How to calculate the takeoff speed for a hypothetical aircraft?

Given some basic information such as:

• aircraft weight
• wing load (including wingspan, and basically the whole wing configuration)
• airfoil profile
• coefficient of lift
• angle of attack

Is it possible to get an estimation of the minimum takeoff speed? And we are not speaking here about the conventional takeoff (until aircraft reaches 15m altitude), but the minimum speed relative to incoming air until the lift force overcomes the weight of the aircraft.

$$L = \frac{1}{2} \rho v^2 A C_L$$ and $$v^2 = \frac{2g W_S}{\rho C_L}$$

where:
$$C_L$$ = coefficient of lift (this, of course would depend on airfoil and angle of attack)
$$W_S$$ = Wing loading

But as I'm just scratching the surface of this field, I am unsure if my logic is solid and I'm here to ask for help.

• Knowing how you intend to use the information once you’ve found it will help decide how good your estimation needs to be.
– Jim
Oct 16, 2021 at 17:03
• With the parameters given, all you can do is to calculate the minimum airspeed. Adding available thrust would help to determine whether the plane would actually be able to climb and now ground effect will lower this speed, possibly below minimum sustained flight speed. Oct 17, 2021 at 9:33

Excluding safety factor of a little excess airspeed before rotation and excess thrust/angle of climb considerations:

Weight = Lift = 1/2×rho×v$$^2$$×Area×Clift and Ws = Weight/Area

Multiplying W by g would convert your weight force into Newtons, otherwise your two formulas are interchangeable.

For these calculations, special attention to the AoA part of the Coefficient of Lift would be important to establish a safety margain. Because Lift is proportional to v$$^2$$, a little extra airspeed can be very useful in reducing drag and improving climb performance.

• Weight and lift are both forces. No need to 'multiply by g'... Oct 16, 2021 at 13:12
• Yep. Weight=mass X g. Oct 16, 2021 at 13:48