Effect of Friction Lines on the Resistance of a Friction Plane

The "C' in Taylor's is a constant depending upon the breadth/draught ratio and the midship section coefficient and lies in the range of 15.2 to 16.5. The graph is complicated and goes around like concentric circles in simplification.

The "C' in Baier-Bragg coeff: C = -0.906385E-5*x^2 + 0.954632E-2*x + 0.776457 as posted by the late Mike D in this forum.

 

I have never used the approximate formulas you listed. I suspect that they give reasonable approximations for vessels that fall within certain bounds on CB and perhaps CP or other principal parameters. You should not rely on (for example), the Holtrop formula for the WSA of fine-bodied kayaks.

 

I'll echo Leo's comments. See if ranges of applicable coeffiencients are listed for any of the formulas. No regression formula is valid for everything. If you can't find an explicit spplicability range then see what context the formulas were derived for. Formulas derived using data from merchant vessels probably don't have much validity for sea kayaks. Another thing to do is compare the results from the formulas with data from existing designs similar to what you are evaluating.

 

Quite agree Leo. You are a mathematician and you use integration from a known mathemathetical function. I recall there are five methods of finding areas, ACAD is one, girthing method is another.

I used to use Simpon's rule before but our draftsman laughed at me. He said "you want volume, I will give it to you, you want area, here. You want centroid?" Forget it. I learned ACAD. But I do ACAD only when I have finished the preliminaries.

 

Not quite. I divide the surface area into small panels and sum them. Or is that what you mean by "known mathematical function"?
Girthing works reasonably well for some geometries, but it is not guaranteed to converge on the exact answer.

Volumes and waterplane areas can be handled very well and much better than surface areas using Simpson's rule.

I guess, as with most things, you have to choose the right (numerical) tool for the job at hand.

Leo.

 

I use Rhino which computes the areas, volumes, moments, centroid locations, etc. using small "elements" based on the precision specified. It provides an estimate of the accuracy of the results when the various area and volume related commands are used for the calculations. I've done some limited checking and the accuracy estimates appear to be correct.

Some other, particularly older, naval architecture software uses much the same proceedures as traditional manual calculations with discrete stations where the properties of the sections at those stations are calculated, and then the appropriate area properties are summed using Simpson's rule or similar to obtain the overal values. Essentially the computer replaces the planimeter and the sheet used to record and sum the planimeter results. The accuracy using that proceedure is limited by the number of stations used. When computers were slower there may have been some advantages to doing the calculations in that manner. Experience with software which works in this manner may lead to different conclusions about the overall accuracy of "computer" calculations than experience with software which works similar to Rhino. (Last comment not directly related to posts above.)