For the CLto (take off lift coefficient), is there some way to estimate this?
I was thinking of using CLmax but wouldn’t this be too big? I was thinking maybe CL cruise?
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For many airplanes the lift-off lift coefficient is determined by the maximum pitch angle before a tail strike occurs (minus some safety margin, of course). Before take-off, the speed which allows flight at this pitch angle is computed so rotation is not initiated too early.
If your configuration allows to be stalled with the achievable pitch angle during ground roll, taking off at this maximum lift coefficient is unsafe and most likely counter-productive. Normally, drag near stall is growing disproportionally with angle of attack, so rotating too early will create high drag which leaves less thrust for further acceleration. Also, any flow asymmetry between the left and right wing near stall might cause an unstable rolling motion which can ruin your day and the airplane with it.
For fast-accelerating airplanes a safety factor of 1.1 for lift-off speed can be considered (which means lift-off occurs at 82.6% of the maximum lift coefficient) and for more conventional types this could be increased to 1.2 (so the lift coefficient is only 70% of its maximum). Details depend on the shape of the drag polar and the stall behavior the particular design.
The lift coefficient for cruise will most likely be too low to allow for a reasonably short take-off distance, unless we speak of a motor glider.
answered Mar 24, 2022 at 9:36
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$\begingroup$ "Normal takeoff attitude for the B737-800 is between 8 and 10 degrees. This provides 20 inches of tail clearance at flaps 1 and 5. Tail contact will occur at 11 degrees of pitch (if the aircraft is still on or close to the ground)." While the takeoff pitch angle is (by my standard) dangerously close to tail strike, it feels like the flight manual is very confident that the airplane is off the ground before rotation completes (which takes 4-5 seconds). [1]: flaps2approach.com/journal/2014/8/4/… $\endgroup$ Mar 24, 2022 at 18:34
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$\begingroup$ I think using tail strike pitch angle (or takeoff rotation angle) as an estimation of takeoff threshold AoA could be quite inaccurate, because liftoff is likely to happen before target pitch is reached, after which the AoA won't raise to target pitch either because the speed vector will also pitch up and eventually catches up with pitch angle. $\endgroup$ Mar 24, 2022 at 18:40
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$\begingroup$ @user3528438 If the B757 flies already at 10° pitch, it will not reach those 11° while still on the ground. Thank you for confirming my answer. And when liftoff happens before target pitch is reached, you rotated too late. Physics cannot be cheated! $\endgroup$ Mar 24, 2022 at 19:52