Two heads - drag forces compared

[Torsten]

Hi,

this is a response to a question from the "Head length vs head weight" - thread here:
viewtopic.php?f=8&t=3606&start=140

Is there a significant difference between the drag forces between two heads with the same mass but different length during the acceleration phase of the line?

I've written a small Python-script, you can find it on my GitHub-account; here is the source code
https://github.com/orsenter/Flycasting- ... uteDrag.py

The output from that script is:

Air density = 1.204 kg/m³
Tangential velocity = 39.95 m/s
Normal velocity = 2.09 m/s
Skin friction coefficent = 0.005
Form drag coefficent = 1.0
Line inclination = 3.0°
--
Line length = 10.0 m
Line diameter = 1.72 mm
Reference area (skin friction) = 0.054 m²
Reference area (form drag) = 0.017 m²
Reynolds Number Re (form drag) = 2.38e+02
Reynolds Number Re (skin friction) = 2.64e+07
Skin friction force Fdt = 0.2596 N
Form drag force Fdn = 0.0454 N
--
Line length = 20.0 m
Line diameter = 1.22 mm
Reference area (skin friction) = 0.076 m²
Reference area (form drag) = 0.024 m²
Reynolds Number Re (form drag) = 1.68e+02
Reynolds Number Re (skin friction) = 5.27e+07
Skin friction force Fdt = 0.3672 N
Form drag force Fdn = 0.0642 N
--
Force difference = 0.1263 N

I've chosen a quite high velocity, I think during the stroke the value will be much lower. Because the line isn't usually exactly straight accelerated to the flow, I've included an inclination parameter.

Now we need to compare the result to the force due to line inertia and that's likely above 1N, so my current guess is, that it's difficult to feel a difference related to the drag force.

Uncertainties are related of course to the simplifications and choice of the drag coefficients. I've chosen typical values for cylinders (form drag) and the measurements from Gaddis for the skin friction. More details later (e.g. turbulent boundary layer etc.pp.)

Greetings,
Torsten

[VGB]

Hi Torsten

Skin friction coefficent = 0.005

Some real life measurements from industry may give you some perspective on the skin drag figures you are using:

In the absence of real measurements for a fly line, I would suggest that the figure of 0.0015 would be more appropriate. I would also add to your list that you are assuming laminar airflow for your form drag figure which also tends to overstate the output value by some margin.

Regards

Vince

[gordonjudd]

In the absence of real measurements for a fly line,

Vince,
The C\(_{dt}\) =.005 value given in the paper by Gaddis was derived from measurements on different lengths of thin wires with diameters of .55 and .88 mm.

Are you implying that the tangential skin drag on a smooth fly line with similar diameters would be different for some reason?
Gordy

[VGB]

Gordy

I'm not implying anything, I am stating that the skin drag coefficent used in Torstens mathematical model appears to have a higher skin drag coefficient that a variety of aircraft structures, I have no idea what Gaddis has measured or how it compares to a fly line, or why you now believe that the Perkins and Gatti Bono values that have underpinned much of the aerodynamic models here were in error.

Nor do I know why laminar airflow has been assumed, I expect all will be made clear in time.

Vince

[gordonjudd]

why you now believe that the Perkins and Gatti Bono values that have underpinned much of the aerodynamic models here were in error.

Vince,
Perkins typically used a skin drag coefficient of .0015 while Gatti-Bono used a value of .015 for the tangential drag coefficient in one of her papers. Since those values are an order of magnitude different I would expect that one or both of them could be in error.

As you noted a better estimate would be expect to come from actual measurements of the axial flow drag one long thin cylinders as was done by Gaddis.

Nor do I know why laminar airflow has been assumed,

At least in the measurements made by Gaddis the opposite was true. He found:

It is clear that there is very little laminar flow. a result anticipated due to the testing in an already turbulent flow which will produce early transition.

Gordy

[VGB]

Gordy

It is clear that there is very little laminar flow. a result anticipated due to the testing in an already turbulent flow which will produce early transition.

The form drag Cd is for laminar flow but you are assuming that the flow is turbulent for the skin drag, why is that? The quote from Gaddis is a bit odd, how long was the test piece?

Perkins typically used a skin drag coefficient of .0015 while Gatti-Bono used a value of .015 for the tangential drag coefficient in one of her papers. Since those values are an order of magnitude different I would expect that one or both of them could be in error.

Or one could be a typo, I can’t see the logic of throwing both out.

As you noted a better estimate would be expect to come from actual measurements of the axial flow drag one long thin cylinders as was done by Gaddis

Do you have a copy of the reference you can share? It would be interesting to see how the figure from Gaddis came about, the test set up and aerodynamic conditions that were tested. It certainly seems an incongruous result when compared with aircraft surfaces that have rivets, gaps in panels, boundary control devices etc.

Vince

[gordonjudd]

Now we need to compare the result to the force due to line inertia and that's likely above 1N

Thorsten,
For what it is worth, I get the same skin drag and form drag values that you calculated for a 3 deg inclined section of fly line with a horizontal velocity of 40 m/s.

On one of Lasse's long casts Tracker gives a line acceleration value of around 237 m/s\(^{2}\) near MRF.

For a 20 meter length of fly line having a mass of .022 Kg that gives an acceleration force of 5.2 N. Thus the drag forces would pale in comparison to the torque the caster would "feel" when accelerating the line in a cast.

Gordy

[VGB]

Sorry, I forgot to mention that the Form Drag coefficient that you are using is for cylinders that are perpendicular to the flow, not 3 or 4 degrees, I’ve provided some examples of the difference that geometry and flow conditions make to the figures.

6071CE79-01AD-40E7-A1D4-A656DA16B9B6.png (34.58 KiB) Viewed 1010 times

Vince

[Torsten]

Vince,

yes, the author of the paper assumes turbulent flow. Actually this is plausible, the *skin friction* coefficient is lower for laminar flow; e.g. compare with the skin friction for flat plates in the literature. Gaddis has measured a 48% higher skin friction coefficient compared to the flat plate. The coefficient could be a slightly bit lower, because I've computed a higher Reynolds Number than for the measurements of Gaddis - on the other hand it's not that likely that the fly line is exactly straight over 20m (and thus a smaller Reynolds Number is more realistic).
Ideally we would know measurements from real fly lines, until then I'll keep the values from Gaddis.

Greetings,
Torsten

[VGB]

Torsten

I have no problem with an assumption of turbulent airflow, as this is the most likely condition in the environment we are casting in. However, you have taken the form drag coefficient that you are using for the line as being in laminar flow, you can’t have both flow conditions simultaneously. I’m sure that you agree that the assumption should be consistent?

Regards

Vince