Was Marchaj having us on?

Two is plural. This discussion started with you stating there was only one. Also, you adding that pressure exerts force on a body. This is a misunderstanding of what pressure is. Pressure, as I have told you several times, is a unit of force per surface area. The pressure is not exerting anything, the gas is.

 

Yes, I know.
Air, a gas, is exerting pressure on the sail. This pressure over the surface of a sail, results in a force.
There's nothing else, apart from a bit of shear stress, that contributes to (or detracts from) the generation of the thrust and leeway/heel force from the wind over the sail.

 

Once we accept that, we can exclude all the complexities of aerodynamics * and recognise the significance of understanding the source of this pressure and then, maybe, we can start to get a handle on why the changes sail trimmers make to the sail shape results in changes to the performance of the yacht .

*like lift, drag, viscosity, boundary layers, circulation, momentum change, starting vortices, vortex sheets, Kutter-Joukowski, Navier Stokes, Bernoulli, Euler equations, flow fields, pressure fields etc.

 

David - The changes in pressure and the changes in velocity are two related effects that happen together. We are considering steady state flow, so nothing is changing with time at any one particular location, but if we were to have a pressure and velocity sensing device that traces the path of a streamline we would see that as pressure increases the magnitude of the velocity simultaneously reduces and vice versa. You could say that a pressure change causes a velocity change, or you could say that a velocity change causes a pressure change, it does not matter, these are just two interelated changes that happen together. Its a bit like a see-saw. I could say that if the left hand side of the see-saw goes down that causes the right hand side to go up, which would be correct. But it would also be correct to say that if the right hand side goes up that causes the left hand side to go down. And it certainly isn't the case that pressure differences occur first to drive changes in velocity! That rather sounds as though you think that if you start to apply force to some mass then after a delay, maybe a second or two, the velocity of that mass starts to change, but surely you don't think that, I hope not anyway!

Placing an aerofoil into an originally uniform flow changes the pattern of the streamlines because the streamlines now have to pass round the aerofoil, they cannot go through it. So in the vicinity of the aerofoil the originally uniform velocity field is changed to some different velocity field. Vector fields can be added together by doing a vector addition at the corresponding locations in each field. So instead of saying 'the uniform velocity field is changed to some different velocity field' we can say 'some additional vector field has been added to the uniform velocity field'. That might sound like a more complicated way to say the same thing, but it does lead to a method for predicting the whole velocity field and hence the pressure field and hence the lift on the aerofoil which is a useful thing to know for designing aeroplanes and things. Without going into the maths, it can be shown that if you add the vector field of a free vortex to the vector field of a uniform flow you get the vector field for flow round a rotating cylinder - i.e. the vector field for a Flettner rotor. If you add in a third free vortex vector field you may well get the vector field for flow round some non-cylindrical object. Continue this by adding in a very large number of free vortex vector fields and choose just the right strength and centre location for each of the added fields and you can model the flow round an aerofoil of the cross section shape that you are interested in. A uniform velocity field and a free vortex velocity field are both velocity fields for incompressible and irrotational flow, so the combined field will also represent incompressible and irrotational flow, which is what we want if we are considering sailing boats. Mach numbers for sailing boats are not high enough for compressiblity to matter (at least not yet!) and the assumption that the flow is irrotational outside boundary layers has also been found to be generally acceptable. The required stength and location of all these added vector fields can be determined mathematically which is the basis of thin aerofoil theory (applicable to thin aerofoils with or without camber) and the vortex panel method (applicable to aerofoils that have thickness, with or without camber). Once the combined vector field has been determined in this way it is relatively straightforward to calculate the pressure field and hence the lift force on the aerofoil and the moment of that lift force.

None of the above is anything new that I have worked out for the purpose of this thread! It was all worked out by some very clever people a hundred or more years ago and it has been correctly explained in various books but I cant easily give you references since as I said, I hardly ever read books these days. These things have also been incorrectly explained in some books, as you have noted! Sailor-Al seems to be inordinately keen to know whether or not any of the books that correctly describe flow over aerofoils are books about sailing, well they might well be but I would not know for sure. I do not recall having read Marchai's book but I did once read some article by Marchai, could have been in a boating magazine. If I remember right he was saying that a crab claw rig is superior to various modern rigs, a crab claw rig being something like a lateen sail but with lower aspect ratio and a very concave leech giving the sail a shape a bit like a claw. I was not convinced by that article, but I had better not start another long thread with that!

 

As I said earlier, I'm not looking to canvas opinions on the source of the pressure differences.
I am trying to determine if there is any sailing publication that explains the source of the pressure difference....

 

That is absolutely wrong. You keep on saying that pressure results on a force. It is the force over an area that results in a pressure. Your lack of understanding of basic principles is the problem. As I told you time and time again, study the fundamentals.

Acceleration, as flow direction is changed, also generates a reaction force. Study the fundamentals. I don't mean read Wikipedia and dumbed down highschool books.

 

Not quite. I am saying a gas can only exert a force on a solid object by pressure (OK, plus a bit of shear stress in the case of relative motion).
A stiletto shoe will generate enough pressure to damage a floor, but the same weight in a flat shoe generates much less pressure and preserves the floor. That is an example of a force (the weight of the person) generating pressure. That's an example of an object transferring a force to another object by pressure.
A big bladder inflated to 600 Pa will lift a Cessna. Here, the air pressure is generating a force of 1,000 Kg weight (~10,000 Newtons) . That is the example of a gas generating a force by pressure.
I'm talking about the pressure, in a gas, being the way that the gas exerts a force on an object.

 

Hi John,

They're two different aspects of the same underlying thing, so they have to be simultaneous, and yet one of them still has a role in causation which the other lacks.

If we have a box with a divider down the middle and we have air filling one half and a vacuum in the other, we can remove the divider and watch what happens. Air will accelerate out of its half of the box to fill the whole box, but the air molecules aren't accelerating: they just keep going at the speed they were already moving at, while the pressure falls because there's less air in a given volume. What is the cause of the action here? There are often multiple causes of events which work together, but a change to one factor can trigger the action. The pressure difference is a driver - it allows air molecules to travel into the void instead of being bounced back, but as soon as they begin to make this extra progress in that direction the velocity of the air as a whole increases, so these two changes are absolutely simultaneous. The initial speed of the air is not a driver of this change though, so even though these two aspects change simultaneously, only one of them is a driver. The triggering cause of the pressure drop and velocity change is the removal of the divide, and then the pressure difference is able to drive the action from there with the velocity change being a consequence. This is what happens over the back part of the top of a wing.

If we start with a bicycle pump maximally extended and then push the plunger in, we accelerate the molecules that are hit by the leading part of the plunger and have an instant change in pressure and in the velocity of the air in the closing space: the pressure's going up while the velocity of the air reduces (relative to the moving plunger). Again there's a pressure difference that comes before the velocity change of the air, but it's disguised because it's pressure applied through the plunger, so it isn't initially a higher pressure in the gas. This is what happens underneath the wing.

With a wing (or sail), what drives the changes in pressure and velocity of the air is the underside of the wing batting some molecules to generate a higher pressure; and the top of the wing directly creating a void for air molecules to move into. Any valid explanation of how a wing or sail works should start with these two primary causes.

The maths fits beautifully, but it wasn't designed to address the issue of causation. Explanations of how need to go beyond maths to pin down the actual chain (or network) of causation. This is something that physicists frequently fail to resolve because they're trained to think in terms of high-level laws and to apply them with all manner of simplifications in their understanding. You can see this with Maxwell's Equations, for example, where they take advantage of the phenomenon of apparent relativity in order to take a simpler form (for example, a distance is always measured as the apparent physical separation distance and not the actual transmission distance through space if the apparatus is moving) and then they are invariably misinterpreted as providing proof that the speed of light is always c relative to every observer. That kind of sloppy thinking is prevalent throughout physics.

 

David
I thought this thread is about steady state irrotational flow of an incompressible fluid over an aerofoil (or hydrofoil maybe). But the examples in your second and third paragraphs are very far from that situation and they are both non steady state and with fluid compressiblity having a very big effect. Also big mechanical energy input with the bicycle pump.

Yes, if we consider what is happening at a molecular level what you say above makes sense. But, keeping to the molecular level, I think there is an alternative and also valid way to look at this. Molecules are impacting the wing surface all over because they are in random motion. These impacts cause changes to the velocity of individual molecules and the frequency and average severity of the impacts is a bit higher on the underside of the wing than on the upper side. (and highest of all at the stagnation point) A bit further away from the wing, molecules that will never reach the wing are hitting those that have already hit the wing so they also get changes in velocity too, but on average those are smaller changes than experienced by the molecules that actually impact the wing. These velocity changes at the molecular level result in changes to the mean flow velocity, so changes to the orientation of the streamlines and the speed of the flow along them. And no streamline can continue from the far field straight through the wing because no single molecule can do that. (well cloth sails might be a bit permeable, but that would be a very sophisticated analysis!) In aerodynamics of sailing boats and suchlike, I think we take the velocity of the air at a point to mean the mean velocity of the molecules in a small region around that point, we are not really interested in the actual velocity of each individual molecule and as you said earlier in this thread the speed of those individual molecules is quite a lot higher than the mean flow velocities that apply to sailing boats. (I think you said it is about 1100m/s?) So all this means that the velocity field in proximity to the aerofoil is different to the 'far field' velocity field and from Bernouli's equation this means that the pressure field is also different. Whereas you prefer to say that the pressure field in proximity to the aerofoil is different to the 'far field' pressure field which means that the velocity field is also different. I think both are correct so no need for us to argue about it!

For me, the idea that the presence of the aerofoil changes the form of the streamlines (because they have to go round it) and hence changes the velocity field and hence changes the pressure field is just a bit more intuitive than the way you choose to look at it. And if we want to use the established and experimentaly verified mathematical procedure (thin aerofoil theory etc.) to calculate lift, that mathematical procedure starts by determining the velocity field, then uses that to determine the pressure field and then the lift (or determines the circulation from the velocity field and the lift from the circulation). So that procedure (sort of) regards the velocity field as the cause and the pressure field as an effect, the opposite to your way of thinking.

I wonder, is there a mathematical procedure that starts with determining the pressure field then derives the velocity field from that?

 

You really need to go and study the basics, starting by units of measurement.
P = F/L^2 This is a normalized unit of measurement.
If you apply pressure to a surface : P*A= (F/L^2) * L^2 = F Therefore, the area cancels out and the applied force is calculated. However, pressure is not the applied force.

 

Why do you need a velocity field?
If you have a pressure field, then applying the pressure over surface area and using the surface normal you have the force vector.
Converting pressure to velocity is just muddying the water.
The fundamental challenge is determining the pressure field.

 

Pressure and velocity are related. You keep on trying to solve a dynamic problem with statics.

 

Whether pressure and velocity are or are not related is irrelevant to the issue.
The thrust and leeway/heel force of the air over the sail has to be due to air pressure (and maybe a bit of shear stress).
There's no other way a gas can exert a force on an object.

 

Accelerating the air also generates a reaction force. Since the airflow changes direction, there is acceleration. However, you keep on misunderstanding the basics. If you refer to thrust, you are implying there is a reaction force due to acceleration. Get you units right.

 

You are right Al, if we knew the pressure field we would not need to work out the velocity field to get the lift vector. But as you say, determining the pressure field is the challenge. If we can somehow manage to find out what the pressure field is then determining the lift vector is not all that difficult, just a matter of integrating the force due to pressure with respect to area over all surfaces of the aerofoil - piece of cake, well a piece of cake compared to the problem of determining what the pressure field is in the first place.

Fortunately some clever people, from about a centuary ago, thought of a way to find out what the pressure field is going to be for any particular 2D aerofoil section at a particular angle of attack (which has to be small enough that the aerofoil is not stalled). However, this method first finds out what the velocity field is (the hard part), then the pressure field follows from that. Or if you only want the lift force and you have got as far as working out the velocity field then you can get the circulation from the velocity field and the lift from that. I think 'thin aerofoil theory' was the first version of this method. I have just done a quick internet search and have learnt that 'thin airfoil theory' was first conceived by Max Munk working at NACA in 1922. Then the theory was refined and extended by the team lead by Hermann Glauert at the Royal Aircraft Establishmet, Farnborough UK.

Of course, these days we have Computational Fluid Dynamics software based on numerical solution of the Navier Stokes Equations that can be used to analyse all sorts of fluid flow situations but studying the earlier methods discussed in this thread arguably provides a better understanding of why fluids flow the way they do.