Swept Volume Theory

You make a number of interesting statements here, but I'm not sure what your point is. Could I invite you to elaborate please? Why, for example is it trivial to identify a frame of reference as being that of the undisturbed air?

 

OK, that is not a reasonable interpretation of my explanation of the source of the low pressure to leeward of the sail (or the top of the wing).

I don't say that. If it did instantly fill with air from nearby, I agree, there would be no pressure region at all. My theory depends on the fact that the air does not instantly fill in.

It is the speed of sound, as is explained in the paper in the section "The Volume Challenge" .
I would welcome any discussion on this section.

 

Okay, so the air cannot fill in the "gap" instantly: it only moves at the speed of sound. How do you derive the speed of sound without recourse to classical fluid mechanics?

Apologies if this has already been answered, I have not read all 20 pages between my comment and your reply above.

 

This is the most insightful question that has been posed in the 18 months of the thread in which my responses to the objections and questions from the forum have often been clumsy, ineffective and sometimes inappropriate, for which I kick myself daily. You have not missed much by skipping the 20 pages.

In a new year's resolution, and in an attempt to see where I lost the plot, I scoured the 20 pages and 300-odd posts and realised your post contained a recognition of the core of my theory, but I had not followed it up.

In my defence, at the time of your post I was aware that further development of the theory required a deeper understanding of thermodynamics, but it was a subject where I previously struggled. I have since studied hard and can claim more than a passing familiarity with the subject.

The speed of sound derives in its entirety from Molecular Theory and classical thermodynamics , and deriving it is quite complex, but can be found in standard physics textbooks.

It is the most amazing relationship. Its simplicity is stunning:


Where

c is the speed of sound in the medium
γ is the ratio of specific heats, specifically the specific heat at constant pressure (cp) to the specific heat at constant volume (cv) for a gas.
R is the universal gas constant 8.31 Joules/mol/°K
T is the temperature of the gas in °K
M is the molecular weight of the gas in kg/mol​

So for air at NTP

T = 15°C , 288.1°K
γ = 1.4 - the standard value for a diatomic gas
M = 0.029 kg/mol
​

So, in response to your question, I hope I have demonstrated that the derivation of the speed of sound owes nothing to fluid mechanics.
I am encouraged that you are comfortable with the concept of the low pressure being generated by the speed of sound limit to the rate at which the gap can be filled.
The principle also applies to the high pressure on the windward side, by limiting the rate at which the squeezing of the air can be relieved.

 

There is quite a strange physics mix here. One basis of the kinetic theory that underlies the calculation of the speed of sound is the "rapid motion" condition (hypothetis) : "Gases expand spontaneously to fill any container".

 

[EDIT] Take another look at the equation. There's no "rapid motion" involved in the calculation of the speed of sound: just γ, R, T and M.

Yes, that's right. Spontaneously means occurring without any external cause. A gas will expand to fill a container without any external cause.
I'm not sure where you're going with this.

 

If a gas fill space spontaneously, shouldn't the rate at which the gap can be filled be infinite ( if we agree on the definition of a rate = volume/time) ? I agree that the word spontaneously has some ambiguities, but the velocity here do not have any macroscopic meaning. No air gap are filled nor emptied at the speed of sound.

 

Nothing in nature occurs at an infinite speed.
If I may quote my physics textbook[1]:" It is impossible for conditions in one part of a medium to influence those in another part of the medium sooner than the arrival of sound wave, so far as pressure, density or temperature are concerned".

Can we stay with my response to @tlouth7’s claim that the speed of sound is derived from fluid mechanics please?

1. Starling S. G. and Woodall A. J. (1950), Physics, Longmans. p. 805

 

Pressure, density and temperature are macroscopic quantities. The speed of sound is derived from the energy conservation equation. And it differs, in general, with the rate at which macroscopic changes occur.

I understand that you have to fill the voids in your theory, but as it relies on mechanics, it will be better, in my opinion, to leave it like this. One of your conclusion is that the lift depends on the geometry and the pressure differential. This is intuitive. And it works for air and water. So why bother with the gaz equations ?

 

To explain the differences between the behaviour of water and the behaviour of air.
Is that really your objection to my theory, or are you just probing my rhetorical competence?

 

Nope, please consider it more like a way to introduce the Dynamic Pressure p = .5 * rho * sqr(u)
This expression has the same form as the one used in gas kinetics, because it is also established from the main Physics principle.
This speed is applicable to moving fluids (or moving bodies through fluid at rest), derived from the principle of conservation of energy, and the Newton's principle.
Here is the speed you need to use, not the "average molecular speed". The general expression of a force is then fully explained :
F = dynamique pressure * Surface * Coefficient.
This Coefficient, by itself, take into account a pressure differential, in relation with the geometry. In essence, this seems to be exactly what you need for your "swept volume theory", if, of course, you are willing to consider the notion of fluid as a continuous medium. With some properties that vary depending on the state of matter.

Edit : please note that this coefficient cannot be fully expressed using the formal expression of the pressure differential, due to the viscous effects, also depending on the shape of the fluid boundaries. The pressure differential is in interaction with the viscous effects, everywhere at the fluid boundaries, in any direction (ie parallel to the flow, but also perpendicular to the flow)

 

Have I answered your objection at #322 about filling the void at infinite rate?
Have I answered your objection at #324 about why I am using the gas equations?
Are you now adding an objection to my theory because it doesn't use dynamic pressure?

 

In short : you cannot use gas kinetics. It is wrong. The diffusion of a gaz into a room doest not happen at constant speed, the speed of sound. Yes, you should use the concept of dynamic pressure.

 

I couldn't agree more. I have no ides what gas kinetics is, never heard of it, and certainly have never suggested it as part of my thesis.

I don't think I ever mentioned diffusion of gaz in a room either.
What I have said is that the low pressure generated to leeward of the sail and the high pressure generated to windward, propagates at the speed of sound. Not the air, but the pressure in the air.

But on a far more serious note, could I ask you to be a little more specific please?
Could I ask you to indicate just where in my thesis I should introduce the concept of dynamic pressure?

 

Could I return to an earlier comment of yours on the Circulation thread

which I replied to on this thread with the following questions:

The choice of the undisturbed air as the frame of reference is fundamental to my explanation, indeed it is the very foundation upon which the hypothesis is built:



You must agree therefore that your statement: " You don't have any referential at rest, only the trivial one, at zero speed." , presents a significant objection to the entire hypothesis, and one which I am obliged to explore.
Could I ask you again to elaborate on your objection please?
I acknowledge that English is not your first language, and that something may have been lost in translation so could I ask you to review your comment: "You don't have any referential at rest,"? I have been poring over it for a long while but am still unsure of its meaning.

[EDIT]
Would your objection be answered if I added the following text to the identification of the Frame of Reference?:
"The centre of a single helium balloon, weighted precisely to have it neutrally buoyant at, say 3 metres altitude, is released at a distance of, say 200 metres upwind of the yacht would serve as the origin of this frame of reference, with its orthogonal axes oriented due North, due East and gravitationally vertical."
[/EDIT]
And could I ask you to explain why my choice of the undisturbed air is " the trivial one"?
[/EDIT2]
The default FoR is the boat, with the wind blowing at the apparent wind speed(AWS) and angle (AWA) and the water flowing at the boat speed (Log) at the leeway angle (Leeway) from the centreline.
In the FoR of the water, the boat is moving at boat speed (Log) at the leeway angle from the centreline (Course), and the wind is blowing at the true wind speed (TWS) and direction (TWD).
In the wind FoR used in the the thesis, the boat is moving at the apparent wind speed (AWS) and direction (AWD), and the water is moving at the true wind speed (TWS) and direction (TWD).
Of course if there is a tidal flow or current then there is a fourth FoR which is the ground, but since the "system" under consideration consists of the boat, the water and the air, we can simplify the problem by setting the tide/current to zero without loss of clarity.

I really do not understand why you suggest the choice of the undisturbed air as the FoR is "trivial".
[/EDIT2]