NACA series 4 aerofoil generator

A NACA series 4 aerofoil generator, based on the equations and methods set out in Abbot and von Doenhoff’s classic student aerodynamicists’ text, Theory of Wing Sections. Although the 4 series aerofoils are rather old (they were developed in the thirties) they are still useful for low-speed applications such as wind turbines or velomobile fairings. They are also tolerant of innacuracies in construction, dirt and insect accumulation, and real-world conditions generally.

I’ve improved on the methods desribed in the book by using Cosine spacing of the samples along the Thickness Distribution, working from Trailing Edge to Leading Edge so that there are more samples at the critical Leading Edge, as well as wrapping the Thickness Distribution around the Mean Line as a single curve from Trailing Edge to Trailing Edge. I’ve also used Fit Curve on the Mean Line to smooth out the bump that inevitably occurs with Abbot and von Doenhoff’s method, and the Flow component to map the Thickness Distribution onto the Mean Line: a lot less fuss than using the mathematical approach that was necessary in the 1930s!

NACA 4 series aerofoil generator - (19.8 KB)


Thanks for sharing!

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My pleasure, Martyn!
Let me know if you do anything useful or interesting with it, or if you have any problems - preferably the former :wink:

Will do Gareth! I’ve used a similar one in the past when designing a hydrofoil board for a kite. i think I just used the generator to create a foil section on the mast as it could generate symetrical foils.

For the main wing and stabiliser wing I imported point coordinates from a text file and created a curve through them. A common one used is and Eppler 817.

I’ve had to park this project for now but if I get time to return to it in the future I would like to figure out how to generate other types of foil instread of importing text files.

If you are not familiar with hydrofoils for kites…

Also attached the other NACA generator I used previously if you are interested. (19.0 KB)

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These are both very interesting - and surprising for me - approaches for generating airfoil shapes.

The surprise is because when I was working in the McDonnel AIrcraft (now absorbed into Boeing) Loft Lines dept. we used the following equation to generate airfoil shapes:

z = ay**3 + by2 + cy +d + ey(1/2) where z is up and y is aft.

This equation has the cube term so the surface could have an inflection point, and the square root term so it would have an infinite slope at the front. For a complete airfoil shape there were 2 equations - one for the top half and one for the bottom half. I’m not sure of all the aircraft this equation was used for, but I know it was used for the wings of the USAF F4, F-15, and (at the time) the Douglas DC-10 wing and flaps.

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Can you give example values for your a,b,c,d,e that would give something that looks aerofoilish? doen’t need to be an actual F-15 wing section :slight_smile:

There are lots of “official” postings based on this equation. Here’s the first one I found:

This one has a 4th order term that I’ve never seen before and, I expect, was probably not used in real applications:

Here’s a PDF about a computer program used to generate airfoil shapes:

The software I used was a series of Fortran programs that were part of something called the IBM Scientific Subroutine Package that I was told had some sort of US Gov’t certification. Back then all the parameters (a - e) were 64-bit “double precision floating point” values.

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The equation with the 4th order term is the equation used to define the thickness distribution of NACA four-digit and NACA five-digit airfoil series. I strongly doubt either series was used for F4, F15 or DC10 wings, etc.

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This page gives reference of airfoil shapes from many aircraft

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I got the Eppler aerofoil from that first airfoiltools website… you can download point coordinates from there and I imported this into grasshopper.

If you search for hydrofoil profiles there are only a few. The challenge is working out which one is best for the application you need! I believe there is software available that lets you simulate the foil and look at lift / drag etc (as that website does for each profile)