ma
New distance will be: 555 meters.... not acceptable for ship take-off....
For TB3, for 300 meters of run, we need an engine power of ~200 hp assuming TB2 uses ~110 hp (too tired to find & check engine manual).
For 300 meters TB2 uses an engine with 110 hp (Rotax 91x)
For 200 meters TB2 needs an engine with 165hp (PD170)
For 100 meters TB2 needs an engine with 330hp... (AI450, 450hp, or maybe a smaller version of this core)
Assuming no weight changes...
For 1200 kg TB3 multiply all with 1.85, assuming again the weight stays same (which is not)...
For 300 meters TB3 needs an engine with ~200hp (PD222)
For 200 meters TB3 needs an engine with ~300hp (AI450 with a small core or 2x PD170)
For 100 meters TB3 needs an engine with ~600hp... (AI750)
And this is with the same stall speed assumption. To get the same stall speed, TB3 wing has to have 1.85 times more area than TB2 wings....
Maybe a constant speed propeller, if not already used on TB2, may help for low speed performance and cut those power requirements from engines a bit (by a factor of ~1.5, so new required engine power will be 133, 200 and 400hp back to single PD222 and AI450 range, example propeller data:
https://www.propellor.com/Content/Images/uploaded/Documents/Articles/Comparison of Fixed and CS propellers corrected.pdf ), helped with not only scaled up but better wings. According to formula d= V^2/2a, speed is more important than acceleration because it is squared, so Tb3 may have nice design changes because there is also a space limit on deck....
I also don't rule out catapult or rocket assisted take-off. Just for backup we should develop that method too. If desperate piston diesel + turbofan/turboprop dual or triple engine configuration can be tried too, UAV can be launched with all engines and the jet engine can be shut down during slow cruise flight for maximum endurance, reignited for high speed...
Calculator used:
https://www.omnicalculator.com/physics/acceleration