BYYB Forums

Greetings all,

From the 2011 edition of the Calendar of Wooden Boats by Benjamin Mendlowitz, we have miss June ...


http://www.woodenboatstore.com/2011-Cale...o/800-211/
and more at http://www.noahpublications.com/

I have bought the calendar for many years now, and Benjamin never disappoints. Benjamin’s photographs do not happen by accident. Careful planning for optimal lighting quality, time of day, sky conditions, sea state, backgrounds, and positioning of the chase boat for proper framing and subject lighting are hallmarks of his work.

The boat is Murmur, a 25’0” x 6’9” Buzzards Bay 15 class sloop (modified) designed by N.G. Herreshoff and built by Artisan Boatworks, Rockport, Main, 2009.

Aside from being art for art’s sake, this particular photograph just happens to be a very good example of a sailboat travelling at hull speed.

A bow wave forms at the stem as the boat pushes through the water. The length of a wave (in feet) is proportional to just over half of the square of its propagation speed (in knots) through the water. Usually you see this formula written the other way around as the speed of the wave in knots equals 1.34 times the square root of the wave length, or



and that is a simplification of velocity = sqrt( (gravity*wavelength)/(2 pi) * tanh( (2 pi) * depth / wavelength). or



The hyperbolic tangent term accounting for drag in shallow water is usually deleted, as the term rapidly approaches a value of one for water deep enough to not drag the rudder.

In short, as the speed of the boat goes up, the length of the bow wave gets longer, right up until the moment where the length of the wave matches the waterline length of the hull. At this point, the hull is resting on two wave crests as if they were saw horses.

If we push the boat any faster through the water, the wave will lengthen with the increased speed, and the second wave crest will slide backwards out from under the stern, dropping the transom down into the trough between the crests. We are now pushing the boat uphill, and the amount of energy required for faster sailing increases exponentially.

Hull speed for a 13 ft waterline Weekender should be 1.34 * sqrt( 13 ) ~= 4.8 knots or 5.5 mph, which is a speed that is achievable with the smallest of 4 stroke engines or a middle of the line trolling motor.

Here is the same photo with the wave crests lined in for clarity.



It's rare to find such a clear cut example, so I thought I would share it with you.

Cheers,
Tom

WOW, that's about as nice as it could be done. Thanks Warren

Beautiful, educational, and inspiring. Thank you!

Tom:  Great explanation!  What's the math tell us about hull speed of a Vacationer?

Dave

Greetings Dave,

The hull speed of a Vacationer will be about 1.34 times the square root of the Vacationer's waterline length.

The Vacationer is 21 feet on deck, and the keel is cut from 19 foot long lumber, so I am going to guess that the waterline length is about 18 feet. The square root of 18 is about 4.25. That times 1.34 gives us a theoretical hull speed of about 5.7 knots, or about 6.6 mph, which is not that much faster than the 5.5 mph we calculated for the Weekender. All other things being equal, if you want to double your speed, you have to lengthen the boat by a factor of four.

Cheers,
Tom

Imperical data supports the math.  Saralee would make 5.8 kt with a good wind.  I had her up to 8.6 down wind with the Honda running at about 3/4 throttle once.  More noise than go!

The 1.35 S/L ratio is purely a hypothetical mathematical "constant". In reality, all boats will travel at a specific wave form pattern, based on many variables (thousands). 1.35 is true of most modern yachts and fairly light shoal hulled craft, but is by no means a true indication of actual S/L ratios. In fact, most sailboats, except racers can not maintain a 1.35 S/L for very long. They can average 1.25 in the course of an afternoon, but most of time they're slower than this, with all but the most attentive skipper. This is especially true of cruisers, novice sailors and gaff rigs. Typically these boats are sailed "leisurely", meaning somewhat less then 1.35 S/L is the result.

Columbus managed a speedy .75 - .8  S/L as he crossed the Atlantic from Europe. Had he taken just the Nina, he would have managed 1, maybe 1.1 S/L, because she was "fast". I've recently purchased a yacht that regularly can reach 2.6 S/L ratio and can motorsail at about 2.9 S/L. For a 65' yacht this means she can motorsail at 23 knots (26 MPH), which is cooking along folks, on her 150 HP diesel. Yep, that's right 26 MPH in a sailboat! Of course this is running WOT and broad reaching, but she can casually do 17 - 18 knots under sail alone in moderate wind strengths. The open "box rule" boats and other ocean racers, can do much better then this, with speeds in the low 30's!

Paul are you getting my e-mails????

Great photo. He is one of the best.

Good explanation tom.

Paul? 23 knots?  The 327 foot Coast Guard cutter I served on would only do 19.  That is really scooting for a sailboat!

Hi Peter, less then 11 tons displacement, less then 12' of beam and a 63' LWL. This means it's hull speed is over 12 knots at a S/L of just 1.35. Since it has a 5.5:1 beam length ratio, the usual hull speed constraints go out the window, so she easily does a 2.0 S/L without much fuss, placing her in the 17 to 18 MPH bracket very easily. Add a tall rig with lots of sail area (1,700 sq. ft. of working sail) her SA/D is 34!, so she doesn't have trouble hauling the mail into the low 20's on a beam reach or motor sailing. She's a handful up wind, being a bit tender and twitchy, but a demon down wind, blasting in the mid 20's in gusts. It's a ridiculous boat, but I can have some fun, make major revisions and upgrades and sell her when the economy turns around for considerably more then I have in her.