A Loaded Question

[George C]

When during a cast does a fly rod begin to unload?
It seems that MCL is routinely taken as the start of unloading, but is this correct? Or is the load just being shifted out the rod and contained more in compression than flexion as the rod straightens?

Please consider the pictures below. A cheap graphite kid’s rod carrying a 4 oz load. It seems the load is constant regardless of how much the rod bends, and for a moment the rod can even carry the load (if in line with the blank) without much bend at all.

So is any of this pertinent to a fly cast?

Thanks
G

Note: pictures have been cropped so magnification varies if measurements are considered

[Lasse Karlsson]

Hi George, try the same with the rod angled towards the weight. The bend then moves further down the rod.
Rod bends from the butt up, and are shitty springs anyway.
But they are pretty and needs magic to really sell

If you also want to have some more fun, instead of taking the pictures straight from the side, angle the camera, so either the butt or the tip is closer to the camera. Makes for some interesting bending profiles, the big spring proponents love

Cheers
Lasse

[Walter]

Hi George,

What you have demonstrated is two concepts.

The first is that the amount of deflection in the rod varies directly with the amount force being applied to deflect the rod. Hooke’s Law.

The second is that force, in this case gravity, is a vector quantity. The amount of force applied to the rod to deflect it will vary with the angle of force being applied to the rod. The mathematical relationship is the amount of force times the cosine of the angle of the rod relative to the force. Example, with a 2 ounce weight hanging from a horizontally held rod the force applied to the rod for deflection is 2*cos(0) = 2 ounces. If the rod is held at a 45 degree angle from horizontal the deflecting force would be roughly 1.4 ounces and for a perfectly vertical orientation the force would be zero but you would have to run the string through the core of the rod to achieve this.

Does it apply to fly casting? Yes. It shows that as the angle between the rod and the line changes the amount of force actually applied to the line changes. Tobias has done some work to show how as the rod unloads the angle of force application by rod the rod on line remains fairly constant even though the angle between rod and line is constantly changing. So the relationship applies to the design of the rod directly and indirectly to the casting stroke.

Not sure what a shitty spring is. As far as springs go it’s just a spring.

[Walter]

George,

By the way, this was a really good question and thanks for presenting it. It made me think of two things:

One is that the rod, by intent or accident, is a really well designed device. Except for materials not much has changed in the basic design over the course of centuries.

The other is that in spite of all the bickering that seems to occur in the physics forum a lot of interesting detail about the rod has been either initially presented here or or found a wider audience on Sexyloops from their initial publication. As Lasse pointed out the way the rod bends is significant to its efficiency and effectiveness for casting and Tobias has elaborated on that significantly to show how the unloading characteristics allow us to recover more energy than we would with a rigid rod. I believe it was Gordy or Gordy and Meriln pointed out that the dynamic nature of the rod allows us to input more work energy into the system than we could with a rigid rod. Server showed us that the rod has a natural frequency that affects the casting stroke and we had some really good demonstrations by others to confirm his work. There have been a number of contributions by science experts like Grunde and Torsten that have helped us understand the basic physics in the cast and the rod. I'm sure there are many others and I apologize if I haven't given proper credit but that's enough for now.

Keep asking questions,

Walter

[Paul Arden]

Hi Walter,

Since the load is dynamic, does this mean that as the angles change and load is reduced on the rod, that it will continue to unload?

Thanks, Paul

[Dirk le Roux]

Hi George

That is a really good question.

Your pictures illustrate the same weight’s ability to bend or buckle the same rod to varying degrees in different supported orientations. Additional to the force vector angular component aspect as Walter explained, there are some structural terms to consider, such as deflection relative to span (and bending resistance) and the moment of a force (effectively torque, but this term is not the preferred one in structural design speak). Both are amplified by an increased distance between load and support force lines of action.

Structurally your scenarios change progressively from that of a tip-loaded cantilevered beam to something like a slightly eccentrically loaded supportive but quite slender column. The rest of this post may be boring.

With your first image, the rod is like a horizontal cantilever (tapered) beam with a point load applied at the (thin) free end, far from where your hand holds the rod virtually clamped. The structural result here is the 1) highest possible deflection and 2) most intense (torque) moment about the support point of any of the four scenarios, and 3) almost zero compressive stress in the rod’s longitudinal axis direction. Neglecting the rod's own weight, the moment about the support point = the sinker's weight x cosine of zero degrees (which is 1) x the distance between your holding support and the line attaching to the sinker. The deflection depends on these factors plus additionally the rod’s moment of elasticity and its cross-sectional moment of inertia. These two additional factors being equal across all four scenarios, the deflection differences are determined by the same factors as for the moment. The longitudinal compressive stress is (almost – due to geometric imperfections) zero by load having almost zero vector toward the held point, the sine of zero degrees being zero.

The rod in your last image is more like a slender column clamped at the bottom with a slightly eccentric load weighing down on it at the top. The structural situation here is the 1) lowest possible lateral deflection, 2) smallest moment about the support point and 3) highest longitudinal compressive stress. The deflection and moment about the support point, in this case, are greatly reduced by 1) the negligible lateral vector component of the force exerted by the sinker’s weight (cosine of 90 degrees is zero) and 2) the smallish eccentricity of the load relative to the support point’s force axis. Similarly, by the downward force vector effectively equaling the sinker’s weight (sine of 90 degrees is 1) and by the load’s small eccentricity to the support force's line of action, longitudinal compressive forces dominate here.

All the best,
Dirk

[Dirk le Roux]

Correction - modulus, not moment, of elasticity

[Walter]

Hi Walter,

Since the load is dynamic, does this mean that as the angles change and load is reduced on the rod, that it will continue to unload?

Thanks, Paul

The narrower the angle between the rod and the string holding the suspended weight the less the deflecting force will be (yes the rod wil continue to unload or straighten).

Given that the weight in this case isn’t a point mass it would be impossible to reduce that angle to zero. There will always be some degree of eccentric load and that will prevent the rod from fully straightening.

If you were to attach the line to the rod tip, run it down through the centre of the rod out the bottom and hang the weight from there you could remove the eccentric load and the rod, assuming it had no major manufacturing flaws, would fully straighten.

With respect to casting and the forces being applied to the line, the resulting counter force on the rod tip, how the rod unloads and how that affects energy transfer to the line during the unload, that is covered in the work Tobias has done. I know it was made available on SL some time ago.

[Walter]

Paul,

I found the video Tobias made on Vimeo. Notice that as the rod unload it forms a semicircular shape that reduces in diameter as it moves up the rod towards the tip. The tip for a large part of the unloading remains at the apex of the semicircle with the line coming off of that semicircle at a tangent. Ideal continuous force application to the line even though the angle between the rod butt and line becomes very narrow.

[George C]

Thank you, Walter and Dirk.
Much to think about.
From Tobias' video, can a case can be made that the rod is fully loaded at the point of maximum deflection and already starting to unload (the red circle moving up the rod) by MCL? As the butt passes perpendicular to the load from the line, the forces on the rod begin to shift from deflection to compression and the rod begins to straighten from the strongest part upwards? Phrased differently, does this mean that the rod is trying to unload thru the latter half of rotation rather than just at the 'stop' at the end of rotation? Or is the total load still increasing but just being moved further out the rod?

Thanks for helping me understand this.
George