Azero score at a checkpoint! This is what a Time Speed Distance (TSD) car rally team works for. Like golf, the lowest score wins. Thus the teams, each consisting of a driver and a navigator, will use all legal means to achieve the elusive "zero-hero" status.
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The basic equation for determining distance, D = Time X Velocity, is also the primary formula for achieving the TSD rally's ideal, or perfect, time. This article describes efforts to develop a GPS-based system for measuring elapsed distances traveled by a TSD rally competitor.
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TSD Rally Overview
A TSD rally is a driving competition held on public roads that challenges the teams to stay on course and on time by following route instructions given out by the rally organizer or rallymaster. These instructions may consist of an explicit command, such as Right on side road (Grass Lake). In other cases the rally team will need to follow an underlying principle, such as: Proceed as straight as possible, if a route instruction cannot be executed. Such underlying principles are also known as primary course-following rules. An important objective of a rally is simply staying on the prescribed course.
An equally important objective is maintaining assigned average speeds over the route. These speed assignments are known as CASTs, an acronym for change average speed to, and each route instruction will have a CAST. So, TSD rallies are based on giving the competing teams a distance (from following the route) and a speed (from the CAST) that will, if followed precisely, result in a team matching the rallymaster's ideal time along the entire route.
A final note: rally workers are positioned along the rally route to check whether the teams are matching the rallymaster's ideal time. These locations are known as checkpoints, and competitors rarely know these checkpoints' locations in advance. The rally workers, using highly accurate timing devices synchronized with the rallymaster's official clock and pneumatic hoses used to trigger the timing device, measure a team's arrival at the various checkpoints.
Each team is assigned a starting time at the beginning of the rally. At each checkpoint the team's start time--and, thus elapsed time spent in this section of the course--can be computed. Each section of the rally so timed is known as a leg, and this interval performance is figured into the team's overall score. After each checkpoint a team will be assigned a new starting time for the next leg.
As all teams are competing on the same course, the checkpoint workers must stage the start of the subsequent leg in one-minute intervals for each team. But, once again, the team has no idea where the next checkpoint will be located along the course. Thus, to successfully compete, a rally team must drive the course to be on time, all the time.
Let's demonstrate the concept of a TSD rally leg with an example as shown in Figure 1. Assuming the rallymaster routed Team A to arrive at the T intersection on the left of Figure 1, the Numbered Route Instructions (NRI) given to the team for this section of the course are shown in Table 1.
Not shown in the route instructions, of course, is that the team won't get to execute NRI 4 before being stopped by the workers at the checkpoint at mileage 2.797. The rally team will receive the precise time of day that they tripped the workers' clock and will be given a new starting time for the next instruction to be followed from the NRIs. They typically will have two to three minutes to prepare for the next leg. So, what is the perfect time for Team A, assigned to leave the stop sign at NRI 1 at exactly 12:01:00, to arrive at the checkpoint? Divide the distance of each NRI segment by the CAST (in miles per hour) assigned to that segment (first multiplying the segment distance by 60 to convert the resulting value to minutes). Then simply add up the segment times to get the total time for this leg. (In most rallies time is measured in minutes and fractions of a minute and not minutes and seconds.)
Using a variant of the TSD formula, DISTANCE-miles X 60 / SPEED-mph = TIME-minutes, we obtain the results shown in Equation 1:
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Note that the CAST did not change at NRI 3 and, thus, the CAST in effect (27) was used both in the second and third fraction.
In order to match the rallymaster's perfect time, rally teams use clocks that display fractions of minutes and not seconds, which will be the format for times shown in this article. Also, the perfect time will usually be truncated to 100ths of a minute, or two places, and these fractions of minutes are known as cents. TSD rally scores represent the deviation in cents from a perfect time. So, for our example, team A's car arriving at the checkpoint at 12:06.72 would score a 0.
A TSD rally is not a race and arriving early is as "bad" as arriving late. For example, if a team arrives 2 hundredths of a minute early (12:06.70), then it receives a score of 2; if 33 hundredths of a minute late (12:07.05), a score of 33. A team cannot make up arriving late at a checkpoint by arriving early at the next, as each leg is scored independently. A rally consists of many legs, and the winner will be the team with the lowest cumulative score over all legs.
Measuring the Distance
The basic idea in rally computation can be stated in one of two ways: Given a starting time and the current time, at the CAST(s) assigned, have you traveled the correct distance? For example, if Team A was to start at 12:01.00 at a CAST of 32 and it is now 12:03.17 has the car traveled 1.158 miles? Or, given the mileage traveled at the CASTs assigned, does the current time match perfect time? For example, if Team A was to start at 12:01.00 at a CAST of 32 and the vehicle has traveled 1.158 miles, is the current time 12:03.17? Both these computations require that exact distance measurements are available to the rally navigator.
In calculating perfect times, the mileage is measured to thousandths of a mile. This is much more accurate than a standard automobile odometer is capable of showing--typically only displaying tenths of miles--but not actually of measuring. The rallymaster will use a precision odometer that reads out to three decimal places to obtain mileage between NRIs and then, using the same method as in the example, compute perfect time.
Most precision odometers work by using a magnet attached to an axle or wheel and a Hall effect sending unit, or transducer, which triggers upon detection of a strong magnetic field. Each turn of the tire will cause one pulse to be picked up by a computer, which will then simply add a value known as the calibration factor distance into the odometer, as seen in Figure 2. This calibration factor is based on the formula: pi X (Tire) Diameter = Circumference.
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The calibration factor is usually expressed as a fraction of a mile, the number representing how far the vehicle travels for each revolution of the tire. What is needed now is the diameter of the tire that is on the vehicle to which the precision odometer is attached. This is found using the formula:
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For a vehicle equipped with tires having a specification of P205/70R15 the formula yields 26.299 inches for the tire's diameter and hence a circumference of 6.8851 feet. Thus, each pulse resulting from the wheel rolling along the road means the vehicle will have traveled 6.8851/5280 or .00130399 miles. This will be the calibration factor used for the precision odometer. Note that this is a theoretical value that won't exactly match the rallymaster's mileages and must be adjusted. All rallies allow for this adjustment in a segment of the rally known as the odometer calibration run to reflect real world conditions, such as tire load, tire inflation and road conditions.
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In the 1980s, several hardware manufacturers--including Alfa, Terratrip, Zeron and Timewise--integrated precision odometers with a device to compute whether a TSD team was on time given the target CASTs. Some of these units are still manufactured and can cost up to $1,000.
The GPS Alternative
John Fishbeck had competed in rallies in the 1960s when all that was available were mechanical calculators, such as a slide rule, along with paper and pencil, to compute in real time how close the driver was to maintaining perfect time. Now in the 21st century, having both a laptop computer and affordable portable GPS receivers available, he decided to develop a custom software-based rally computer, the SWRallyComp.
