half breadth station width calc

I should have given more attention to high school calculus
Can you tell me an easy way to find the "X" measurement
Maybe a picture to help give me an idea of the approach in figuring this measurement for each of the curved bow area stations?
The aft section is easy because it's rectangular...
Having trouble with the curves...
Should I use graph paper and scale it up??
I am not using CADs yet

 

What is the half breadth at the stern?
Or the length overall?
It shows up on my computer screen as 7.25" long.
If the length of the vessel is (say) 14.5', then the scale is 1:24.
And once you know the scale, then the X measurement is the dimension multiplied by the scale.

Or have I totally misunderstood your question?

 

Thank you for offering to help
The drawing is not accurate it is only an illustration, I will need to refine the curve, may look at a few different styles
Stations 7-12 width is what I need help finding, they will be different based on how I draw the curve,
For discussion, the half breath at the stern is 6" and the overall length is 48"
0-6 stations are mostly the same width...

 

Are you looking to calculate the area under the curve using Simpson's Rule, and hence you need to find the half breadths at each station?

You could try drawing it on plain paper at 1 : 2 scale - you would need a sheet of paper a bit longer than 24" (it does not have to be graph paper), and you might need to stick a few standard 'letter' size sheets together to do this.
Then draw a rectangle on the paper that is 24" x 3" in size.
You have 13 stations - but the station spacing is not uniform. Is this intentional?
If they should be uniform, then your station spacing is approx 1.85".
If you draw in your curve, then you can measure the offset to the curve at each station.

 

I am attempting to find the LENGTH not the area of the stations (half of the "bulkheads")
The drawing in the fist post is crude, only something to get out quick...
I am working on a graph paper drawing by hand, with equal station spacing.
Thank you for explaining the scale also, I feel I have a good base for scaling upwards and can get accurate measurement by taping multiple sheets together,

I guess my question at this point is how to mathematically check what each station width would be?

Usually I use some geometry triangle theorems to get the V hull shapes on the transom, the curves at the bow I dont understand...hope that make sense

 

Sorry, but I am still a bit baffled.

Can you post any other info or sketches of this boat please?

Re mathematically checking the width of each station, you will want the curve to be nice and fair, such that if you look along it there are no wiggles or wobbles in it.
Once you have a nice fair curve, you can measure the offset at each station, and then calculate what it is by using the scale?

 

It's not too difficult to measure the breadth of the section and multiply it with the scale...

...or you should redefine your question.

Maybe you want a curve that follows a mathematical (parabolic) function for example f(x)=sqrt(x) ?

 

Exellent
I think you are right - I am over complicating this - I can simply draw the curve and then measure with a ruler to the curve
It may be most accurate depending on the size initially or how I scale from there

I think if I bring functions into this that will be a whole new thing to worry about !!

 

Thank you both for mentioning the scale, I believe that was the challenge I was having, and by not starting too small at first

 

I still use paper and pencils. You need to decide what scale you want to work in, and you need a scale rule. Station spacing is usually consistent in helping to draw up lines to develop off-set measurements, they do not have to be where you may want a bulkhead for example, as any dimension you need can be taken off a developed set of lines.
My initial answer to your question of measuring X, would have been to use a ruler, but that figure is meaningless without scale.

 

A few years ago I did an Excel folder to determine the coordinates of bended deck beams for boats. You pick out of three geometrical shapes (circle, parabola and ellipse), put in the span of the beam, the hight of it at maximum and the width of steps for calculation. You get a table with values (up to 200 steps or intervalls) and (if you click it) a graph.

The y coordinate eaquals the half breadth of a station.

This is for example a quarter of an ellipse.

If someone is interested, its free (without liability, the instructions are in German).

 

Buy yourself an engineers scale. You can get one on Amazon, or if you prefer a regular store, I have seen them for sale in art stores, or even Michaels. Shouldn't cost much. The local art store here has them for a little over $11.00 If there is a University or college near you they sell them too but usually more expensive. They already have the scales of 1:10, 1:20, 1:30 , and so on, on the device. You can get them in standard units or metric. You draw a base line (on boats usually the center line) and measure the distance from the base to the curve. The best way is to use a drafting compass (with points, not pencil lead) to measure the distance and then measure the compass width on the engineers scale. Or if you don't have a compass, just measure it with the engineers scale. Not as accurate but close. Hope that makes sense.

 

Very helpful Thank you !

 

Or you can do what Naval Architects did for generations that didn't require a compass. Tick strips. Cut out some strips of paper . Width doesn't matter. Label them with the name of the project, for instance "20 meter boat" and the station number. Lay it on the drawing alongside the station line. Put a tick on the strip where it meets the centerline. Put another tick on the strip where it meets the curve. Then measure the distance with the engineers scale..

In 1984 the Coast Guard transferred me to HQ in Washington DC. We rented a house in Bethesda, MD. When we moved in I found a box in the basement with a lot of those strips in it. I asked my landlord who was the previous occupant. He was a Naval Architect that worked at the Naval Research Laboratory. So you can guess what he did in the basement in his spare time. I set up my drafting table in the basement in the only spot big enough. Probably the same spot he used. I used to have dozens of those tick strips from designs I did in a course I took.

 

The fairing is exactly what I am looking to perfect - I guess without mathematically calculating, my curve drawings need to be accurate and hopefully the wood will curve the same way. Seems like I might only be able to get somewhat close on paper and fine tune the plug bulk heads after