Swept Volume Theory

A 15 second search on the internet found me this -

 

Despite his commentary at 0:43 where says: "Here you can see it speeds up as it approaches the airfoil" But the video doesn't actually show that. If anything, the air slows slightly as it approaches.
Sure, it moves faster than the air over the bottom, (where that air actually decelerates) but it doesn't move faster than the ambient air at the top or bottom of the screen.
He is effectively disproving the equal transit time myth, but has failed to notice that he's also disproving the "accelerating over the top" myth.
(I have had a long and spirited discussion with him about this, he claimed that it's an experimental error!)

 

Dammit! I have been once again inveigled into arguing against Aerodynamics.
My hypothesis does not rest on Aerodynamics.
Please can we return to the subject of the thread.
I am explaining the source of the pressure difference.
You may have your own alternative theory that you may wish to publish. But can you do it on your own thread?

 

I should have replied along the lines:
Yes, but who says they are insignificant?
Is it significant or insignificant that it only takes 0.5% of atmospheric pressure to support a C172?
And a 0.5% variation in temperature (from 300°K) is only 1 1/2 °C
I think "insignificant" changes in temperature and density may well be sufficient to generate the "insignificant" pressure variations around the sail.

 

We are in the hydrodynamics and aerodynamics section of the forum, so I thought we were discussing aerodynamics. My apologies.

OK, so regarding the differential change in pressure, lets look at it from you perspective. Take the equation PV/T = constant, since we are only talking about relative values. It raises some questions:

1) What is causing the pressure change? Is the volume changing, or is the temperature changing, or a bit of both?
2 What are you defining as your volume? I'm unclear about the extent of the working volume. Is there one on both sides of the sail? I assume there must be if we are raising the pressure on one side and lowering it on the other.
3) The working volume would need some kind of boundary I assume. What is creating the boundary?
4) If the volume is changing, How does that occur? Is it an instantaneous change, or does it happen over time? What is the mechanism?
5) If the temperature is changing, and the volume is constant, there would need to be a heat source and a cooling source. Is there is an external source of heating and/or cooling what is providing that? If the heat is being transferred from the low pressure side of the sail to the high pressure side, what is the mechanism for that?
6) If both the volume and temperature are changing, and assuming the pressure is also changing because that is the thing we are trying to prove, what is the relationship between them?

The definition of the extent working volume is important because it determines how much heat energy we need to supply or transfer to get the required temperature change, and hence pressure change. If the volume is the thing that is changing then heat is not required, but we need to understand the mechanism for the volume change..

 

PV=nRT does not have anything to do with flow rates. The equation deals with a closed/contained volume.
Take a 1 cubic foot volume of air, heat it up the pressure goes up.
Without losing any molecules of air, reduce the volume, the pressure and temperature goes up.
This is straight forward. Nothing to do with your sail

 

You are correct, and my hypothesis is neither hydrodynamics nor aerodynamics, but it this forum seemed to be the best place to discuss the physics of the force that the wind provides to propel a yacht.
Your questions are insightful, and, if I may, I would like a few days to work up a suitably thoughtful response.
But, be assured, that response will be forthcoming and will quite possibly form part of an explanatory section of a revision of my paper.
I will welcome any assistance offered to work up the appropriate replies.

 

But my hypothesis embodies a demonstration that PV=nRT does have everything to do with a sail. I just don't have the knowledge to work out the physics yet. I am hoping that by engaging the wisdom and intelligence of a community of technically minded sailors such as this, a fuller account of the maths can be achieved.
As I say in my conclusion:
"The theory has been presented in an entirely qualitative manner. Whilst some numbers have been provided to describe the experiment, no attempt has been made to ascribe values to the size of the pressure variations. The purpose of the exercise was to establish a fundamental principle; the work of calibration and quantification is yet to be undertaken."

 

In reaching out for assistance, may I submit three thoughts:
1) I suggest that instead of considering the formulation of the Ideal Gas Laws as PV = nRT, the density-base version avoids the tricky question of having to define the volume.
The Ideal Gas Law can be stated PM = dRT , where
P = Pressure in Atmospheres
M = Molar mass of the gas
R = [EDIT] 0.0821 not 0.821[/EDIT] atm litres/°Kelvin
T = temperature in °K
d = density in grams/litre.
2) Rather than considering the velocity of the gas in cm/sec, we should be concentrating on its mass flow rate, in grams/second.
3) And finally, and more challengingly, I suspect the the size of the pressure differences is related to the speed that these pressure changes, both the high pressure to windward and the low pressure to leeward, are propagated through the air.
And that introduces the speed of sound!
Please, let's not get caught up with shockwaves! The speed of sound is the speed with which a disturbance of pressure or density in one part of a medium can influence the pressure or density in another part of the medium. Shockwaves are a special case where the disturbance is moving through the medium faster than the speed of sound. The sail is moving at considerably less than that speed, however, it is still causing a pressure and density disturbance in the air. Just observe the deformation of the hexagonal bubbles ahead of and behind the foil.

 

Ah, but when you use the density version of the Ideal Gas Law: PN= dRT where d is density, or even better when you have tied down your gas to air (mol weight = 28.9) , we can use: P = cdT where c = 2.88 10^6 cm^2/sec^2, you can forget volumes altogether!
Now, I think, with some clever thermodynamics, you will find that it does directly relate to my sail.
I am working on it.
Stay tuned.

 

These insightful questions have motivated me into a six-month deep dive into thermodynamics, the result of which is a major revision of the Swept Volume Thesis in which your questions are addressed and I think, resolved.

The pressure change is the direct result of the volume changing. The volume is being changed by the sail sweeping into the air to windward, in front of the sail, and out of the air behind the sail, to leeward.

The volume is the region between the sail and the pressure wave front that propagates as a high pressure wave to windward and a low pressure wave behind the sail to leeward.

The boundary of the working volume is the pressure wave front, beyond which, due to the speed of the disturbance due to the sail's movement through the air (the speed of sound) has not had time to penetrate.

The volume is changing as the high pressure front propagates to windward and the low pressure front propagates to leeward. This is a continuous process, so the volume is changing continuously as the pressure wave propagates and the sail sweeps through the air.

The volume is not constant.
The volume is changing as described above.There will be some temperature change due to this volume change, but due to the relatively small changes in volume and pressure, the temperature changes will be small. Calculations indicate that at sailboat speeds the temperature changes will be around 3° higher to windward and 3° lower to leeward. The process will be almost adiabatic, since there will be minimal heat exchange generated at the speed that the sailboat works.

The relationship between changing pressure, temperature and volume of air is provided by Thermodynamics.
Since we can deal with the air operating around a sailboat as an ideal gas (relatively low pressure and temperature), and the process as being adiabatic (very small temperature changes), thermodynamics provides the relationship between pressure, temperature and volume of an ideal gas in an adiabatic process as PV^γ = constant, where γ is the adiabatic constant (Cp/Cv) which, for air has the value 1.4.

There is no heat energy being supplied. Due to the low levels of temperature change, the process can be considered adiabatic, i.e. no heat transfer in or out of the system.
Any temperature change is due to the effect of the volume change (compression ahead and expansion behind) in the swept region.
The volume is being changed not by the transfer of heat (heating or cooling) but by the movement of the sail through the air, which is at the core of the swept volume hypothesis.

Thank you for raising these insightful questions, I hope you find the revised paper provides a good explanation of the source of the pressure differences around a sail.

 

Here is a summary of the thesis:

1. We know that the wind provides the force to drive a sailboat.
2. The experimental evidence confirms that air pressure alone generates all the force.
3. There is no satisfactory explanation for the source of the pressure differences in the technical literature.
4. The source of the pressure differences can be shown to be the volume of air swept by the sail.

Some encouraging "back of the envelope" calculations indicate that thermodynamics could provide the framework for calculations.

As long as we focus on flow rather than pressure, little progress can be made to explain how the shape of the sail affects the boat's performance.

I look forward to your feedback.

 

I have been monitoring the "reads" of this thread and can see that there has been some significant activity since I posted the response to @MalSmith's questions two weeks ago. Also, the thesis itself has had a reasonable number of views since then. However, despite the thread having attracted considerable interest last year and earlier this year, there has been no response at all by forum members.
Is that because:

1. You have read the thesis and agree with it. Great, please make contact. You may be able to assist in developing and refining the physics.
2. You have read the thesis but don't understand it. If so, please let me know, either by comment here or by making contact through the email on the thesis.
3. You have read the thesis and disagree with it. Please, criticism is fundamental to the advancement of science.
4. You have not read the thesis. Please, take a few minutes to familiarise yourself with the proposition.

 

I agreed with it before you even started, so I was surprised that it wasn't already a named theory. What your experiment's done though is correct one place where I'd been misled by the mainstream theory relating to air speeding up over the top of a wing where it's now clear that it the air can slow down over the top of the wing too, merely doing so less than the air passing under the wing, though this only applies to the front half of the wing, because the air going over the top slows down more at the back end of the wing while the air going underneath speeds back up there. These changes in speed are now easy to account for though, because it's all about pressure and vacuum: there's a vacuum over the top which allows the air to flow in fast but slows it down on exit as it's held back there by the vacuum, whereas under the wing there's high pressure which slows down the air coming in but pushes out the air that's leaving at the back of the wing: that likely accounts directly for at least 90% of the speed changes in air flow. So, over the wing we have a vacuum causing the air to be accelerated or decelerated in line with --> <---, while under the wing we have high pressure causing the air to be accelerated or decelerated in line with <--- --->. It's that simple.

 

I know from your earlier posts that you are an adherent of the concept of the sail leaving a hole behind it: (the low pressure side of what I term the swept volume), and I suspect the theory has not gained traction because it is not intuitive.
It is more intuitive to think of the force as being caused by the airflow around the sail, but this is not the case. Any airflow around the sail is actually caused by the pressure differences, not the other way around.
The air moving in to fill the space is what creates the lower pressure. The air being pushed out in front of the sail causes the higher pressure. The pressure differences are what cause the force. Any airflow is simply a consequence of the pressure differences.
If we're looking to uncover the nature of the aerodynamic force, and the source of the force is clearly the pressure differences caused by, as you put it, the air moving in to fill the space, then there is no need to further complicate the issue by talking about airflow. We have the components:

• The force is caused by the pressure differences.
• The pressure differences are caused by the sweeping of the sail through the air.

We now need to concentrate on physics, through thermodynamics to more precisely determine how the shape of the sail and its speed and angle relative to the undisturbed air generates the pressure differences that ultimately generate the aerodynamic force.