Michigan Windsurfing

Windsurfing & Stand-Up Paddleboarding in Michigan

Windpower = 1/2 (sail area) . (air density) . (windspeed) 3

Author: Jeffrey MacIntosh

Here’s some interesting tidbits from the world of science. The equation governing the power of the wind is -

P = ½Apv3 where P is power, A equals the area over which the wind passes, p is the density of the air, and v is the wind speed

This means the following:

1. When the wind speed doubles, the power of the wind increases by 8 times!

-a wind speed of 15 mph generates about 2.3 times the power of a 10 mph wind
-a wind speed of 20 mph generates 8 times the power of a wind speed of 10 miles per hour
-a wind speed of 30 mph generates about 3 ½ times the power of a 20 mph wind
-a wind speed of 30 mph generates a whopping 27 times more power than a 10 mph wind

2. So when we go from a 10 mph wind to a 30 mph wind, why doesn’t the sail become 27 times smaller? Part of the answer lies in modern twist-off sails. A twist-off sail twists at the top as the wind increases, dumping wind. This effectively makes your sail smaller, since the top of the sail is no longer “working” to supply power. It’s just flapping in the breeze.

3. Those who used to use very low-aspect non-twist off sails will remember how impossible a sail became to use when the wind speed increased by only a few mph. Twist-off sails have a much greater wind range because the functional area of the sail decreases as the wind gets stronger.

4. Adding downhaul loosens up the leech (the back side of your sail, from the clue to the top of the mast). This increases the twist-off effect. It also flattens the sail and makes it a less efficient airfoil, decreasing the power of the sail and making it easier to hang on to. Thus, downhauling the sail when the wind picks up is equivalent to rigging a smaller sail.

5. Pulling on the outhaul actually increases the functional surface area of the sail, increasing the power. But the increase in power is more than offset by the flattening of the sail, which makes the sail a less efficient airfoil. However, it is noteworthy that tightening the downhaul both flattens the sail and increases the twist-off affect. This means that downhauling is generally more effective than outhauling at reducing sail power.

6. Most of us don’t have adjustable downhauls that can be adjusted on the fly (except you diehard racers). But adjustable outhauls are readily available and easy to use. They can be a very effective way of extending your sail’s wind range and allowing you to keep sailing when the wind picks up without going in and rigging a smaller sail.

7. Another part of the explanation of why we don’t need to go down in sail size 27 times when the wind increases from 10 mph to 30 mph has to do with a change in the sail’s “angle of attack”. The angle of attack is the angle between the wind and the sail. In low winds, the wind tends to hit the sail at a higher angle. This generates greater lift or power in the sail. When the wind picks up, the angle of attack naturally tends to decrease, lowering the power generated by the sail (and making it easier to hang on to).

Here’s a slightly more technical explanation. The “true wind” is the wind that you feel if you are standing still. But when you are sailing, the wind that your sail “feels” is the “apparent wind”, not the true wind. The apparent wind results from the fact that as you move forward, you generate your own wind, blowing in exactly the opposite direction.

It’s like the wind you experience in a car. Let’s say that the true wind is zero. But if you accelerate to 60 mph in your car and stick your hand out the window, you feel an “apparent” wind that is generated by the forward motion of the car. The apparent wind blows in exactly the opposite direction to the car’s motion.

So, as you move forward on your board, the apparent wind acting on your sail is a combination of the true wind and the wind resulting from the forward motion of the board. The faster you go, the more the apparent wind shifts toward the front of the board. And the more the apparent wind shifts toward the front of the board, the lower the angle of attack between the sail and the wind, and the less the power in the sail.

This means that going faster is just like rigging a smaller sail, since the total surface area of the sail that is perpendicular to the wind (“A” in the above equation) gets smaller. One implication of this (which may seem counterintuitive) is that, in a high wind, the faster you go, the easier it is to hang on to the sail.

8. The winds in autumn and spring are cooler, and therefore denser than the winds in the warmer summer months. According to the formula above, this means that they pack more power at any given wind speed. For example, wind at 10° F (4.4° C) is about 10% more dense than air at 90° F (32.2° C). So the 10° wind is 10% more powerful than the 90° wind, for any given wind speed. This may affect the choice of sail that you rig in the fall versus the summer months.

Found this at Windsurfingcanada.com

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I wonder if it's time to resurrect Jim Drake's Physics of Windsurfing

Attachments:

Good lord! Canadians are as bad as the Brits, analyze the sh@@ out of everything until they come up with a thesis!!! Answer buy a modern sail and if your falling in on your back rig bigger if your getting launched over the handlebars, rig smaller!!

Don, truth is there are a lot of geek windsurfers!

Cracks me up sometimes when I hear people agonize over whether to sail a 6.3 or no,, maybe I should take the 6.5 sail???  Granted if one is a speed sail or the other is a wave cut it may make a difference, but in general I find downhaul tuning and to some degree outhaul tuning can usually save you  a lot of rigging and de-rigging as the article explains.

 

With all of this going on, it's amazing that we can, with consistent winds and everything in balance, briefly sail w/o hands on the boom.

But there's also the times when nothing seems to work...

comment one:

Math and science physics , have little to do with windsurfing, some of the formulas for board liter size, sail size , fin size, and size size are vaguely useful as a guide. There are too many variables for mat to work .

The equation takes NOT in account the altitude , can it be the same at 11,111 feet as 1 feet above sea level ?

Sails size, rig something you can be assured it will work at least part of the time, sail re rig time  10 minutes or so.

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