# Thoughts of resistance and leeway

Discussion in 'Hydrodynamics and Aerodynamics' started by TeddyDiver, Aug 10, 2014.

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### tspeerSenior Member

That formula looks to be based on the side force characteristics for a specific boat. There's a lot packed into "K". The 1/boat speed^2 factor comes from the fact that lift scales with the square of the speed. The heel angle factor probably comes from the stability of the boat - the greater the side force from the rig, the more the boat will heel. Since the side force from the keel has to equal the side force from the rig, the hydrodynamic side force will scale approximately with heel.

Since the formula is used as an instrument calibration to get an approximate value for leeway, and the leeway angle is expected to be small, it doesn't need to be very accurate. And it needs to be based on things that are observable, such as the heel angle and speed.

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### JoakimSenior Member

Crew weight spoils quite badly that approximation. You can sail without or with minimal heel and still have a lot of leeway. You can also introduce more heel in light wind without adding leeway.

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### jlcongerJunior Member

Since I can calculate the side force generated by the sails, I could come up with a better method of estimating leeway. However, I would need some method of measuring leeway on the real boat to validate the work. Here in SF Bay we have so much current that the GPS track is difficult to use. Any ideas?

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### tspeerSenior Member

All true. There are much better algorithms for estimating the leeway, if you have more information. For an instrument system, though, it may be good enough to have a very approximate value for leeway, especially if the algorithm is calibrated for the boat and how it's sailed, and if the leeway angle is small. Any errors in estimating the leeway then become small differences of a small quantity and are a higher-order effects that become submerged in the other noise sources.

I think it's important to distinguish between the definition of leeway, the prediction of leeway during the design phase, and the estimation of leeway based on measured data. Those can be three very different things.

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### jlcongerJunior Member

I'm doing this on conjunction with a CFD simulation of the sails, but I am not currently simulating the hull under the surface. The leeway angle has a large impact on the calculated VMG and generally pushes the VMG to tighter apparent wind angles. Many thanks if you can point me to other people's work in this area.

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### tspeerSenior Member

I think you're going to need to create a velocity prediction program (VPP) to get the interaction between the aerodynamics and hydrodynamics. It's not possible to optimize either one separately. The leeway angle will fall out naturally as a result of doing the force balance in the VPP.

It's straightforward, but labor intensive, to generate tables or curve fits of aerodynamic and hydrodynamic forces and moments, and then put them into a spreadsheet. Excel's Solver can be used to solve for the equilibrium speed, sail trim, heel, leeway, rudder trim, etc., for a given true wind angle.

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### gonzoSenior Member

Doesn't the foil section of the keel also affect leeway at different speeds?

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### tspeerSenior Member

No. All decent (meaning the flow is attached) sections have essentially the same lift-curve slope, so the leeway will be the same. Theoretically (for ideal flows), thick sections have a little higher lift curve slope and therefore slightly less leeway. However, in practice, thick sections also have thicker boundary layers at the trailing edge (owing to a higher peak velocity and therefore a more adverse pressure recovery region), and the displacement effect of the boundary layer pretty much cancels out the higher lift curve slope.

The only difference section shape makes is in the profile drag and stall characteristics. And if the boundary layer is essentially fully turbulent (a pretty good assumption for the vast majority of keels), the minimum profile drag scales with thickness and is nearly independent of shape for a given thickness.

That's why there are so many different section shapes. If it actually made a difference, evolution would rapidly settle on a winner.

Where section shape does matter is if you are after some specific requirements. If you can maintain laminar flow, then section shape is used to control the pressure distribution and thereby extend the laminar region. Or reduce it, if laminar separation is an issue. Section shape is important for avoiding cavitation. And section shape plays a big role in controlling separation at high angles of attack.

Essentially, section designis all about the care and feeding of the boundary layer. If you're in the operating range where the boundary layer characteristics are not critical, then section shape is not a driver.

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### gonzoSenior Member

How about when the foil starts to cavitate at high speeds?

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### brian eilandSenior Member

I have a relatively new member that has some very specific questions he wishes to ask concerning these subjects.

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### erdbenJunior Member

Thanks Brian for opening this old thread, here is my post copied from the other thread:

As a winter project, I got the rudder and centerboard off my boat to do some repairs/improvements. Since it's too cold in the garage now, instead of getting the epoxy out, I started reading about foil shapes and optimal planform area, then one thing led to another, and I ended up making a VPP for my boat so I can play with different foil shapes and centerboard sizes.

Let's say the question is what's the optimum centerboard size for a boat to achieve best upwind performance.

I understand that changing leeway angle by changing the size of the centerboard just rotates the hull relative to direction of movement, which will influence resistance of the appendages and the hull, and generally you'd try to find the centerboard size that gives you the best lift/drag ratio.

However, what I haven't seen to be discussed in detail is how the leeway affects the performance of the sails. In the VPP, I use the ORC sail coefficients to calculate aerodynamic forces, and those tables are based on apparent wind angle.

Should the AWA input for these aerodynamic calculations be corrected by the leeway angle?

Are the CL and CD numbers given for varying AWA in these tables independent of hull dimensions and sheeting angles (most importantly minimum sheeting angles)?

Here is an example: the max CL for the jib is at 27 degrees of AWA from the ORC tables. For angles less than 27 degrees, CL drops very quickly. Let's say my boat sails at 42 true wind angle, 12 kts true wind speed, at ~ 6.5 kts of boat speed with an AWA of 27.6 degrees. Leeway is ~5 degrees.

Would you calculate the main and jib CL / CD values from the 27.6 deg AWA or because the hull is rotated into the wind by 5 degrees, from an AWA reduced by the leeway (22.6 deg)? It makes a pretty big difference!

If the AWA for the sail forces need to be corrected by leeway, should it be done for all sail angles or only for angles where hull/rig geometry limits trimming of the sails? Should it be done only for the genoa, which is limited by the shrouds or the main, too? The main could theoretically be oversheeted with the traveler, but its interaction with the genoa will change, since the genoa can't be sheeted in more.

Considering the effect of leeway this way, would greatly influence optimum size for a centerboard, since leeway will not only affect hull/centerboard resistance, but also sail forces.

I'd be very interested to hear your opinions.

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### JoakimSenior Member

If your boat just had a mainsail, that would be easy. You are interested in the force vector parallel with the velocity vector, not the one paralle to keel line. So you shouldn't reduce AWA by leeway, you are just using the traveller.

With jib and main you have forestay and mast on the keel line, which makes it impossible to turn the whole sail area with leeway. So using the AWA as it is, is not 100% correct, but still much closer to reality than reducing by leeway. You can sheet in the jib and use the traveller.

With an overlapping jib there will be a limit to the sheeting angle and that needs to be considered. When you would need to sheet the jib in more than physically possible, you will not get the optimum sail forces predicted by the coefficients.

So I would say that AWA should not be corrected for leeway, but you may need to start to reduce the sail forces at some point to reflect the unoptimal sheeting.

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### erdbenJunior Member

Thanks. Yes, this is kind of what I was thinking, I just wasn't sure, since I haven't seen this discussed before.

It's also interesting that the general thinking is that you should center the boom while sailing upwind, but on a boat that sails at a relatively large leeway angle, it may be justified to "over-sheet" the main by that 5-6 degrees of leeway angle.

I remember that there was once a picture of a super-maxi or a tp52 on sailinganarchy sailing upwind in light winds with weirdly over-sheeted main and jib. It just looked wrong, but someone confirmed that it is in fact the way to sail these boats in light wind. Maybe it was just the excessive leeway due to low speed and sails trimmed correctly relative to the direction of the velocity vector and not the keel line.

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### JoakimSenior Member

The mainsail is just a "trailing edge" of the whole sailplan, thus its angle to wind or keel line shouldn't be thought the same way as jib or boats with just a mainsail. The latter would never sheet the boom above keel line.

Also it is just the boom. There is always some twist and the leech will not be windward of the keel line further way from the boom.

It is quite common to sheet the boom to windward of the keel line in many modern boats.

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