Calculating speed of boat by sail alone

[zappattack]

Hello all,

I know this is probably very simple stuff, but I'm a mature student, and a bit rusty.

Essentially, I need to calculate the following: a sailboat of mass 52 tonnes, dimensions 50m x 6m x 2m, and square shaped sail of 150 m^2 is sailing by wind alone, which has a speed of 15 m s-1.

How do I calculate the max speed the boat can travel under sail? Do I assume the hull to be 1/2 the area of a circle and use stokes law for drag in liquids? How do I convert wind speed to force in forward motion for drag to go against? How does the drag alter if moving against current?

The last couple of questions is prob unnecessary, as I need this to be v simple illustration of time it might take to get from a to b via steady wind power...

Thanks!

 

[K^2]

It all depends greatly on the course you take. The sail is effectively a wing. It generates lift and drag. At close haul, you are using component of lift to push you forward. At broad reach or running, the sail is "stalled" and you are using aerodynamic drag.

Body drag is going to depend greatly on the shape of the boat. For some boats, the direction of the wind will matter too, but unless we are talking about a multi-hauled boat, that probably won't make too much difference.

For estimate on the body drag, you should probably use a drag formula. But what the drag coefficient is going to be like depends on the shape and size of the boat.

 

[DaveC426913]

Hello all,

I know this is probably very simple stuff, but I'm a mature student, and a bit rusty.

Essentially, I need to calculate the following: a sailboat of mass 52 tonnes, dimensions 50m x 6m x 2m, and square shaped sail of 150 m^2 is sailing by wind alone, which has a speed of 15 m s-1.

How do I calculate the max speed the boat can travel under sail?

Where I come from, you need one variable: length at waterline.

For a sailing vessel of 50m (164') length, max hull speed is 17knots.

v = 1.34 * LWL^1/2



Oh. Max speed in a wind of 15ms-1. Never mind.

 

[zappattack]

Thanks guys,

Maybe try a formula. But there are so many variables! F = 1/2 pu^2cdA, where p = density of water, u is velocity of object relative to fluid, cd is drag coefficient, A is frontal area of object.

Say I did find a suitable value for cd... what's thehecking velocity of the object relative to fluid? Surely that depends on the drag...the value I'm trying to find? If I were to assume the boat was on a frictionless river, how then would I convert wind speed to calculate terminal velocity of boat?

It's 2.30am and I'm trying to decide whether to pull and all nighter or if a few hours sleep would help!

 

[russ_watters]

Where I come from, you need one variable: length at waterline.

A quick explanation: It isn't friction drag that limits the speed of a displacement vessel, it is the creation of and riding on the boat's own wake. At the speed described by Dave's equation, the boat sits in a trough created by the bow wave. In order to go faster, the boat must start climbing up the bow wave and literally lifting itself out of the water, which is something the wind (or even powerful engines) can't do to a displacement hull vessel.

 

[K^2]

Oh, right. Wave drag. That's making things much more complicated.

In that case, I'm out.

 

[DaveC426913]

A quick explanation: It isn't friction drag that limits the speed of a displacement vessel, it is the creation of and riding on the boat's own wake. At the speed described by Dave's equation, the boat sits in a trough created by the bow wave. In order to go faster, the boat must start climbing up the bow wave and literally lifting itself out of the water, which is something the wind (or even powerful engines) can't do to a displacement hull vessel.

Correct.

Unless, like me, you happen to have a sailboat with a planing hull.