Ideal aspect ratio - aspect ratio dilemma

[philSweet]

Foils become more efficient as aspect ratio increases; but for a fixed area, this implies a lower Reynolds number (Rc). Foil efficiency (L/D) decreases as Rc decreases; so there is an ideal aspect ratio that depends on the relationship of velocity to area. I have not found any info on this, but several references to others asking the same question. A study was done on model gliders but its results seemed to be dominated by the manner the tail section was varied as AR was varied. Using available test data, a surface plot of the form below could be created with a spreadsheet. A series of these plots for various angles of attack would be useful for setting starting points in the design of high performance rudders and small propellers for HPVs. A sense of how linear the change in performance is with change in size would help decide on the importance of the relative size between rudder and main foil.

The spreadsheet method assumes a fixed foil type. Better would be to allow a foil optimizer to compute new foil geometry for each aspect ratio based on the Rc implied by that aspect ratio, and then reduce the performance by the amount appropriate to that aspect ratio. I suspect this method would be quite a bit better than the spreadsheet. The effect seems to be recognized by the designers of micro UAVs, but again, no plots.

Any one seen anything on this.

[DCockey]

What is constrained on the foil, span/draft or area? Classic aircraft design treats area as a constant, but for many boat design situations span/draft is the constraint. Or to put it another way, how will aspect ratio be changed, by changing span/draft or planview area?

For a given lift (as opposed to lift coefficient) and planview shape induced drag decreases if span/draft increased. Induced drag stays (almost) constant for a given span/draft as area is changed. Considerable discussion of this in: The Myth of Aspect Ratio

Drag of a foil section increases faster than lift as lift increases from the section design lift, typically the drag change is close to the lift change squared or more (outside of a drag bucket). See the CD vs CL plots for sections in Theory of Wing Sections for examples. Note that this is a 2-D viscous effect, different than the 3-D, inviscid induced drag though the two are frequently lumped together as "induced drag".

So for a given water/air speed and density, lift, profile and planview shape the optimum area and draft/span can be determined. Pick an area and aspect/ratio. Calculate the required lift coefficient of the foil to achieve the required lift. Calculate the induced drag. Determine the corresponding sectional lift coefficients and look up the corresponding drag coefficients. Calculate the sectional drag based on the drag coefficients. Sum the induced drag and sectional drag for the total drag. Repeat for the next area and aspect ratio combination.

Optimization becomes more complicated when it's recognized that keels and rudders need to perform at a range of speeds and lifts. A keel or rudder optimized for a given lift may not have sufficient margin for higer lift and/or lower speed situations.

[philSweet]

I was considering small, low powered vessels on the scale from HPVs (1 man, not triremes) up to small sailing skiffs. Quite a bit of data is available regarding the rules of mechanical similitude used for scaling down a hull to a smaller size, but scaling down the highly engineered foils on a performance skiff is a bit of a black hole (at least to me it is).
So draft constraints don't really come into play. I'm trying to figure out at what size scale the practical structural limits on aspect ratio cease to be an issue due to the physics of the situation. I'm still dredgeing the web and am starting to find some links to low Reynolds number data dumping grounds. The micro UAV guys are working down around R=10^4. There seems to be a hole in the data centered around 10^5. So far, every case I've found where low aspect ratio has been employed, there has been some rule bias toward low aspect ratio.

[Erwan]

Hi PhilSweet,

Please find attached a pdf file workpaper from M Selig & Guglielmo.

You will discover that some asymetric wing sections (only a few) can exhibit a decreasing lift curve slope with increasing Reynolds, but only around a small range of Reynolds.

Otherwise, you test your wing section with XFOIL @ different Reynolds

hope it can help

Cheers

EK

[Erwan]

Hi again,

With regards to the propeller problem, the "efficiency" of the propeller should consider the following parameters
Prop diameter/ rpm / boat speed.
A larger and low rpm prop will fit better a slow boat than a small prop @ 5000 rpm.

But may be there is an alternative to prop for low Reynolds

Cheers

EK