Discussion of the speed-curvature Power Law

This is a typical example of the discourse dysfunctions discussed in another thread (http://discourse.iapct.org/t/discourse-dysfunction/15960)

It seems(!) like Rick is so sure about being right that he cannot understand what Martin means by his criticism and so he (Rick) just repeats his original claims.

I try to help.

In the eq. 4 the dotted xs and ys are measurement values by which the relationship between V and R are calculated in the trajectory which is under study. Those measurement values are specific to just that trajectory and they determine the specific relationship between V and R in just this trajectory. I repeat: relationship between these two variables: V and R in this specific trajectory, and not in some other trajectory. (So it is possible to determine the relationship between V and R if it is done in one specific trajectory and if those x and y (dots) values are available!)

Instead eq. 5 is a general truth about the relationship between these THREE variables: V, R, and D in any possible trajectory, but it says nothing about the relationship between V and R. (I thought you had already understood this in your earlier reply to my criticism.) From this equation you can, however, infer that if D remains stable then also the relationship between V and R remains stable and obeys 1/3 power law, but this is a full tautology.

This situation is analogical to a much simpler case of determining the relationship between the height and width of a changing rectangular. Analogically with the eq. 4 you can calculate the relationship from then x and y components of the heights and widths of differently sized rectangulars. Instead, with the equation: width x height = area you cannot determine that relationship because it fits to all possible rectangulars independently of their form. But if you know that the area of a changing rectangular remains stable, then you know that there must be a linear reversed relation between width and height.

(I hope but quite weakly that this is of any help.)