Age grading interpolation
Some of the factors for age-grading are interpolated, namely:
– the Serpentine Handicap (6975 metres)
– 20 miles
– 40 kilometres
There’s also an option (here) to calculate your age graded time based on any arbitrary distance, which also requires interpolation.
In the past, I’ve used linear interpolation. This basically draws a straight line between the observation before and observation afterwards:
IT = LT + (((ID – LD) / (HD – LD)) * (HT – LT))
IT = Interpolated time; LT = Lower Time; HT = Higher Time
ID = Interpolated Distance; LD = Lower Distance; HD = Higher Distance
But I’ve realised that isn’t very sensible when we have a better model, namely the Riegel Formula.
The Riegel Formula is HT = LT * (HD / LD)^n (where n is approximately 1.06)
I have adapted this to do non-linear interpolations of the age-grading formula. The formula calculates n by comparing the times above and below.
Rewriting the equation above:
n = (ln HT – ln LT)/(ln HD – ln LD)
Then we can use that n to calculate the intermediate time.
Non linear interpolation
Working from the lower bound:
IT = LT x (ID/LD)^((ln HT – ln LT)/(ln HD – ln LD))
or, working from the higher bound:
IT = HT / (HD/ID)^((ln HT – ln LT)/(ln HD – ln LD))