35737RE: [SabreSailboat] Re: Cowl Vents - 4" with a little extra work?
- Jan 5, 2012
OK, let’s try a thought experiment. First, choose as big a dorade cowl as you like. To simplify matters, instead of the baffle assume the dorade just funnels down into the cabin. Now, put a plate across the opening into the cabin, sealing it. What you now have is a giant pitot tube. The pressure at the dorade side of the plate is the stagnation pressure for the opening of the cowl. Assuming uniform flow outside the boat, it doesn’t matter what size the cowl is the pressure is still the stagnation pressure. The pressure on the other side of the plate is the static pressure in the cabin. Now drill a small hole in the plate (and be sure the companionway is open so the cabin remains at static pressureJ). The flow is going to be controlled by the hole size and can be calculated as flow thru a hole with the stagnation pressure on one side and static pressure on the other. As you enlarge the hole more air flows, and the static pressure on the upstream side of the plate drops, but continuity says the static plus dynamic pressure are constant. If we look at the cowl inlet when we put a small hole in the plate, most of the cowl frontal area is still nearly stagnant air. That is why you can’t assume that greater cowl area equals greater flow. The cowl is positioned like a probe in a free air flow. With a restriction further downsteam inside the cowl some of the free air flow impinging on the cowl flows outside of it so the flow into the cowl entrance is not the free air velocity times the cowl cross sectional area. The limiting case is where the opening is closed and all air impinging on the cowl flows around it.
I hope this helps. No Cessnas were crashed in the preparation of this e-mail.
From: Sabresailboat@yahoogroups.com [mailto: Sabresailboat@yahoogroups.com ] On Behalf Of Jim Starkey
Sent: Wednesday, January 04, 2012 3:29 PM
Subject: Re: [SabreSailboat] Re: Cowl Vents - 4" with a little extra work?
OK, let's work this through. The venturi that sucks air through the gyros on your rustic Cessna 170 has one funnel facing into the airstream connected to another smaller funnel facing downstream, and a hole in the middle connected by cracked Tygon to a dying directional gyro. The constriction of the forward facing funnel increases the air pressure in turn accelerating the air through the constriction. The pressure measured in the constriction relative to cabin pressure (assuming neither your instructor or your passenger is yelling at you) is lower, drawing air (not vacuum, ladies and gentlemen) through the gyro cause the rotor to spin sufficiently to keep the dirty side down, even in the clouds.
I submit that a) a Sabre isn't a Cessna 170, b) the cowl / dorade / interior vent is not a venturi, and c) Mr. Bernoulli has as little to do with it as he has to do with keeping your Cessna 170 in the air (which, technically, is held up by the declining balance in your checking account). I further submit that the pressure inside the dorade is higher than cabin pressure, for if it were not, air would flow from the cabin to the dorade causing it to explode or morph into a black hole.
Perhaps we might agree on a simpler analysis, if not arithmetic. Air comes in the cowl, through the dorade box, through the internal vent, and into the cabin. I hope this is self-evident. The amount of air passing through this system is a function of a) the frontal section of the cowl, b) the speed of the air relative to the cowl, c) the obstruction of the interior of the dorade box, and d) the size of the interior vent. Increase the frontal section of the cowl, the speed of the cowl relative to the outside air, lower the air resistance of the dorade box, or increase the size of the interior vent and you get more air passing through the cabin, the ultimate goal of this exercise.
Of these options, the only feasible on is increasing the frontal section of the cowl. I have no doubt that Roy Lopresti could design a more efficient cowl/dorade/vent system, though doing it postmortem would be a trick. That said, his famously efficient cowls were round, which is where we started.
I graciously concede the 7.07 square inches. You are of course correct.
(Note: no comparisons between sail and wings were tortured by this post.)
Founder and CTO
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