I just want to point out, this notion of exceeding the wind speed is often misunderstood. Yes, it is absolutely possible and routinely done. But, there are some caveats here. First, not all boats are capable. High-performance and/or planing boats are much more capable. Displacement hulls and underpowered sail area make it much harder or impossible.
With a displacement hull, one must recognize that there is a very narrow window for this to occur. That is, let's say the boat has a hull speed of 6-7 kts (pretty typical). That means that, for the boat's speed to exceed wind speed, the wind must be under 6-7 kts, but high enough to allow sails to perform optimally. So, that pretty much means that winds need to be right about at 3-5 kts. Any less than 3 kts and most boats will struggle to maintain a good enough sail shape in most real-world conditions. The water needs to be rather smooth. (Lake sailors will enjoy the fact that calm winds usually coincide with calm waters. Not always the case on bigger water.)
So, with a displacement hull, when we talk about exceeding the wind speed, we are really talking about sailing just a little faster than a 3-5 kt wind. Because of the way drag works, as the water speed approaches hull speed, the forces at play are greater to overcome, making it less optimal for this phenomenon.
Also, on most boats (regardless of hull type), you are most likely to be able to exceed wind speed on a beam reach (or a slightly broad reach). The easiest way to understand this is to recognize that, on a beam reach, you are not "fighting" any headwind. The boat is free to move sideways to the wind without being translated downwind. So, all lift generated by the sail is converted into forward motion. (This is not a true statement because of what's happening under water, but is a simplified explanation. In reality, there is leeway and associated drag.)
Going upwind at a speed exceeding wind speed ... this isn't that easy on most displacement hull boats. Going a little upwind, you can enjoy the conditions of a beam reach with just a little more headwind to overcome and a slightly less-optimal wind angle. But, as you pass through a close reach, this phenomenon becomes out of ... reach ... for most displacement hulls. Close-hauled, I would be highly skeptical of any claims.
Though it is theoretically possible, in practice, any claims of a displacement monohull exceeding wind speed in anything other than ideal conditions and anything other than something very close to a beam reach ... these are probably misperceptions rather than accurate observations. (I am not talking about high-performance displacement monohulls. I am talking about most folks' boats.)
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Only keep reading if you are a math geek ...
The way to determine if you can exceed wind speed looks something like this:
- Calculate the apparent wind speed and apparent wind angle based on a hypothetical boat speed. I don't know a good way to represent the trig functions to calculate these in this editor, but the formulae are easy to find online. You just need the true wind speed and direction, and the boat's speed and direction.
- Calculate lift and drag based on the coefficients of lift and drag for a given sail configuration. These formulae are pretty simple:
L = (1/2) * p * A * Cl * V2 [V squared]
D = (1/2) * p * A * Cd * V2
Where:
p = air density
A = sail area
Cl = the sail's coefficient of lift
Cd = the sail's coefficient of drag
V = apparent wind speed
- Calculate driving force. Driving force is the component of the lift force the propels the boat forward. That formula is pretty simple:
F = L * cos(Wa)
Where Wa is the calculated apparent wind angle from step #1.
Then, you can calculate the net force propelling the boat forward:
Fnet = F - Dh - D
- Using Newton’s second law (F=ma), the boat’s acceleration (and thus speed) can be calculated. Though, for a steady speed, Fnet must equal zero, so:
F = Dh - D
If you make these calculations for most displacement monohulls, you find that, at best, there is a very narrow theoretical window in which the phenomenon is possible. Or there is no window at all where it is even theoretically possible. These calculations assume perfect sail trim, a perfectly clean hull with no surface friction, and perfectl flat seas. Real-world conditions pretty much close that window entirely.