measuring (mechanical) work

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

Quoted message said:

I am interested in measuring the work (energy, measured in Joules, or "watt-hours"😉 used when
riding a bike, in a certain time interval.

What I need to monitor is the tension in the chain (the stretching force in the chain) and chain
speed (see below).

Chain speed can be measured optically, with a photo-cell for example.

How can tension in the chain be measured? I can imagine an arm with a spring and wheel that
presses down on the chain; the angle of the arm is proportional to the tension in the chain.
Sounds impractical.

-- Are there more practical ways of measuring or estimating the amount of work spent?

Power is also torque * rpm (with appropriate unit conversions), so:

Speed can also be measured by wheel or pedal rpm, and you could measure crank strain (bend) with a
strain gauge as a measure of applied torque. Then with a bit of math and a couple of calibration
checks you can calculate power.

....

--
Dave Kerber Fight spam: remove the ns_ from the return address before replying!

REAL programmers write self-modifying code.

223rem said:

I am interested in measuring the work (energy, measured in Joules, or "watt-hours"😉 used when
riding a bike, in a certain time interval.

What I need to monitor is the tension in the chain (the stretching force in the chain) and chain
speed (see below).

Chain speed can be measured optically, with a photo-cell for example.

How can tension in the chain be measured? I can imagine an arm with a spring and wheel that
presses down on the chain; the angle of the arm is proportional to the tension in the chain.
Sounds impractical.

-- Are there more practical ways of measuring or estimating the amount of work spent?

Thanks very much.

PS: "Proof".

Work = Force * displacement = Tension in chain * chain displacement (assuming force = constant)

The instantaneous power (at moment t) is: Power(t) = Force(t) * chain_velocity(t)

Then total work from t1 to t2 is

W12 = integral of Power(t) from t=t1 to t2.

Polar already does this with the power measurement option on their high-end heart monitor (720?).
They use a magnetic pickup on the upper run (the tensioned side) of the chain. Normal road roughness
will make the chain vibrate. The chain's resonant frequencies depend on its unsupported length, its
linear density, and its tension. The length is almost constant, and the linear density is fixed if
you ignore dirt buildup and wear. Polar measures the speed of one of the jockey pulleys, IIRC, to
measure chain speed. I don't think they make any attempt to subtract the tension in the lower chain
run from that in the upper, but it shouldn't make much difference.

Dave Lehnen

David Kerber said:

Quoted message said:

I am interested in measuring the work (energy, measured in Joules, or "watt-hours"😉 used when
riding a bike, in a certain time interval. What I need to monitor is the tension in the chain
(the stretching force in the chain) and chain speed (see below).

Quoted message said:

Quoted message said:

Chain speed can be measured optically, with a photo-cell for example.

Quoted message said:

Quoted message said:

How can tension in the chain be measured? I can imagine an arm with a spring and wheel that
presses down on the chain; the angle of the arm is proportional to the tension in the chain.
Sounds impractical.

Quoted message said:

Quoted message said:

-- Are there more practical ways of measuring or estimating the amount of work spent?

Quoted message said:

Power is also torque * rpm (with appropriate unit conversions), so:

Quoted message said:

Speed can also be measured by wheel or pedal rpm, and you could measure crank strain (bend) with a
strain gauge as a measure of applied torque. Then with a bit of math and a couple of calibration
checks you can calculate power.

Others have had similar interests and for that purpose a system was developed for measuring power
expended while riding a bicycle. See:

analyticcycling.comPowerTapFeatures.htmlOpen ↗

Jobst Brandt [email hidden]

Quoted message said:

Normal road roughness will make the chain vibrate. The chain's resonant frequencies depend on its
unsupported length, its linear density, and its tension. The length is almost constant, and the
linear density is fixed if you ignore dirt buildup and wear.

That's a very elegant solution!

I've estimated power (and energy) using the output from a GPS. The GPS records position and altitude
as a function of time. My power output can be estimated knowing my weight, the bike's weight, speed
and slope (I assume wind speed is zero).

The results are disappointingly small numbers.

Kirby

Quoted message said:

Quoted message said:

Polar already does this with the power measurement option on their high-end heart monitor (720?).
They use a magnetic pickup on the upper run (the tensioned side) of the chain. Normal road
roughness will make the chain vibrate. The chain's resonant frequencies depend on its unsupported
length, its linear density, and its tension. The length is almost constant, and the linear density
is fixed if you ignore dirt buildup and wear. Polar measures the speed of one of the jockey
pulleys, IIRC, to measure chain speed. I don't think they make any attempt to subtract the tension
in the lower chain run from that in the upper, but it shouldn't make much difference.

Dave Lehnen

Do a clean chain and a dirty chain have the same resonance behavior for the same tension ?

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

Quoted message said:

Quoted message said:

Quoted message said:

Polar already does this with the power measurement option on their high-end heart monitor
(720?). They use a magnetic pickup on the upper run (the tensioned side) of the chain. Normal
road roughness will make the chain vibrate. The chain's resonant frequencies depend on its
unsupported length, its linear density, and its tension. The length is almost constant, and the
linear density is fixed if you ignore dirt buildup and wear. Polar measures the speed of one of
the jockey pulleys, IIRC, to measure chain speed. I don't think they make any attempt to
subtract the tension in the lower chain run from that in the upper, but it shouldn't make much
difference.

Dave Lehnen

Do a clean chain and a dirty chain have the same resonance behavior for the same tension ?

No. Dirt will add to the mass and to the frictional losses, which will reduce the resonant frequency
and increase the damping respectively (the latter may be negligible, but I doubt the former would
be). That's why he said you have to ignore the dirt buildup.

--
Dave Kerber Fight spam: remove the ns_ from the return address before replying!

REAL programmers write self-modifying code.

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

Quoted message said:

I've estimated power (and energy) using the output from a GPS. The GPS records position and
altitude as a function of time. My power output can be estimated knowing my weight, the bike's
weight, speed and slope (I assume wind speed is zero).

The results are disappointingly small numbers.

Unfortunately, this doesn't take into account the power expended against air resistance and
frictional losses, so your actual output will be greater than what this calculates for you, often
significantly greater when on relatively less-steep hills.

--
Dave Kerber Fight spam: remove the ns_ from the return address before replying!

REAL programmers write self-modifying code.

David Kerber said:

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

Quoted message said:

I've estimated power (and energy) using the output from a GPS. The GPS records position and
altitude as a function of time. My power output can be estimated knowing my weight, the bike's
weight, speed and slope (I assume wind speed is zero).

The results are disappointingly small numbers.

Unfortunately, this doesn't take into account the power expended against air resistance and
frictional losses, so your actual output will be greater than what this calculates for you, often
significantly greater when on relatively less-steep hills.

Right. But there are another source of error.

I guess the OP used: Power(t) = Mass * Acceleration(t) * Velocity(t)

Acceleration(t) can be derived from Velocity(t). You also have to account for gravity.

When you go downhill, gravity does part of the work, so you have to subtract g*sin(slope) from
Acceleration. You add that when you go uphill.

When you brake, Accelaration(t) comes from the brakes, not from your legs, and this will contaminate
your results.

Thats why bikes are so great!

So how much horsepower do you have? Way back in highschool we did an experiment by a timed run up
some stairs - where it apparently makes some difference if you take them 2 at a time. Can't remember
the outscome or the formula.

take care Liz

Hey! Look what "Kirby James" <[email hidden]> wrote :

Quoted message said:

I've estimated power (and energy) using the output from a GPS. The GPS records position and
altitude as a function of time. My power output can be estimated knowing my weight, the bike's
weight, speed and slope (I assume wind speed is zero).

The results are disappointingly small numbers.

Kirby

I do include an estimate of air resistance - but don't take into account acceleration.

I mainly do 1-2 hour rides for pleasure and typically my average power output is around 100 watts
with peaks of over 300 watts.1 horsepower (hp) is 746 watts. If you are reasonably fit you can
output 1 hp for a short time
(e.g. running up two flights of stairs). It is reckoned that utility cyclists can maintain an output
of about 75 watts.

Kirby

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

Quoted message said:

Thats why bikes are so great!

So how much horsepower do you have? Way back in highschool we did an

experiment

Quoted message said:

by a timed run up some stairs - where it apparently makes some difference

if you

Quoted message said:

take them 2 at a time. Can't remember the outscome or the formula.

take care Liz

Hey! Look what "Kirby James" <[email hidden]> wrote :

Quoted message said:

I've estimated power (and energy) using the output from a GPS. The GPS records position and
altitude as a function of time. My power output can

be

Quoted message said:

Quoted message said:

estimated knowing my weight, the bike's weight, speed and slope (I assume wind speed is zero).

The results are disappointingly small numbers.

Kirby

Kirby James said:

I do include an estimate of air resistance - but don't take into account acceleration.

You dont? How exactly do you calculate power, and energy? You integrate the temporal changes in
potential and kinetic energy?

223rem said:

I am interested in measuring the work (energy, measured in Joules, or "watt-hours"😉 used when
riding a bike, in a certain time interval.

What I need to monitor is the tension in the chain (the stretching force in the chain) and chain
speed (see below).

Chain speed can be measured optically, with a photo-cell for example.

How can tension in the chain be measured? I can imagine an arm with a spring and wheel that presses
down on the chain; the angle of the arm is proportional to the tension in the chain. Sounds
impractical.

-- Are there more practical ways of measuring or estimating the amount of work spent?

It's been done many times so far, and there are commercial companies offering on-the-bike power
meters. Google Up on the following products:
* Polar S720 - an HRM, about $700 with power meter, measures chain tension via chain
vibration frequency
* PowerTap - about $800, strain gauges in rear wheel hub, reputably most accurate
* SRM PowerCranks - $1500 and up, strain gauges in the crank
* Ergomo - $1200, optical strain gauges in the bottom bracket

Don't reinvent the wheel, read up on what the others have done.

Kacper W said:

Quoted message said:

It's been done many times so far, and there are commercial companies

offering on-the-bike power meters. Google Up on the following products:
* Polar S720 - an HRM, about $700 with power meter, measures chain tension via chain vibration
frequency
* PowerTap - about $800, strain gauges in rear wheel hub, reputably most accurate
* SRM PowerCranks - $1500 and up, strain gauges in the crank
* Ergomo - $1200, optical strain gauges in the bottom bracket

Don't reinvent the wheel, read up on what the others have done.

For comparisons of the data produced by each: mywebpage.netscape.comwattageOpen ↗

"Robert Chung" <[email hidden]> wrote in message "]news:[email hidden]...

Quoted message said:

Kacper W said:

Quoted message said:

It's been done many times so far, and there are commercial companies

offering on-the-bike power meters. Google Up on the following products:
* Polar S720 - an HRM, about $700 with power meter, measures chain tension via chain vibration
frequency
* PowerTap - about $800, strain gauges in rear wheel hub, reputably most accurate
* SRM PowerCranks - $1500 and up, strain gauges in the crank
* Ergomo - $1200, optical strain gauges in the bottom bracket

Don't reinvent the wheel, read up on what the others have done.

For comparisons of the data produced by each: mywebpage.netscape.comwattageOpen ↗

Thanks. I particularly liked the Rosetta stone comparison. Well done.

Mike Kruger said:

Quoted message said:

For comparisons of the data produced by each: mywebpage.netscape.comwattageOpen ↗

Thanks. I particularly liked the Rosetta stone comparison. Well done.

You're welcome. I have an analysis of the Ergomo compared to the PT Pro up now.