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Heckie
11-14-2000, 05:36 AM
All over the Internet I find links to the article of Paul Zander, “Design and construction of centerboards and rudders”(march 1996). Having a heavily restricted design class boat, I tried to work out the formula for the parallel sided foils. Unfortunately I have to conclude they are not perfect. The original formula for the leading edge reads:

y = (t/2) * ((8*sqr(x) / 3sqr(Xle)) - (2*X / Xle) + ((x^2) / (3*Xle^2)))

where x is the position along the chord from 0 to 1
y is the thickness at a given value of x
t is the maximum thickness as a fraction of the chord and
sqr is the square root function.
The above taken from the earlier mentioned NACA-formulation, and
Xle is the distance that the leading edge is faired.
Using these variables will not give proper figures!

My calculations show that the formula for the leading edge should be:

y = (t/2)*((8*SQRT(x) / (3*SQRT(Xle)))-(2*x/ Xle)+((x^2)/(3*(Xle^2))))

where
t = total thickness of the profile (mm).
x = the position along the chord of the fairing (mm).
Xle is the distance that the leading edge is faired (mm).

Also, the formula for the trailing edge doesn’t seem to give proper results:

y = (t/2) * ( (1- 3x^2) / 2*Xtl + x^3 / 2*Xtl^3 )

where x is the distance from the start of fairing.
Xtl is the distance the trailing edge is faired.

Or in Excel-language:
=(t/2)*((8*SQRT(B44)/(3*SQRT(fairing)))-(2*B44/fairing)+(POWER(B44,2)/(3*POWER(fairing,2))))

Having learnt from the leading edge I presume all distances should be in real length (mm). But that still doesn’t get me the right results. And also I feel the formula should be something like:

=(t/2)*(1-(((3*X^2))/(2*Xtl))+(((X^3)/(2*(Xtl^3))))))

Or, in Excel-language:
=( t/2)*(1-(((3*POWER(D44,2))/(2*fairing))+((POWER(D44,3)/(2*POWER(fairing,3))))))

This at least gives me a starting point at the thickness of the foil. But I still can’t get it right; I need a correction-factor. But then I’m not shure I have the right profile...

Is there anybody who can help me with this one?

Thanks,
Eric

scottek
11-14-2000, 10:21 AM
Eric,

I am working on it, will get back to you later...
-YF Scott

H Downey
11-14-2000, 12:11 PM
The leading edge equation worked fine for me. My Excel formula read:
=(t/2)*(8*SQRT(X)/(3*SQRT(Xle))-(2*X/Xle)+(X^2/(3*Xle^2)))
But, t is actual thickness, in whatever units you wish, X is in same units. I tried a thickness of 25mm, and over a length of 50mm, and it looked fine.

The trailing edge formula appears to be missing a square of Xtr in denominator of the first term. My formula in excel read:
=(t/2)*((1-3*X^2)/(2*Xtl^2)+X^3/(2*Xtl^3))
This appears to give the amount to remove, because it yields -t/2 at X=Xtl. Again, use real dimensions.

John B
11-14-2000, 01:24 PM
I had stuff like that come up on my cellphone once when it got wet. Don't tell me its really an artificial intelligence,(A.I.) with a desire to design boat parts.
THAT would be too good.

Steve McMahon
11-14-2000, 05:51 PM
The old boat designers and builders that I have been a groupie to over the years have all used the "Mackerel Formula" They took a look at the top veiw profile of a fresh caught mackerel and tried to copy the shape. I'm just kidding... well...sort of just kidding. Oh yea - don't leave it in the sun too long or it will kind of bloat up on ya and you'll get the shape all wrong. http://media4.hypernet.com/~dick/ubb/wink.gif

Heckie
11-15-2000, 06:23 AM
Thanks Mr Downey. It works!! It runs back to zero beautifully now.
I'm not shure if it looks like a freshly caught mackerel, but it looks fine by me. I never knew you could do these kind of calculations on a wet cellphone. Maybe in the States you're way ahead of us here in Europe...
The thing that's puzzling me now, is how much less drag will this new foil produce???

Eric

[This message has been edited by Heckie (edited 11-15-2000).]

Oyvind Snibsoer
11-20-2000, 06:34 AM
A physicist, lying on his deathbed, was asked whether he would ask God about fluid mechanics.
"No" he answered, "I wouldn't want to embarass him".