# Cosine Wherry Explain me : Hand Calculator and Fair Line Drawing

Discussion in 'Boat Design' started by mustafaumu sarac, Feb 2, 2018.

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### mustafaumu saracSenior Member

I read wooden boat cosine wherry article and designer had had been wrote a program to get the lines from the scientific hand calculator. I can understand cosine curve,I can understand each section area rule with related cosine curve height. But I cant understand , how to get line drawings from calculator which is fair.

Is there a formula , algorithm to program the calculator designs line drawings all fair to each other ?

How he did 40 years ago with calculator ?

Umut
Istanbul

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### HeimfriedSenior Member

I don't know how this paticular designer did it, but to calculate fair lines it is possible to use cubic splines as any graphic software does as far as I know.

I did this in Excel-VBA and it is a nice tool around boat building. For example you can check the accuracy of an offset table or check measurements along a fairly curved line.

40 years ago we used programmable scientific calculators from Texas Instruments. There were certain limits of code lines given (I don't remember, how much), but basically it would have been possible to calculate such splines.

If you are interested, the excel folder is attached.

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• ###### Splines3_v2_engl.zip
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Last edited: Feb 2, 2018
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### mustafaumu saracSenior Member

Thank you very much.

Lets say we have a sine curve and we know each of every section - sliced bread - area.

Now we have cubic spline which will calculate the correctness of fairness with a long curve placed on section lines.. Thank you explaining to me.

But how a calculator can draw 2d line shape of each sliced bread ? There are zillions of things can be drawen ?

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### HeimfriedSenior Member

Regularly there will be only one solution. This is because there are some rules stated: The shortest possible curve meeting all given points is required, between neighboring points the curve is a polynomial function of (or up to) 3rd grade, the value, the slope and the curvature of the arriving function f1(x) at given point is identical with the value, the slope and the curvature of the following function f2(x) at the same point. In the given case of natural splines there is no curvature at starting point and at ending point of the whole curve. The functions are worked out by methods of matrix algebra.

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### mustafaumu saracSenior Member

Thank you so much , thank you very much. I will try to understand above with google searches. Where can I find an article which will explain above with examples ? Or a book ? Can you confirm , all of your line drawing calculations and fair line drawing calculations could be done on casio cheap programmable calculator ? There is 3500P2 and can make integral and differantial.

And If you cant find any article , tutorial or book , can you please calculate an example ? I know its difficult but very important to non engineers.

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### HeimfriedSenior Member

An example for checking offsets:
In George Buehlers book "Buehlers Backyard Boatbuilding is an offset table dispayed for the cutter Njord. The stations versus height of chine reads (converted to millimeters) as given below (pic 1).
The calculated values shown as graph are in the next pic below.
After erasing the wrong height, the graph looks like the 3rd pic.

(The display of the curves occures in respect of the given screen area. Therefore they are horzontally compressed. But in spite of that the check of fairness is easy possible.)

The reason was just a typo 4-9-0+ instead of 4-8-0+ .

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### mustafaumu saracSenior Member

Let me brief what I understood,

we want to design a rowing boat.
we want to design it as the nuclear submarine design research results.
we decided to distribute the displacement as submarine bulb distributes the displacement.
we drawn a cosine curve and decided to distribute the displacement like the curve heights and lenght.

than we make a matrix calculation and every lines appears because there is only one solution.
than we check the fairness with spline .
is it true ?

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### HeimfriedSenior Member

Sorry, I really don't know, if your calculator would be capable doing this. It is merely a question of the max allowed number of code lines. The math is not difficult but all the formulas have to be very well arranged. To learn about it, I used a few university scripts, I found in the web. I will attach the best of them, but it is in German. Maybe you will find other scripts in english (or turkish).

#### Attached Files:

• ###### Splines_WW.pdf
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1.1 MB
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### mustafaumu saracSenior Member

Helmfried,

Can you confirm my post ?

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### HeimfriedSenior Member

Sorry, I can not at all confirm it (as far as I understood your posting). You very much overstressed the capability of this tool, I think.

A spline table is not a kind of boat design software. All it does, is to find a fair curve meeting all points of your input. And if you put in 10 pairs of value (x and y), the curve will consist of a set of 9 polynomes like f(x) = A + B * x + C * x^2 + D * x^3 .

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### mustafaumu saracSenior Member

how can we do what boat design software can do with hand calculator ?

I think you described the fair line drawing drawing. How can we go from sliced bread areas to line drawing ? I thought you said there was only one solution as line drawing to this problem and I could calculate the 2d shapes of each slice ? Am I wrong ?

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### alan craigSenior Member

Partial quote from a post by Stuart Young on another forum:

The Cosine Wherry was designed by John Hartsock and is fully described in WB100. Hartsock used Colin Archer's Wave Form Theory as a starting point and designed the boat so that the curve of the underwater areas followed a Cosine Curve (The cosine of an angle plotted against the angle inself). Having fixed that parameter (the reverse of the usual design cycle) he used John Gardner's and Willit Ansel's research work to determine the final dimensions of the boat.

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### gonzoSenior Member

I read the article when it was published. I think it is more of a mathematical exercise than one of good boat design practice.

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### keith66Senior Member

It turned out a very good boat, A standard Cosine wherry the Maggie has won the Great River race in London on & off for many years. She has a very strong & fit crew but to do that year on year against the cream of the UK's traditional fixed seat boats & crews takes some doing.

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### tspeerSenior Member

Does this approach help? You can draw conic sections using classic drawing instruments without doing any numerical calculation. IIRC, the P-51 Mustang was the first airplane drafted using conic section lofting, and part of its performance has been attributed to the fairness of its lines. You can measure cross sectional areas with a planimeter, so the amount of numerical calculation doesn't have to be very much.

The key to creating fair lines numerically is to describe smooth section shapes parametrically, and then vary the parameters smoothly along the length. This is easily done by using low order formulae to vary the parameters. Once you have generated the offsets, you section the surface in different directions to create classic lines drawings.

The way I've matched the prescribed cross sectional area distribution is to make an initial guess at the section size and calculate the cross sectional area. Then I compare that area with the desired area and scale the section accordingly. Given smoothly varying section characteristics and a smoothly varying cross sectional area specification, the end result turns out to be pretty fair.

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