Ok, how embarrassing. After writing that, I realized that I should have googled Bernoulli for incompressible fluids, instead of rudder design. I found out that the Bernoulli equation is actually for incompressible fluids; there is a special form to handle gases. So, please ignore that question.
It did however lead to another one. One of the explanations of lift is the Kutta effect, which seems to be based on the reverse flow from the trailing edge of an airfoil. The closing statement in the wikipedia article is this:
The Kutta condition gives some insight into why airfoils always have sharp trailing edges, even though this is undesirable from structural and manufacturing viewpoints. An aircraft with a wing with a smoothly rounded trailing edge would generate little or no lift.
So, that leads me to the question of asymmetrical rudders for proas. Both their edges would be somewhat rounded, I assume. Does that mean that these
rudders would generate no lift? Likewise a keel or leeboard designed to work in either direction would generate no lift?
Is that the reason that Rob keeps using standard rudder foils on his design? (Rob, you still here?)
- Gardner
--- In
harryproa@yahoogroups.com.au, Gardner Pomper <gardner@...> wrote:
>
> Hi,
>
> I have been trying to read alot about rudders and foils and lift and such,
> trying to understand what shape an asymmetrical rudder should be, when I
> realized that I am missing something fundamental.
>
> I don't see how a rudder (or a keel) generates lift. I understand how a sail
> does it, but the bernoulli equation only applies to a gas (if I remember my
> college physics; it has been 30+
years). The idea of the flow around the
> outside of a sail reducing the pressure implies that the density of the gas
> decreases. Since water is incompressible, I don't see how that applies, as
> the density remains constant.
>
> It seems to me that keels and rudders act by introducing resistance to the
> leeway producing forces generated by the sails, resulting in an effective
> force vector in the direction of motion by cancelling out leeway forces, not
> by adding lift in the opposite direction.
>
> If this is right, then the shape of the keel/rudder should not be critical
> for lift, but only to prevent seperation of flow from the rudders surface so
> that you don't get turbulence or a gap that can suck air down and reinforce
> the separation.
>
> I am somewhat encouraged in this view by this
> article<
http://www.animations.physics.unsw.edu.au/jw/sailing.html>I
> found from the school of physics in NSW, Australia that mentions lift
> from
> the sail, but does not mention it in relation to the keel.
>
> Am I right about this? If not, can someone point me to a good explanation of
> how a keel/rudder generates lift?
>
> Thanks,
> - Gardner
>