(I deleted the first attempt at posting as the post was clipped at the first inserted image.)

I've started exploring foil design - both lifting and rudder foils for proas.  This and completing the wing rig design being the remaining elements required for the 16.8m proa I'm building.  The principal objective being to establish two way proa foils that are sufficiently efficient to permit foiling with only two leeward foils and eliminating the need to rotate through 180 degrees.

Working to Tom Speer's proa series 3 boards, I've created an ellipse based mathematical model in which to design the section shapes.  The low pressure side of the board is similar to Speer's proa boards but the high pressure side represents a significant departure being much flatter, and consequently, simpler to build.

My initial XFLR5 results are extremely positive.  Somewhat astonishingly, the blunt ended proa boards are outperforming the Eppler e817 and Speer's H105 on all scores once the lift angle exceeds 5 and 3 degrees respectively.  The rudder foils are also outperforming the Speer proa boards, I'll post some info on these once I've done a bit more modelling.

I want to qualify my claims in three ways.  Firstly, I have only tested my designs in XFLR5 and would like to corroborate my findings in a CFD application and perhaps through third party examination.  I'll probably send the modelling to Tom Speer - at least before I publish these ideas more widely.  Secondly my models are smoother than those obtained from Speer and Eppler offsets - both mathematically and through the number of points defining the section.  To what extend does this smoothness contribute to the results?  Thirdly, in defence of Tom Speer's modelling: his proa board results were obtained using an ncrit number of 9 and I'm not sure re the H105.  In more recent times its been established that modelling in water should use ncrit between 1 - 3; ncit being a measure of propensity of the fluid environment to become turbulent across a lifting surface.  Tom Speer's results were also obtained at lower Reynold's numbers (from 150,000 to 1.5million) than I am interested in.  With a foil of 0.4m chord, the Reynold's number is 1.8 million at 10 knots.  Reynold's numbers are proportional to foil chord, so for a proa of the size I'm building,  I'm only interested in modelling from near the top of Speer's range and beyond.

I've attached images of the foil sections and results obtained at a Reynold's number of 2 million.  The results are similar across a range Reynold's.  This isn't the best environment for detailed images, so I may need to look into attaching or uploading files to the forum.

The first image shows two P5 (my designs) cross sections in red and green the Eppler is pink.

The second image shows Cl plotted against Cd. The P5 boards again in red and green.  The e817 and the Speer H105 in pink and blue.  The P5's can't match the more conventional sharp trailing edge boards at low lift characterised by fully attached laminar flow.  They come into their own beyond a Cl of 0.4 - the low drag bucket clearly evident.

This third curious plot shows the Cl/Cd ratio plotted against Cl.  In the most efficient range Cl/Cd exceeding 60, the P5 foils are unmatched.

The final plot shows Cl/Cd plotted against angle of attack.  This graph is problematic in that angle of attack differs from lift angle.  Observe that all the foils generate lift at negative attack angles.  It would make more sense to draw this graph with all foils showing zero lift at zero degrees - what I term, lifting angle.  These results are a function of the coordinates supplied to the program, so only really make sense if we mentally shift all curves to share a common Cl/Cd point.  That said, its instructive to observe that the P5 foils maintain lift through a wider range of angles of attack.

I'll post the rudder info in a day or two, as commitments permit.

Regards,

David

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