Sailboat Speed Potential


Presented by Cory M. Wisnia, A MendoWorld Science & Math Tech Guy
cwisnia@mcn.org
Mendocino Middle & High School, Mendocino CA 95460

http://www.mcn.org/ed/cur/cw/cwhome.html

The "Speed Potential" of a sailboat might be given as a relationship between the SAIL AREA and the HULL UNDERWATER VOLUME. This sort of measurement comes up while the America's Cup Race is being planned for by sailing group Challenger/sponsors, and has led to design innovations.

Suppose for the purposes of this problem that:

Where:

x is the sail area
y is the volume of the hull underwater (HUW)
S is the speed potential

Two boats have the following values:

L'il Suzy: Sail (triangular) measures 8.5 by 11 meters high; HUW measures 8 by 3 by 2 meters (consider it to be a box)

Red Ryder: Sail (triangular) measures 9.5 by 9.5 meters high; HUW measures 7.5 by 3 by 1.75 meters (again, consider it a box)

Questions:
Which boat will have the best Speed Potential? Why or why not does this make sense when you consider the sail and hull values? In what way SHOULD the sail area and hull values be DEPENDENT, if at all?

A MORE ADVANCED SAILBOAT PROBLEM

Suppose that the relationship between the HUW and the Sail Area were ruled by 4 Guidelines, so that for any boat in competition, the following rules applied:

1. Sail Area (x) is less than or equal to 100 square meters
2. Hull Under Water (y) great than or equal to 25 cubic meters
(Thanks to Jonah Steinbuck of Mendocino High for catching an error that was here earlier, when it was mistakenly listed in feet and square feet!)

And they need to be related by the following inequality

3. The Product of the Sail Area by the HUW is greater than or equal to 1500 and less than or equal to 2600.
4. The ratio of Sail Area divided by the HUW is greater than or equal to .8 and less than or equal to 1.3.

Questions:

1. Do EITHER of these two boats above meet these guidelines? Show why or why not.
2. What would be the BEST boat possible to make which was still "legal" for this competition? What are the DIMENSIONS for the sail and hull under water? In other words, can you make a boat which is better than the two examples and yet meets all guidelines and is there a BEST set of values?

PS: this isn't necessarily a trivial question, as several years ago at least one or more boats in the America's Cup were disqualified for having not met requirement limits with regard to their hull specifications!

Please note: these are new problems and MAY have some bugs! If you tackle these problems, see if you can make improvements on them, and let the Wizard know by e-mail or snail mail. Tell how you arrived at your solution(s) so that others may follow your thinking, and include any graphs you may have as GIF files. If you wish to "snail mail" in graphs and solutions, here is the address:

The Wizard's Math Page
Mendocino High School
P O Box 226
Mendocino CA 95460

Please include permission to put your solution, or part of it, on the page if you wish to be acknowledged! Also include your school or city and state. BACK TO TOP

Do You Have NEW POWs or Enhancements or solutions? We will publish these for you! Mail them to cwisnia@mcn.org aka "The Wizard!"

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