The group height of spicules links their acceleration and velocity

This study reveals a new feature of many solar jets: a group height, which links their acceleration and velocity. The acceleration and velocity (a,V) for jets such as spicules, often displayed as scattergraphs, show a strong correlation. This can be represented empirically by the equation, V = pa + q, where p and q are two arbitrary non-zero constants. This study reanalyses the (a,V) data for nine different groups of jets, in order to test an alternative proposal that a simpler relationship directly links (a,V) to the mean height for the group of jets, without needing the empirical constants p and q. A standard mathematical test: plotting log(a) against log(V) , tests whether V ~ a^n and if so, gives the value of n. When this is done for a wide range of jets the index n is consistently found to be close to 0.5 The nine groups of jets include spicules, macrospicules and dynamic fibrils. The result, V ~ a^0.5, or equivalently V^2 = ka , with only one constant, provides as close a match to the data as the equation V = pa + q, which requires two unknown constants. It is found that the constant k, is a known quantity: just twice the mean height, s, of the group of jets being analysed. This then gives the equation V^2 = 2as for the jets in the group. This more succinct relationship links the acceleration and maximum velocity of every jet in the group to a well-defined quantity: the mean height of the group of spicules, without needing extra constants.