Re: Analysing loop propagation
Posted: Mon Sep 14, 2020 9:36 am
Wave, energy or momentum, it depends of the type of approach, qualitative or quantitative.
I consider wave as a qualitative one. I agree that a mend is a transverse wave but the loop is not, the displacement is not perpendicular to the medium. The string analogy may be a trap since it does not handle “dynamics”. I mean that most of the time string studies refer to “stranded waves”, some type of “steady state” situation by opposition to a situation where accelerations and decelerations take place. The whip analogy looks better, but it is far from being that simple. Maybe the loop is a “longitudinal wave” in some aspect; anyway it is a strange wavy flying object.
If we aim at quantification then we have to use momentum variation in time (horizontal, vertical, angular) and energy balance. There must be a number of equations equivalent to the number of unknowns (among them: leg speeds, rod leg sag, line inclination at both ends of the loop, loop radius, etc. ) and you usually have to use simplifying assumptions or software able to handle a number of ODEs simultaneously. For example, morphing is included within the angular momentum problem but to make that easily usable for a simple model you assume that the loop does not morph. Such quantitative approach involves tension in the line, this tension varying along the line itself.
If you consider “tension” as something more global, then you are back into the qualitative approach (remember Berlin?).
You need something qualitative for teaching and it should ideally be based on a quantitative approach, as accurate as possible. Tension could be an example of a parameter linking both approaches.
You cannot solve the loop propagation technical problem by wave only, momentum only or energy only appraoches, IMHO.
Merlin
I consider wave as a qualitative one. I agree that a mend is a transverse wave but the loop is not, the displacement is not perpendicular to the medium. The string analogy may be a trap since it does not handle “dynamics”. I mean that most of the time string studies refer to “stranded waves”, some type of “steady state” situation by opposition to a situation where accelerations and decelerations take place. The whip analogy looks better, but it is far from being that simple. Maybe the loop is a “longitudinal wave” in some aspect; anyway it is a strange wavy flying object.
If we aim at quantification then we have to use momentum variation in time (horizontal, vertical, angular) and energy balance. There must be a number of equations equivalent to the number of unknowns (among them: leg speeds, rod leg sag, line inclination at both ends of the loop, loop radius, etc. ) and you usually have to use simplifying assumptions or software able to handle a number of ODEs simultaneously. For example, morphing is included within the angular momentum problem but to make that easily usable for a simple model you assume that the loop does not morph. Such quantitative approach involves tension in the line, this tension varying along the line itself.
If you consider “tension” as something more global, then you are back into the qualitative approach (remember Berlin?).
You need something qualitative for teaching and it should ideally be based on a quantitative approach, as accurate as possible. Tension could be an example of a parameter linking both approaches.
You cannot solve the loop propagation technical problem by wave only, momentum only or energy only appraoches, IMHO.
Merlin