## Sail Size vs. Wind Speed

### Sail Size vs. Wind Speed

Does anyone know if thee is some relationship or rule of thumb that compares
sail size (power) to wind speed.  In other words, using the same board, sailor
and sail design, if a 7.0 produces a certain amount of power at 12 kt, how much
wind does it take for a 6.0 to produce the same power?  A 5.0? and so on.

### Sail Size vs. Wind Speed

Sail thrust is proportional to Area x windspeed*squared, all other things being
equal. Thus IF all these sails were identical except for size, the thrust from
each sail = Area times windspeed*squared times some constant your question

So any sail has twice the power of an identical sail half its size in the same
wind, ideally.

And any sail has four times the power that same sail has in half as much wind
.... ideally.

But don't go buying sails based too seriously on these facts, because there are
MANY factors complicating this theoretical ideal. IOW, all other things are NOT
equal.

Mike \m/

### Sail Size vs. Wind Speed

Good as far as you went, but you forgot drag.  The thing that makes you go
faster is the difference between the force (thrust) a sail generates and
the drag (from all sources, aero and hydro) that holds you back.   If such
were not the case, then if an 8.0 was good for 10 knots, at 12 knots a 5.5
would work.  We all know that's not the case.

Some rules that can be counted on:

Bigger riders need (can hold down) bigger sails.
Less wind means more sail.
You can never have too many sails (or boards).

The best sail sizes to own will be dictated by where and when you sail, how
much you weigh, what kind of sailing you do, and how much money you have to
spend.

Frank Weston

Quote:
> Sail thrust is proportional to Area x windspeed*squared, all other things
being
> equal. Thus IF all these sails were identical except for size, the thrust
from
> each sail = Area times windspeed*squared times some constant your
question

> So any sail has twice the power of an identical sail half its size in the
same
> wind, ideally.

> And any sail has four times the power that same sail has in half as much
wind
> .... ideally.

> But don't go buying sails based too seriously on these facts, because
there are
> MANY factors complicating this theoretical ideal. IOW, all other things
are NOT
> equal.

> Mike \m/

### Sail Size vs. Wind Speed

It is interesting to note that the maximum power (rather than the force, i.e. Watts or horse power,  rather than Newtons) you can
extract from the wind goes as the 4th power of the velocity!

Kit.

### Sail Size vs. Wind Speed

Quote:

> It is interesting to note that the maximum power (rather than the force, i.e. Watts or horse power,  rather than Newtons) you can
> extract from the wind goes as the 4th power of the velocity!

> Kit.

I'd have guessed the 3rd. Is the power extracted defined as what's
required to move the hull against water resistance?

Ian

### Sail Size vs. Wind Speed

This is the reason I was wondering.  The v-squared approach would suggest that
very small differences in wind speed would equate to much larger differences in
sail size, which is counter to experience.  I figure that sailing upwind all
the force comes from lift, which is proportional to velocity squared, going
downwind, all force comes from push, which I figure is proportional to velocity
alone.  Everywhere in between, it seems like the force should be a combination
of push and lift.  At top speeds (reaching) it seems like the two forces should

Also, drag, sailor size, capability, wind variability, etc would come into
play.

I realize this is esoteric, but I was a physics major in college and stuff like
this fascinates me.

Quote:
>Good as far as you went, but you forgot drag.  The thing that makes you go
>faster is the difference between the force (thrust) a sail generates and
>the drag (from all sources, aero and hydro) that holds you back.   If such
>were not the case, then if an 8.0 was good for 10 knots, at 12 knots a 5.5
>would work.  We all know that's not the case.

### Sail Size vs. Wind Speed

Quote:
> Does anyone know if thee is some relationship or rule of thumb that
compares
> sail size (power) to wind speed.  In other words, using the same board,
sailor
> and sail design, if a 7.0 produces a certain amount of power at 12 kt,
how much
> wind does it take for a 6.0 to produce the same power?  A 5.0? and so on.

A pretty good model relating sail size and wind speed for equal force is:

(Sail Area # 1 / Sail Area #2) = (Wind Speed #2 / Wind Speed #1) ** N

Ideal fluid aerodynamics predicts that N=2, but in real life N is something
like N=0.6.  This number is empirical.  It depends on your weight, and
what type of sail you use (slalom vs. wave).

Have fun.

Andrew

### Sail Size vs. Wind Speed

Quote:
> I figure that sailing upwind all
>the force comes from lift, which is proportional to velocity squared, going
>downwind, all force comes from push, which I figure is proportional to
>velocity

Actually, lift is defined ast the force perpendicular to the direction of the
relative wind. Drag is defined as the force generated in the direction of the
relative wind. On a reach, only a portion of the lift is directed in the
direction of  travel of the board, and only a portion of the drag is opposed to
the the direction of the board. The sum of the remainder of the forces of lift
and drag is directed perpendicular to the direction of travel, and is
counteracted by the fin.

>I was a physics major in college and stuff like

Quote:
>this fascinates me.

As a physics major, you should find it easy to do the vector diagrams of the
above. And maybe you can tell me if it is possible to calculate the fastest
point of sail. Experience says it is a broad reach. But how many degrees off
the wind, and why? I would think 120 degrees would be optimum, but can't quite
work out the math.

Bob Jacobson

### Sail Size vs. Wind Speed

Yes, 20 years ago (when I graduated) I probably could have figured it out.
This much I think I do know: I agree that a broad reach is the fastest point of
sail from both experience and every book on the subject that discusses it.  I
think (based on my vector diagram) that the optimal angle of sail to relative
wind is 45 degrees.  That is because the component of force from the sail in
the direction of travel is sina*cosa*force(push) + cosa*cosa*force(lift), where
a is the angle of relative wind to the sail.  Since the above maxes out at 45
degrees, this should be the best angle to hold sail to wind.    Now, I haven't
figured out how to go the next step.  However, I would guess that the answer is
to sail 135 degrees off the wind for fastest point of sail.

Anyway, its been too long to figure out the vector diagrams and formulas, and
the best laboratory is on the water.

Quote:
>As a physics major, you should find it easy to do the vector diagrams of the
>above. And maybe you can tell me if it is possible to calculate the fastest
>point of sail. Experience says it is a broad reach. But how many degrees off
>the wind, and why? I would think 120 degrees would be optimum, but can't
>quite
>work out the math.

### Sail Size vs. Wind Speed

Quote:
>Yes, 20 years ago (when I graduated) I probably could have figured it out.
>This much I think I do know: I agree that a broad reach is the fastest point
>of
>sail from both experience and every book on the subject that discusses it.  I
>think (based on my vector diagram) that the optimal angle of sail to relative
>wind is 45 degrees.  That is because the component of force from the sail in
>the direction of travel is sina*cosa*force(push) + cosa*cosa*force(lift),
>where
>a is the angle of relative wind to the sail.

What is this push you keep writing about?  The sail only sees the relative
wind, which causes low presessure on one side of the sail and high pressure on
the other. The pressure differential causes a force to be generated
perpendicular to the relative wind, and this force is called lift. No Push.
Bob Jacobson

### Sail Size vs. Wind Speed

Quote:
> As a physics major, you should find it easy to do the vector diagrams of
the
> above. And maybe you can tell me if it is possible to calculate the
fastest
> point of sail. Experience says it is a broad reach. But how many degrees
off
> the wind, and why? I would think 120 degrees would be optimum, but can't
quite
> work out the math.

There are a lot more than vectors involved.  I don't pretend to be able to
do the modeling required or to own a computer capable of the calculations,
but I can say with some certainty that the optimum angle off wind for
maximum speed depends on the wind speed.  The higher the wind, the greater
the angle.  If it's blowing 15, the angle might be about 100 degrees, if
it's blowing 150, the angle might be closer to 180 degrees.

Frank Weston

### Sail Size vs. Wind Speed

Quote:

> As a physics major, you should find it easy to do the vector diagrams of the
> above. And maybe you can tell me if it is possible to calculate the fastest
> point of sail. Experience says it is a broad reach. But how many degrees off
> the wind, and why? I would think 120 degrees would be optimum, but can't quite
> work out the math.

> Bob Jacobson

the optimum sailing angle can not be determined from a simple vector
analysis, i.e a decomposition of the net-force-vector.

There are several reasons for this, but the most obvious one is that
the magnitude of the net-force-vector is itself a function of the
sailing angle.

in practice many factors will influence the optimum sailing angle,
and it is probably best determined empirically.

here is another way of looking at it:
if the optimum sailing angle could be determined by a vector analysis,
then
all boats would have the same optimum angle, and boat design would be
irrelevant.
Emprical evidence that this is not the case is easily obtained by
watching big
boat racing. In races with different types of boats, one finds that when
sailing
downwind, different boats sail different angles. of course this is
slightly more
complicated, because they are seeking to maximize their downwind vmg
(velocity
made good, i.e. their component of velocity in the downwind direction),
not their
speed. moreover, this optimum angle changes when the wind speed changes,
a fact
not compaptible with a 'vector decomposition' analysis.

designers of racing boats generally provide their clients with what is
known
as a "polar diagram". plotted in cylindrical coordinates, these diagrams
show
boat speed vs. sailing angle for a variety of wind speeds and sail
plans. these
polar diagrams are usually computer generated, but are updated by
on-the-water
testing, and they can be quite accurate. a look at these polar diagrams
shows
that the optimum sailing angle (in terms of both raw boat speed, and
vmg) varies
dramatically with both boat design and windspeed. again, this would not
be the
case if a simple vector analysis could obtain the optimum angle.

jeff

### Sail Size vs. Wind Speed

Of that I have no doubt!!!.  And even knowing the vectors probably doesnt help
one sail very well.
Quote:
>There are a lot more than vectors involved.

### Sail Size vs. Wind Speed

When sailing on a run (sail 90 degrees to the actual wind), the only force is
the wind pushing the sail from behind.  Like a leaf blowing in the wind, the
only speed you could hope for is to equal wind speed, drag would slow you down.
When close hauled the force is all lift.  Based on my windsurfing books when
you are on a broad reach you get some of both.
Quote:
>What is this push you keep writing about?

### Sail Size vs. Wind Speed

Quote:

> >the optimum sailing angle can not be determined from a simple vector
> >analysis, i.e a decomposition of the net-force-vector.

This is a correct statement as there are a myriad of variables.

Quote:
> But vector analysis ---snip--- use some help...

You can get pretty close to it using vector analysis as there will be a
point in the polar VMG diagram where the available driving force due to
the velocity squared (apparant wind) function is balanced by the course
dependent forward component of the lift vector. However, you will have
to know or make some assumptions regarding lift/drag coefficients,
sheeting angles, wind speeds, drag from the board and fin, degree of
side 'slip, degree of 'perfectness' of air as a fluid, water surface,
etc.

AND, the biggest variable will be the response of the board as a
function of driving force, as the faster you go the more the apparant
wind moves forward.

This is all a good rainy day exercise and perhaps an interesting
Master's Thesis, but a lot more fun on the water. Just get on a solid
close reach and start bearing off. It will become obvious within a few
seconds for your particular set of variables and best of all, porter
beer belliedness is automatically included...

I believe Sailquik has done this with his GPS (for his set of
variables.) Roger?

- Bill Hansen
Sail Design/R&D
Windwing