Sailboat rudder physics, and water flow estimate

[Neeps]

Hi. I'm a computer science student developing a kalman filter for autonomous sailboat, but I severely lack knowledge of the physics behind sailboats. I have a wind sensor giving data about wind speed and wind velocity, problem is the data is unreliable.

So i thought that i could estimate what the next value of wind direction would be based upon boat velocity, rudder angle, previous wind direction, previous coordinates (decimal degrees), and boat's compass course.

Sounds easy.. but problem is I don't know what the compass course and wind direction would be after x time.
Time intervals will be at most 5-10 seconds, to save some processing power. Would this be a circular motion?

What I'm after is some equation that returns a estimate of current state of "rotation/circular motion" in degrees
of boat caused by rudder angle, where time would be a factor.

Also, is it possible to estimate water flow based upon wind & GPS data?

 

[OrangeDog]

What you are trying to do is extremely complicated. I really don't think you should try the method you are suggesting (predicting the wind). However, for your curiosity you can very easily obtain windspeed and direction data at local weather monitors. This will usually be at least 50 feet above the ground though and will probably be higher than the velocity experienced at sea level / the ground.

If the sensor you are using is unreliable that is a very big problem - much more so than coming up with a type of filter. You will probably need a sensor that will do a good job of capturing the average wind speed but will not be sensitive to freestream turbulence or short term gusts. The pitot probe (can be really damn expensive) is good for 1 directional measurements, however can be inaccurate with large fluctuations in wind direction. The kiel probe does a better job of taking average measurements but can also be wildly inaccurate when the wind direction changes significantly. I suspect this might be the problem you are experiencing with your sensor.

You might want to go with a simple weather vane/anemometer combination. The interesting problem is that you will have to take into account the vibrations and change in orientation of the boat.

 

[A.T.]

What I'm after is some equation that returns a estimate of current state of "rotation/circular motion" in degrees
of boat caused by rudder angle, where time would be a factor.

You can find the turning radii at different speeds and ruder settings experimentally. Then interpolate or fit some function into the data.

 

[OrangeDog]

You can find the turning radii at different speeds and ruder settings experimentally. Then interpolate or fit some function into the data.

This will only work if he is in a low sea state. If this is a model then I say go for it.

 

[Jezza]

When you turn a boat, it pivots around the centre of lateral resistance (usually this will be somewhere near the centre of the keel), but there is also a tendency for the boat to slew towards the outside of the bend (Though this can be neglected for small angles at reasonably high speeds). The rudder works simply by deflecting the flow of water to one side, from flow parallel to the boat, to flow parallel to the rudder. This force can be resolved laterally and then the position of the rudder with respect to the centre of lateral resistance can be used to calculate a turning moment due to the rudder's angle. With a value for the moment of inertia of the boat, you can calculate the rate of turn of the boat from rudder position. It would be a question of exactly how much water is deflected by the rudder that determines the difficulty of this problem.

The rudder and keel are teardrop shaped, which greatly increases their efficiency and ability to deflect water at higher speeds (>3-4 knots) (when compared to laminas). The shape means water will tend to flow evenly over both sides of the keel and rudder even when not presented perfectly parallel to their direction of motion through the water. These become more efficient as you get faster. Further complications will come when you find that the centre of effort of the wind on the sails is rarely vertically in line with the centre of lateral resistance, so the rudder will have to be off centre to compensate. Then there's the consideration that as the boat heels, the rudder and keel become less effective since their effective area decreases. Another problem is that with a curved hull, when you heel you present an asymmetric profile to the water so you get uneven flow around the boat, This will cause the boat to turn towards the wind, and rudder correction will be needed for that. Again, this effect becomes more pronounced at higher speeds.

If you can overcome all the inevitable difficulties, then I think the problem will boil down to knowing what mass of water the rudder will influence and therefore deflect.

Many GPS systems will report rate of turn data, speed and course over land and through water (this requires a physical sensor, the log, which almost all boats have), tide, wind - apparent (this will rely on your anemometer of course) and true (which is calculated from apparent wind, speed and course over ground) and position. You could use the speed and course through the water to calculate a simplistic water flow prediction.

I think the bottom line is that there is no simple formula and you'll have to have a decent understanding of the physics. This looks quite interesting and like it might be of help to you:
https://books.google.co.uk/books?hl=en&lr=&id=6e_mkgRPVkUC&oi=fnd&pg=PP1&dq=the+hydrodynamics+of+rudders+and+keels&ots=nFRwsNk4VY&sig=h1FZHBWnk3g0ebkCpkW_9wEVWkE#v=onepage&q=the hydrodynamics of rudders and keels&f=false

 

[A.T.]

When you turn a boat, it pivots around the centre of lateral resistance (usually this will be somewhere near the centre of the keel), but there is also a tendency for the boat to slew towards the outside of the bend (Though this can be neglected for small angles at reasonably high speeds). The rudder works simply by deflecting the flow of water to one side, from flow parallel to the boat, to flow parallel to the rudder. This force can be resolved laterally and then the position of the rudder with respect to the centre of lateral resistance can be used to calculate a turning moment due to the rudder's angle. With a value for the moment of inertia of the boat, you can calculate the rate of turn of the boat from rudder position. It would be a question of exactly how much water is deflected by the rudder that determines the difficulty of this problem.

The rudder and keel are teardrop shaped, which greatly increases their efficiency and ability to deflect water at higher speeds (>3-4 knots) (when compared to laminas). The shape means water will tend to flow evenly over both sides of the keel and rudder even when not presented perfectly parallel to their direction of motion through the water. These become more efficient as you get faster. Further complications will come when you find that the centre of effort of the wind on the sails is rarely vertically in line with the centre of lateral resistance, so the rudder will have to be off centre to compensate. Then there's the consideration that as the boat heels, the rudder and keel become less effective since their effective area decreases. Another problem is that with a curved hull, when you heel you present an asymmetric profile to the water so you get uneven flow around the boat, This will cause the boat to turn towards the wind, and rudder correction will be needed for that. Again, this effect becomes more pronounced at higher speeds.

To make it even more complicated, there is also some vertical torque from the sail, that tries to turn the boat.

 

[Nidum]

@Neeps

http://students.asl.ethz.ch/upl_pdf/155-report.pdf

 

[CWatters]

To make it even more complicated, there is also some vertical torque from the sail, that tries to turn the boat.

Indeed, on a well trimmed boat its sometimes possible to steer without a rudder, just using the sails.

 

[gleem]

What is the physical size of the boat i.e. hull length. What is expected of the boat with regard to holding course and changing coarse.

You will need some control over the position of the sails. Trimming them in as you go toward the wind and easing them out as you come off the wind. Proper trim will depend on the apparent wind direction and speed. You will need heel sensor to keep the boat tipped to an efficient angle. If you could get a hold of an RC boat you could learn a lot. Actually go sailing its will teach you a lot and its fun.

 

[Svein]

Hi. I'm a computer science student developing a kalman filter for autonomous sailboat, but I severely lack knowledge of the physics behind sailboats. I have a wind sensor giving data about wind speed and wind velocity, problem is the data is unreliable.

So i thought that i could estimate what the next value of wind direction would be based upon boat velocity, rudder angle, previous wind direction, previous coordinates (decimal degrees), and boat's compass course.

I had that kind of steering on my previous sailboat - it was an Autohelm setup. I set the general course on the autopilot and told it to use wind information. It worked a charm!

 

[A.T.]

@Neeps

http://students.asl.ethz.ch/upl_pdf/155-report.pdf

@Neeps also:

http://students.asl.ethz.ch/upl_pdf/110-report.pdf