TGJB Wrote:
-------------------------------------------------------
> EZ-- you probably think that's a simple question,
> right? You forget what industry we're in.
>
> As I've posted before, a length in this business
> is a measure of time, not distance, and there is
> no official designation of how much time. The
> different teletimer companies use different
> formulas, and won't reveal what they are, although
> Equibase assures me they are close.
>
> We eyeballed it a long time ago (before we knew
> how complicated the question is) as roughly 10
> feet, and a path as somewhere around 3 feet or a
> little more, and using pi times diameter, worked
> out it was approximately a length. (I actually
> came up with that way back at Ragozin's, and found
> out he was using almost exactly that, something
> like .96). As a practical matter, the ground info
> is limited in accuracy (trackman don't tell you
> the horse was in the 2.9 path), so it's never
> going to be super accurate, but it's pretty close.

I was thinking more in aboslute terms with respect to the TVG Brother Derek & Barbaro question... we had a similar problem at work today figuring something out for the path of a mobile scientific instrument and related it to the distance a horse travels around the track (really, an ellipse). Assuming the path along rail is exactly one mile, like CD, how much farther in feet did a horse 2w 2w run than the horse 1w 1w.

It is in fact, a very complex problem as measuring the perimeter or cirumference of an ellipse (the shape the horse is tracing as it runs) is a high level calculus problem if you want an exact answer. For approximations, you'd need to measure the two radii from the center of the ellipse. This can be difficult to figure for racetracks, as we all know, not all one mile tracks are created equal.... this is easy to show by the distance of the homestretch.

The approximation equation is pretty straightforward, but not sure how you'd measure a and b

P ~ pi*(2(a2+b2) - (a-b)2/2)^1/2

I'll play with Google Earth and some GIS tomorrow to get the Churchill Downs info and maybe we can get an approximate answer for the difference in distance run by BD than Barbaro.