Fossati's Aero-Hydrodyamics

I don't see much of a problem with the definition of CP on page 20, other than that the text uses delta for submerged hull volume while formula 2.19 uses uses the inverted delta for immersed hull volume. Other than a small typo, the written text, the formula, and the illustration all correspond to the definition of prismatic coefficient:

 

I am buying Fossati's explanation and your interpretation here.

I buy your interpretation here, and the manometer readings in the photo and your 'graphical experiment' both support the data. Think of the flow field above the airfoil as a 'virtual venturi,' if you will. The 'top wall' of the venturi is the horizontal freestream flow far from the airfoil. The local velocity along the streamlines very close to the airfoil surface can be higher than the freestream velocity over the entire length of the airfoil. That equates to local pressure along the airfoil top surface that will always be less than the freestream pressure. Sure, the local pressure toward the back end of the airfoil is higher than the local pressure near the nose, but the local pressure anywhere along the top surface can be lower than the freestream pressure.

Your going down this rabbit hole and correlating manometer photo readings to the airfoil diagram with numerical integration and vector addition is very cool. Fossati is not wrong, he just doesn't cover the answer in-depth. That's why you look at other work beyond relying on one author to answer all of your questions.

 

@Sailor Al -

I've attached 3 more screenshots from a run of Martin Hepperle's JavaFoil applet that might help:

tsAGI 12% foil section at 8 degrees AOA with pressure vectors at the surface and streamlines. This is pretty much the info Fossati is presenting in his visuals:



tsAGI 12% foil section at 8 degrees AOA with pressure field around the airfoil and streamlines:



tsAGI 12% foil section at 8 degrees AOA with pressure vectors at the surface, pressure field around the airfoil, and streamlines:

 

While the outcome of the calculation may give the correct result,it has been more usual to express the Prismatic Coefficient as a ratio of the immersed volume to that of a prism of the greatest cross section extended to the length of the waterline.Why would you refer to a cylinder?

 

I've seen the term 'cylindrical volume' applied to the definition of CP in more than one case. The term refers to taking any sectional area and extruding it along one axis to define a volume. I've seen the term used in several books on computer graphics programming and CAGD as well. Perhaps it's poor translation, or Fossati is using a term that is acceptable but not what you are used to seeing. Because the illo describes CP correclty and I've seen the term 'cylindrical volume' before, I never gave it a second thought that it is used incorrectly.

 

I think this is what you are describing?
Images from Fossati Figs. A 1.10 and A.1 13

Or, with the top wall modified to be straight instead of curved, I think it would still generate the pressure differences of a venturi:

 

Very close - You probably got it. Fossati's illo of the venturi tube isn't great, so it may be obscuring a few things.

Here's a close up view from Java Foil analysis for a NACA 0022 symmetrical section at AOA =0 degrees. Flow field and streamlines are turned on:



Same analysis zoomed way out. Flow field and streamlines are turned on:



The top of the frame is essentially the top wall of your wind tunnel test section or 'split venturi' diagram. Bottom of the frame is the bottom wall. Symmetry and AOA = 0 makes for easier discussion. Note the flowlines curve and the pressure field still varies at top and bottom of the frame in the close-up. The zoomed out view shows straight streamlines and no pressure variation at the top and bottom of the frame. In reality, the disturbance in the field around the foil out to the 'true freestream' takes quite a distance to dissipate. Air isn't much of a 'wall' as compared to a solid material!

Here's one more with the pressure filed turned off, but surface pressure vector values turned on, along with streamlines:



That's to make it obvious there really is pressure lower than '0' along almost the entire length of the test section, both top and bottom.

 

OK, then this is my problem with Fossati's explanation (apologies for ignoring your artwork, but I really do want to get to the bottom of Fossati's explanation).
Here's what he says:
"It is in fact evident that where the section where the flow passes narrows because of the conservation of fluid flow there must be an acceleration of the flow which must correspond with a reduction in pressure"
But as my analysis shows, whilst the the pressure variation is an under-pressure where "the flow passes narrows" (sic) , where the flow passes widens (to use the same tortured language) the pressure variation remains an under-pressure, not and over-pressure.

If the pressure variations were due to the venturi effect according to Bernoulli's Principle then the experimental data would have been very different, with the last three pressure taps on the upper surface reporting over-pressure (which would be illustrated in red) not the (blue) under-pressure actually detected, more like this:

And that is just the upper surface. I am not inclined to speculate what would occur on the lower surface.
So that's my problem.
It seems to me that Bernoulli's Principle would have generated positive over-pressures, not the experimentally reported under-pressure. I don't understand why Bernoulli's Principle has been invoked as an explanation when it clearly does explain the experimental data.

 

If you superimpose Fossati's venturi tube sketch over the his airfoil +streamlines sketch expecting a resolution to your question, it won't work. You have to get past that. The screens depicted by Martin Hepperle's JavaFoil app or the XFLR5 program (based on XFOIL code written by Mark Drela) give a much better visualization of what is going on and are not close to being mere 'artwork.' Fossatis' sketches are 'poor artwork' by comparison, if you want to push the analogy.

BTW, both Hepperle and Drela are both reknowned aerodynamicists. They know this stuff inside-out and every which way. I can't be of any more help, other than to say 'let it go and look for answers outside the couple of little diagrams in Fossati you are getting hung up on.'

 

Yes, that is exactly my problem

Why?
I am trying to understand the science behind the aerodynamic force on a sailboat. Fossati was a full professor with a PhD in Applied Mechanics and renowned authority on the subject. His book is a worldwide reference text for sailing yachts theory. That's why I am reading it.

Your advice :

suggests that maybe you are not someone who I was addressing in my OP :

 

You suggested mistranslation being the explanation:

I wonder if you might have a better interpretation that somehow is supported by the experimental data?

 

I did indeed suggest mistranslation,but I don't have any concerns about what is actually happening.It can't be easy finding translators with the depth of knowledge of aerodynamics needed for the task.Would it be simpler for you to learn Italian in order to read the book's original text than to continue to struggle with the translated version?

 

I'm pretty sure there was no Italian language edition of the book. I can find no evidence in library searches. My technical Italian would be quite capable of doing the translation myself.

Are you able then to suggest a way of connecting the venturi explanation with the experimental data that I asked about?

This is one of the challenges I alluded to in my OP. I just don't understand how the venturi example can be used to explain the under-pressure that is reported at the back of the foil.

 

Does the length of that arrow ( I referred to as "rogue" since there was no pressure tap at that location) indicate the magnitude of the over-pressure?

 

"His book is a worldwide reference text for sailing yachts theory."

(!?)

I was very fond of Fossati. But let's face it: that's not a book.

It consists of a photocopy of a long article on hydrodynamics published by Prof. Keuning of Delft and a few pages on the wind tunnel in Milan.

I don't know how Professor Keuning had the courage and serenity to preface 'that'.