It’s all about the Reynolds number . . .
So out of curiosity I wondered – what really is the difference in performance between a flat plate and a basic NACA type symmetrical foil? Was it even a close choice in some circumstances or was it that “foils are better in every way”, as is reasonably thought?
. . . and it seems as if it depends! - on the velocity of the water past the rudder: it depends on the width of the rudder combined with the speed of foil type: – the speed length ratio or the Reynolds Number . . .
A typical rudder is about 3” or 7.5 cm wide and for this post’s purpose let’s say the speeds involved go from 1mph to 10mph which give a Reynold’s Number range of 2.44 x 10^4 = 24,000 to 2.44 x 10^5 = 240,000 [3mph gives a Reynolds Number about 80,000 for that rudder].
So the typical discussions about flat plates vs foils show performance graphs that look something like this for Coefficient of Lift versus Angle of attack. I couldn`t find a graph for a symmetrical NACA foil, but for the sake of argument it’d be safe to assume they’d be fairly similar [but slightly lower lift coefficient] and the reason for considering that foils give superior results. Here we see 2 foils giving higher lift coefficients plus stalls delayed compared to a flat plate. Interestingly, the flat plate has a wider stall envelope than the foils.
So something like that is what one would expect . . . for higher Reynolds numbers. But kayaks operate over a speed range and the lower speed range falls under LOW Reynold’s Numbers – say 3mph and below – and here is the shocking result . . . flat plates perform equivalently to foils and at real low speeds, it even appears as if they outperform foils! I've included a paper showing and discussing these effects:
here's the abstract:
and here's interesting results at ReN 20,000 to 80,000:
Now this is not the whole story: there’s drag to consider as well as many discussions I’ve read about flat plates having quick and unpredictable stalls versus the more predictable foil type that initiates at the tail of the foil. But it really points to the fact that a flat plate rudder for general kayaking is essentially an effective, economic and reasonable choice. Who’da thunk?
[edited to add: the paper is about control surface effectiveness as control surfaces have to operate in either direction and so for this case are symmetric, ie NACA 00xx type foils. The suffix xx12 and xx06 refer to the foil chord thickness that these foils have at the 20% chord location [if I remember correctly] from the nose. ]