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Bernouli works b/c of pressure differential produced by longer/shorter flow paths created by varying angles of attack.


Will, Bernoulli has nothing to do with the longer/shorter flow path. The length of the flow path over the leeward side of a fabric sail is the same as the windward. Bernoulli is simply an expression of the conservation of energy along a single, particular flowpath. It works for determining the conversion of potential energy (pressure) to and from kinetic energy (velocity) for a particular packet of air as it approaches, passes over and leaves the wing surface. The simplified form applicable for us is,

P1 + 1/2 ro V1^2 = P2 + 1/2 ro V2^2

P - pressure
ro - density
V - velocity

The two conditions, 1 and 2, are for one packet of air moved from one location to another at two points in time, not two packets of air in two different locations at the same time. Section 3.4 in See How It Flies goes over the Bernoulli Equation. In that section, he does mention comparing two different packets of air. However, it's dangerous to get into that without first accepting as true the single packet/two locations principle and how flowpath length differentials don't apply. The way it works is,

P1 + 1/2 ro V1^2 = P2 + 1/2 ro V2^2
and
P3 + 1/2 ro V3^2 = P4 + 1/2 ro V4^2

where 1 and 2 are on one flowpath and 3 and 4 another. Above, below the wing, doesn't matter. But, let's assume that states 1 and 3 are in undisturbed fluid well in front of the wing and therefore, equal. That makes the total energy states at 2 and 4 equal. What this means is that you can take a pressure probe and poke around anywhere in the flowfield and knowing the flow state at 1-3, you can calculate the velocity. Or, conversely, if you measure the velocity, you can get the pressure. But you do not get lift from this and as you can see, flowpath length doesn't enter into the measurements or calculations anywhere.

I apologize to all the people looking at algebra before having a cup of coffee.

Last edited by steveh; 08/25/05 12:58 AM.