I'm currently trying to write a script in python that I can use to optimalise a flying wing aircraft. I've run into a problem when trying to use data from airfoiltools.com. I've tried to calculate the zero lift drag coefficient using a value for Cd and Cl found on airfoiltools.com, I used the following equation:

Cd = Cd0 + Cdi

Cd0 = Cd - Cdi -> I then substituted the induced drag coefficent:

Cd0 = Cd - Cl**2/(piARe)

The symbols are:

Cd0 = zero lift drag coefficient

Cd = total drag coefficient (from airfoiltools.com)

Cl = Coefficient of lift (from airfoiltools.com)

AR = The aspect ratio of the wing

e = The oswald efficiency factor

The problem is that this equation gives me a negative value for Cd0, which is not possible for obvious reasons.

Please, does anyone see my mistake here? I'm not formally schooled in aerospace engineering so I don't know all the theory behind these equations, thus I may not understand wether I can or cannot use them in this situation.

Thank you in advance and kind regards, Remco van Woerkom


Induced drag is only produced when real lift is created. In 2D flow, when only the airfoil drag is given, there is no induced drag even for discrete lift coefficients. 2D flow assumes an infinite aspect ratio which results in zero induced drag.

Your zero lift drag coefficient should be the airfoil drag coefficient at the actual lift coefficient at the wing station when the airplane is in flight. Do this for several stations over span since the lift coefficient varies over span. Plus the contributions of fuselage, tail and whatever is added to the configuration, of course.

  • $\begingroup$ Ahh that makes a lot of sense! Thank you that helps out a ton. However could you elaborate on how the lift coefficent changes over the span of the wing? Or maybe reccomend a paper or article to read that explains this in more detail? I would love to understand it. Thanks!! $\endgroup$ – Remco van Woerkom Dec 19 '20 at 10:09
  • $\begingroup$ @RemcovanWoerkom I recomment this and this answer. $\endgroup$ – Peter Kämpf Dec 19 '20 at 11:25

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