Alpo Posted September 1, 2019 Share Posted September 1, 2019 How would one figure the length of the long leg of a right triangle, if the hypotenuse had a curve? I am attempting to determine the length of a small boat made from a single sheet of plywood. > A small flat-bottom boat of shallow draft. Specifically, a flat-bottom boat made of one four-feet by eight-feet piece of plywood, the bottom being a two-feet eight-inches wide eight-feet long pointed-ends lengthwise-centered oval cut from the piece, and the boat's sides being comprised of the two remaining pieces attached lengthwise to the outside edges of the oval. < If you cut an 8" strip from each side of a 4 foot wide piece of plywood, you can attach these two 8" strips to the sides of the wider 2'8" bottom. If, however, you "oval-cut" the 2'8" x 8' bottom, so that it comes to a point at each end at the center line, the circumference of the bottom will now be greater then 192". If, instead of doing an oval, the boat was diamond-shaped, simple a² + b² = c² (actually c² - a² = b²) gives a maximum length of 90.5". That, however, is with a straight hypotenuse. A curve would certainly be longer, requiring a shorter length. I could figure it if it was a circle, but a "pointed oval" I probably could have done it back when I was taking 10th grade geometry, that was nigh on fifty years ago. I just don't recall how. Thoughts? Link to comment Share on other sites More sharing options...
bgavin Posted September 1, 2019 Share Posted September 1, 2019 Can you "stick build" it by laying out on the garage floor and tracing the curve with a string, then measuring the string? Link to comment Share on other sites More sharing options...
Alpo Posted September 1, 2019 Author Share Posted September 1, 2019 I'm sure I could, but I have no interest in building the boat. I'm just trying to figure out the math involved to come up with it. That section I quoted - between the > < - seems to be saying the boat will be 8 feet long. Mathematically it can't be. But I don't remember, if I ever knew, how to figure the length of that curve. I thought someone here might. Link to comment Share on other sites More sharing options...
Texas Lizard Posted September 1, 2019 Share Posted September 1, 2019 If both legs of right are equal...Finish the circle...If not then then add another right angle to other side and finish circle...See what kind it is and go from there...Should be a formula for a race track design....Then take 1/4 of it.... Texas Lizard Link to comment Share on other sites More sharing options...
Marshal Mo Hare, SASS #45984 Posted September 1, 2019 Share Posted September 1, 2019 4 hours ago, Alpo said: I probably could have done it back when I was taking 10th grade geometry, that was nigh on fifty years ago. I don’t think so. Link to comment Share on other sites More sharing options...
bgavin Posted September 1, 2019 Share Posted September 1, 2019 As you mentioned above, if the curve is a circle calculating the length of the arc is straight trig. However, it sounds like the curve is an ellipse.. meaning more digging to see if there are any arc length calculations for ellipse. Link to comment Share on other sites More sharing options...
Alpo Posted September 1, 2019 Author Share Posted September 1, 2019 Why trig? Wouldn't πd work? Go from your center point to any spot on the circumference. That's r. Double it. That's d. Multiply by π. That's the circumference. Divide by 4. That's the length of ¼ of the circle. I never took trig, but that seems like basic geometry. Link to comment Share on other sites More sharing options...
Marshal Mo Hare, SASS #45984 Posted September 1, 2019 Share Posted September 1, 2019 You have a curve. Is it actually part of a legitimate ellipse or circle? What are the Fock, major and minor axes? I doubt you actually have 1/4 of the perimeter. the calculations are challenging, not high school geometry. https://www.mathsisfun.com/geometry/ellipse-perimeter.html Link to comment Share on other sites More sharing options...
Michigan Slim Posted September 1, 2019 Share Posted September 1, 2019 And THIS, ladies and gentlemen, is why I bombed high school. I have a headache. Link to comment Share on other sites More sharing options...
Marshal Mo Hare, SASS #45984 Posted September 1, 2019 Share Posted September 1, 2019 20 minutes ago, Michigan Slim said: And THIS, ladies and gentlemen, is why I bombed high school. I have a headache. Not really. That math would be encountered in a good graduate school math course in geometry. I know. BS, MS, PhD Link to comment Share on other sites More sharing options...
Assassin Posted September 1, 2019 Share Posted September 1, 2019 The problem with math class was the lack of explanation. I passed all the word problems. All the other crap above normal mathematics made no sense. Why don't they teach us why we need to know this stuff rather than x + y = z, what the heck does that mean without telling the kids they are building a boat. All theory and nothing practical. Then, they'd tell me, you got the word problems correct why can't you figure out the easy stuff. Every algebra/trig teacher was like Ben Stein. Link to comment Share on other sites More sharing options...
Tom Bullweed Posted September 2, 2019 Share Posted September 2, 2019 Also, I would calculate based on all three legs being straight line segments and add a fudge factor to allow for the curve. In a boat, it is like more of a spline than a fixed radius curve. Link to comment Share on other sites More sharing options...
Alpo Posted September 2, 2019 Author Share Posted September 2, 2019 2 hours ago, Marshal Mo Hare, SASS #45984 said: You have a curve. Is it actually part of a legitimate ellipse or circle? I was replying to bgavin, when he said " if the curve is a circle calculating the length of the arc is straight trig" I know that, for this boat, it is NOT a circle. 13 minutes ago, Tom Bullweed said: Also, I would calculate based on all three legs being straight line segments and add a fudge factor to allow for the curve That's what I did to come up with 90.5". Hypotenuse can't be longer than 48. Short leg is half of 2'8", which is 1'4", or 16". That gives you a long leg of 45.25". Double that, because it's only the front half of the boat, and you get 90.5", instead of 96" - 8 feet. Link to comment Share on other sites More sharing options...
Marshal Mo Hare, SASS #45984 Posted September 2, 2019 Share Posted September 2, 2019 17 minutes ago, Alpo said: I was replying to bgavin, when he said " if the curve is a circle calculating the length of the arc is straight trig" I know that, for this boat, it is NOT a circle. But, is it even a conic section? Or just a free hand drawn curve? Link to comment Share on other sites More sharing options...
Red Gauntlet , SASS 60619 Posted September 2, 2019 Share Posted September 2, 2019 Math through Geometry, Algebra III, and Trig was fun and easy. Algebra IV and V and Calculus and Analytic Geometry were hard. I had A's through Trig; C's ever after. Link to comment Share on other sites More sharing options...
Joke 'um Posted September 2, 2019 Share Posted September 2, 2019 The process you are asking about is called, I believe, lofting. Traditionally performed by laying out the boat in a large, open room (loft) on the deck. You can do it by building a model to your chosen scale from cardboard. When done, take it apart, measure and multiply. Easy, peasy. It is easy enough that simple (no math degree) boat builders have done it for centurys. Many 'how to' books will tell you how to too. Link to comment Share on other sites More sharing options...
MizPete Posted September 3, 2019 Share Posted September 3, 2019 No. Just no. The hypoteneuse can't have a curve & it's still a triangle. Link to comment Share on other sites More sharing options...
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