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 ?
