I Am asking about the takeoff power here not how the aircraft takes off.
What do I need if I want to calculate the power required by an aircraft to take off?
What parameters should I consider?
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In the physics realm $Power$ = Mass x Acceleration x distance/time
To many it means "how much throttle" , which is how much fuel/time.
"Throttle" x prop efficiency = $Thrust$
This gives you a unit of Force that can be directly compared to glide data as follows:
Potential energy Mass x Gravity x altitude loss = $Thrust$ x horizontal distance flown
This rearranged to $Thrust$ = Mass x Gravity x altitude loss/horizontal distance flown
$Thrust$ = force required for straight and level flight, expressed in "pounds or Newtons"
So if your plane weighs 10 lb and glides 5:1, you need 2 lb of thrust for straight and level flight.
One would at least double, or even triple this for "takeoff power", depending on your performance preferences. Sufficient "takeoff power" will give a safe climb rate to avoid difficulties with downdrafts.
For example: my plane glides 5:1 at 60 mph or around 5000 feet/minute and loses 1000 feet/minute. At 10 lbs it was calculated to need 2 lbs of thrust for straight and level flight.
How much more thrust do we need to climb 500 feet per/minute. Again, the glide data provides a very good estimate, 2 lbs x 500 fpm/1000 fpm = 1 lb additional or 3 lbs total at 60 mph. Higher speeds with more drag, or lower speeds "behind the power curve" will require more than 3 lbs of thrust.