Was Marchaj having us on?

In the case of a sailing yacht in steady motion, the thrust is balanced by the drag of the hull, the leeway is balanced by the lift of the keel and the heel (moment) is balanced by the bulb at the end of the keel. It's a bit more complex than that with rudder, superstructure and mast drag etc, but it covers the big picture.
No acceleration here (apart from gravity). The system is in equilibrium.
A force does not need to generate an acceleration.

 

Can you explain a change in direction of a fluid flow without acceleration?

 

Hi John,

With a wing you also have an input of energy from a propeller or gravity with a glider, while for a sail you're tapping energy from the relative movement of the air to a surface (water/ice/ground). Without that, the wing would slow down and be at rest relative to the air. It's only because we have energy maintaining the speed that we have a steady state flow, but it's actively tapping that energy that's being put in: it needs that input to keep pushing the pressure up under the wing and to keep opening up a void over the back of the wing. You also see the beginning of the causation involved in this more easily if you start with the wing at rest in the air and then accelerate it to get the flow started, and the pattern of flow changes for a while before it locks into an steady state.

Your description is fine. If we still have a disagreement, it would be about the order of causation, but you didn't include that there.

Well, that's the bit where the story often has the molecules in the streamlines say to each other, "Obstacle ahead, guys - looks like we're going to go over the top of a wing, so we need to speed up and reduce pressure." Your wording is better than that as you do say that the presence of the aerofoil changes the form of the streamlines, but I think the description needs to be more specific than that: it is actively hitting air to a higher pressure underneath and generating a void overhead that is the creation of a low pressure. Surely that needs to be spelt out as the cause of everything that is then driven by those pressure differences?

Well, that's the danger of thinking through high level concepts which incorrectly describe the path of causation. The causation under the wing is from the wing driving the pressure up and the velocity down (relative to the wing) by batting it while both of those consequences happen simultaneously. The causation over the top is from it generating a void directly to create low pressure without changing the velocity because there's no air there to have a velocity until it moves in there to take up the space, so the vacuum can have low (zero) pressure without the air content having a speed (due to it not being there). What then happens as a consequence is that molecules find their way into that space and bring a velocity with them.

I think you'd need detailed directional-pressure information in order for the data to be complete. To give you an example of what I mean, if you blow between two parallel sheets they get sucked together by the lower pressure that you generate between them, and yet there's higher pressure air beyond the plates which can't push back into that low pressure area because the low pressure air behaves as if it has a higher pressure than the higher pressure air ahead of it due to its speed of movement in that direction. If the only data you have is the simplistic pressure information at each location, there's probably insufficient information there to generate the velocity field. As it stands, I think it's a one way process from the velocity field to the pressure field with some information thrown away.

 

Why would I want to do that? The system we’re interested in is the yacht in equilibrium and the forces and moments acting on the yacht.
Elements in the environment outside our system, the wind and the water, are clearly not in equilibrium. They are not stationary or in steady motion.
However any acceleration that occurs in the air only contributes to the pressure that the air exerts on the sail.

 

Wow, that is a hodgepodge of claims.

 

1. The system under consideration is the yacht and the forces and moments acting on the yacht.
2. The system is in equilibrium: it is in steady motion: there is no net force on the system to cause it to accelerate. All the forces acting on the system are equally and oppositely opposed, all the moments are balanced.
3. There are elements in the environment that are not in equilibrium. But as they are outside the system, they are not under consideration.
   
4. Any acceleration that occurs in the air (outside the system) only contributes to forces on the system, namely from the pressure (both dynamic and static) that the air exerts over the area of the sail.

That seems pretty straightforward. What's the problem with that?

 

So this is an open system with exterior forces acting on it.

You claim it is in dynamic equilibrium

If you don't care where the forces come from, what is the point of this thread?

You are having a hard time understanding what pressure is. I think that is at the core of your lack of understanding of everything else. Pressure is a unit of force per surface area. It is not restricted to gasses. A rock on top of your foot is applying pressure. If it lays flat, the pressure is less than if it sits on its point. The force applied is the same.

 

It's a system with forces acting on it. I don't know why you choose to embellish it with adjectives.

It is in equilibrium. Again, you are embellishing with adjectives.

The force on the sail comes from the pressure of the air.

Correct, the force of the rock, that is its mass x the acceleration of gravity, can be resolved either as a pressure over the area of your foot, or, as a point force at the centre of effort.
You can't do that with a gas. The force a gas exerts, either static or dynamic, is entirely dependent upon the area of the surface over which it is acting.
The 600 Pa in the big bladder I described earlier, when spread over the 16 square metres of the Cessna's wing provides a force of 10,000 Newtons, which is sufficient to support the 1,ooo Kg plane.
If the bladder was smaller, say just big enough to cover the fuselage, say 5 square metres, and still inflated to 600 pa, it would only produce 1,200 Newtons, which would only lift 150 Kg, not the 1,000 Kg plane.
A solid can exert a force by pressure, and the size of the pressure depends on the area over which the force is applied. The bigger the area, the lower the pressure, but the force is the same.
A gas can only exert a force through pressure over an area. With a given pressure, the size of the force depends on the area.
With a gas, the bigger the area, the bigger the force.
With a solid, the size of the area does not affect the size of the force.

 

You got it backwards. A force is not exerted or applied by pressure. Pressure is a normalized unit of measurement.

 

I should have accepted the private advice that there is no point discoursing with you. Logic will not sway you.
Let others judge.
I'm tapping out.

 

Unless you understand units of measurement, you won't be able to understand more complex things.

 

I know this thread is old, but it continues to fascinate me.
Does anyone have access to the source of the figure that is presented on p. 212 as Fig 2.15 B Included in my attached image)?
It is referenced as "ARC Reports and Memoranda, Aeronautical Research Council, England-N01353, 1931" by "the late T Tanner", but I am unable to source the report in order to access the Theory referred to in the text.
I have digitised the graph and have deduced that Marchaj's Fig 2.16 A does not represent the data in Fig 2.15 B.


which is a pity as it is the image that Fossati used, unacknowledged, on p. 316 of his Appendix A :

 

(Ref 2.11)

- The text is quite clear: in one case it is a RAF 30 airfoil with an Angle of Attack of 7 degrees, and in the other case it is a pedagogical example of an airfoil with an Angle of Attack of 15 degrees.



(CA Marchaj)

 

CA Marchaj made a striking and patient pedagogical effort, if you don't like his effort, then argue with the original sources starting for example with Mr. Kutta and Mr. Joukowski

Kutta–Joukowski theorem - Wikipedia https://en.m.wikipedia.org/wiki/Kutta%E2%80%93Joukowski_theorem

and then you can continue with Ludwig Prandtl and Max Michael Munk and finish your intellectual journey with Alan Pope

 

The drawing that worries you is on page 104 of Alan Pope's book, fig 6.4, which comes from his previous book on Wind Tunnel