Longboard Rocker and the Universal Numbers

I have compared the rockers of four different longboard designs of varying vintages (Phantom 380, IMCO, Tiga 330 and [an old] Wayler). Guess what? All of the rockers can be described by a single set of simple mathematical functions which can be related to the board characteristics for sailing upwind with the sailor in the forward footstraps and the mast step fully forward; and planning downwind with the sailor in the back footstraps with the mast track fully back. The functions are fully consistent with the discussion in an early post regarding the need for a three-part rocker to correctly transition the board handling characteristics between these two extremes of upwind and downwind sailing.

The following figure (thanks German Windsurfing Association for all of the photos in this posting) shows the typical distribution of the centre of mass and centre of effort for upwind sailing in approximately 12 knots of wind with the board and rig powered up.


As you would expect, the centre of effort is approximately located at the point of maximum chord on the centreboard and this will line up with the point of maximum depth in the sail (which probably lies about 30% back from the mast. The centre of effort in the sail and the centreboard have to line up in order for the sailboard to track in a straight line (ignoring leeward drift) and not round up to windward or bear away to leeward. Note that the centre of effort lies about 40% forward from the tail of the board on the Phantom 380 (for a fully rotated centreboard).

Now I would expect that the centre of mass would lie forward of the centre of effort under these conditions. Visualise yourself being on the water in 12 knts of wind. Everything is fully powered up, and if its not too rough then you are sailing with legs and hands close together as shown in the figure above (sans the hand). However, in order to balance the weight of the wind on the sail you are not only leading outward, but also forward (at least that is what I do). Under these conditions, the centre of mass is probably sitting about mid-way along the board (50%).

Lets relate this back to the rocker. Under these conditions, it would be logical to locate the point of maximum rocker under the centre of mass because this is the point about which the board will pivot in a fore and aft position in response to the chop when sailing to windward. So a schematic diagram of how this looks is as follows.

What you want in this situation is a rocker shape that is locally symmetric about this pivot point, so that the board rocks easily backwards and forwards without 'slapping' and generating extra drag in the chop.

So this is the first, and probably the most important component of the 3-part rocker on a longboard.

Now lets consider the situation in which you are powered up and sailing downwind on a reach. You're on a longboard of course (what else!) and so the centreboard is fully retracted, the mast base is at the back of the mast track, you're hooked on to 9.5 m^2 of sail with the feet in the back straps and with the board skipping along on the first two metres of the tail, desperately hoping that the water flow around the fin stays laminar and doesn't detach and spin you out.

.So in this situation, the only component of the board which is relevant to the rocker shape is located within 1-2 metres of the tail (barring a catastrophic nose dive in which case it is the first metre at the nose of the board which is important!).

For powered-up reaching conditions, it would be expected that a pretty flat, to a slightly curved rocker shape would be optimal. Flat would be fastest under optimal conditions, however a small amount of curvature is probably required in order to aid with gybing, to provide a smooth fore-and-aft response to the chop and also to reduce drag when the board is sailing upwind. Care must also be taken to ensure that the tail rocker transitions smoothly into the mid-point rocker as described above.

The front part of the rocker provides a transition between the mid-point rocker and that safety valve- the nose rocker; and also generates lift for planning under marginal conditions. Here the aim is to minimise the rocker as much as practical in order to maximise the waterline for windward sailing (particularly when railing). However, eventually the rocker has to sweep up to the bow and hence provide some protection against the nose dive.

All of this information can be represented in the following schematic diagram.


Our mid-point rocker is represented by a curve which goes from x1 to x2 and has the deepest point at xc. Our tail rocker goes from x0 to x1 and starts with a value of r0 and a slope of r0'. Finally our nose rocker goes from x2 to x3 and finishes with a value of r3 and r3' at the nose of the board.

The curves that we use to describe the rockers have a quadratic shape for the tail and the mid-point rocker and a cubic shape for the more complicated nose rocker. The curves are constrained to match the local rocker and rocker gradient at the transition points.

So all we need to do to fully describe the rocker for our longboard is to prescribe the tail and nose rocker and the points of transition between the tail, centre and nose rocker. Now I've tested this model against a set of best estimates of the actual rocker for an IMCO (thank you for the pictures John), Phantom 380, Tiga 330 and a Wayler and the result of this testing is shown below.

So you can see from the images that the three part conceptual rocker model matches the actual rocker very well. What is particularly useful is that in all cases, the transition from the tail to the mid-point rocker occurs about 40% forward of the tail, the point of maximum rocker occurs about 50% forward of the tail and the transition from the mid-point rocker to the nose rocker occurs 60% forward of the tail.

The slope of the nose rocker varies between 20% (380) and 35% (IMCO; Tiga) and the slope of the tail rocker varies between 1% (IMCO), 5% (Tiga; 380) and 7.5% (Wayler). This seems consistent with the knowledge that the IMCO is pretty flat towards the tail (see an earlier post on this), and that the Wayler, being an older, displacement type board has the largest rocker in the tail. Note also that the 380 has the smallest nose rocker which may be an attempt to maximise the water line.

The result of this work is a simple and self consistent mathematical description of the longboard rocker which can be used for the design of a longboard. And the universal numbers? 40:50:60.

Bye for now.