Wind Angle X Upwash of the Sails

Answer By Paul Bogataj

QUESTIONS:

1. The wind that the luff of the sail “sees” is some degree further aft than that at say the top of the mast (indicated by the mast fly) because of upwash right? The wind as it is entering the front of the sail is bent aft? How can you figure out how much? Will the difference between the real (unaltered by sails) apparent wind angle and the upwash wind angle change as the boat’s speed increases?

2. Does the upwash angle change from top to bottom of the sail? I.E., is there more upwash at the top of the sail where the wind is going faster?

3. The other thing I think is interesting is how the path that the wind takes over the surface of the sail has to change radically as the boat heels. What happens to the shape of the airfoil the wind sees as the boat is heeled over? Becomes longer and deeper? I can’t quite visualize it.

The apparent wind angle seen on the mast head fly includes the affect of the tip vortex. That is due to air flowing around the top of the sail from windward to leeward (higher pressure to lower pressure). When you add that component to the freestream flow component, the flow around the top is at a higher angle than on the sails. Because of this, generally upwash increases in angle moving upward along the sail toward the tip.

Maybe the two images above can help. The wake is following a path that indicates the flow direction downstream of the sails. You can see that there is also a significant vortex around the bottom of the sails. The colors on the sails are the pressure difference across the sail (pressure on the leeward side minus the pressure on the windward side at that point). The color range has red being less difference and blue being higher difference, with black being the most extreme. Upwash is caused by the low pressure on the leeward side sucking more air around to that side. Since the pressure differential is lower toward the top of the sails, the upwash will be larger toward the top.

So far these explanations relate to how the sails are influencing the flow through the pressure changes that they produce. Another change in direction that occurs moving up the sails is that because the true wind speed increases moving upward, the apparent wind angle is more aft. You can see this by adding a true wind vector of a given length to a boatspeed vector (remember to draw the boatspeed vector toward the boat in the direction of the wind created by the boat moving) and then drawing a longer true wind vector. This is because the boatspeed is the same all the way up, but the true windspeed is not. Thus, the apparent wind angle is higher where the true wind speed is higher. This is the twisted flow that occurs due the boat moving through the sheared (merely in velocity) flow near the earth's surface.

There are also interactions between the main and foresail, such that the upwash is increased on the forward sail due to the addition of the upwash from the main, and the upwash is reduced on the mainsail due to the downwash behind the foresail.

Maybe another way to think about heel is that the sail shape is the same, but as the boat heels, the apparent wind angle is reduced. This is obvious if you consider an extreme heel angle like 90 degrees where the sail would probably luff. As the boat heels, the flow probably moves more along the spanwise direction of the sail then when the boat is more upright.

Paul Bogataj is an aeronautical engineer, specializing in sailing applications. He was responsible for appendage development for Team Dennis Conner and Young America in the 1995 and 2000 America's Cups, respectively. He approaches sail and keel design from the perspective of using advanced aerodynamic technology and methods that have been developed for the aircraft industry. He previously worked for Boeing and has consulted independently for a variety of sailing design projects. He currently works for North Sails One Design analyzing sails for one-design boats.

He has employed his knowledge of how sailboats function to win the North American Championship of two different classes, and numerous fleet and district championships. Paul combines his practical understanding of sailing from his experience as a successful racing sailor with his awareness of fluid dynamic principles as an engineer to provide explanations of how sailboats work that are understandable to the average sailor.

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