The simple practical answer is that when a boat tries to turn up into the wind ('to weather') and you have to pull up on the tiller to steer the boat straight, then that's called 'weather helm'. But in naval architectural terms, it's when the effective Center of Pressure of the sails (CP) is behind the effective Center of Lateral Resistance (CLR) of the underwater body and its foils. (The word 'effective' is used, as the measured position of both these centers actually move when the boat is sailing—and to complicate things, they do not move equally.) Also, the CP is effectively to leeward of the centerline of the boat due to sail position and heel and this produces a turning moment into the wind. This is balanced +/- by the pure side force of the wind on the sail, that tends to turn the boat downwind—all relative to the CLR. This means that designers have to estimate where the CP will act and then arrange the CLR relative to it, so that the helm is nearly balanced. Something much easier to state on paper than to achieve in practice.
If one wonders just why that is, well the CP is mathematically an integration of thousands of variable pressure points that sails are subjected to as the boat bucks and heaves into constantly variable air pressure, with changing attack angles and varying sail shape. The shape of sails will change the location of the CP and its position will move with changing relative-air-velocities and direction.
So how do designers deal with this? Well, as it is totally impractical if not impossible to calculate the true CP of any specific sail plan, they have to simplify the case, by starting with a calculation of the more theoretical Center of Effort (CE). This is found by calculating the center of area of all sails under consideration as if they were flat sheets, and then drawing a vertical line down to the keel from this integrated 'center of area'.
Having done that, the designer then calculates the CLR of the underwater lateral areas in a somewhat similar manner. The keel is normally included with 100% of its area and generally, so is the lateral projected area of the hull. Some designers only include a percentage of the hull area, while others, consider all of it. (For example, a V-section hull might justify a higher percentage than a deep U-shape or flat bottom shape that has little lateral grip.)
Variations can also occur with the rudder. While a fixed fin will generally be included 100%, the rudder may be only partly included (perhaps only 50%); or may even be totally excluded from the calculation. With such variable ways to calculate this, one starts to wonder how a designer can be reasonably assured of ending up with a decently balanced boat!
Well, it generally falls to their experience with a certain type of sailboat. Typically, a designer will follow their own personal set of ground rules and then, having established the CLR on the sailplan, draw a vertical line up from the CLR to the waterline, with a line parallel to the one coming down from the previously calculated CE.
The horizontal (lengthwise) distance between these two lines, is commonly called 'the lead' and it's the lengthwise position between these two theoretical points (the CLR and CE) that the designer will need to vary, to get the boat to balance as he wishes. Often this 'lead' is expressed as a percentage of the waterline length and for monohulls that heel, will almost always be forward of the CLR. Yet on some boats sailed upright with narrow hulls (like multihulls), it could even require to be slightly aft—and by varying amounts too. This is where past experience comes in and often designers guard their own know-how by not publicizing these 'lead percentages'. Within closely related types, the percentage might be fairly constant though and if the designer has kept of track of how past, similar designs have balanced in practice, then he or she can locate the keel or sailplan with some confidence. Even if 'you know' what % of lead a designer has used, one would still have to know what percentages of the rudder and underwater areas were previously included in the calculations to make useful sense of the figure. Different rigs, different cuts of sails and different boat forms will vary this lead percentage, and as heeling and trimming a boat also changes it, it's no wonder that there are so many boats out sailing that do NOT have ideal helm balance! Sailors even disagree on what IS ideal. Some say that it's just safer or that a substantial weather helm is actually faster for racing upwind. But how can that be?
If the boat is trying to turn into the wind, the tiller must be pulled to windward and then, the rudder will go to leeward. With the boat in forward motion, that will apply a force (greater pressure) on the leeward side of the rudder and push the rudder and the stern with it, further up towards the wind, so seemingly counteracting the normal drift to leeward.
But if the rudder is now significantly off the line of water flow down the hull, the rudder then also effectively acts as a partial brake, with higher than normal resistance to the forward motion we seek. Over 50 years ago now, I personally did some fairly controlled tests on the effects of a near vertical foil, angled in relation to the keel center, so see if the 'lift' the foil gave, made up for the loss of speed due to higher forward resistance. Despite many runs, I was never able to prove that it did and from there on, always aimed at reducing any significant weather helm to a relatively mild amount, as it was certainly less tiring to sail a boat like that. But for sure, I would never want a boat with lee helm—although this can still happen downwind and particularly in waves, is sometimes momentarily unavoidable.
I have personally found that boats that round up TOO fast when the helm is let go, can be even more dangerous than those that round slower, as they often pass instantly through the eye of the wind and then get hammered on the new tack with the same squall. The tiller will also go crashing across with powerful force. All of this can be dangerous for both equipment and crew and I personally prefer to have the boat go where I want it to go, rather than have the boat sail in new directions by some default.
PART 2 will give suggestions on how excessive weather helm can be reduced.
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