Distal taper on the tuberculed spitfire fin for the olo of the sun

The tuberculed spitfire fin for the olo of the sun showing non linear distal taper.

The addition of leading-edge tubercles

"The addition of leading-edge tubercles to a scale model of an idealized humpback whale flipper delays the stall angle by approximately 40%, while increasing lift and decreasing drag"

Fluid Physics

"a staggering 32% reduction in drag, 8% improvement in lift, and a 40% increase in angle of attack over smooth flippers before stalling"

http://www.asknature.org



"The swirling vortices inject momentum into the flow," said Howle. "This injection of momentum keeps the flow attached to the upper surface of the wing and delays stall to higher wind angles." 

http://www.scienceagogo.com

Olo of the Sun 19 foot surfboard , Spitfire cutaway fin, foiling tubercules

Foiling tubercules on the spitfire cutaway fin,  for the Olo of the Sun 19 foot surfboard ,

http://olosurfer-woodensurfboardsatpipeline.blogspot.com/2010/12/olo-of-sun-19-foot-surfboard-spitfire_02.html

Olo of the Sun 19 foot surfboard , Spitfire cutaway fin

Here's the 13 inch spitfire cutaway fin for the Olo of the Sun taking shape,  when set into the board the tab below the cutaway won't be seen.



The faceted cutaway is a development of the radial cutaways used on previous fins, and is of the type used in 1940's spitfire tailplanes.



Leading edge tubercules will be added next...

More wavy sword blade, wing, and fin theory

  In order to get a feel for the sort of  air resistance generated by a wide blade which is stalled ( keeping in mind that tubercules reduce drag even when not stalled ) one can swing a lightweight wooden staff or batten with a similar width. A flat sided batten will work best.



In doing so it's immediately apparent that the maximum speed of the cut is determined by air resistance.



In support of this we can note that air resistance goes up with square as speed increases. Also  as discussed  the drag caused by the outer part of a completely stalled wide cutting blade   is definitely very significant in proportion to the muscular energy  available to power the sword.



Once a sword is in a continuous circular arc motion  ( excluding air resistance ) it takes a lot less energy to keep it in motion than it does to accelerate it in the first place. Thus continuous arcs are not necessarily very tiring, as long as the air resistance is low. 



Air resistance is the catch. Air resistance saps energy very quickly. I've found this also with shorter weapons. For example it is less tiring to do fast whirling staff escrima drills with thin  heavy sticks than it is with  thicker lighter sticks. When such drills are done slowly the lighter thicker sticks are much easier to use, but once going fast air resistance soon limits the top speed. . .  and that's when doing very tight small radius arcs spirals figure eights and so on, it's even more the case with longer weapons.  With simple strikes where the weapon travels through a shorter arc ( e.g 90 to 180 degrees ) this isn't as apparent, the lighter stick feels faster as the limiting factor then is inertia during acceleration.



With longer weapons the most energy efficient redirections are larger arcs which maintain the speed of the weapon rather than shorter stop/start turns with greater acceleration/deceleration and consequent energy sapping inertia issues .  During larger arc redirections and turns  air resistance needs to be addressed partly because the speed is higher and partly because the blade is experiencing relativley high angles of attack even in a large arc turn.



During WWII it was discovered that the spitfire could turn more quickly than the ME109 as even though it did larger arc turns it did so with greater airspeed due to more efficient lower drag elliptical wings. Turning tightly is not always the fastest way to turn, it uses more energy.  Of course if anything gets in the way of the fast  moving blade during a turn it is going to be damaged a lot more than by a slowly moving stalled blade attempting a tight turn, and that is no doubt  a bonus when 'hedge trimming' a wall of opponents

Stall reduction via a wider range of air flow angle of attack is also useful due to the fact that pre stall and stall situations create vorteces which tend to make the wing or blade oscillate uncontrollably. . . so it's good for control as well.



One way of avoiding air resistance and stalling problems is via a narrow thicker blade tip, however with these types cutting efficiency is lost, and the pointed tips create very significant tip drag vorteces which spatulate tips largely avoid. So all things considered, for the control of 360 degrees of territory I'd design  a long wide bladed cutting blade with leading edge undulations. . . . ..   and behold such types exist !



There is another reason why undulating blades experience less drag, to do with  air flow from the strong of the blade to the weak. During cuts ( particularly the long continuous arc type )  the majority of the time the blade is presented strong first, with the weak trailing behind. This creates air flow towards the tip which makes  a big increase in the drag inducing tip vortex as the air flows off the blade at the tip. Leading edge tubercules help to prevent this flow to the tip, and spatulate  blade tips deal with it better than pointed ones.



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Tuberculed cutaway spitfire fin, simplicity vs complexity and the myth of Occam's razor.

Here's the tuberculed cutaway spitfire fin resin coat with the second resin coat.

Recently a critic of the tuberculed fin ( Our friend Mr Black from the 'Surf a Pig blog http://surfapig.blogspot.com/2010/07/tubercules-and-other-gimmicks.html  ) complained that it is overly complex and that simpler solutions are better, in an attempt to apply Occam's razor to fin design.



It was suggested that this ( very nice ) fin is simpler:

The concept of simplicity is however problematic as it's impossible to determine what is simplest. Such judgements are arbitrary. There's no evidence to support the idea that simplicity is more efficient, and in fact simplicity is a very complex and problematic concept to use as it is impossible to know what it means in practice.



From Wikipedia:



"  When scientists use the idea of parsimony, it only has meaning in a very specific context of inquiry. A number of background assumptions are required for parsimony to connect with plausibility in a particular research problem. The reasonableness of parsimony in one research context may have nothing to do with its reasonableness in another. It is a mistake to think that there is a single global principle that spans diverse subject matter.[10]

 As a methodological principle, the demand for simplicity suggested by Occam’s razor cannot be generally sustained. Occam’s razor cannot help toward a rational decision between competing explanations of the same empirical facts. One problem in formulating an explicit general principle is that complexity and simplicity are perspective notions whose meaning depends on the context of application and the user’s prior understanding. In the absence of an objective criterion for simplicity and complexity, Occam’s razor itself does not support an objective epistemology.[9]

The problem of deciding between competing explanations for empirical facts cannot be solved by formal tools. Simplicity principles can be useful heuristics in formulating hypotheses, but they do not make a contribution to the selection of theories. A theory that is compatible with one person’s world view will be considered simple, clear, logical, and evident, whereas what is contrary to that world view will quickly be rejected as an overly complex explanation with senseless additional hypotheses. Occam’s razor, in this way, becomes a “mirror of prejudice.”[9]

 

It has been suggested that Occam’s razor is a widely accepted example of extraevidential consideration, even though it is entirely a metaphysical assumption. There is little empirical evidence that the world is actually simple or that simple accounts are more likely than complex ones to be true.[21]"





http://en.wikipedia.org/wiki/Occam%27s_razor

Resin coating the tuberculed cutaway spitfire fin for the 7'8" Jet

Resin coating  the tuberculed cutaway spitfire fin for the 7'8" Jet today.

More biomimetics and fin tubercule theory. . .

Given that the tubercules give an efficiency advantage, it's like money in the bank which can be 'spent' in various ways.



For example the advantage could be used entirely to increase the angle of attack capability. Alternatively it could be used just to reduce drag, or to increase lift.



Adding the tubercules to an existing fin should give some of each of the three advantages, but by altering the fin size or thickness the fin can be tweaked to weight the tubercule gain towards one or two of the parameters more than the other(s).



As an example if one just wanted to reduce drag then the fin could be made thinner with tubercules, because the tubercules give back the aoa capability lost by making the fin thinner. Also the fin can be made 5 percent or so smaller because that's the gain in lift given by the tubercules. . . if we give it back by reducing fin size we also reduce drag.



Biomimetics in practice: