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I have hear of RTOW charts but I haven't seen any calculations with the runway length or slope. What is the formula or equation to finding flex temperature and V-Speeds?

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The RTOW (regulatory takeoff weight) charts are runway and configuration specific, so the length and slope (and permanent obstacles) and all taken care of (see red box below).

There is no manual formula, either the charts or a performance calculator such as the Airbus FOVE or the company's proprietary software.

This is what an RTOW chart looks like:

enter image description here

The information needed (example):

  • Takeoff from Paris-Orly, Runway 08
  • Slat/Flap configuration: 1+F
  • Actual TOW = 66 tons
  • OAT = 24ºC
  • Wind = +20 Kt headwind
  • QNH = 1013 hPa
  • Air conditioning: Off
  • Runway state: Dry

Source: Getting to grips with aircraft performance (Airbus via skybrary.aero)

Here's why there is no equation, from the Boeing book Jet Transport Performance Methods:

Here’s the complication: for the very first increment of time after engine failure, one second, we need to calculate the average acceleration in order to find the airplane speed after one second.

But we can’t find the average acceleration because we don’t know the thrust after one second. And we don’t know the thrust after one second because we don’t know the speed after one second. And we don’t know the speed after one second because we don’t know the average acceleration.

What they end up doing is iterative calculations and flight tests to come up with the graphs / tables.

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