Two speedometer quirks?

Carl Fogel said:

For the last few years, I've used cheap speedometers from
Nashbar and Performance, setting them to whatever my front
tire sizes ranging from 2109 mm to 2143 mm.

The MPH speed steps puzzle me. The numbers go in roughly
half-MPH increments that vary from 0.5 MPH to 0.4 MPH. I
just spun my wheel by hand and saw these steps:

3.7 4.1 4.6 5.0 5.5 6.0 6.4

The drift continues throughout the speed range. Yesterday
it went from 22.3 to 22.8.

Does anyone know the explanation for this drift? Do better
speedometers read in regular 0.5 MPH steps?

My other question is related. Long ago, my first cheap
speedometers read in smooth 0.1 MPH steps up to 21.4 MPH,
where they hesitated and then began reading in regular half-
MPH steps at 22.5 MPH--23.0, 23.5, 24.0., 24.5, and so on,
in an xx.0, xx.5 pattern.

But they never showed 21.5 or 22.0. Instead, they skipped
this range, as if the change in calculation from tenths to
half-MPH around 21.5 to 22.0 required a reset.

My current cheap speedometers read in roughly half-MPH
steps, not tenths, but they still hesitate and waver
around 21 to 22 MPH.

Does anyone know why there's this rough patch around 21 to
22 mph where cheap speedometers seem to change their gait?
And do better speedometers read smoothly all the way up to
40 or 50 MPH and back down?

Carl Fogel

Annoying, isn't it? Supergo's cheapest computer acts about
the same way. What follows is pure speculation.

To reduce build cost and increase battery life, these
computers probably use not-very-many-bit microcontrollers (4
or 8 bit?) running at very low clock rates. Both timer
resolution and ability to do high-precision calculations are
severely limited. It's also possible they don't scour the
planet for the best software developers. Anyway, the odd
steps look like roundoff or truncation from low-precision
calculations.

If timer resolution is not very good, it won't be possible
to get fine resolution of higher speeds without making the
number of wheel revolutions per calculation excessive.
Flakiness at some particular speed could be due to switching
from one low-precision algorithm to another.

Of the cyclometers I've owned over the years, the Cat Eye-
Velo CC-1000 took 2 AA cells, had wheel size selection with
a rotary switch, and when in MPH mode, reported speed in
units of 0.6 mph, probably using 0.6 mph = 1 Km/h as its
conversion factor. The Cateye Micro only reported to the
the nearest mph, no tenths. Same for the Sigma BC-800, and
the Avocet Altimeter 50. The Cateye Mity 3 reads in tenths
up to 20 mph, and then in 0.5 mph steps. The Shimano Flight
Deck reads in tenths at least up to 50 mph if not over its
whole range.

Dave Lehnen

Open up a broken one. Look at the microprocessor used
inside. My wild guess is that they are using a four bit
processor.

In article
<[email hidden]>, Carl
Fogel says...

Quoted message said:

For the last few years, I've used cheap speedometers from
Nashbar and Performance, setting them to whatever my front
tire sizes ranging from 2109 mm to 2143 mm.

The MPH speed steps puzzle me. The numbers go in roughly
half-MPH increments that vary from 0.5 MPH to 0.4 MPH. I
just spun my wheel by hand and saw these steps:

3.7 4.1 4.6 5.0 5.5 6.0 6.4

A few years ago I had a Bell that did that. Most every Bell
product I have bought has proven inferior to other brands.

Congratulation on your new bike. If you need a speedometer
with 0.1 increments you can sometimes find Cateye Mity 3 on
sale for $15. But that would still cost an extravagant 30
percent of the cost of the bike.

Ed <[email hidden]> wrote in message news:<[email hidden]>...

Quoted message said:

In article
<[email hidden]>, Carl
Fogel says...

Quoted message said:

For the last few years, I've used cheap speedometers from
Nashbar and Performance, setting them to whatever my
front tire sizes ranging from 2109 mm to 2143 mm.

The MPH speed steps puzzle me. The numbers go in roughly
half-MPH increments that vary from 0.5 MPH to 0.4 MPH. I
just spun my wheel by hand and saw these steps:

3.7 4.1 4.6 5.0 5.5 6.0 6.4

A few years ago I had a Bell that did that. Most every
Bell product I have bought has proven inferior to
other brands.

Congratulation on your new bike. If you need a speedometer
with 0.1 increments you can sometimes find Cateye Mity 3
on sale for $15. But that would still cost an extravagant
30 percent of the cost of the bike.

Dear Ed,

Actually, I should have made it clear that I'm not
complaining about the speedometer, which is more than
accurate enough, just puzzled by the odd pattern, which
didn't seem to round up or down.

I doubt that Dave Van Tol can be persuaded to fund any
further extravagances. I dread writing the grant
application for the bicycle research department of PSU if I
get a flat tire and need to buy a 26" replacement tube at
$2.25 plus 7.4% sales tax. Luckily, the tires on my
Roadmaster Fury seem to have been stolen from a Hummer and
may well be bullet-proof.

Here's a longer list of the speedometer steps, which may
show that there is a pattern:

reading increase .9
1.3 0.4
2.8 0.5
3.3 0.5
4.7 0.4
5.2 0.5
6.7 0.5
7.1 0.4
8.6 0.5
9. 0.4
10.5 0.5
11. 0.5
12.4 0.4
13.9 0.5
14.4 0.5
15.8 0.4
16.3 0.5
17.7 0.4
18.2 0.5
19.7 0.5
20.1 0.4
21.6 0.5
22.1 0.5
23.5 0.4
24. 0.5
25.5 0.5
26.9 0.4
27.4 0.5
28.8 0.4
29.3 0.5
30.8 0.5
31.2 0.4
32.7 0.5
33.2 0.5
34.6 0.4
35.1 0.5
36.5 0.4

I set up a spreadsheet to let me plug in a trial value and
show how close steps of the trial size would be to the
speedometer's steps:

home.comcast.netSpeedo.wk1Open ↗

A value of 0.4599999999999999999 keeps the trial steps
within 0.1000, plus or minus of the speedometer steps.
Probably someone can figure out the odd 0.459999... value.

Math is hard, as Barbie says. Time to go shopping at
Performance over the internet.

Carl Fogel

Carl Fogel said:

A value of 0.4599999999999999999 keeps the trial steps
within 0.1000, plus or minus of the speedometer steps.
Probably someone can figure out the odd 0.459999... value.

It's just 0.46 as represented by a piece of software too
stupid to round its output. You could do this more quickly
by observing that the speedometer goes from 0.9 to 17.5
mph in 36 steps which are equal up to rounding, so the
interval is
(17.5-0.9)/36 = 0.461 mph, or 0.206 m/sec.

The computer must be counting N wheel revolutions within
some fixed time interval T. For wheel circumference C, speed
V is given by

V = N * C / T

The key here is that N is an integer, giving discrete
steps. The increment of speed dV is given by dN = 1.
Solving that equation for T, T = C / dV. If you put in a
circumference of, say,
18.13 meters, the sampling time T is about 10.3 sec. With
this bare-bones sampling - basically a moving average - a
longer time T would give more accurate V but since the
speed is smoothed over T, it would be slower to respond
to changes in speed.

A better programmed or more capable computer could use a
more sophisticated sampling algorithm to produce more-
accurate values without slowing the update. This is not
rocket surgery.

Ben
B.S., Reverse Engineering

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