Curve fitting

[Johnny Boivin]

Hello. I'm not a mathematician and I'm designing a sailboat hull. I have to test the shape of the underwater portion of the hull, at different hell angle ( angle of the hull in relation to the plane representing the water surface). To do so, I have the constraint to keep constant the volume of the underwater portion of the hull at different heel angles. So I'm using a polynomial curve fitting approach where I have the  X value representing the depth of the submerge portion of the hull  and the Y value corresponding to the volume of the submerge part . I sample 100 of these x,y values on my drawing  and I fit  curves  of different degrees . To test which degree is the best to allow to  predict the volume according to a certain depth ( or vice versa) , I split the  sample into a training set of 75 x,y values)   and one test set of 25  x,y values . With this, I determine the best polynomial degree to use to get the most precise prediction . I still get  an errors of about +- 1.5 pounds of water over a target of 1750 pounds of displace water . Is there anyway to get more precise results ?

[studiot]

15 hours ago, Johnny Boivin said:

Hello. I'm not a mathematician and I'm designing a sailboat hull. I have to test the shape of the underwater portion of the hull, at different hell angle ( angle of the hull in relation to the plane representing the water surface). To do so, I have the constraint to keep constant the volume of the underwater portion of the hull at different heel angles. So I'm using a polynomial curve fitting approach where I have the  X value representing the depth of the submerge portion of the hull  and the Y value corresponding to the volume of the submerge part . I sample 100 of these x,y values on my drawing  and I fit  curves  of different degrees . To test which degree is the best to allow to  predict the volume according to a certain depth ( or vice versa) , I split the  sample into a training set of 75 x,y values)   and one test set of 25  x,y values . With this, I determine the best polynomial degree to use to get the most precise prediction . I still get  an errors of about +- 1.5 pounds of water over a target of 1750 pounds of displace water . Is there anyway to get more precise results ?

 

Hello John and welcome.

I am suprised some sailors have't yet replied.

Anyway I think I can see what you are trying to do, but I have a couple of comments / questions to clear up,

1. I am suprised you are not satisfied with =/- 1.5 lbs as that is less than 0.1% variation. Someone's sandwiches will be greater than that.
    
2. You seem to have contradicted yourself. You say you are keeping the underwater volume constant but also seem to refer to it as the Y value?
    
3. I am guessing that you want to keep this volume constant to keep the bouyance force constant in magnitude, though obviously its application point will change wilh heel angle.?
    
4. However this will only keep it in force for a stationary boat. As soon as the boat moves momentum forces will enter and change the dynamics. Also I would not expect a stationay boat to be heeled over.
    
5. 1750 lbs displacement means a what, 12 to 15 foot boat ?