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Why synced clocks aren't as important as you think they are

If you hang around registration at a rally, you'll see the codrivers anxiously looking for where the official time is. Then, they'll spend quite a lot effort to make sure their watch is exactly synchronized to the official time. Stick around a little longer, and you'll witness one of the volunteers carefully making sure all the clocks used for official time are ticking perfectly in beat with each other.

But really... neither of these matter.

Part 1
Let's look at the first instance, the racer's watch. Within a second or so is close enough, and even less accuracy is needed if you can just remember which way it's off. The only time you really use it is checking in to a control. And for any check in, you can always ask to see what the official clock being used says. So if in the only situations you need the official time, official time is provided to you... your own copy of official time doesn't need to be very precise.

Where else does a racer use their own copy of official time? Counting down how much time is left in service. Within five seconds is fine here. New racers will often record their stage times. Old timer racers will too, but the old timers know that as far as anything official, like protesting an inaccurate stage time, the "well, MY clock said..." isn't given anything more than "oh, that's interesting" weight when considering the results. That's because, well, then next part.

Part 2
The official clocks. Let's start with a couple of facts:

  • The clocks are never perfectly synced.
  • They start drifting apart as soon as you sync them.

    What does this mean, exactly? Well, there are a variety of methods of synchronizing clocks. The critical thing to realize is that they all just sync to within some range of the reference time. That range might be very small, like three milliseconds. TimeWise clocks are supposed to be able to manage three milliseconds. This means that, if the reference time happens to be 0.000 seconds, one clock might be at 0.001 seconds, another might be 0.003, and another might be at 0.000. The real point is that if you look at anything close enough, they're not EXACTLY synced. One sync method might get you to within 3mS, another might be within 100ms.

    Now, what about the drift? Any clock will have some drift, where after a day, or a year, it's not exactly right anymore. Rally clocks are no exception. It's typical to get 0.5 to 1 second drift over 36 hours, which is a usable measure of time. Usually the clocks are synced sometime the day before the rally, handed out to the volunteers, and then used the next day. So by the end of the rally, they've been going in their own direction for 36 hours, or maybe 60 for a two day rally. Keep in mind that two clocks might go in two different directions. One could drift a second forward, on could drift a second backward.. OMG THIS COULD CHANGE YOUR STAGE TIME BY TWO SECONDS!

    Now, let's get down to why this doesn't matter. It's important to begin with a statement of "What are we trying to do here?" The whole purpose of a rally race is to figure out who, at this event, with the machinery they have, is the fastest. Keep that in mind as we work through some examples.

    Let's imagine a 10 mile stage. Racer A averages 60 mph, and so completes it in 10 minutes and zero seconds. Racer B is a little faster, he averages 61 mph, so he completes the stage in 9 minutes, 50 seconds. All on perfect clocks. So B beat A by 10 seconds.

    Ok, now let's have that clock drift. Let's say the start is early, and the finish is late. both by a second. Racer A would have a recorded time of 10 minutes and 2 seconds. Racer B would get 9 minutes and 52 seconds. Racer B still wins by the exact same amount!

    And so we have arrived at the idea that "it doesn't matter if the clock is off, because it's off for everybody" and this is very true. Clocks that are off won't affect the prime objective of the rally, which is determining a winner.

    Now the astute reader will recognize that the clock is actively drifting, which means that the drift amount won't be the same for Car 1 as it is for Car 60. That's true. Let's take a look. If a clock can drift a second per day, then the difference might be, over the course of an hour, 1/24th of a second, or 41 milliseconds, or 4 hundredths of a second. At least in the US, where even tenths of a second have, over a decade, never actually affected who the winner of the rally was, 4 hundredths are meaningless. However, a little more thought has to go into this: Car 1 isn't racing Car 60. Car 1 is racing Cars 2 through 10.

    How much would a clock have to drift before it became an issue? A racer is usually only in competition with other racers within 10 cars before or after them. Statistically tenths of a second have been mathematically shown to not make a difference to the outcome. Thus we can safely rack up at least a tenth, probably more, without making what we're trying to do (see who's fastest) any more difficult. A tenth of a second every 10 minutes is six tenths an hour, or 21.6 seconds over 36 hours. And since you need to share that across two clocks, you would want each clock to maintain 10.8 seconds over 36 hours.

    That, remember, is only to satisfy the proven "tenths don't matter" tenet. The math hasn't been done on "half seconds don't matter", but if that were true, then the 10.8 seconds allowable drift would be five times larger, nearly a minute of drift each day.

    And it turns out that pretty much any digital clock can manage ten times better than 10.8 seconds over 36 hours.