Masthead31_Sept2014.pub - page 16

The Masthead
Know It All Contest Solution
to the June 2014 Question
On Speed/Length Ratio, Reynolds Numbers and Model Tests
(This issue’s new Know it All question is on page 20)
The Know It All questions and correct answers are important design tips for students as well
as other marine professionals. We suggest that you file them away for future reference.
The Question Was:
As the chief engineer for Majestic Sea Yachts, you are designing their new 78-foot Sea Ranger model expedition
voyager. The boat is 71 feet 8 inches on the waterline, and you have arranged for towing-tank tests to observe
performance and check on your computer speed-and-powering calculations. The towing model is to be 1/12th size.
What speed should the model be towed at to run at the equivalent top speed as the 12.68 knots your computer
calculations indicate that the boat can achieve? What is the Reynolds number of the full size boat at this speed and
the model at its speed, and what does this mean with regard to the model-test results?
The Winner Is:
We received several answers to the June 2014 Know It All question but only one of them covered all the aspects of
the question and was both complete and accurate. This was from Westlawn student Will Sturdy. As a result of his
remarkable demonstration of insight, brainpower, sagacity and gumption, we have no choice but to award Will with
the official title of “Know It All.” Henceforth, he should be addressed only as “Mr. Know It All” by all and sundry. Of
course, a Westlawn T-shirt, cap and Know It All certificate are on their way to our winner.
The Answer Is:
The speed/length ratio the Sea Ranger is operating at is:
71 feet 8 inches is 71.67 feet waterline.
If we wanted to conduct towing-tank tests on a 1/12th-
scale model of this boat, the model would need to be run
at the same SL Ratio, which is:
71.667 ft.
÷
12 = 5.972 ft. WL model length
By Froude’s laws of similitude, the wave patterns around
the 5.972-foot waterline model and the 71.667-foot
waterline boat will be the same at these respective
speeds because the SL Ratios will be the same. We can
now see how the Reynolds numbers compare for the
model and the full-size boat.
Reynolds Number (Re)
Re = (V x L)
÷
Where:
V = boat velocity, ft./sec.
L = Wetted length (LWL), ft.
12.68 kts
= 1.498 SL Ratio
71.67 ft. WL
1.498 SL Ratio x 5.972 ft. WL = 3.66 kts
Sept. 2014 Page 16
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