A Loaded Question

[gordonjudd]

Maximum rotation speed: peak torque for the caster

Merlin,
Would the maximum torque being applied to rotate the rod correspond to MAV or 50-60 ms before that point where the maximum angular acceleration is reached in most distance casts?

Here is a plot of the angular acceleration of and angular velocity that I measured for one of Henry Mattel's 5 wt. distance casts while the US casting team was practicing at the Long Beach Casting Club last summer. As with most rotational systems you can see the angular acceleration will be zero at when the angular velocity is at its maximum.

forward_omega_accel.jpg (56.62 KiB) Viewed 1640 times

I don't know if that maximum angular acceleration point would mark the time when the maximum perpendicular tip deflection (MRF) is reached in a cast.

Even less certain is when the maximum acceleration force is being applied to the line since as Lasse noted the rod is a shitty spring due to its considerable mass in relationship to the mass of the line it is accelerating. Spolek estimated that 30-40% of the rod tip deflection we see in a cast is due to the inertial bending of the rod associated with its distributed mass. Thus unlike the ideal situation we assume in the simple harmonic oscillator model not all of the deflection of the rod can be attributed to a corresponding acceleration force on the line based on the measured spring constant of the rod.

Gordy

[Merlin]

Hi Gordy

The difference in time between MAV and peak torque varies with the type of cast. For a fishing one I have some 50 ms (peak torque before MAV), whilst for a competition one I have only 5ms difference (peak torque after MAV).

For the competition cast peak torque is close to max perpendicular deflection, nearly spot on, but for a fishing cast the maximum perpendicular deflection occurs 70 ms after maximum torque. Generaly speaking, the rod response is always delayed by comparison to the input.

Among the various reasons why a simple idea does not explain resluts, there is also uncertainty due to modeling, you know.

Merlin

[gordonjudd]

Generally speaking, the rod response is always delayed by comparison to the input.

Merlin,
Does that mean there would be some lag for the rod's deflection due to some applied torque at the butt?

As noted in a Google search for "angular acceleration vs torque" the first result says:

In the angular version of Newton's 2nd law, torque τ takes the place of force and rotational inertia takes the place of mass. When the rotational inertia of an object is constant, the angular acceleration is proportional to torque.

I would think the reverse would be true as well and imply the maximum torque would match the point of maximum angular acceleration regardless of the type of cast.

For a fishing one I have some 50 ms (peak torque before MAV), whilst for a competition one I have only 5ms difference (peak torque after MAV).

How are you calculating the applied torque to get such a timing difference for different types of casts?

Since the butt of the rod could be considered to be a rigid body, I would expect that the maximum angular acceleration would be reached when the maximum torque is being applied to rotate the rod and MAV would occur some 50-60ms after that point as shown in the above plot for a competition distance cast of Henry Mattel's.

Does the typical proportionality between applied torque and angular acceleration not hold in your model because the rod is not a rigid body?

Wikipedia notes:

For rigid bodies, angular acceleration must be caused by a net external torque. However, this is not so for non-rigid bodies: For example, a figure skater can speed up her rotation (thereby obtaining an angular acceleration) simply by contracting her arms and legs inwards, which involves no external torque.

Thanks for explaining this to me.
Gordy

[Merlin]

Gordy

The rotational inertia of the fly rod and line system is not a constant since the rod is far from being rigid. That makes the calculation difficult to take on board the changes in inertia (changes in equivalent inertias values for example). Then stiffness variations and non linearity variations due to the changes in pull angle and force at tip intensity, have to be estimated to get a best guess of the torque value. Consequently, depending on the cast and on the rod (sorry for forgetting that point before), the calculated peak value for the torque does not match the peak acceleration one.
The difference in between peak acceleration and peak torque is about 70 ms (HT6 competition cast) to 120 ms (fishing cast with #5 rod).

I would expect that the maximum angular acceleration would be reached when the maximum torque is being applied to rotate the rod and MAV would occur some 50-60ms after that point as shown in the above plot for a competition distance cast of Henry Mattel's.

Not peak torque, Gordy, peak acceleration. It is 62 ms in the case of the competition cast I am using, close to your values then.

Merlin

[gordonjudd]

but for a fishing cast the maximum perpendicular deflection occurs 70 ms after maximum torque.

Merlin,
Here is a plot of the relationship between the angular velocity (omega in rad/sec) and the perpendicular tip deflection (in meters) for the haul cast that Mathias Lilleim made with the Paradigm rod that was used in Grunde's high speed video experiments. The blue line shows the perpendicular deflection of the tip relative to an imaginary extension of the measured butt angle in that cast.


You can see the maximum tip deflection occurred about 20 ms after MAV in that cast. I don't know when he applied the maximum torque to the rod but the calculated time for the maximum angular acceleration of the rod butt was measured to be about 210 ms before RSP1 in that cast.

ang_accel_defl_paradigm.jpg (55.75 KiB) Viewed 1428 times

Gordy

[Merlin]

Gordy

The reason why maximum torque does not take place at maximum acceleration in rotation time is the fact that the rod bends.

Merlin

[gordonjudd]

The reason why maximum torque does not take place at maximum acceleration in rotation time is the fact that the rod bends.

Merlin,
Is that because the MOI of the bent rod is smaller than a straight one or is the reduction in the radius to the line mass when the rod bends a bigger effect?

You can see from the calculation below that the MOI of the Paradigm rod (about a center of rotation at the elbow) was about 90% of the MOI of a straight rod when the rod was at its maximum deflection point.

paradigm_moi_about_elbow.jpg (35.41 KiB) Viewed 1365 times

Gordy

[Merlin]

Gordy

Since the rod bends the rotation speed of each individual piece of rod varies. For example it is not the same at the tip top compared to the butt. So each individual piece of rod has its own acceleration profile (rotation) and the torque is a function (integral) of individual MOI / acceleration along the rod shaft. It is a pretty different situation compared to rotating a rigid rod.

Merlin