# Some questions on polars and upwind/downwind performance

Discussion in 'Sailboats' started by Tedd McHenry, Sep 7, 2021.

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### Tedd McHenryJunior Member

I made the polar below using ORC Sailboat Data. I picked the Nordic Folkboat only because it's a boat I like and is of the size and configuration that most interests me. (And the data was readily available.) I've marked the points of maximum upwind and downwind VMG, by eye. I have two questions about this (below) and I'm also interested in other thoughts from people with experience using polars.

1. I've fitted a radial line through the upwind VMGmax points, by regression. They all lie close to 53 degrees. What strikes me about this is how far maximum VMG is from the minimum beat angle--nearly 10 degrees in some cases. Is that typical for a boat like this, or is my methodology somehow exaggerating the difference?
2. I'm also intrigued by the downwind VMGmax points. For 10 kt and below, they lie well away from a dead run. It's not obvious to me why that would be, but one explanation that occurred to me is that a spinnaker might have been used for the 10-kt and below data points. I would have thought that an asymmetrical spinnaker, especially, would tend to give VMGmax at some angle away from a dead run. Does that make sense, or is there a better explanation?
I originally attempted to do this analysis by fitting various nth order polynomials through the data. That allows the VMGmax points to be accurately determined by finding the zero points on the derivative of the polynomial. But I found that it wasn't possible to find polynomials that gave a good fit. Lower order polynomials rounded off the curves too much in the beating area while higher order polynomials introduced wavy bits in the downwind and broad reach areas. So I settled on spline curves so that I at least know the curve matches the data at the actual data points. Unfortunately, I've yet to work out how to find the equation used at each point in the spline, so I have to eyeball the VMGmax points instead of using calculus. I've got a reference for working out the actual spline equations but I haven't digested it, yet.

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### BlueknarrSenior Member

1. Very typical results.

2. Your explanation is probable. Could also be result of further reduction in sail area from reefing the main. Surfing dead down wave could also change vector of vmg

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### Tedd McHenryJunior Member

Thanks for your thoughts, @Blueknarr . I hadn't even thought about waves and following seas but I agree, that could be quite significant.

I still remember the first time I found myself going downwind at above hull speed in a keel boat. At that time I'd never even heard of "surfing" in a sailboat.

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### DolfimanSenior Member

Your results upwind are intriguing, not usual I would say, the usual optimum VMG with a modern sailboat is obtained with twa from ~ 44 deg with 6 Knots of wind to ~39 deg with 20 Knots. Example of the Sydney 38 :
Downwind, it also depends of the capacity to go fast when closer to the wind, same example : twa ~ 140 deg with 6 Knots to ~ 170 deg with 20 Knots (0r less, see also the targets which assume to go planing ?) .

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### AJBJunior Member

Tedd,
You need to get out more!

But seriously...

Upwind
Your regression around TWA is a source of confusion, not enlightenment. A useful approach is to calculate the AWA for the optimum VMG numbers.

So, for example in 10 knots TWS, BS is 5.0 and AWA is ~ 35 degrees, at 52 degrees TWA from the graph.

This AWA kind of summarises the lift/drag characteristics of the whole apparatus; and what you will probably find is that the AWA for optimum VMG across the range 6 - 20 TWS does not vary by more than about 2 degrees.

This AWA tells us that the foil and underwater surfaces are not very efficient; from a modern standpoint, the wetted surface of the Folkboat is very high. For reference, a 'modern' upwind AWA would be around 25 degrees. Ballpark estimate for your wetted surface drag is around 2/3 of the total hydro drag.

Downwind VMG
These are flat water polars, so no surfing is involved. The ORC downwind aero coefficients are a fair way away from reality, particularly for the VMG run part of the spectrum.

But two major points:
1. Because attached flow generates aero force that is a multiple of stalled flow, some degree of gybing downwind will always be better than DDW, i.e. sailing with TWA at 180, where the proportion of unstalled flow over the sails becomes very low. So for most boats (with spinnakers, asymmetric or symmetric) the optimum AWA for VMG running in less than 8 knots TWS is around and even less than 90 degrees. The AWS might be more than double that of the boat trying to sail DDW. Aero force is proportional to V^2.... so the aero force might be 4 times as large...
2. Because the hydro drag of the relatively heavy design rises rapidly as the speed exceeds about 5 knots, the downwind gybing angles in good breeze (say 14 knots and up) will be quite small. But there is plenty of evidence to suggest that around 165 degrees TWA is a good rule of thumb maximum ; i.e. minimum gybe angle of 30 degrees.

For some larger modern designs with large masthead spinnakers, the ORC VPP continues to predict zero gybe angles for VMG run, when if fact, the aero force of the spinnaker in that situation will lead to sufficient windward heel and force misalignment as to propel the yacht into an involuntary gybe! The more accurate designer VPPs have the maximum TWAs at around 165 and AWAs not greater than about 155, for moderately heavy designs.

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### gonzoSenior Member

Downwind, the boats speed gets subtracted from the windspeed. As the boat accelerates, the apparent wind decelerates slowing the boat until it reaches a balance. At lesser angles, the boat speed adds to the windspeed, so the apparent wind is higher than the actual windspeed. As the boat reaches "hull speed", the power needed to go faster increases exponentially, so the difference in apparent wind does not make as much of a difference.

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### Tedd McHenryJunior Member

Thanks for the Sydney 38 data, @Dolfiman . I plugged it into my spreadsheet so I could see all the curves. It certainly looks more like what I expected to see, with max. VMG upwind at the minimum beat angle and max. VMG downwind at 180 degrees (for most wind speeds).

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### Tedd McHenryJunior Member

I do. But I'm not currently working and I'm between boats, so what the heck else am I going to do?
That is a great idea, I will do that. I started out only interested in where maximum VMG would lie relative to TWA, but I think you're right that considering AWA will provide more insight. I'm also going to apply the same analysis to a few different boats. Since I can't currently sail anything that will have to substitute for experience!
Are the ORC numbers not actual measurements? I assumed that they were.

I'm going to have to think about your last two points for a while. But thanks very much for the input!

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### AJBJunior Member

All good Tedd

ORC is just reheated IMS, not really very sophisticated - just a bunch of spreadsheets, no actual performance feedback.

Which is why, with good resistance, flow and dynamic performance models the leading designers can game it very significantly.

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### Tedd McHenryJunior Member

Hi @AJB ,

Is this the kind of thing you expected to see? This is from the Sydney 38 data that @Dolfiman linked to. It seemed to be good quality data so I used it. The polar below is based on AWA, and the scalar quantity is the boat-speed/wind-speed ratio. As you predicted, the maximum point for each wind speed is found in a pretty narrow range of angles.
View attachment 171421
[Attachment updated with better version. This version uses 4th order polynomial fit to the original data, rather than a spline curve. I think that reflects reality more closely and also allows the maximum speed ratio points to be calculated from the polynomial.]

#### Attached Files:

• ###### Sydney_38_AWA_Polar.png
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Last edited: Sep 11, 2021
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### AJBJunior Member

Tedd,
Nice!

If only the real world was quite so smooth!

Now you should consider the VMG vs VMC speed downwind for offshore stuff...

You can find the Farr 40 polars on the class website; and they are well closer to reality than ORC or the Sydney 38 numbers.

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### Tedd McHenryJunior Member

Thanks again, @AJB . Now that I have the spreadsheet as a template I can easily plug in the Farr 40 data. And I'll have a look at downwind, as well.

Yes, fitting polynomials creates unrealistically smooth data, but I think it's fine for conceptual purposes. I'm not trying to learn anything about any particular boat, but more just get a sense of how all the parameters work together.

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### tlouth7Senior Member

Polars should always be created with respect to TWS/TWA not AWA. Otherwise if you aren't sailing to the target speed you can't use the polar at all.

Folkboats have long keels so a wider optimum close-hauled angle than modern boats doesn't surprise me much. The downwind angles don't surprise me either - at low windspeed the boat is sailing an appreciable proportion of the windspeed, so AWS is very low and there is a comparatively big increase in AWS from heading up a few degrees. For higher windspeed the subtraction of STW has less effect, so the advantage of heading up is reduced. It is a general rule that whether under white sails or spinnaker, boats benefit more from sailing angles (and those angles are wider) in light than strong winds.

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### Tedd McHenryJunior Member

Thanks for your comment. The purpose of looking at the effect of AWA, as @AJB mentioned above, is to gain an understanding of how the L/D of the entire system (sails and hull) perform under different conditions. It's not so much something a sailor would use, as you noted. But it is of interest from the perspective of boat design.

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### Tedd McHenryJunior Member

@AJB ,

Here's what I got from the Farr 40 data.

• "SRmax" is the point where the ratio of boat speed to wind speed is maximim, for the given wind speed.
• "VMGmax" is the point where VMG is maximum, for the given wind speed.

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