# Getting sailboat velocity from wind speed and direction

• kubassek
In summary, you would need to use the polar to find the maximum possible boat speed relative to true wind, and then use that speed to find the corresponding course.
kubassek
I am trying to figure out how to calculate the boat velocity using wind speed and wind direction. I have tried to find sources online but this is the only useful site I managed to find:
Unfortunately it has been a while since I did maths and I'm struggling with understanding how the VB (boat velocity) in the examples on the website is calculated and was wondering if anyone could explain it at all? The results don't have to be 100% accurate so as long as a rough estimation of speed is achieved that's fine.

The part I am most struggling with is how the VB is calculated using a - apparent wind as I though you needed the boat velocity (VB) to figure out a.

Thank you in advance for any help.

You need to do a vector sum. Not just the speeds, but the speeds and directions. The pictures below illustrate. Does that answer your question?

kubassek said:
I am trying to figure out how to calculate the boat velocity using wind speed and wind direction.
What about the course? Do you have a target that you want to reach as fast as possible?

Or do you want to maximize speed no matter the direction?

https://en.wikipedia.org/wiki/Saili...heorem_and_Maximum_speed_course_sailing_angle
http://www.onemetre.net/Design/CourseTheorem/CourseTheorem.htm

You will need more parameters, at least the lift/drag ratios to the air and to the surface (efficiency).

I can't decide what information you have about the situation. You are basically dealing with a vector equation with three vectors. You need to know two of the vector quantities in order to work out the third.
You can measure apparent wind speed and direction on the boat but what about true windspeed and direction? Would you assume that the Windfinder information is accurate enough? It sounds to me that it's an ill conditioned problem. Buy a second hand Garmin gps and that will tell you what you want.

CWatters
It is impossible to calculate boat speed from just the wind speed and wind direction. The crew also have a say in such matters!

If you have info on the true and apparent wind then it's a simple vector sum as the drawing anorlunda posted shows.

BillTre
I agree with CWatters.

The design of the boat (think about those American Cup boats) will also matter, as well as other things.

I think of the vectors more as reflecting the relative amounts of force derived from the wind, which through the action of the boat, crew, water conditions, etc. generates a speed.

I had the luxury of a boat that went so slowly that real and apparent wind were never very different. "A bit for'ard" was accurate enough for me.

Nugatory and BillTre
sophiecentaur said:
I had the luxury of a boat that went so slowly that real and apparent wind were never very different.
The other extreme are sailcraft where real and apparent wind have opposite directions.

https://en.wikipedia.org/wiki/Blackbird_(land_yacht)

CWatters and BillTre
Hi - I am trying to solve the same problem as kubassek above for historical ships, using the equations given on the blog he/she referenced.
I have determined paths and each cell I have values for the wind speed (Vt) and direction (gamma) (among many other factors that are less relevant to this question). I also know the direction of the ship and its speed in the previous cell. I can determine some kind of efficiency coefficient (eta) using historical data for these ships, and I have a polar for relatively similar square-rigged ship.
What would then be the equation that would give me the ship's speed based on these parameters? Any help would be greatly appreciated. Many thanks.
Alexis

litvine said:
Hi - I am trying to solve the same problem as kubassek above for historical ships, using the equations given on the blog he/she referenced.
I have determined paths and each cell I have values for the wind speed (Vt) and direction (gamma) (among many other factors that are less relevant to this question). I also know the direction of the ship and its speed in the previous cell. I can determine some kind of efficiency coefficient (eta) using historical data for these ships, and I have a polar for relatively similar square-rigged ship.
What would then be the equation that would give me the ship's speed based on these parameters? Any help would be greatly appreciated.
The polar gives you the max boat speed as function of course relative to true wind. Calculate that relative course and get the corresponding max speed from the polar.

If you want to compute realistic acceleration between different conditions, then you will need a more complex simulation based on Newton's Laws, which also requires more information. But this only matters if the wind changes a lot and/or in a non-smooth manner. Otherwise you can ignore this and assume max. possible speed at all times, or do some interpolation.

It depends on the data and the application what is acceptable here.

Use the polar as a look-up instead of an equation.

sophiecentaur
Thanks to both - the problem is that the polar has only curves for three wind speeds, hence I cannot use it for *any* windspeed I have in my data. I don't mind having max speed but I'd still need a way to derive the boat speed from wind speed. Ideally, I'd like to do something similar to what is done in this article (I have current speed and mean wave height, but I'd prefer to start with a simplified model to calculate wind-based speed only). AS for the friction I can obviously not measure it but I can infer a coefficient for different wind directions based on the polar and historical data. Am I getting this wrong?

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litvine said:
Thanks to both - the problem is that the polar has only curves for three wind speeds, hence I cannot use it for *any* windspeed I have in my data.
You could interpolate/extrapolate them.
litvine said:
AS for the friction I can obviously not measure it but I can infer a coefficient for different wind directions based on the polar and historical data.
A polar is the result of many parameters. Trying to reverse-engineer their individual values from the polar might be under-determined.

Last edited:
sophiecentaur
You might find the web site given below useful in gaining an understanding of hull resistance. I think finding the propulsive force of the sails is then the next step. To do this you need to fix the wind direction and course steered (not track).
The below-water foils and hull behave as wings of an aeroplane; the side thrust of the sails is equivalent to the weight of the 'plane and the forward thrust is equivalent to the engine thrust. The angle of attack of the wing (keel or centreboard) equates to the glide angle of the 'plane, and for a boat this is the same as the leeway.
https://www.usna.edu/NAOE/_files/documents/Courses/EN400/02.07 Chapter 7.pdf

litvine said:
the problem is that the polar has only curves for three wind speeds, hence I cannot use it for *any* windspeed I have in my data. I don't mind having max speed but I'd still need a way to derive the boat speed from wind speed. Ideally, I'd like to do something similar to what is done in this article
Even if you have equations, you still need values for all the coefficients in those equations. The following sentence is quoted from the article you linked.

The presented mathematical model of ship speed forecasting in real weather conditions has been verified on the basis of experimental model tests.

The polar curves you have also come from testing, probably with a dose of judgement and data smoothing imposed.

I think your best chance for success, without millions for a testing program, is to use curve fitting or linear interpretation on those polar curves to use them for any wind speed.

Even then, your results apply only to the particular hull design used to make the polar curves. To make conclusions applicable to a range of hull designs you need a corresponding range of polar curves.

Therefore any result predicted by your models will have a large error bar associated with it, and estimating the size of those error bars would be another big project.

How much effort and money are you willing to invest for how much accuracy of prediction. That's the key question to ask yourself.

## 1. What is the formula for calculating sailboat velocity from wind speed and direction?

The formula for calculating sailboat velocity from wind speed and direction is V = (Vw * cos(ϴ - α)) + (Vc * cos(β - ϴ)), where V is the sailboat velocity, Vw is the wind speed, ϴ is the wind direction, α is the angle of the sailboat relative to the wind, Vc is the current velocity, and β is the angle of the current relative to the wind.

## 2. How accurate is the calculation for sailboat velocity?

The accuracy of the calculation for sailboat velocity depends on various factors such as wind and current conditions, sailboat design, and instrumentation. Generally, the calculation can be accurate within a range of 5-10%.

## 3. Can this calculation be used for all types of sailboats?

Yes, this calculation can be used for all types of sailboats. However, the accuracy may vary depending on the sailboat design and conditions.

## 4. Is the calculation affected by the size of the sailboat?

Yes, the size of the sailboat can affect the calculation to some extent. Larger sailboats may have a higher windage and require more wind to reach a certain velocity compared to smaller sailboats.

## 5. How can this calculation be used practically for sailing?

This calculation can be used practically for sailing by helping sailors determine the optimal angle and trim of their sails for a desired velocity. It can also be used to plan and adjust sailing routes based on wind and current conditions.

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