Area Tool
The diagram hopefully makes things clear; you can estimate the bottom surface area of a surfboard by using rectangles, and the Area Tool offers a quick way to do just that. The tool uses a well know and established way of obtaining quick area estimates, (see any introductory Calculus book.)
You can make your estimates more accurate by reducing the width of the tool from 4 in to 2 or even 1 in. Though I’ve shown the tool using inches, you could use the metric system instead (e.g. centimeters). You could also make the Area Tool out of Plexiglas; it will make reading the various h values a lot easier. Of course, if you’re clever and understand the concept, you don’t even need a special tool, a simple ruler will do.
… Segue Into Design
The bottom area is of particular importance if propulsion in surfing is derived from the flow of water in a wave (see ‘Dynamic – The Trim Equation’.) Given that force is equal to pressure times area, the pressure coming from the flow in a wave, area becomes a design tool.
F = PA
(See, ‘Dynamics – The Trim Equation’ for way to estimate P using wave particle velocity.)
Increasing the area, for a given pressure would increase the force.
Though matters are rarely that simple, nevertheless comparing a fish to a standard shortboard, and then possibly to a gun, is likely to be interesting exercise. (I suggest exploring how surface area increases from the tail end forward, and correlating it with where the surfer usually stands while riding the respective board.) Fishes were designed for low flow conditions –i.e. small water particle velocities, whereas for guns, the opposite. Smaller water particle velocities means less pressure, the fish strategy compensating for this by using greater area. Higher water particle velocities means you can reduce the area and still have sufficient propulsion. Of course these are not the sole determining factors in the design of these two solutions (fishes and guns.)
But you could take this a little further. Narrower rear section boards, unless they are ridden on sufficiently large waves, tend to push the surfer to ride more forward on the board. Boards with wider rear sections tend to allow the surfer to surf farther back, but in general, tends to cause problems on larger waves (you generally loose the ability to remove or bring surface area on line –i.e. you loose a degree of control over propulsion.)
Of course, I am sure there are other explanations as to why surface area matters. This is just one take from a given perspective –i.e. if propulsion was derived from the flow in a wave. Also, the above discussion on area as a design tool is in no way complete, nor does the above discussion prove or disprove anything.
(Edit:Remove this line. 06/18/06, KC)
The next step will be an attempt to explore how propulsion as outlined in ‘Dynamics - The Trim Equation’ might impact design through bottom contours.
(Edit:Add this line. 06/18/06, KC)
The next step will be an attempt to explore how bottom contours might impact propulsion as outlined in ‘Dynamics - The Trim Equation’ .
Kevin
PS
My apologies for the edit. I’m not very good at proof reading my own work.