[AusRace] Co-efficient of Uncertainty (3)

[Tony Moffat]

Continuing - from Maths for Games Part 8 by Lowell Harbison(Munro) (NZ)

Race time and sectional time became available in NZ before it was common
place elsewhere
The technical authority governing racing (dog, harness, thoroughbred) was
the same across all codes
and what was good and expected for harness came to be expected amongst the
other codes.

Those harness racing people live for and fairly salivate over 'mile rates'.
They might be onto something?

Mr Harbison used race time, sectional time (perhaps 400 metres) and seems to
have introduced the following:

HIDDEN SPEED

The maths used are the authors. The explanation of them are mine (sorry)

The overall race time is a given, the timing from start to finish.
The sectional time was for the agreed last part of the race, his sectionals
may have been 400 metres

He makes a claim that there is a portion of the race that is untimed
specifically but might be faster than either time shown for the race,
overall or sectional

This is the interim distance, the distance between the sectional time
commencement and the start of the race. 

He managed to find several names for it, this time over a differing
distance. I liked 'Hidden Speed' which conjures up a possibility of
something unknown, unexpected, mysterious and scientific
(a) Record the overall race time (and distance)
(b) Record the sectional time (and distance)

Take distance (b) away from distance (a) and there is the 'Hidden' distance.
You have the 'Hidden' distance and it should be easy enough to work out the
time
to cover that distance using (i) the overall speed and (ii) the sectional
speed.

Mr Harbison did both calculations (overall and sectional) 

Eg 1600 metres with 600 metre sectional - 96.96 overall, 35.71 seconds
sectional
To get the 'Hidden Speed' distance - 1600 minus 600 = 1000 m
To get the 'Hidden Speed' velocity: 96.96 - 35.71 = 61.25 = 1000/61.25 =
16.32 (metres second) which is slow.

There are now three values
1600/96.96 = 16.50 metres second
1000/ 61.25 =16.32 metres second
600/35.71 = 16.80 metres second

His reckoning was that the runner appears to have 'loafed' along from the
start until a point 1000m out at 16.32 metres second
Then sped using the fraction 16.50/16.32 = 1.05 > 16.50 *1.01 = 16.68 metres
for a distance in order to score the final sectional of 35.71 metres second.

That 16.68 metres per second is f a s t (and hidden as it happens)

I don't agree with his arithmetic

Another way - you would hope

Cheers

Tony



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