***For casting geeks only***
Simple harmonic motion has been mentioned in the 'what makes a fast rod fast' and the 'why is fast better than slow' threads (and not just be me
). I therefore thought I'd try and explain how SHM may (note the 'may' there) influence the loading/unloading of the rod and the line speed.
This is obviously taking this board into 'Sexyloops' territory and I should point out that there are plenty of people over there that think this concept is utter tosh!
In order to make the maths easier the problem is simplified to a mass (equivalent to the fly-line) being towed by a spring (to represent the flexible rod) which is driven by a car that can be linearly accelerated or decelerated (representing the casters input). This then results in a differential equation that can be solved for mass position, mass velocity, mass acceleration etc.
Now, you can drive massive holes through this if you want to, and I'll do my best to point out some of the inadequacies as I go, but try and suspend your disbelief that fly casting can be represented in such a manner
.
Firstly, let's assume that the spring (rod) is very stiff. Hopefully simple logic will tell you that if the spring doesn't extend at all, then the mass will move in a way that reflects the drive (the car, or the caster), as it is connected with a rigid connection. The model (the solution to the differential equation) shows this:
This chart shows velocity (vertical) versus time (horizontal). The black line shows the drive linearly accelerating up to just over 16 m/s, followed by a stop at about 0.35 seconds and then a period of deceleration (that the velocity doesn't get back to zero doesn't matter - if I ran the calculation for longer it would obviously get there). The red line shows the calculated velocity of the mass. You can't see this because it sits exactly underneath the black line - as logic says it should (it is connected rigidly after all). [I should also point out that the drive accel/decel is variable and can be changed, the values selected reflect those measured from a real cast].
If the rigid connection is replaced by a 'springy' one then the answer gets a lot more interesting. This chart uses exactly the same drive profile (in black) as the one above:
It's clear from this chart that the model predicts the mass will attain a velocity in excess of that achieved by the drive. This is a obviously a good thing as far as fly-casting goes, and maybe explains why we want the rod to bend during casting.
Another point of interest in this result is the time at which the mass velocity exceeds the drive velocity - this happens before the stop
. This obviously isn't the point at which the mass overtakes the drive, merely the point at which it starts catching it up. The equivalent in the fly cast would be the point at which the rod-tip, instead of bending more, first starts to straighten.
Ok, so if bendy rods are good why not make them very bendy? What the model allows is for the 'springyness' to be specified. This is called the spring constant or
k in technical terms. Now here lies a significant issue in that (at the moment)
k is entered as a constant. In a fishing rod this is not the case - the rod gets stiffer the more it bends therefore
k isn't a constant, it increases with load (because of the taper of the rod).
Ignoring that fact, if you calculate maximum (mass) velocity as a function of
k you get this:
Again this is calculated with the same drive as above. The red line shows the maximum velocity of the drive, the same 16+ m/s as before. The blue line is the maximum velocity of the mass. Low
k values (to the left) means the spring (rod) is very bendy (think limp spaghetti on the extreme left), and high values mean it is stiff (think telegraph pole on the extreme right).
What is of interest is the
k values where the maximum (mass) velocity exceeds that of the drive i.e. not too bendy nor too stiff
Note this result is for the drive conditions specified. The curve will move if the drive is changed, and thus the
k values that produce high velocities will also change slightly (hopefully you can see the logic in this also).
I'll get my anorak and go...
Simple Harmonic Motion
Linear Mode
