jurgen
Daily Rider
The GPS determines its location from the time it takes a signal from at least four different satellites to reach it. Technically, three satellites would do but the fourth signal is needed to synchronize the clock of the GPS with those onboard the satellites.
GPS locations are accurate within 30 ft or lower, sometimes less than 10 ft. The calculations have a certain error, i.e. the calculated location lies anywhere within a given radius around the true location. Let's assume this error is truly random.
The GPS updates its location at certain time intervals, let's say every second.
Let's assume that we are riding exactly on a straight line.
The first location is called point A. A lies on the line, but due to the error, it is 10 ft behind the motorcycle. The next point, B, is fixed one second later and its location is right on the line, but 5 ft ahead of the bike.
Let's say the bike travels at 60 mph or 88 feet per second (60 x 5280 / 3600)
The distance A-B would be 88 ft plus 10 ft plus 5 ft = 103 due to the GPS errors. Therefore, the GPS calculated a speed of 70.2 mph. That's how those crazy "Max Speed" readings get computed.
Say, after the next second, the GPS calculates Point C as lying on the straight line, but 10 ft behind the bike. Therefore, between B and C, the GPS calculates 88 ft + 5 ft - 10 ft. 83 ft convert to a speed of 56.6 miles calculated by the GPS. However, if I went back to calculate the speed based on the distance between points A and C, I would get 176 ft + 10 - 10 = 176 ft in two seconds or exactly 60 mph.
You can play this game with different time intervals but as long as the location errors are truly random, the speed will average out to be exact, and the distance travel will also be exact. The error becomes smaller if the distance between points gets longer, and the GPS may have a "smoothing" function that averages the indicated speed over several location points. If you own a Garmin, you can look at the speeds calculated between each pair of points along the tracked line of travel if you download the GPS information to Mapsource.
There are only two small problem causing systematic errors:
First, our assumption that the calculated locations lie exactly on the line of travel is not correct. In reality, nearly all of the calculated points lie to either side of the line. Therefore, if one would connect the calculated dots it would look like a zigzag line crisscrossing the path of travel. So, what the GPS calculates is the distance along the zigs and zags, i.e. between points NEAR the path of travel. These distances are always slightly longer than the true (straight) line. If the GPS location is 10 ft off to the side on a 100-ft segment (the following point being right on the line), the line between the GPS points will be 0.5 ft longer (SQRT (100^2 + 10^2) = 100.5). These errors to the sides will not be compensated over time, leading to a slightly faster speed indicated by the GPS. This error is less than 1% in most cases. This error gets smaller, the longer the distances are between points calculated.
Second, if the bike travels through a curve, the path of travel along the curve is longer than the straight lines connecting the locations that the GPS calculates. Due to this error, the GPS will read slightly lower than the true speed. Again, without going through the geometry, this error is negligably small. It gets smaller, the more readings the GPS calculates.
To make it even more complicated, a motorcycle cannot travel along a straight line because it has to be balanced with slight left-and-right movements of the handlebars. So, one might ask, which is the true speed - that of the front wheel following these oscillations or that of the rear wheel (making similar, but much smaller oscillations) or the speed of the center of gravity of the bike and rider? This gets a bit academic...
So, for most of us, the speed indicated by the GPS is dead on - it's probably the best speed indicator one can build.
If you are passing a radar speed indicator you will find that, in most cases, your GPS is spot on. If there is a significant difference (more that 1 mph) my bet would be that the radar gun is out of calibration. I was traveling on I80 in Wyoming, following a truck and had my cruise control set at 83 mph as indicated by the GPS. I got a ticket for going 83.
Regarding the speedo discussion, German law requires that a speedo may not read below true speed but is allowed to read up to 7% high to compensate for tire wear (I'm sure the US and other countries have similar rules). New tires can have 2-3% higher circumference than worn tires, and +-3% is probable the mechanical accuracy to which a mass-produced speedo can be engineered and built. So, the manufacturer aims at 3.5% high with tire wear at mid-level, and with new tires, the indicated speed will still be within the allowable tolerances.
GPS locations are accurate within 30 ft or lower, sometimes less than 10 ft. The calculations have a certain error, i.e. the calculated location lies anywhere within a given radius around the true location. Let's assume this error is truly random.
The GPS updates its location at certain time intervals, let's say every second.
Let's assume that we are riding exactly on a straight line.
The first location is called point A. A lies on the line, but due to the error, it is 10 ft behind the motorcycle. The next point, B, is fixed one second later and its location is right on the line, but 5 ft ahead of the bike.
Let's say the bike travels at 60 mph or 88 feet per second (60 x 5280 / 3600)
The distance A-B would be 88 ft plus 10 ft plus 5 ft = 103 due to the GPS errors. Therefore, the GPS calculated a speed of 70.2 mph. That's how those crazy "Max Speed" readings get computed.
Say, after the next second, the GPS calculates Point C as lying on the straight line, but 10 ft behind the bike. Therefore, between B and C, the GPS calculates 88 ft + 5 ft - 10 ft. 83 ft convert to a speed of 56.6 miles calculated by the GPS. However, if I went back to calculate the speed based on the distance between points A and C, I would get 176 ft + 10 - 10 = 176 ft in two seconds or exactly 60 mph.
You can play this game with different time intervals but as long as the location errors are truly random, the speed will average out to be exact, and the distance travel will also be exact. The error becomes smaller if the distance between points gets longer, and the GPS may have a "smoothing" function that averages the indicated speed over several location points. If you own a Garmin, you can look at the speeds calculated between each pair of points along the tracked line of travel if you download the GPS information to Mapsource.
There are only two small problem causing systematic errors:
First, our assumption that the calculated locations lie exactly on the line of travel is not correct. In reality, nearly all of the calculated points lie to either side of the line. Therefore, if one would connect the calculated dots it would look like a zigzag line crisscrossing the path of travel. So, what the GPS calculates is the distance along the zigs and zags, i.e. between points NEAR the path of travel. These distances are always slightly longer than the true (straight) line. If the GPS location is 10 ft off to the side on a 100-ft segment (the following point being right on the line), the line between the GPS points will be 0.5 ft longer (SQRT (100^2 + 10^2) = 100.5). These errors to the sides will not be compensated over time, leading to a slightly faster speed indicated by the GPS. This error is less than 1% in most cases. This error gets smaller, the longer the distances are between points calculated.
Second, if the bike travels through a curve, the path of travel along the curve is longer than the straight lines connecting the locations that the GPS calculates. Due to this error, the GPS will read slightly lower than the true speed. Again, without going through the geometry, this error is negligably small. It gets smaller, the more readings the GPS calculates.
To make it even more complicated, a motorcycle cannot travel along a straight line because it has to be balanced with slight left-and-right movements of the handlebars. So, one might ask, which is the true speed - that of the front wheel following these oscillations or that of the rear wheel (making similar, but much smaller oscillations) or the speed of the center of gravity of the bike and rider? This gets a bit academic...
So, for most of us, the speed indicated by the GPS is dead on - it's probably the best speed indicator one can build.
If you are passing a radar speed indicator you will find that, in most cases, your GPS is spot on. If there is a significant difference (more that 1 mph) my bet would be that the radar gun is out of calibration. I was traveling on I80 in Wyoming, following a truck and had my cruise control set at 83 mph as indicated by the GPS. I got a ticket for going 83.
Regarding the speedo discussion, German law requires that a speedo may not read below true speed but is allowed to read up to 7% high to compensate for tire wear (I'm sure the US and other countries have similar rules). New tires can have 2-3% higher circumference than worn tires, and +-3% is probable the mechanical accuracy to which a mass-produced speedo can be engineered and built. So, the manufacturer aims at 3.5% high with tire wear at mid-level, and with new tires, the indicated speed will still be within the allowable tolerances.
