Spanish experiment

[gordonjudd]

The easiest way to understand the difference would be look at the frequency domain rather than the time domain.

Walter,
That may be true, and you would find that the sin(x)/(x) like response for those two cases (zero rise time or 50 ms rise time) would be nearly the same.

But that is missing the point. You and Vince need to realize that the rise time of the applied acceleration used in casting is much smaller than 1/(loaded frequency) of the rod and line. Consequently, Vince's statement that:

For a gradually applied force such as a fly cast, the amplification factor is less than 2 and related to the rise period.

Is not true. We do not "gradually apply" the torque used to accelerate the rod rotation. Rather once a good caster starts rotating the rod (after a drag phase with little or no rotation) he gets to a sizable angular acceleration level rather quickly as shown in the angular acceleration curve that Grunde measured for the Paradigm cast that is shown below. From that graph you can see that Mathias reached his nominal acceleration value of around 1000 deg/s^2 in about 50 ms. The loaded frequency of the rod and line for that cast was around 1.2 Hz. Thus that "rise time" was about 1/24 of the loaded frequency period, and thus is far from being "gradual."


If you had a better understanding of Merlin's model would you would understand that the near 2x increase you get for the force applied with a flexible rod depends on the magnitude and duration of the applied acceleration not on its relatively short rise time.

Gordy

[Merlin]

Alejandro,

Congratulations for making the experiment real and exploring the intricacies of the system. Yes, the string can be better than the spring and vice versa, it tells you that there is an optimum somewhere, and that our rods are optimized (up to some point) to make casting easier.

Merlin

[James9118]

This has been posted before but I thought I'd put it up again as it predicts the 'tuning' behaviour seen in Alejandro's experiment. Maximum 'mass' velocity in blue, whereas the red line denotes the max velocity of the drive (again with the usual caveat that this is a set of drive conditions defined be me).

[Walter]

Walter,
That may be true, and you would find that the sin(x)/(x) like response for those two cases (zero rise time or 50 ms rise time) would be nearly the same.

But that is missing the point. You and Vince need to realize...

Gordy - you need to realize that you seem to be putting words in my mouth again. You have made a statement that seems to say that how I apply force to a rod, or add input to a system, is more important than the actual forcing function. I've simply stated that, for modelling purposes, the opposite is true. A simple way to look at it is to look at the frequency domain. This would allow you to easily determine the response of a system to a different input. If you wish to avoid this and simply make the statement that a ramp function with a rise time of 50 ms is so close to zero rise time that it is essentially a step function then I'm actually okay with that. I call that an assumption and I don't think it's an unreasonable one unless we are concerned about what happens in the first 50 to 100 milliseconds of the cast.

[gordonjudd]

You have made a statement that seems to say that how I apply force to a rod, or add input to a system, is more important than the actual forcing function.

Walter,
I don't understand what you mean in that sentence. I am saying the torque input to the rod/line system does determine the acceleration forcing function using in Merlin's model. Why would you contend that how we apply the input would be more important than the forcing function? To me the forcing function has to be related to the input.

To me how we apply torque to accelerate the MOI of the rod and also produce the varying acceleration force on the line through the spring in the rod does determine the forcing function (either a constant or varying acceleration) to Merlin's model. Consequently, the torque used to rotate the rod and accelerate the line is intimately related to determining the angular acceleration we would compute from CA data. How could it be any other way?

A first order approach to computing the torque required to produce a given acceleration input for Merlin's model is discussed here if you are interested in seeing an example of what I am talking about.

Here is the approximate torque curve (shown in red) that Merlin calculated using the measured data from the Paradigm cast.

I've simply stated that, for modelling purposes, the opposite is true.

Why do you think that how we apply torque to rotate the rod does not determine the acceleration forcing function that is used in Merlin's model? I may be putting words in you mouth but I do not see the distinction you are making.

Merlin is using one dimensional translation values (m, m/s, m/s.^2) rather than the one-dimensional phase values (radian, radian/sec, radian/sec.^2) you would use in a model based on rotation analysis, but the form of the ODE used in either model is the same. The two approaches are just related by the effective length of the rotating rod.

Gordy

[Walter]

Gordy - I can see you are confused. Sorry - I'm never quite sure what level to gear my responses to you at. In this case I was obviously too cryptic. I'm talking about using the Laplace transform. This is used when you have a system for which you have a known response to a known input but you do not know the actual transfer function of the system. Use the Laplace transform to look at the system in the frequency domain rather than the time domain. This will convert a system which is characterized by differential equations into one which can be manipulated algebraically. This allows you to fairly easily separate the input function from the transfer function and introduce a different input function of your choice. The reverse transform then provides you with the time domain response of the system with the new input function, for example - you can determine how your system responds to a step input if you know how it responds to a ramp input. How the input is physically created is not important in this case, the function that describes the input is important.

[gordonjudd]

I'm talking about using the Laplace transform.

Walter,
I would expect that those skilled in the art of using Laplace transforms could use that to get more insight into the problem, but I do not think it would change any of the results.

The ODE45 solver in Matlab is a direct, easy way to solve the SHO ODE for arbitrary acceleration profiles, so I will stick with that method to provide a direct way to solve the SHO differential equation. If you are an expert in using Laplace transforms, then it would be great for you to use it to verify that the method described here is a valid model for arbitrary measured acceleration functions.

Merlin's model says the short rise times we see with the applied acceleration curves used by good casters would produce maximum acceleration forces (from rod whose spring constant is matched to the magnitude and duration of the acceleration profile for a cast) that are much larger than the value you would get using a broomstick driven by the same acceleration profile. Whether the rise time is zero, or 50 milli-seconds I do not think it would have much of an effect on what is going on.

It would be great if you would do the calculation for yourself and show some results that would either verify or contradict that results that Merlin and Grunde are getting with their approach to the problem.

I would think you accept Merlin's and Grunde's model as being a reasonable first order model to understanding how line speed is produced in casting, but with the comments that you make I am never sure. Your statement in the other thread that:

In the massless case and using Newtonian mechanics the magnitude of F1 and F3 will always be equal.

and the use of f=ma as being as useful as a real free-body diagram for the lead mass, tells me you did not understand what was going on with the force applied to the brick by the spring or the net force on the falling lead mass in this "Spanish" experiment.

The intent of Aitor's experiment was to do a controlled experiment (using a fixed amount of input PE) that would help to verify that Merlin's one-dimensional SHO model is a useful approach to understand how the deflection in the rod varies to a given acceleration function in casting and how that impacts the resulting line speed. I hope that Alejandro's results show that is the case, and everyone now understands why the spring in a flexible rod will produce more line speed than a broomstick for the same angular acceleration of the butt.

Gordy

[Walter]

Gordy - Since you seem to be in a who said what and what does it mean frame of mind then I must say that your statements:

If you are an expert in using Laplace transforms, then it would be great for you to use it to verify that the method described here is a valid model for arbitrary measured acceleration functions.

and the use of f=ma as being as useful as a real free-body diagram for the lead mass, tells me you did not understand what was going on with the force applied to the brick by the spring or the net force on the falling lead mass in this "Spanish" experiment.

Tell me that, as usual, you don't know what you are talking about and as usual you would like to see me wasting my time on fluff that you dream up rather than trying to understand what I am saying. Maybe you actually get some benefit out of looking at a picture of a box with a couple of arrows attached to it but many of us graduated past the need for that sort of tool in high school.

The intent of Aitor's experiment was to do a controlled experiment (using a fixed amount of input PE) that would help to verify that Merlin's one-dimensional SHO model is a useful approach to understand how the deflection in the rod varies to a given acceleration function in casting and how that impacts the resulting line speed.

And what do Aitor's results tell you? Do you think it is worthwhile having Alejandro build two rods and to have Alejandro and Aitor run their proposed experiment based on the results from Aitor's proof of concept? Or do you think the proof of concept needs a bit more refinement and testing? Do you think the spring effect has been sufficiently separated from other variables in Aitor's experiment to make the results meaningful? Do you understand the concept of statistical significance or are you going to rely on Matlab to tell you what it is? There is significant cost in time and materials in what they are proposing. They have approached this forum for advice regarding the experiment. I'm providing some, i.e. how to tell if results have statistical significance and the potential impact of one input function vs another. Sorry if you are troubled by that.

[VGB]

But that is missing the point. You and Vince need to realize that the rise time of the applied acceleration used in casting is much smaller than 1/(loaded frequency) of the rod and line. Consequently, Vince's statement that:

For a gradually applied force such as a fly cast, the amplification factor is less than 2 and related to the rise period.

Is not true.

If you had a better understanding of Merlin's model would you would understand that the near 2x increase you get for the force applied with a flexible rod depends on the magnitude and duration of the applied acceleration not on its relatively short rise time.

Gordy

Gordy

I'm not sure whether you did not understand what I wrote or are deliberately trying to twist it.

Do you know a case where DAF reached more than 2 and how close to 2 does the model say you can get?

As for the last sentence did you understand the ramp step and the implications of t/T?



Vince

[VGB]

Alejandro

Thank you for your experiment

regards

Vince