Cycle computers - what do they measure?

Tank-slapper

My cycle computer is a Garmin Edge 500. To measure distance and speed, it counts wheel rotations using a magnet attached to a spoke (like most computers). Distance is calculated as:

number of rotations x wheel circumference = distance.

However, wheel circumference varies depending on wheel diameter, tyre size, tyre pressure, weight carried on the bike, etc. In the past, I always measured the actual circumference of the wheel and entered it into the computer in the belief that this was more accurate. Measuring is done by putting a chalk mark on the ground, moving the bike forwards 1 wheel rotation, putting another mark on the ground and measuring the distance between the marks. Traditionally, I have done this with an unweighted bike. But then I had a thought - when out riding, the bike is weighted and the wheel circumference is smaller - so does that make the distance shown on my computer wrong? Should I do the measurement with the bike weighted? And how much difference does tyre pressure make?

So, this morning I had some spare time and did some measurements of the circumference of my wheel. It is an Olympic 26" rim with a Nobby Nic 2.25" tyre. Here are the results:

Unweighted = 210cm

Weighted 25psi = 205cm
Weighted 30psi = 206cm
Weighted 35psi = 207cm

OK the difference is not huge, but it does work out at about 2%, or 20m per kilometre, or for every 50km ridden you get a freebie kilometre.

Is this something worth worrying about? Or should I get out on the bike more?

cooldad

I would get out more. It's a mountain bike.
Is it important?

pugaltitude

Got to agree with cooldad.
My mate and I have the same type of speedo from tesco, same tyre size so computer is programmed to the same setting and mine is about 1 mile in distance out compared to his.
I just use it for approx readings
The instructions in the packet is all I use to set the computer.

cee

cooldad wrote:

I would get out more. It's a mountain bike.
Is it important?

this.

and......

it would probably be different over quite a number of wheel rotations on uneven ground. the tyre will change shape as you cross rocks, roots and even bumps, so your precision goes right out the window.

It only needs to be precise enough as a rough guide to your perfromance.

until you are trying to get the very last drip of perfromance out of your body or the bike....it will be plenty accurate enough to not need to worry about it.

theres a big difference between technically correct and pragmatic.

nicklouse

but as the front wheel travel further than the rear, and that is the one that is doing the work does it matter?

Anonymous

All speedometers have accuracy issues. Including those on cars. They're not a scientific instrument.

rhext

I thought all Garmins used GPS to work out speed/distance. Mine doesn't have any magnets, but I was always under the impression that those which do, have them only to use as backup for when they can't lock onto the satellites!

Anonymous

rhext wrote:

I thought all Garmins used GPS to work out speed/distance. Mine doesn't have any magnets, but I was always under the impression that those which do, have them only to use as backup for when they can't lock onto the satellites!

GPS has a 10-metre tolerance. Best using wheel sensors for low-speed vehicles.

rhext

yeehaamcgee wrote:

rhext wrote:

I thought all Garmins used GPS to work out speed/distance. Mine doesn't have any magnets, but I was always under the impression that those which do, have them only to use as backup for when they can't lock onto the satellites!

GPS has a 10-metre tolerance. Best using wheel sensors for low-speed vehicles.

That would be true if you were looking at instantaneous measurements. The computers have integration algorithms which smooth out noise in instantaneous measurements of position: the end result is pretty accurate measurement of distance covered, while speed measurement is a little sluggish to react to acceleration and deceleration, but is pretty accurate otherwise.

Anonymous

rhext wrote:

yeehaamcgee wrote:

rhext wrote:

I thought all Garmins used GPS to work out speed/distance. Mine doesn't have any magnets, but I was always under the impression that those which do, have them only to use as backup for when they can't lock onto the satellites!

GPS has a 10-metre tolerance. Best using wheel sensors for low-speed vehicles.

That would be true if you were looking at instantaneous measurements. The computers have integration algorithms which smooth out noise in instantaneous measurements of position: the end result is pretty accurate measurement of distance covered, while speed measurement is a little sluggish to react to acceleration and deceleration, but is pretty accurate otherwise.

Bang on. "pretty accurate". Which is what wheel sensors give us.

rhext

yeehaamcgee wrote:

rhext wrote:

yeehaamcgee wrote:

rhext wrote:

I thought all Garmins used GPS to work out speed/distance. Mine doesn't have any magnets, but I was always under the impression that those which do, have them only to use as backup for when they can't lock onto the satellites!

GPS has a 10-metre tolerance. Best using wheel sensors for low-speed vehicles.

That would be true if you were looking at instantaneous measurements. The computers have integration algorithms which smooth out noise in instantaneous measurements of position: the end result is pretty accurate measurement of distance covered, while speed measurement is a little sluggish to react to acceleration and deceleration, but is pretty accurate otherwise.

Bang on. "pretty accurate". Which is what wheel sensors give us.

Perhaps depends on how sensitive you are to 'the truth'. Over 10 miles, the GPS will show variance of less than 1/100th of a mile, regardless of what bike you're on. As observed above, your wheel sensors will give you more variance than that if you've got a few less PSI in your tyre than usual.....

rhext

...anyway. That's perhaps not the point. The point is that they're pretty accurate at the basic measurements, and you don't need to faff around with magnets or worrying about how big your tyres are. Just turn them on and go.

Anonymous

rhext wrote:

Perhaps depends on how sensitive you are to 'the truth'.

That's funny
I have no idea what the hell you mean by it, but it's a hysterical turn of phrase.

No, GPS will not be that accurate. I you were taking one datum point, and then measuring another single point a hundred miles away then, yeah, great.
That's not how it works though. Every direction change, every velocity change, each measurement, is subject to a degree of accuracy.
Basically you'll get around the same accuracy as a wheel sensor.

rhext

yeehaamcgee wrote:

rhext wrote:

Perhaps depends on how sensitive you are to 'the truth'.

That's funny
I have no idea what the hell you mean by it, but it's a hysterical turn of phrase.

No, GPS will not be that accurate. I you were taking one datum point, and then measuring another single point a hundred miles away then, yeah, great.
That's not how it works though. Every direction change, every velocity change, each measurement, is subject to a degree of accuracy.
Basically you'll get around the same accuracy as a wheel sensor.

That's true to a degree, but at least as far as distance is concerned, the noisy measurements cancel each other out. I ride the same route in to work every day. GPS logs the distance to 1/100th of a mile. Every day the measurement is exactly the same, no matter how fast/slow, what the headwind is, what bike I use. It's sensitive enough to pick up minor variations in route (so if I divert 20m to go see if the gate on the short-cut is locked), it'll show that and show it consistently. Your point about 'very accurate over 100 miles' is correct...but you get that degree of accuracy whether you make two point measurements or whether you track continuously over the course of the journey between them.

Anonymous

rhext wrote:

but you get that degree of accuracy whether you make two point measurements or whether you track continuously over the course of the journey between them.

Bullcrap.
I'll believe that when I see it. I've been through several GPS and Sat-Nav devices and have never seen anything approaching that accuracy.
Anyway, like I said, the slower you're going, the less accurate GPS meters become, because of their inherent accuracy limit.
The faster you're going, or the further you're going, the bigger the changes between measurements are compared to the inherent errors. It's basically increasing the signal to noise ratio of the system.

There is absolutely no way in hell that you are covering exactly the same distance to 100th of a mile on a daily ride. Slight deviations in course all add up.
The only way I can imagine a device getting the same results consistently is if it has on-board mapping, and uses the map plot to calculate the distance between two points (your home and work)

rhext

yeehaamcgee wrote:

rhext wrote:

but you get that degree of accuracy whether you make two point measurements or whether you track continuously over the course of the journey between them.

Bullcrap.
I'll believe that when I see it. I've been through several GPS and Sat-Nav devices and have never seen anything approaching that accuracy.
Anyway, like I said, the slower you're going, the less accurate GPS meters become, because of their inherent accuracy limit.
The faster you're going, or the further you're going, the bigger the changes between measurements are compared to the inherent errors. It's basically increasing the signal to noise ratio of the system.

There is absolutely no way in hell that you are covering exactly the same distance to 100th of a mile on a daily ride. Slight deviations in course all add up.
The only way I can imagine a device getting the same results consistently is if it has on-board mapping, and uses the map plot to calculate the distance between two points (your home and work)

The point is that slight deviations do not add up, they cancel out. And i'm not making it up: if I cycle the same route I get the same mileage measurement. I have three years worth of data logged. I do have a few different route variants I do regularly, and I can tell exactly which variant I've done simply by looking at the last couple of digits of the total. It really is that consistent. It's a simple Edge 205 unit, no on-board mapping at all.

Incidentally, I spent some of my formative years working on pulse radars: they suffer the same 'problem' as GPS units, in that individual measurements are pretty inaccurate. Add lots of measurements together and average them out though (as a GPS unit will do), and they can be quite spectacularly accurate.

rhext

yeehaamcgee wrote:

rhext wrote:

but you get that degree of accuracy whether you make two point measurements or whether you track continuously over the course of the journey between them.

Bullcrap.
I'll believe that when I see it. I've been through several GPS and Sat-Nav devices and have never seen anything approaching that accuracy.
Anyway, like I said, the slower you're going, the less accurate GPS meters become, because of their inherent accuracy limit.
The faster you're going, or the further you're going, the bigger the changes between measurements are compared to the inherent errors. It's basically increasing the signal to noise ratio of the system.

There is absolutely no way in hell that you are covering exactly the same distance to 100th of a mile on a daily ride. Slight deviations in course all add up.
The only way I can imagine a device getting the same results consistently is if it has on-board mapping, and uses the map plot to calculate the distance between two points (your home and work)

The point is that slight deviations do not add up, they cancel out. And i'm not making it up: if I cycle the same route I get the same mileage measurement. I have three years worth of data logged. I do have a few different route variants I do regularly, and I can tell exactly which variant I've done simply by looking at the last couple of digits of the total. It really is that consistent. It's a simple Edge 205 unit, no on-board mapping at all.

Incidentally, I spent some of my formative years working on pulse radars: they suffer the same 'problem' as GPS units, in that individual measurements are pretty inaccurate. Add lots of measurements together and average them out though (as a GPS unit will do), and they can be quite spectacularly accurate.

Anonymous

I'd like to see an explanation on how adding errors together can eliminate them.

rhext

Imagine throwing darts at a bullseye. If you're crap at darts (like I am) then they'll go anywhere on the board except for where I'm aiming. But if I throw 100 darts and they land randomly on the board, then the average position of my darts will start to centre very closely on the bullseye.

It's like that with a Garmin. It takes lots of measurements every second. The first measurement might be 10 meters behind the real position, the second one 3 meters in front, and 4 meters to the left, the third one 7 meters in front and 5 meters to the right. Add them all together and average them out though and the aggregate measurement can be very accurate indeed.

Anonymous

Ah. That makes sense yes.
But why do the units not update several times a second then? The polling interval seems to be about once every two seconds or so.

rhext

It's down to the integration algorithms. In order to get accurate measurements, they have to do the adding and averaging over time. If they just splurge out the raw measurements they swing about all over the place, so they have to take some time smoothing things out. Speed is particularly difficult for them because individual measurements swing about a lot. So they have to collect quite a bit of data before they can be sure that they're dealing with real position change instead of noise. If you look at a GPS while accelerating down a hill, for example, it'll be quite clear that it's lagging by a second or more. Instantaneous speed measurements are consequentially quite inaccurate (probably worse than a traditional cycle computer). But average speeds and distances can be very good indeed.

Anonymous

Fair enough.
Your example has absolutely zero bearing on any GPS device I've used though.
(and the "accuracy" figure on any of the ones I've used that actual;ly state their "accuracy" is never less than 10 meters. Garmin even state that 10 meters is the limit of accuracy on their website)

rhext

...we're in the mountain bike forum: not my normal 'commuting' stamping ground. I do the same journey every day - and I'm a sad git with an interest in physics and and almost obsessive urge to keep track of how far I cycle every year.

When I'm actually mountain biking, not only do I never do the same route twice, but I don't really care that much about how far I've travelled. Somehow it seems more important when I'm commuting, but that's probably down to the fact that when you're pounding down the same piece of tarmac every day anything which keeps you motivated is worth trying

rhext

Re the 'accuracy' statements on the devices. Standard use of GPS is to tell you your position. And in order for your position to have any meaning it has to be related to a map. I think that the 'accuracy' statements are a reflection of how accurately measured GPS position and map position can be aligned. Certainly I've been in situations in the past where, were my GPS to be believed, I'd have been driving in a river! Distance travelled measurements do not require relating to a map.

Anonymous

What? The accuracy figures are given when the device is giving your position using latitude and longitude readings. What the hell does that have to do with a map?
Map accuracy would be a figure for the maps, not GPS.

rhext

yeehaamcgee wrote:

What? The accuracy figures are given when the device is giving your position using latitude and longitude readings. What the hell does that have to do with a map?
Map accuracy would be a figure for the maps, not GPS.

Lat/long are map co-ordinates. I use the term 'map' in the context of an origin and co-ordinate system. You don't need the origin for distance measurements.

Anonymous

rhext wrote:

yeehaamcgee wrote:

What? The accuracy figures are given when the device is giving your position using latitude and longitude readings. What the hell does that have to do with a map?
Map accuracy would be a figure for the maps, not GPS.

Lat/long are map co-ordinates. I use the term 'map' in the context of an origin and co-ordinate system. You don't need the origin for distance measurements.

Excuse me?
Latitude and longitude readings are based on an imaginary grid of the globe. Maps use those to mark out where the map is relevant to.
It is THE way that location systems work. It is how location is measured.

rhext

What is a map but an imaginary grid imposed on a topography?

But it's back to the dartboard. The average distance by which each of my darts misses the centre of the dartboard could be several inches (a measurement of the accuracy of my throw). But the average position of my darts would be the bullseye (lots of positional errors all cancelling each other out).

Anyway - unfortunately I'm going to have to sign off and head for home now. So I'd like to say 'thank you' for an interesting debate! Have a great weekend!

delta5

yeehaamcgee wrote:

I'd like to see an explanation on how adding errors together can eliminate them.

Here goes: Because of the relatively low resolution of commercial GPS (as you say about 10m) it doesn't add the readings, it averages them - something like plotting a curve through a scatter graph where the plotted points represent each satellite reading. GPS therefore tends towards consistency, and (as with any data sampling process) the more points sampled (longer distance) the more reliable (accurate and consistent) the results will be.

With a magnet sensor-type speedo all the little front-wheel deviations are added to the total. Also, any variance (error factor) in the circumference setting is cumulative, and deviation from "the truth" is therefore linear or a % of distance. Magnet speedos can still be reasonably accurate though. To calibrate find an accurately measured distance of at least 1 mile (easier said than done), ride it 10 times or more, calc your average distance reading, determine the variance from the 'measured' distance, then use this to work out a correction factor for the circumference setting. Not sure I cba to do this myself though - as long as I can roughly compare one ride distance to the next I'm happy!

PS - a case of fast thread, slow fingers . . glad it's the weekend.

Anonymous

rhext wrote:

What is a map but an imaginary grid imposed on a topography?

But it's back to the dartboard. The average distance by which each of my darts misses the centre of the dartboard could be several inches (a measurement of the accuracy of my throw). But the average position of my darts would be the bullseye (lots of positional errors all cancelling each other out).

Anyway - unfortunately I'm going to have to sign off and head for home now. So I'd like to say 'thank you' for an interesting debate! Have a great weekend!

But lat/long is the very means of describing position. It has a link to cartography, but apart from that, they are the units in which location is described. It is the data that the GPS works from.
I understand the scatter graph approach, that is a good example (ignoring the fact that a person may throw all darts too low and to the left for example ), but even when taking that into account, 10m is the highest degree of accuracy that Garmin, and I am led to believe, any GPS system can deliver.

ellieb

What various people are missing out here is that the 'dartboard' is moving so that the average is not the 'bullseye', because the bullseye is moving and the inaccuracies are constantly changing.
GPS inaccuracies are caused in part by the differing positions of the satellites in relation to the unit. In some configurations, if, for example, the satellites are in a line rather than scattered around the sky then you aren't going to get a good fix. Other inaccuarcies caused by the update rates (when you turn at right angles around a corner while the GPSdraws a straight line) are never going to be picked up. GPS was designed to tell you where you are. It wasn't designed to tell you how fast you are going.
The name 'Global Positioning System' is the giveaway