OK, where to start...
peanut said:
digital or analogue makes not a jot of difference
That point I was talking about an analogue gauge vs a digital display. It's much easier to accurately read a digital display than it is an analogue gauge.
A digital display that reads "23.4" doesn't make people go "23, err, could be 24 though" unlike an analogue speedo does.
Completely separate to this:-
peanut said:
the input is still revolutions counted against time .
The electronics in the average cycle computer is pretty crude . It is also only as good as the information input.
Counting the revolutions of a wheel against time is hardly an accurate way of measuring speed and acceleration av speed etc.
It is a very accurate method, which is why most cycle computers accept wheel dimensions in mm. Cheap electronics to perform sub-second timing has been around for years, in the 80s there were cheap digital watches with stopwatches that can time to within a 100th of a second, whether they were accurate and consistent is another matter.
Speed is easily measured, at 20mph a 700c wheel rotates roughly 4 times a second, so each revolution takes about 1/4 of a second. Looking the figures more closely:-
20mph = 8.9408m/s
My 700c x 25mm tyre has a circumference of 2105mm according to a rollout test.
So the wheel rotates every 0.235437545 seconds (2.105 / 8.9408)
If we assume it's accurate to a thousandth of a second then:-
0.235 seconds per revolution works out at 2.105 * (1/0.235) m/s in mph = 20.037mph (3.d.p.)
0.236 seconds per revolution works out at 2.105 * (1/0.236) m/s in mph = 19.952mph (3.d.p.)
So that's a 0.085mph difference, or 0.425%, at 20mph.
And that's if the cycle computer measures intra-pulse timings at just the thousandth of a second. There's a good chance it'll do it much more accurately than that. Reliable 5kHz quartz timing chips cost nothing and that'd reduce the possible error to under 0.1%.
Note that what the cycle-computer measures and calculates internally may not be what it displays. It does work by counting each wheel revolution (hence it knows whenever I travel 2.105m) but only displays (in odometer mode) tenths of a km (or 100m).
Average speed is trivial to calculate (note, not measure) as it is simply distance traveled (a multiple of the number of wheel revolutions detected) divided by the time elapsed (basic clock circuitry).
I don't know of any cycle computer that measures or displays acceleration, so I'll ignore that red herring.
peanut said:
Its not necessary for a cycle computer to be any more accurate than 10% ie 15mph +/- 0.5mph is plenty accurate enough.
That may be true, but it doesn't mean that they are inaccurate.
In fact, they're surprisingly accurate. The only alternative is that all cycle computers I've got (and I use 3 different ones plus a GPS) are all equally and similarly inaccurate as they all produce reliable similar figures when doing the same route over and over again. My cycle-computer readings are easily to within 0.5% of the same readings from my GPS for both distance travelled and speeds.
peanut said:
All measuring equipment has what is called an operating tolerance . Check your computer to see what the tolerance is or accuracy
A digital counter, such as on a cycle computer, isn't affected by measuring tolerances; it's a pulse counter. Distance wise, it's simply counting pulses from the magnet/reed-switch and then applying a bit of computation (multiplying by the wheel circumference) and then it feeds the display a scaled down version of this number (in km or miles). The binary input (a single pulse) isn't going to be affected by a measuring tolerance.
The timing circuitry may have a slight inherent inaccuracy, as described above, but there'll be hardly any noticeable effect on calculated values, certainly not the odd 10% figure you are quoting.
Finally, observation rules the day. I do long distance cycling. On one 307km ride my cycle computer (and GPS) matched the distances on the routesheet almost perfectly (barring a couple of typos). These distances were taken from the organiser's cycle computer when riding the route to prepare the routesheet. The distances of 15 riders at the finish were all within 1 or 2 km of the 305km distance (some variation is expected as some riders do have a habit of going off route and having to backtrack when they realise). This is over a spread of makes and models of cycle computers.
