Steve,

I read over the articles you are referencing. They state that the original definition contained circles:

"The values of leading-edge radius of the derived airfoils, published in references 9 to 12, were initially determined by plotting
the ordinates to a large scale and fairing in the best circle fit by hand."

I know from many documents and experience that the le and te are based on circles of a specified radius, made tagent to the rest of the airfoil definition. Perhaps you are confusing what some NASA engineers are doing in a Fortran code 50 years later to what the original designers specified. I am using the original NACA 65A009 definition. I am not going to recode this NACA Fortran code you are referencing. It offers me no benefit. There already exist many NACA airfoil plotting codes for one thing. I recommend Hanley Innovations VisualFoil Plus. You can not only plot the airfoil but get data for it at transonic speeds. I don't have $700 dollars to spend on it. Thus I am using the NACA definition and data.

I appreciate people trying to help. However, what you have been doing I do not perceive as help. Thus my frustration at this point. I am a retired engineer who has designed and worked on a number of real aircraft propellers. I am well aware of what I am doing. You can take that as hard heading if you like. When someone is insisting I am doing something wrong, I don't know how you would like me to take it. Plus, not showing how to do it supposedly right, until I request it. I have worked with a number of people that think being a road block is an accomplishment, that is how you are coming off to me.

No one needs to use this script if they don't want to. Nor develop it for that matter. I could care less. I thought it would be useful to people, thus the request. If you think its wrong, fine don't use it. But enough already. You are beating a dead horse.

Anthony