The problem of bulb optimization is a very interesting one but much more complicated than it seems at first glance.

A ) for a bulb shaped body there are two kinds of optimization :

a1:minimum drag for a given sectional area ( such as a engine nacelle fairing on a multiengine airplane )

a2 : minimum drag for a given total volume of the body ( this is a problem that was deeply analyzed to improve old airship performances )

This is our situation.

B ) for a given volume :

b1: increasing lenght to diameter ratio, wetted surface is increasing and drag coefficient is decreasing ( a slim body is more “slippery” )

b2: decreasing lenght to diameter ratio, wetted surface is decreasing and drag coefficient is increasing ( a blunt body has more drag )

total drag depends both on drag coefficient and wetted surface

Somewhere it should be a L/D ratio that is the best one

C ) for a given speed

c1: increasing bulb lenght, reynolds number is increasing , and frictional coefficient is decreasing

c2: the opposite is true decreasing bulb lenght

Just to make things more complicated this effect is variable with speed, it is cross connected with point B, and there is also an abrubt change of coefficients with transition from laminar to turbulent flow

D ) for a given volume and lenght

bulb cross section can be modified from height to width ratio 1 ( a circle ), to something that is wider and lower.

d1 :a low and wide bulb has more wetted surface but lower center of gravity

d2 :a “rounder” cross section has less wetted surface and higher cg

E )Last but not least, a bulb shape and size is affecting keel lift changing its effective aspect ratio due endplate effect

F)Looking to improve ( at least on paper ) keel performances, it should also be considered that when not going downwind, few degrees of leeway are to be expected and for this reason flow will not a perfect axial one

G)If you are in the wake of somebody else, or just due to wave turbulence water flow on the leading edge of bulb and kell will be not a perfect one, and unknow amount of existing eddies are not to be forgotten

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Conclusions

looking at americas cup very different solutions on boats designed by very skilled naval architects, for very well defined conditions ( valencia ) , it seems obvious that a final word on bulb shape optimization doesn’t exist

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My way

after a careful analysis of existing experimental data , and an optimization worksheet, it seems to me that for an “average” footy ( 200 gr of lead @ 0.6m/s ) drag is decreasing going up to a L/D ratio around ten

exceeding ten, the curve is almost flat and is not worth to have a longer bulb

somewhere I have plotted a graph L/D versus drag ( given speed and weight )

I will try to do my best to find it ( among an unbelivable amount of other stuff ) in order to publish my data on the forum

Flavio

Folgore ITA-5