Thursday, February 05, 2009
Sunday, December 14, 2008
Thinking about Pi
Looking at some chart comments recently, I found a dog with a w-i-d-e running style and wondered out loud how many lengths he was giving away to his opponents by racing with his right feet nearly on the grass. A sure sign I had too much time on my hands this morning was the thought that I should try to figure that out.
My last taste of Pi in a formal math class was in 1972, so I needed a little review. The formula for measuring the circumference of a circle is c = 3.1415 x d, where d is the diameter of the circle. Using Lincoln's 110 foot radius as an example, the circle formed by the two turns equals a diameter of 73.3333 yards for a circumference of 230.3765 yards. By adding one yard of radius, and therefore two yards of diameter, we can calculate how many extra yards a dog traverses in a race for every yard it runs from the rail:
1 yard = 236.6595
2 yards = 242.9425
3 yards = 249.2255
4 yards = 255.5085
5 yards = 261.7915
6 yards = 268.0745
In other words, for every yard that a dog runs wide, it has to cover 6.28 more yards than the dog one yard closer to the rail. For 3/8ths races at the same track, a dog negotiates three sets of bends instead of two, so it must cover 9.42 more yards for every yard out from the rail.
1 yard = 6.28 yards
2 yards = 12.56 yards
3 yards = 18.84 yards
4 yards = 25.12 yards
5 yards = 31.40 yards
6 yards = 37.68 yards
Multiply these figures by 1.5 to get the distances for a 3/8ths race.
Of course, these numbers don't take into account the conditions of the track. A dead rail can make a wider route the fastest way around, but imagine the handicap for wide runners where the inside is the place to be.
Lastly, these figures are for Lincoln. Distances at a tight track like Palm Beach will be slightly smaller, and for bigger tracks like Southland, a little higher.
My last taste of Pi in a formal math class was in 1972, so I needed a little review. The formula for measuring the circumference of a circle is c = 3.1415 x d, where d is the diameter of the circle. Using Lincoln's 110 foot radius as an example, the circle formed by the two turns equals a diameter of 73.3333 yards for a circumference of 230.3765 yards. By adding one yard of radius, and therefore two yards of diameter, we can calculate how many extra yards a dog traverses in a race for every yard it runs from the rail:
1 yard = 236.6595
2 yards = 242.9425
3 yards = 249.2255
4 yards = 255.5085
5 yards = 261.7915
6 yards = 268.0745
In other words, for every yard that a dog runs wide, it has to cover 6.28 more yards than the dog one yard closer to the rail. For 3/8ths races at the same track, a dog negotiates three sets of bends instead of two, so it must cover 9.42 more yards for every yard out from the rail.
1 yard = 6.28 yards
2 yards = 12.56 yards
3 yards = 18.84 yards
4 yards = 25.12 yards
5 yards = 31.40 yards
6 yards = 37.68 yards
Multiply these figures by 1.5 to get the distances for a 3/8ths race.
Of course, these numbers don't take into account the conditions of the track. A dead rail can make a wider route the fastest way around, but imagine the handicap for wide runners where the inside is the place to be.
Lastly, these figures are for Lincoln. Distances at a tight track like Palm Beach will be slightly smaller, and for bigger tracks like Southland, a little higher.
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