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I want to be able to calculate the take off runway distance that a plane needs depending on factors such as weight and plane size, etc. I know that graphs exist in the pilot handbook to do this but is there a specific formula that I could perhaps put into a program?

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These calculations are quite complex because they take into consideration a lot of different variables, just off the top of my head:

  • Take off weight, which includes FOB
  • Runway length
  • Runway condition
  • Field elevation
  • Air temperature
  • Air pressure
  • Wind
  • Engine type and airplane configuration

Based on those (and I am sure many more), you have to calculate at minimum V1, VR and V2, and possibly others.

These calculations are looked up from a table.

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It's not just one single formula, there is a whole procedure that needs to be followed in order to get to the TO distance. From Torenbeek Appendix K:

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For a given configuration of weight, altitude, temperature and aeroplane configuration (flap setting), compute:

  1. The takeoff run: compute the distance required to accelerate to the moment of lift-off, plus part of the airborne distance to a height of 35 ft.
  2. Emergency distance: distance to accelerate to critical engine fail speed, plus distance to brake to a standstill.
  3. The TO field length is the greatest of the emergency distance, TO distance to 35 ft with engine failure, and (all-engine TO distance times 1.15) to reach 35 ft.

The Appendix K referenced above contains a more detailed procedure for carrying out these steps.

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