The goal of Classic ARDF is to find all the transmitters required for your age/gender category in the least-possible amount of time. Period. Full stop. End of story. If you can accomplish that feat, then you should always be pleased with your performance: only your physical limitations kept you from doing better, so you need only improve your strength and endurance.
But with five transmitters to locate, there are 120 (5!) fox-order permutations you can take on your journey from Start to Finish. Choosing which of those 120 routes to follow is key to minimizing your time.
It is tempting to assume that the route with the shortest total length will result in the shortest-possible time. But that is true only if you can run at maximum speed regardless of gradient and obstacles, and can locate transmitters with equal ease whether they are on the air, or silent. So there are at least three factors that contribute to your total time:
o Total route length (shortest is best)
o Ease of traversal (easiest running is best)
o Timing of arrival (arriving to within “striking distance” of each transmitter when it just starts its 1-minute transmit period is best)
The first two factors (total route length, and ease of traversal) are readily understood, though not always easy to gauge using just map and signal readings. The third factor (timing of arrival) is less obvious, and often overlooked in the calculation of best-possible route, but no less important when performing route-choice calculations.
To illustrate the role of timing of arrival, it can be helpful to imagine the case where total route length, and ease of traversal, play no part. Consider a perfectly flat landscape with no obstacles to avoid. Now pretend that you are the “Usain Bolt of ARDF”, and can cover the distance between any two points on the course in two minutes or less (roughly two transmit periods for a fox). Even Usain can’t do that? Then make yourself the Roman god Mercury instead.
Since all routes are equally runnable, and you can arrive at any two points in a 2-minute time interval, your only concern is to have the transmitter you are chasing be on the air at the moment you find it. You are a Roman god, but that only makes you fast, not omniscient – so the transmitter must be on-the-air in order to “sniff it out”, unless you are simply lucky and find its flag off cycle. Lucky is good too, of course, but harder to perfect.
Like all your competitors, you start the course from the Start when Fox #1 begins its transmit cycle. Feeling fresh, and with your lightning speed, you traverse the distance from Start to Fox #1, finding it in the middle of its second transmit period at minute 6, 5.5 minutes into the competition. With the bearings and signal strength readings you took during the first 5-minute transmit cycle, you have a good estimate of the approximate locations of all four remaining foxes; accurate enough that you can identify locations that would place you within a 1-minute sprint of each one.
So the question is: in what order should you attempt to find the remaining foxes? There are 24 possible permutations. Let’s examine two of them.
You’ve got 30 seconds before Fox #2 begins to transmit, so let’s examine the choice where you take it next. You head in the direction of Fox #2 and travel in that direction for 30 seconds before it begins to transmit. You use its signal to guide you as you run, but one minute later you arrive within final sprinting range of Fox #2 just as it goes off the air. Now you must wait four minutes for Fox #2 to come on the air again so you can sniff to its exact location. Suppose you find Fox #2 the next time it transmits during minute 12, at 11.5 minutes into the competition. Following the same strategy you select Fox #3 next, and with similar results you locate Fox #3 at 17.5 minutes. Fox #4 then is found at 23.5 minutes, and Fox #5 at 29.5 minutes. After a 1-minute dash to the finish your total time is 30.5 minutes. That’s good enough to beat most mere mortals, but could you have done better?
Let’s look at another route order. Suppose standing at Fox #1 at minute 6, you had instead decided to head toward Fox #3. You would have traveled for 90 seconds before Fox #3 began its second transmission at minute 8 into the competition. You would be assured of arriving to within sprinting distance of Fox #3 after traveling 120 seconds, and you still would have 30 seconds of transmit time before Fox #3 goes off the air. Chances are good (at least 50:50) that you will find Fox #3 before the end of minute 8. Suppose that you succeed, and then choose Fox #2 for your subsequent destination. You will start to travel from Fox #3 toward Fox #2 at the start of minute 9, and arrive within sprinting distance of Fox #2 by the start of minute 11, about one minute before Fox #2 comes on the air. After waiting one minute you then will locate Fox #2 during minute 12. Then you will choose Fox #5, which you are likely to take during minute 15. Then you’ll find Fox #4 at minute 19. Even if it takes you 2 minutes to dash to the Finish from Fox #4 your total time is about 20.5 minutes. By choosing more optimum timings of arrival, you succeeded in shaving 10 minutes from your time. Good enough to beat all but Neptunus Equester.
The example above illustrates the benefits of factoring in transmit timing to determine an optimum time of arrival. Minutes can be saved when choosing the route with the best timing advantage, from two or more routes that are otherwise similar in length and difficulty.