On implement weights or how even brilliant men can be mistaken

A. Juilland, in the book that gave the name to this blog, is discussing the choice of weights for the various implements used in throws. He argues that, since the idea behind the choice of the weights for women's implements was dictated by the desire to have roughly the same throw lengths at world record level, the current choice of weights is not optimal. While for shot put and discus throw the choice is more or less right, the matter is more complicated for hammer and javelin. Of course, hammer throw was a very young discipline at the time of Juilland's article and since that time the feminine world record is no more that far behind the masculine one.

However things are quite different for javelin. Juilland argues that women must use a lighter implement, of roughly 500 g. Moreover his estimates are based on the old javelin, still in use for women at that time, and a world record of 80 m. With the current world record of 72 m a lighter javelin, of roughly 450 g, would have been proposed by Juilland, had he been still among us today.

The photo is that of my preferred javelin thrower Mariya Abakumova.

Unfortunately the grand master of athletic provocation is wrong in his estimates. I have written an article on the influence of implement weight on the length of the throw which will appear shortly in New Studies in Athletics. (I do not link to it here. If anybody is interested in having a copy, I will gladly provide it. It suffices to send me an email at the address: basigram at gmail dot com). One does not have to go through the physics of the article in order to understand the basic point: even when we try to throw a very small weight, there is a limit to the velocity we can impart to it, limit due to the speed at which we can move our arm. This is something far from negligible. In fact as shown in my article the length of the throw is inversely proportional to the sum of the mass m of the implement and something that we could qualify as the effective mass of the arm. In my analysis of shot put I found that for male throwers this effective mass term f had a value around 6-7 kg. One expects this value to be somewhat smaller for javelin throw, because of the different gesture, and even smaller for women. So let us assume a value of 4 kg and see where this leads us. 
We start with an expression for the length 

$$ L = a/(m + f )

For the current world record of roughly 72 m and a javelin of 600 g we find a value of a=330 kg m. Thus, even with a featherweight javelin, women would have trouble going over 80 m. So, let us be optimistic and divide f by 2. In this case a=188 kg m and an almost-zero-weight javelin would reach 94 m. However with a more realistic 450 g javelin (the one the calculations of Juilland would suggest) the record distance would be a mere 77 m. Even with f=1 the record would still be below 80 m. We are very far from a parity of men-women records in javelin throw and moreover it does not look as if the gap will ever close (unless one accepts to go back to old-style aerodynamics for women's javelin, something quite improbable).