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How should I do the math to find the CLmax of a wing that has more than one airfoil, each with a different CLmax?
I am trying to make a model with a portion of the wing tip with a airfoil that has a low Cm, but it has a low CLmax too. So...how can I calculate my CLmax?
The result depends on the wing twist and its taper ratio. You will never get the full 2D lift with a 3D planform, and how much you get depends on the details of your wing. The first step would be to apply Hans Multhopp's methods for calculating the lift distribution of wings (Subsonic Lifting Line Theory), and a search on Github shows a variety of codes to try. Factor in the different airfoils with local twist according to their zero-lift angle of attack.
Lifting line theory does not deal with flow separation and stall, so you need to interpret the results. Ideally, your airfoils will reach their stall angle of attack with a straight lift curve slope, and this stall angle of attack is reached at the same time over the whole span. This should maximise the lift from that wing. Adjust taper and twist until you reach this result (and subtract the twist from the differences in the airfoil's zero-lift angle to arrive at your geometric twist distribution).
However, if you also care about handling, leave some margin at the outer wing in order to have stall start first at the root. Also, you might want to add the effects of aeroelastic deformation in order to avoid unpleasant surprises.
I believe you just blend the two Cl values based on their proportionate share of the wing area. Say 20% of the wing area is 1.4, and the other 80% is 1.6, so you use a blended value of 1.56 for a number to plug in when calculating stall speed.
