Sorry ACW, you are right, so let's try to come to an end with an embarassing question as quickly as possible.
I really like that answer.
When I read that I thought to myself “the teacher will stick you in the corner”. Now I have a better overview of the issue and I shall not talk about calculations details here, if you want to do so, I recommend doing it outside the Board, no one cares about it in the forum and it is a source of disinterest for readers. The Board has a long (bad) list of useless contest stories. You have my mail details; I do not have yours as far as I remember, so the ball is on your side to sort things out. And yes, I misunderstand English sometimes, it is not my native language and I encourage you to write me in French to avoid such misunderstandings, if you prefer.
To pay my dues to physics I am going to make an overview of the issue, starting by some basics on waves (sorry for non physicists, but I shall try to make that simple). Then I rely on (professor?) Graeme to tell me if I reported his view correctly. As I said a wave is a disturbance in a medium, the medium itself being stable. For example, you pluck a long string under tension and a (transverse) wave travels along it. The issue becomes more complex if you generate a sufficient number of waves (named stranded waves) to put the medium under some kind of resonance: then the entire medium is affected by many waves. Stranded waves are shown at the beginning of the video (the yellow zebra on the pic).
First question: does a cast belong to the stranded wave’s category which may turn into resonance eventually or is it a solitary wave travelling alone?
• To me it belongs to the latter category, a cast is a transitory motion and never sees any beginning of a resonance or stranded wave, the tip just moves in one direction, then the line rolls over and the cast ends, and then you can repeat it in the other direction. There is no chance to see a stranded wave and to generate a resonance.
• For Graeme the cast comes from some stranded wave in a long virtual vertical line and this is why this was written:
I'm saying that's only because the medium is not long enough for them to be measured; increase the length of the medium and those aspects could be measured.
But our medium (the fly line) is finite, and has no virtual part. The concept is thus difficult to understand, staying two feet on the earth.
Now we come to tension (yes, a vector). In the usual representation, the tension is aligned with the medium so it is horizontal if the medium is horizontal and vertical if the medium is vertical. There can be both forces on a line: the force due to the tip (horizontal to make things simple) and the gravity (vertical). So force at tip is the source of tension for transverse waves travelling horizontally and gravity is the source of tension for a transverse wave travelling vertically but then you have to imagine that the line is vertical at the beginning of things. The problem is that at the beginning of an ideal cast, the line is “horizontal” and that gravity just wants to put it on the ground. How can one justify the consideration of a “vertical” tension on a supposed to be vertical long virtual line under casting conditions where the line is horizontal?
The document I use for my explanation comes from Harvard (David Morin). To get the wave equation the author determines the tension in a horizontal line (the tension follows the medium axis if I can say so, even if it is a vector). So a disturbance slightly deviates the tension vector from horizontal to make it follow the medium axis. The question is then to evaluate the tension within the disturbance and its effects. To make a long story short the longitudinal components are equal and approximately match the tension of non disturbed parts of the medium, but their vertical component is the source of wave travelling speed and it is by considering those transverse components of (deviated from original axis) tension that one ends with the expression of the travelling speed of the wave = SQRT (tension/mass per unit of length). The tension vector follows the medium axis, even within the wave; otherwise there is would be no expression of the travelling wave speed. I leave that to your representation of tension vectors Graeme, and I can forward the document to you if you give me your coordinates.
Second question: can we have a medium with at the same time a tension component along its (original) axis and a tension component perpendicular to it? You put a string in between two pegs and you generate tension along the string (for example you create tension before fixing one of the pegs). How can you generate a perpendicular tension? You then consider gravity as the source of the vertical tension, but it is negligible by comparison to the tension you created along the string, and you cannot generate vertical waves as long as the medium is not vertical. Here you consider a virtual vertical medium which does not exist but in your mind, so the vertical tension has no impact as long as the medium is not vertical.
If I consider a (horizontal) fly line, the (vertical) field of gravity is “g” (9.81 m/s^2). When we cast a line we generate easily 10 times “g” more or less horizontally and more than 20 times in a distance cast. This means that the dominant force is due to line acceleration and not gravity which can be completely ignored (this is the case in most scientific fly line studies). Remember, the medium should be vertical then, which is real at the very beginning of your video, but soon after, the axis of the medium is turned from vertical to horizontal.
Line flight can be fully explained and described by considering it in the direction of the cast (to make things simple, you consider the line to be horizontal). Up to now I never met anything resisting to that even if they are limitations given the complexity of some calculations (I can send you a number of papers on the subject), excepted for morphing. The transverse vertical wave in a virtual vertical long line may be a nice intellectual concept (consider a vertical virtual long line under stranded waves), but he does not add anything to the understanding of line behavior, it just creates confusion. So why bother casting students with that? They do not ask, no problem, we can stay with the projectile and the loop mechanisms, which match the essentials (straight line path, you know). If one asks the original question of this thread, I recommend saying no, whatever the beauty of the intellectual virtual vertical transverse wave concept is. Stay simple please, and I would not mind if students would not be aware of such discussion, I feel concerned if we invent something to fool them instead of giving the basic and practical explanations.