# Was Marchaj having us on?

Discussion in 'Hydrodynamics and Aerodynamics' started by Sailor Al, Apr 12, 2021.

?

## Did Marchaj know he was wrong when he claimed, on P199 in my post #63, that "A arrives ...before B".

100.0%

0 vote(s)
0.0%

0 vote(s)
0.0%
4. ### He confused A with B. (The pic shows B arriving at the TE before A!)

0 vote(s)
0.0%
1. Joined: May 2008
Posts: 2,458
Likes: 267, Points: 83, Legacy Rep: 1082
Location: Beaufort, SC and H'ville, NC

### philSweetSenior Member

Ah, but we do. All we need to do is find the function that causes the oncoming air to travel around the foil without passing through the foil, because it can't do that. And that is sufficient to define the entire field in a potential flow domain. It's purely a function of the foil geometry, the fluid velocity, and any other passive objects like the walls of a wind tunnel. What we end up with is the original fluid velocity and a whole bunch of little perturbation velocity fields that when all added together satisfy the boundary conditions on the problem. You end up with a system of equations that might have 200 equations and 200 unknowns, and you set up a matrix and solve it. So your function ends up being very long, but also very simple to evaluate because we chose the perturbation fields to be stupid simple that way.

More starting vortex evolution from a 2015 paper
Causal mechanisms in airfoil-circulation formation
by Zhu, Liu, Liu, Zou, and Wu. (Paywalled)

2. Joined: Feb 2021
Posts: 124
Likes: 9, Points: 18
Location: Sydney

### Sailor AlSenior Member

As I said, that's another story, and I'd love to explore it in a separate thread. Can you post a non-paywalled link to that paper please and let's start another thread. FWIW, my view is that the all those functions rely on the airflow moving faster over the upper surface than the lower surface. The unexplained part is what causes that difference.

My point is that what Marchaj was referring to as "circulation" had little to do with the vector calculus version of circulation.

Last edited: Apr 23, 2021
3. Joined: Oct 2009
Posts: 4,984
Likes: 481, Points: 83, Legacy Rep: 1485
Location: Midcoast Maine

### DCockeySenior Member

Further study on the part of Sailor Al is in order.

4. Joined: Feb 2021
Posts: 124
Likes: 9, Points: 18
Location: Sydney

### Sailor AlSenior Member

Did you not comprehend the contradictions I pointed out in post #89?

5. Joined: May 2008
Posts: 2,458
Likes: 267, Points: 83, Legacy Rep: 1082
Location: Beaufort, SC and H'ville, NC

### philSweetSenior Member

True enough. The terminology confusion didn't start with him and there is no end to it in sight a century later.

If you are still trying to figure out what is going on as far as the spinning cylinder dragging air around with it and somehow generating lift, and how that relates to an airfoil not spinning and not dragging air around with it and somehow generating lift, you have a valid question and Marchaj can't help here.

The answer is that a spinning cylinder creates an entrained volume of air around it that stays with the cylinder. The un-entrained flow has to go around both the cylinder and the entrained volume of air. The kinematic balance between the un-entrained air and the entrained air creates an unsymmetrical boundary shaped like a really fat airfoil. And it's that boundary shape that induces the farfield circulation that produces lift in the lifting line model.

The rotating cylinder is just powering a pneumatic pump that inflates the entrained air to a lifting shape. The entrained air being dragged around the cylinder is inside the boundary and it doesn't count. By which I mean that the entrained air's circulation doesn't count towards lift, only the un-entrained air's circulation counts towards lift. Marchaj probably didn't know that.

Neither do some people at NASA, apparently - Lift of a Rotating Cylinder https://www.grc.nasa.gov/WWW/K-12/airplane/cyl.html. This has been a misunderstanding that has persisted for about a century now.

Last edited: Apr 23, 2021
6. Joined: Feb 2021
Posts: 124
Likes: 9, Points: 18
Location: Sydney

### Sailor AlSenior Member

Again, no. I'm focussing on Marchaj's book which, among its many oddities, does a disconnected segue from the rotating cylinder to lift on a wing (P 198 quoted in initial post), and trying to get a consensus from the forum on whether he knew it was crazy and was intentionally having us on, or not (see the choices in the poll).
Along the way, it would be interesting if we could get a consensus on the actual cause of the aerofoil force that generates the thrust on a sailboat, but that would just be a bonus!

7. Joined: Aug 2017
Posts: 549
Likes: 230, Points: 43
Location: Littleton, nh

### Will GilmoreSenior Member

I'm on your side because I like the way you think. However, I don't think Marchaj was having us on, even if he was wrong.

I am not an aeronautical engineer and I haven't read any more than this thread about Marchaj, but it doesn't seem as though he was anything but a serious and well educated scientist at the time of his writing.

My post was to point out that, while 'Through the Looking Glass' was a whimsical story for children, it had some true wisdom to impart and Marchaj seemed to enjoy using it to illustrate his meaning. I thought his references were very appropriate to help the uninitiated to open their minds to see the mysterious and unseeable forces at work.

8. Joined: Mar 2002
Posts: 1,447
Likes: 243, Points: 63, Legacy Rep: 158

### BarrySenior Member

Through all of the posts, it appears that there has not been a mention regarding the simplest explanation and that is that the upwind side of the sail takes a mass of air and changes the direction of outflow.
F =ma, pretty much a proven equation, (and we can use m dot, or mass flow rate, )
Velocity has two components to be called velocity, the first being speed and the second being direction.
So if you are driving at 60 mph, you do not (if you want to be accurate ) refer to it as velocity, but rather the speed component. If you are driving at 60 mph North, then you have defined a velocity

So if you change the direction of a moving object (or the mass of the wind in this case) then you have accelerated it (though the speed will/can be the same) (certainly some other influences as the wind inlet is not a nozzle) and the result is a force on the sail. The specific direction can be determined with some accuracy though it is not always at 90 degrees to the chord depending on the shape of the vane. I am taking chord the line between the stagnation point and the trailing edge

The upside force on the sail is for arguments sake and on the absolute scale, ie atmospheric 14.7 psia, STP, you have the 14.7 psia plus the force generated from the change in direction of the air mass,

On the back side of the sail, depending on shape, you will have an area of say 13 psia, slightly less than the upside 14.7 psia, and not sure what that might be due but obviously somewhat less than the 14.7 acting on the outside of the sail as evidenced by the sail producing a concave shape. While one might call this drag in many other instances, this drag is in the direction of the down wind force generated by the change in Velocity on the upward side so this lower than atmospheric pressure increases the thrust of the sail

So two processes are producing the force on the mast.

After reading through the posts, it appears that Sailer Al is suggesting that his targeted author is saying that circulation means that air is moving forward and around an axis somewhere. But the wind tunnel smoke
streamlines do not show any evidence of this.

There are a couple of thoughts also floating around that the air molecule has velocity when impacting the leading edge of the wing. Certainly in wind tunnels this is the case and is a good method of evaluating forces/flow on wings. But the air molecules for the most part move up and down, they do not have a say a 600mph speed when referenced to earth. Is this relevant? I would say that it is and perhaps this is the reason that the Bernoulli equation has been beat to death about its participation in lift. But if the molecules basically move up and down (some movement say left to right due to the stagnation point compression) as compared to having an initial velocity of 600 mph and hitting an airfoil.

A contributor showed a smoke line that almost disappeared close to the stagnation point. This would be expected as at high speeds the stagnation point sees high pressure and as air is compressible, the smoke thread will obviously become more compressed and hence less visually apparent. Generally, ( only because I can not think of a case but want to cover my ---) when you have somehow created a high pressure area, in the case
the stagnation point, in a compressible fluid, the pressure will try to reduce by way of fluid movement to a lower pressure area. In order to do this there will be a higher velocity between the stagnation point
and say a foot or two over the top and bottom of the wing as it attempts to equalize itself with the adjacent air

Sailor Al in a different thread attacked the term lift with respect to a sail. Some authors have used lift to relate to a sail boats force. While it is to each his own, I would just use force, resolve it if necessary and leave lift to be related to the VERTICAL force that an airplane wing for simplicity. A Boeing 777 300 ER weighs in at about 760,000 pounds. Take off angle is 12 1/2 degrees, The engines will provide 210,000 pounds of thrust.
At 12 1/2 degrees of angle the vertical component of the engine provides 210,000 x Sine 12.5 or about 45,000 pounds. (and this is probably quite a bit off as at take off the airplane is accelerating and drag is increasing) So the 760,000 pounds less the 45,000 leaves us with the wing producing 715,000 pounds of lift,***** not perpendicular to the cord but 715k pounds directed vertically.
(****** of course I had omitted the lift generated by the hull of the air plane due to the angle of attack, so the total combined life of the wings and fuselage is 715,000 )

Back in the day, we had to work through various turbine blade calculations with alternating stators to develop thrust values with compressible and incompressible fluids. There never was mention of lift in the calculations.
Inlet and outlet velocities to determine the force on the high pressure side of the vane, low pressure on the back side and you could get a pretty good idea within a magnitude of accuracy. . And of course stator calculations. The shape of these vanes were close to the profile of a sail as compared to a wing air foil

I would suspect that the resultant forward thrust is due to the opposing pressure on the keel from the water that drives the boat ahead. Without water, the sail boat would just move downwind. A couple of contributors
introduced this.

Last edited: Apr 24, 2021
9. Joined: Feb 2021
Posts: 124
Likes: 9, Points: 18
Location: Sydney

### Sailor AlSenior Member

That's because the thread is about Marchaj, and he didn't use that theory.

Yup: that's pretty much what Marchaj was saying, and it's poppycock! The question is whether he knew it or not.

But, we're a sailing forum, not an aeronautical one. Lift relates to the beneficial resolution of the aerofoil force that opposes the weight of the plane! Nothing to do with sailing boats!

Classic error #1:
The resolution of the hydrofoil force from the keel in the lateral direction opposes the leeway/heel component of the aerofoil force.
The resolution of the hydrofoil force from the keel in the direction of travel is a resistance which adds to the hull and rig resistance.
The keel just stops it going any more sideways than the leeway angle (which it has to have for the keel to generate hydrofoil force).
The keel does not contribute to the thrust of the boat.
But that's also a whole other story!

Last edited: Apr 24, 2021
10. Joined: Feb 2021
Posts: 124
Likes: 9, Points: 18
Location: Sydney

### Sailor AlSenior Member

Thanks for that, it's been hard work, but fun.
And yes, I'm also coming to the opinion that he wasn't a comedian after all, just plain wrong.

No, nor am I, although this exercise has prompted me to delve a little into the arcane world of vector calculus and fluid dynamics.
I first accessed the book on-line because he was quite widely quoted as an authority and I didn't have the \$100 to buy it from Amazon, and then a sailing mate lent me his copy. You should check it out, it's a fascinating read, lots of crazy ideas, but a few good ones as well.

But the Queen referred to "impossible things" not mysterious and unseeable things!

11. Joined: Mar 2002
Posts: 1,447
Likes: 243, Points: 63, Legacy Rep: 158

### BarrySenior Member

Without the keel the boat would not move forward

Will Gilmore likes this.
12. Joined: Feb 2021
Posts: 124
Likes: 9, Points: 18
Location: Sydney

### Sailor AlSenior Member

Yes, I know, and that is the common intuitive objection because it seems an obvious conclusion.
I wish I had the intuitive, simple analogy that covers it, but I don't.
Maybe someone can come up with one.
But really, the first two lines of the response:
"The resolution of the hydrofoil force from the keel in the lateral direction opposes the leeway/heel component of the aerofoil force.
The resolution of the hydrofoil force from the keel in the direction of travel is a resistance which adds to the hull and rig resistance."​
completely account for the the hydrofoil force from the keel. Neither of them contribute to the thrust. You can't agree with the first two lines without accepting the conclusion.

[EDIT]
"The keel (and rudder) allow the boat to be steered at the upwind angle to the wind which allows the thrust from the sails drive the boat forward against the underwater resistance of the hull, keel and rudder, and the above water resistance of the hull and rigging."?

Last edited: Apr 24, 2021
13. Joined: May 2008
Posts: 2,458
Likes: 267, Points: 83, Legacy Rep: 1082
Location: Beaufort, SC and H'ville, NC

### philSweetSenior Member

Those aren't mistakes, they are choices. It's perfectly possible to build highly accurate and useful models using them if you do so in a consistent manner within the model. You are also free to do that differently if you wish.

In the end, there is one total force and one total moment on the boat that determine its linear and rotational acceleration (see Kirchhoff's equations for fluid-body interactions). We may conveniently decompose it into Hydro and Aero components. We can further decompose those into orthogonal components aligned with some reference frame. There are maybe eight useful reference frames depending on what you are doing. Often, a frame is chosen to simplify the math associated with one of those components. Thinking there will always be a simple physical explanation for the other components is the fallacy.

We often start by concentrating on simplifying the lift calculation. If that is what you are doing, don't worry about what the other components are. We have names for them and, as it turns out, formulas for some of them, but it's your job to stay focused on what you are trying to do and not end up in the weeds.

14. Joined: Aug 2017
Posts: 549
Likes: 230, Points: 43
Location: Littleton, nh

### Will GilmoreSenior Member

We are looking at two wedged coming together at an angle, almost like scissors, the boat, caught in the middle, being driven foreword. One wedge is driving against the other, from one frame of reference, but from the boat's frame of reference, both wedges are driving the boat.

15. Joined: Sep 2018
Posts: 169
Likes: 53, Points: 38
Location: MO

### HowlandwoodworksMember

Sailor AI,
Here is something that help me.
There is no "lift"...there is only "drag" in the direction you want to go. (jehardiman)