Bow Wave angle vs Boat Speed

In summary, one of the hobbies of the author is sailing, and they are interested in improving their tactical decisions by applying science to the situation. They believe that there is a simple relation between bow wave angle and boat speed, and they would like to understand how this is determined. They think that it would be worth the effort to make crude measurements with a GPS while out on the water, bearing in mind that they could repeat the excercise in different conditions.
  • #1
YellowPeril
12
0
Hi

From this post you will deduce that one of my hobbies is sailing, I believe that applying a bit of science to the situation will improve my ability to make better tactical decisions on the spot.

I have a GPS but am interested in getting a quick visual of boat speed related to the angle that the bow wave makes to the boat. Is there a simple relation between bow wave angle and boat speed? The type of hull that I am interested is a catamaran hull (long and thin) so it can never plane and the speed range I am interested in is about from 10 to 20 knots (~20 km/h to 40 km/h)

Also I have heard in conversation that there is a maximum speed associated with a specific type of hull. (Hobie 16 catamaran for example) I would like to understand how this is determined, if it is at all possible. A hobie 16 hull does not have a centerboard like most hulls but is designed with an aerofoil shape. When one hull is flying (term used when one hull is raisd above the waterline), the other hull is in the water and the lift generates the stabalising influence (through hydrodynamic lift) that would normally be generated by a keel on a monohull. The hobie hull can be approximated by a long thin aerofoil dragged through the water in section. I think that there is a penalty incurred in the speed for this type of design, once again heard from somewhere. I would be interested to know what the lift and drag relations would be in relation to hull speed and how to determine them.
 
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  • #2
For a given wavelength, wave speed varies with water depth. So you'd have to know the water depth and you'd have to be able to detect at least one single frequency. More would add to your accuracy. This is certainly doable but it would probably take some fairly fancy image processing software. Once you know the spectrum (or at least one main frequency), angle, and water depth (assuming it doesn't vary much or your software knows the variations and accounts for them), then you could make a calculation for each wavelength speed using the equations in this wiki article:
http://en.wikipedia.org/wiki/Ocean_surface_wave#Science_of_waves

Then use trigonometry to figure boat speed (probably averaging multiple frequencies to add accuracy). I suppose in theory you might even see a hull signature in the spectrum and angles!

Its an interesting idea, but I think it would be hard to implement in practice.
 
  • #3
Dang, I skimmed your post and thought you wanted to figure the speed of some distant boat! Ok -- watching your own wake makes it easier, and let's assume its nice deep water (much deeper compared to any wavelength you watch). In that case, pick a wavelength (preferably one much shorter than current water depth), calculate its speed from the simplified equation:

[tex]WaveSpeed = 1.25\sqrt{Wavelength}[/tex]

(meters and seconds)

Then use this equation to calculate boat speed:

[tex]BoatSpeed = WaveSpeed * tan(\pi/2 - Angle)[/tex]

Where Angle is the angle from the boat's path, in radians.

OK, that's the theory. However, I would seriously consider taking empirical data and recording it in a table of angle vs. speed! That way certain other unknowns are accounted for (like inaccuracies/distortions in your visual cortex, inaccuracy in recognizing a wavelength, shock waves, water makeup and temperature, etc.). Come to think of it, salt content would change things a lot, I think.
 
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  • #4
Thanks Fleem,

Empirical measurements were what I had in mind. I just needed some background on the variables to see if it would be a worthwhile excercise. From what you have told me it could be worth the effort to make some crude measurements with the GPS while out on the water. Bearing in mind to repeat the excercise in different conditions, I should be able to get what I am after.
 
  • #5
fleem said:
https://www.physicsforums.com/latex_images/22/2294452-1.png [Broken]
[/URL]

Alternatively,

Vboat = Vwave / tan(θ)​
is a somewhat more direct calculation (no need to subtract θ from π/2 or 90°)
 
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What is the bow wave angle and how is it related to boat speed?

The bow wave angle is the angle formed between the bow of a boat and the crest of the bow wave created by its movement. It is related to boat speed because as the boat moves faster through the water, the bow wave angle increases.

What factors can affect the bow wave angle?

The bow wave angle can be affected by various factors such as the shape and size of the boat, the speed and direction of the boat, and the density and depth of the water.

What is the significance of the bow wave angle for boat design?

The bow wave angle is an important consideration in boat design as it can impact the boat's stability, efficiency, and performance. A larger bow wave angle can create more drag and slow down the boat, while a smaller angle can improve speed and fuel efficiency.

How can the bow wave angle be measured?

The bow wave angle can be measured using a protractor or angle gauge placed on the boat's bow. It can also be calculated by measuring the boat's speed and the distance between the bow and the crest of the bow wave.

Is there an ideal bow wave angle for maximum boat speed?

There is no single ideal bow wave angle for maximum boat speed as it can vary depending on the boat's design, size, and speed. However, in general, a smaller bow wave angle is preferred for faster speeds and better performance.

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