The following examples are used to explain a method for creating ellipse based surfboard rockers. These rocker examples are for illustration of the method. Actual ellipse heights and lengths must be adjusted to create rockers that are suitable for specific surfboard designs.
The blue ellipse-based rocker shown above was done with 2 ellipses of different sizes joined at the (vertical) midline when completed. Both Ellipses have the same width (same as board planshape). Pick the desired nose and tail rocker heights. Draw a straight line the length of the board -- I used a rectangle instead of a straight line. Mark where the surfboard wide point would be on that straight line. Align the (vertical) midline of each ellipse with the widepoint mark on the straight line. Now place marks (or boxes) of the desired nose and tail rocker heights at the appropriate ends of the straight line. Stretch the length of each ellipse, independently of one another, until each elliptical curve touches the corner of both the nose and tail boxes. Join each of the half-ellipses at their midlines. Trim the ends of the ends of the ellipses off at the points where their curves are touching the box corners at each end of the straight line. This creates an ellipse-based surfboard bottom rocker.
Hope this makes sense. Turned out wordier than expected. Very simple when viewed and created as a graphic (below). Purple is the nose rocker ellipse and red is the tail rocker ellipse. Green boxes are 2.0" high (tail rocker) and 4.7" high (nose rocker). Board length is 7'6". Line widths were increased from 1.0 pt to 1.5 pt for blog posting.
Combining Ellipses with Different Heights
Thanks to Ryan for bringing up ellipse height and rocker shape in his comment below. I chose ellipses equal to board width in the example above for the purpose of discussion. Varying ellipse height changes the shape of either nose or tail rocker curve. Increasing ellipse height will make the curves rounder. Decreasing ellipse height will make the curves flatter. That is, as ellipse height gets closer to its length, the curves become more circular. As ellipse height approaches zero, the curves become flatter. While the ellipse curve becomes flatter overall, with decreasing height, the curves near the tips become steeper. Also, with ellipse height fixed, the curve becomes more circular as the length shortens and flatter as length increases.
The figures below all have the same tail ellipse (height = board width). Board length is still 7'6" (blue rectangle). Two of the nose ellipse heights are greater (top figure) or less (bottom figure) than board width. Ellipse lengths must be stretched or compressed accordingly. (Ellipse heights cannot be less than 2x nose or tail rocker height.)
Links to the other elliptic surfboard design posts:
Ellipse-based rails
http://ellipticsurfboard.blogspot.com/2015/11/ellipse-based-rail-profile.html
Ellipse-based planshape
http://ellipticsurfboard.blogspot.com/2015/11/ellipse-based-surfboard-planshape.html
Ellipse-Based Fin
http://ellipticsurfboard.blogspot.com/2016/03/ellipse-based-surfboard-fin.html
Ellipse-based tail template
http://ellipticsurfboard.blogspot.com/2015/11/ellipse-based-tail-templates.html
The figures below all have the same tail ellipse (height = board width). Board length is still 7'6" (blue rectangle). Two of the nose ellipse heights are greater (top figure) or less (bottom figure) than board width. Ellipse lengths must be stretched or compressed accordingly. (Ellipse heights cannot be less than 2x nose or tail rocker height.)
Links to the other elliptic surfboard design posts:
Ellipse-based rails
http://ellipticsurfboard.blogspot.com/2015/11/ellipse-based-rail-profile.html
Ellipse-based planshape
http://ellipticsurfboard.blogspot.com/2015/11/ellipse-based-surfboard-planshape.html
Ellipse-Based Fin
http://ellipticsurfboard.blogspot.com/2016/03/ellipse-based-surfboard-fin.html
Ellipse-based tail template
http://ellipticsurfboard.blogspot.com/2015/11/ellipse-based-tail-templates.html
