hi brian,

i think i know what you mean now. are you referring to the updated tangent points having more significant digits? if so, the added numbers are for the added precision needed to fix the error you found. i was previously using the same precision as the naca points. but to get it to work out, i had to add as much precision as i could with the tools I have available (i.e. MoI and a pocket calculator). though, even that precision is far less than that which i normally use.

normally i use double precision (16 significant decimal digits). the updated tangent points are single precision (7 significant decimal digits). the naca points are only three significant decimal digits. as i eluded to in a previous post, they were using slide rules back then. no pocket calculators or computers, since they hadn't been invented yet. so this is why i have been curve fitting their numbers, rather than taking them literally. they don't have enough precision to be taken literally. the rail points, on the other hand, i compute with double precision. so they can be fitted using the control point option.

also, keep in mind, you do not need to use the tangent points. i thought it would make things easier for you by adding them. but if you want to calculate the tangent points yourself, with the theorem you found, that is fine with me. so you really have three options right now. any option you choose should work out. so pick whichever option is most appropriate for you.

hopefully, you found the latest version of the Fortran codes and they help you out. hope you have a happy new year.

anthony