Parasitic drag from catamaran hulls and beams

[DSmith]

I have calculated the parasitic wind drag from the hulls and cross beams of a beach catamaran by equating it to a flat plate with a width equal to the projected width of the total platform (perpendicular to the apparent wind) and a height equal to the height of the hulls. Especially when going to windward, this works out as a larger % of the total drag than I expected.

Do people think that this is a reasonable approximation? If not, do you have any suggestions.

Thanks

Dave

[frosh]

Sounds approx right, but was is the practical significance? Can we reduce it much; I think not. Anyway at sailboat speeds it is not nearly as significant as the drag forces on the immersed hull, nor the drag force on the sails and rigging. Please explain why you are concerned about it.

[gggGuest]

Yes you'd expect it it be very signficant, which is why it is well worth working on the sections, joins and things and generally tidying it up. Probably only really a concern for high end racing though as I doubt its that huge in percentage terms of total drag.

[DSmith]

Originally Posted by frosh

Sounds approx right, but what is the practical significance?

Well, this beachcat is on foils so when off-the-wind, the hulls will be out of the water. I've found that this parasitic drag is about 17% of the total drag. I'll need to check my arithmatic again but I thought I had it correct.

[grob]

You are spot on, I have an article somewhere on the C class cat Miss Nylex where they performed measurements and found that drag of hulls and beams was 17% of the total drag.

According to John Shutleworth's study (http://www.john-shuttleworth.com/Dogstar50-article.html) The drag of the hulls in the air is even more significant, although he is talking about a 50ft cat.

I think what this shows you is that if you are designing a foiling cat, you want to keep the hull size to a minimum for drag as well as weight.

Gareth

[frosh]

If you read the background about Julian Bethwaite designing the 49er you will see that he gave a lot of thought to this exact problem. In a way he streamlined the hull in its entirety even the parts that are above the waterline. He eliminated vertical bulkheads and created low freeboard, and wings that the crew trapezes off, that were very different to the conventional tubular structures.
I don't know the proportional reduction in parasitic air drag acheived, but obviously he knew that he had a very quick design and that at high boat speeds, air drag on the hull, and above water structures does matter.

[tspeer]

Originally Posted by DSmith

I have calculated the parasitic wind drag from the hulls and cross beams of a beach catamaran by equating it to a flat plate with a width equal to the projected width of the total platform (perpendicular to the apparent wind) and a height equal to the height of the hulls. Especially when going to windward, this works out as a larger % of the total drag than I expected.

I think you're on exactly the right track. Racers are very concerned about every ounce of weight, especially aloft, but I think they ought to be adding up their frontal area, too.

And don't forget about the windage of the crew!

A good source of information on information on windage is Hoerner's book, "Fluid Dynamic Drag". You can find it on used book sites or in engineering school libraries.

Hoerner shows the forces on circular cylinders, wires and cables is

CD = 1.1 sin^3(alpha) + 0.02
CL = 1.1 sin^2(alpha) cos(alpha)

with the reference area being diameter * length, and alpha being the angle between the axis of the cylinder and the flow. The dependence on angle of attack would be the same for all cylinder shapes, and you only need change the "1.1" - the cross-flow drag coefficient.

For sharp-edged (corner radius < 10% of the width) square cylinders, the cross-flow drag coefficient is 2.0, but it drops to 0.11 if the corner radius is 20% of the height or more. For a rectangle with the narrow side to the flow, the coefficient drops from 1.4 to 0.7 by rounding the corners. So round the gunwales! But you can still leave the center 60% of the deck flat without a significant drag penalty.

A hull that's in the water behaves like a cylinder of twice the width, because all the air has to go up and over the top of the hull. But once it is airborne, the drag quickly becomes that of a cylinder of the same width. Shuttleworth has an illustration showing a cross-flow drag coefficient of 1.5 for a sharp-edged hull in the water, 1.3 for a hull with rounded decks, and 1.1 for the hull clear of the water. He doesn't say just what the geometry is, but it looks like the freeboard/beam ratio is about 1 in the water and the height/beam ratio is 1.5 - 2 out of the water. So flying a hull not only reduces wetted area, but windage as well.

For one body shielding another, Horner has a drag coefficient of 0.6 for two circular cylinders in tandem, based on the total area of bot cylinders, rising to 0.75 with three diameters separation between them, after which it stays constant. So effectively the drafting cylinder has a drag reduction of 91% when it's touching the windward cylinder, and a reduction of 64% when it's drafting more than 3 diameters further downstream, assuming the drag of the windward cylinder doesn't change (which is not quite true, but it makes the bookkeeping simple). You might be able to adapt these factors to hulls, although Shuttleworth apparently just uses the exposed frontal area at the apparent wind angle.

I'd say if your hulls are only 17% of the total drag, you're doing very well.

[Chris Ostlind]

The Nacra A2 does a pretty good job of making a point about hull windage. see below for photo.

The designers, Morrelli/Melvin, http://www.morrellimelvin.com/ also managed to eliminate the dolphin striker from the mix by going to carbon beams. A really tricked-out A2 could probably benefit from having better, more organically shaped, beam ends at the hull mounting points, but the hull itself sets a new standard for a production cat that pays attention to what happens above as well as below the waterline. http://www.morrellimelvin.com/a2/

http://www.nacraa2.com/ this site has an interesting Power Point show about how one of these bad boys is put together at the factory.

Chris Ostlind
Lunada Design

[DSmith]

Originally Posted by tspeer

A good source of information on information on windage is Hoerner's book, "Fluid Dynamic Drag".

I will have to get a copy. I used your references to it on your website for calculating the spray drag and junction drag of the foils.

Originally Posted by tspeer

For sharp-edged (corner radius < 10% of the width) square cylinders, the cross-flow drag coefficient is 2.0, but it drops to 0.11 if the corner radius is 20% of the height or more.

Is that correct or did you mean 1.1?

Originally Posted by tspeer

I'd say if your hulls are only 17% of the total drag, you're doing very well.

Upon checking, I am actually getting 36% to windward and 10% to leeward. I had actually halved the drag coefficient from 1.17 for a flat plate to 0.6.

What do people think would be a reasonable drag coefficient for the equivalent frontal area perpendicular to the apparent wind for a well rounded hull like the Nacra A2 shown above? 1.17 might not be too far off when considering both hulls. It is certainly a large proportion of the total drag though.

[tspeer]

Originally Posted by DSmith

...
Is that correct or did you mean 1.1?

Oops. 1.1 (pg 3-13, Fig 23)