By Christopher Cole
I’ve noticed that a lot of races recently seem to be using Time on Time (ToT) instead of Time on Distance (ToD) to correct time. I have a problem with that. ToT greatly favors the boats with higher PHRF ratings in every condition.
In a fairly average race in average conditions that went a very typical eleven miles in a quite common two and a half hours, we recently beat the second place boat by over ten minutes on actual elapsed time (00:10:28). Using the standard ToD formula, we would have won by 00:02:24 on corrected time. Under the ToT rule, however, in average conditions, we gave up another two minutes (00:10:04 total) and won by a mere 24 seconds!
I would think that in average conditions, a boat’s standard PHRF would be as close to fair as possible. But that is not the case. In fact, every commonly used “B factor” gives a significant advantage to boats with a higher PHRF!!
In light air under the ToT rule, with a B factor of 600, we would have gained only about half a minute and would have beaten the second place boat by about only one minute! And that’s in conditions that greatly favor the smaller boats!
Again, under ToD, we would have won by about two and a half minutes, light air or not!
The ToT formula is supposedly based on the assumption that smaller boats will do less well the more time that a race takes. But races often last a long time simply because the wind is light, and that favors the small boats, which accelerate more easily in puffs. Meanwhile, as the smaller boats slowly pull ahead, the larger boats can only sit and watch and roll about, their advantage of potential hull speed rendered meaningless.
In heavy air with a B factor of 480, the smaller boat would have beaten us by about a minute despite our having finished 00:10:28 ahead. We essentially would have given them well over a minute per mile rather than 43 seconds that derives from the straight PHRF numbers.
In addition, many large, heavy boats have high PHRF
numbers because of their performance in light and average conditions, but they excel in heavy air. PHRF numbers already give many of these boats large time allowances, and the ToT formula only adds to that advantage in heavy air, when their long waterlines give them more potential speed and their displacement helps them power through chop.
ToT seems just a clever way for race organizers with slower boats to cheat the PHRF system! In the example below, taken from the aforementioned recent race, I call my boat Boat Alpha and the second place boat Boat Beta.
Time on Distance (TOD)
Boat Alpha PHRF rating: 105
Boat Beta PHRF rating: 148
The difference is 43, meaning 43 seconds per mile, so for an 11 mile race, Boat Alpha would owe Boat Beta 43×11=484 seconds, or 00:08:04 Using the standard ToD formula, then, Boat Alpha would have beaten Boat Beta by 00:02:24 on corrected time.
Time on Time (TOT)
Corrected time = Elapsed time X 650/(B + PHRF)
Commonly used “B Factors”
The formula is easier to solve if we set it up to give a Time Correction Factor (TCF) thus:
TCF = 650 / (B + PHRF)
Given average conditions, the formula would look like this:
TCF = 650 / (550 + PHRF)
The denominator, B + PHRF, is the number of seconds it takes to sail a nautical mile in the expected conditions. That is, 3600 divided by the denominator is the average boat speed in knots in those conditions (about 5.5 knots for Boat Alpha in average winds). To get the corrected time, simply multiply the elapsed time by the TCF. Boat Alpha elapsed time: 0:02:32:55 corrects to 0:02:31:45 TCF = 650/(550+105) = 0.9923664122137405 (rounded up to 0.9924)
Boat Beta elapsed time 0:02:43:23 corrects to 0:02:32:09
TCF=650/(550+148) = 0.9312320916905444 (rounded down to 0.9312) Boat Alpha elapsed time: 0:02:32:55 corrects to 0:02:31:45. Boat Beta elapsed time 0:02:43:23 corrects to 0:02:32:09.
Based on the ToT formula, Boat Alpha owed Boat Beta 00:10:04 – a whole 2 minutes more that under the ToD rule. So under ToT, Boat Alpha gave up almost a minute per mile and won by a mere 24 seconds – in average conditions!
Oh, I should have mentioned that boat Beta beats us more often than not, even under the ToD rule! Something is amiss.
Christopher Cole is a teacher in the Connecticut Technical High School System, the guitarist and vocalist for The Lone Wolf Trio, and the U.S. rep For Loong Sails. He sails his Tripp 37 Ticker out of New London, CT and is a member of the Mudheads and Thames Yacht Club.