thanks brian,

that information allowed me to create a whole ellipse which was one of my goals. i used the conic tool to make the first arc as usual. then i mirrored/rotated the arc. then based on what you said i found you could use the conic tool to draw the remaining arc by simply using the ends of the first arc, the tan/tan point of the first arc, and the apex of the mirrored/rotated arc. i didn't need to enter a rho value to do that step. so two simple additional steps to get a full ellipse. you can then confirm the ellipse by using the center width and height.

the only thing i still can't figure out is what information one would need to duplicate the ellipse manually. without any nice computer tools like an ellipse button or a conic section button. i have the center, width, height, and i calculated the foci, and calculate the rho value. but none of that really helped me duplicate the ellipse manually. i keep trying stevens' method but can't get the same ellipse with that method. i guess i'm just curious that if i was a naca engineer back in the day, what info would i need to recreate an elliptical leading edge. i'm also puzzled as to why they define the leading edge with a circle if they were putting ellipses in there (i'll probably never know the answer to that question).

i guess i'm wondering if i could add some sort of simple information into the naca definition that could be used to put an ellipse in manually. i know we don't need it for your script. but i'm just wondering about it in general.

update; i found some equations that could be used. that would satisfy my question about how you could define this, in the old days, without too much difficulty. now the only thing i'm curious about is if i can somehow re-create the ellipse, in moi, without using the ellipse or conic section tool. mainly out of morbid curiosity.