Team NYYC

NZK

Anarchist
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Roaming
@Rasputin22 after the Xmas regatta maybe this is more accurate?

images.jpeg

 

MaxHugen

Super Anarchist
Not quite. You (roughly) double the aspect ratio if the foil is end plated, not the span.  That means you double the span after squaring it - otherwise you’ll quadruple the AR. 
In this Span Squared | North Sails article they illustrate that the 'reflected' span is included in "span" measurement prior to the drag calc. Span in my calcs is sail height, so now I've doubled it before it gets squared. Seems right, the drag distribution is looking far more realistic:

image.png

 
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Board skiff

Super Anarchist
1,606
672
In this Span Squared | North Sails article they illustrate that the 'reflected' span is included in "span" measurement prior to the drag calc. Span in my calcs is sail height, so now I've doubled it before it gets squared. Seems right, the drag distribution is looking far more realistic:

View attachment 419211
That North article is good, and it is ultimately span that matters not AR. But end plating one end of a foil will not quadruple the effective aspect ratio.  In reality it won’t even double it. See NACA Tech Note 2440, Table 1 for example. http://naca.central.cranfield.ac.uk/reports/1951/naca-tn-2440.pdf
 

6F14B46C-3736-4234-A576-AF461702FE70.jpeg

 

MaxHugen

Super Anarchist
That North article is good, and it is ultimately span that matters not AR. But end plating one end of a foil will not quadruple the effective aspect ratio.  In reality it won’t even double it. See NACA Tech Note 2440, Table 1 for example. http://naca.central.cranfield.ac.uk/reports/1951/naca-tn-2440.pdf
Hmmm... that's from 1951.

North Sails appears to use Span*2 (shown as 'b' below) but there is no specific reference to end-plating of a sail.

image.png

Not easy finding anything specific on this topic!

 

erdb

Anarchist
806
619
Hmmm... that's from 1951.

North Sails appears to use Span*2 (shown as 'b' below) but there is no specific reference to end-plating of a sail.

View attachment 419223

Not easy finding anything specific on this topic!
Max, it doesn't matter how you calculate AR - whether you use span / mean chord or span^2 / area. It's the same thing once you replace area with span x mean chord.

When you double AR assuming a perfect seal under the sails, you can use 2 x (b/c)  or 2 x (b^2/A) or  [(2b)^2] / 2A. It all gives the same number.

 

MaxHugen

Super Anarchist
Max, it doesn't matter how you calculate AR - whether you use span / mean chord or span^2 / area. It's the same thing once you replace area with span x mean chord.

When you double AR assuming a perfect seal under the sails, you can use 2 x (b/c)  or 2 x (b^2/A) or  [(2b)^2] / 2A. It all gives the same number.
It makes a huge difference when calculating the Di using the equations from @Basiliscus.  As per my original query, applying a doubling of the Span before or after squaring is quite crucial for balancing longitudinal forces etc, since I'm calculating these myself.

 

erdb

Anarchist
806
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It makes a huge difference when calculating the Di using the equations from @Basiliscus.  As per my original query, applying a doubling of the Span before or after squaring is quite crucial for balancing longitudinal forces etc, since I'm calculating these myself.
They are mathematically the same thing. If you are getting different results, then there is an error somewhere in your calculations. Just put some numbers in the three versions I posted above. You should get the exact same AR with either of them.

 

MaxHugen

Super Anarchist
They are mathematically the same thing. If you are getting different results, then there is an error somewhere in your calculations. Just put some numbers in the three versions I posted above. You should get the exact same AR with either of them.
The equation I'm using is exactly as presented by B - which as he explained, does not use non-dimensional values such as AR, CL, etc:

Di = Lift2 / ( PI * e * 0.5 * Density_Air * Velocity2 * Span2 )     I have changed the Span part to (Span*2)2. 

Would be interesting to know how Vortex handles end-plating re Span when calculating Di - to double or not, or use a deduced  'factor' instead?

 

erdb

Anarchist
806
619
The equation I'm using is exactly as presented by B - which as he explained, does not use non-dimensional values such as AR, CL, etc:

Di = Lift2 / ( PI * e * 0.5 * Density_Air * Velocity2 * Span2 )     I have changed the Span part to (Span*2)2. 

Would be interesting to know how Vortex handles end-plating re Span when calculating Di - to double or not, or use a deduced  'factor' instead?
OK that's just written in a different form, but it's the same thing as calculating cdi first as cdi = cl^2 / PI * e * AR , and then Di = 0.5 * cdi * dens * A * v^2

So using your version, the (span*2)^2  is correct if you want to double the AR.

Vortex does handle end-plating, you have to specify if the wing is on a solid surface, but in addition to that and the AR, it also considers the shape of the planform (which is factored in as 'e' in the other equation). The advantage is that you can input the dimensions of the whole rig (jib and main), so I think it's more accurate than calculating induced drag separately for each sail.

 

pluscount

Member
341
31
Idaho
The equation I'm using is exactly as presented by B - which as he explained, does not use non-dimensional values such as AR, CL, etc:

Di = Lift2 / ( PI * e * 0.5 * Density_Air * Velocity2 * Span2 )     I have changed the Span part to (Span*2)2. 

Would be interesting to know how Vortex handles end-plating re Span when calculating Di - to double or not, or use a deduced  'factor' instead?
image.png

 


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