No worries Barny,

Glad to be of assistance!

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Barny, I feel, once you answer the question of How long is a race? then you may start to unravel the distance and time riddle.
For simplicity if you multiply your benchmark time by your measured distance this will give you a figure called a Track Constant, for simplicity one would just divide time of each runner into the track constant to give the actual distance completed against the benchmark horse, that would give you one of the three crosshairs in finding a horses performance envelope.

Also your other assertions re racing on the fence, would usain bolt have run quicker in the 200m event on the inside lane, rather then a middle lane. Also there is a formula for centripetal speed that can assist in your studies

A very interesting topic Barny.

I don't think it can be quantified as an exact formula due to the many variants that need to be considered. Recently I have watched a lot of international racing live from the UK and USA and bearing in mind the live racing from here, I have managed to deduce a number of things from this.

It would be easy "on paper" to work out distance travelled given the layout and circumference of a track. But this formula would be flawed in reality. The example of athletics is a good one, because it cannot translate to racing.
In athletics the track is smaller, each athlete sticks to their lane and there is no pace, it is flat out all the way, albeit with a finishing burst. One can note that in a sprint in athletics there is no staggered start, yet anything longer than a sprint there is. The track has much tighter bends than a racecourse. One of the main differences is the speed at which an athlete travels is a whole lot less than a racehorse, therefore the effects of centrifugal force are also less.

If a horse were to race five wide the whole trip, it would be severely disadvantaged due to centrifugal force pushing it further out on the bends.
It also depends on where the best going is on the track, it could be that in later races or rain affected tracks being on the fence is a disadvantage.

However, the point to make here is that if a horse has been racing one or two out the whole trip, but the pace has been kind, it can fan five wide on the home turn with little disadvantage and still win.

A very good in running lay method both at the races and the trots is to find a favoured runner that is wide or takes off at the begining of the turn, not the home turn. A lot of favoured runners lose that way.

So I don't think there is an exact answer to your question unless it's on paper.

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