Need Help with Varying arcs

Question

I am working on modeling a ship and all the decks are cambered for water runoff.

there are a given number of stations which got wider or narrower according to its position on the ship.

the widest part of the ship gives a dimension for the base of the camber.

EX: Highest point of the arc across is 12" @ 39'

that is pretty self explanatory however I then have to go maybe 20 shorter widths of stations to the front or rear so I may have a 28' width, 22' width etc down to say 6" width.

so my question is what formula do I need to calculate the new height of the arc based on the station width keeping with the ratio of height to width originally listed for the center so that when finished will generate a smooth transition from station to station

thanks

Joe

Answer 1

For the first arc, using strictly feet, we have y = 1 -  x² / (19.5)².  In order to scale this for width, I'll use half-width W (to make the formula simpler), then the formula becomes:

 

y = (W/19.5)(1 -  x² / W² ).   (in feet)

 

The W²  in the denominator scales the width, while the (W/19.5) term scales the height at the top.

 

Now, that assumes that you want the height at the center to simply vary proportionally with the width, which may work considering the curvature of the side of the ship will than translate to the camber of the deck from fore to aft.