How accurate are power meters?

On Thursday, December 26, 2013 12:10:38 PM UTC-5, JoeRiel wrote:

An easier way to think of this is to consider the situation with the
treadmill tilted but not running. I hope you agree that the cyclist
has to apply a continuous torque to the wheel to remain in one
position. That is not the case when the tilt is 0. Applying that
torque, with the treadmill not running, takes zero power.

With the treadmill running, the cyclist has to continue to apply that
same torque. But now, because the treadmill is running, the wheel must
turn to remain in one position (relative to the outside). The power the
cyclist must exert is then the constant torque times the angular
velocity of the wheel.

Nice explanation.

- Frank Krygowski

Phil W Lee writes:

Joe Riel considered Thu, 26 Dec 2013 09:10:38 -0800
the perfect time to write:

Phil W Lee writes:

Basic physics tells us we need not apply any energy to remain at the
same speed and direction,

Only if there are no external forces. There is one in this case,
gravity.

so whatever force we are having to overcome
must be applied by the mechanism, not by the attitude of the bike.

Any gravitational component of the force the mechanism applies (the
"rollback" force) could be overcome by holding onto a handrail,

Of course. But the cyclist is not allowed to hold onto a handrail.

think it's fairly obvious that the inclination would need to be pretty
extreme before that sapped very much energy.

An easier way to think of this is to consider the situation with the
treadmill tilted but not running. I hope you agree that the cyclist
has to apply a continuous torque to the wheel to remain in one
position.

Yes - unless it's a track bike the brakes should be more than capable
of that task.

That is not the case when the tilt is 0. Applying that
torque, with the treadmill not running, takes zero power.

Pushing the treadmill surface downhill doesn't take any power if it is
being driven by the mechanism anyway.

We aren't talking about riding downhill.


With the treadmill running, the cyclist has to continue to apply that
same torque. But now, because the treadmill is running, the wheel must
turn to remain in one position (relative to the outside). The power the
cyclist must exert is then the constant torque times the angular
velocity of the wheel.

The only value of the inclination is to stop the cyclist shooting off
the front if he applies more power than is necessary to remain in the
same place.

Don't you find it strange that they would go to all the expense of
building a tiltable treadmill when tilting it, according to you,
has no effect on the situation, other than to provide some additional
safety not already provided by the harness? Much simpler would be
to put some kind of gate at the end.

The same could be done with a sprung roller with a scale,
which the rider was required to exert a particular force against (or
indeed a tow rope with a scale behind).

Ah, but how can he apply continous power, since once the spring is
stretched a given amount, no additional energy will be stored in it?
This is a retorical question---I know the answer. It's not clear that
you do. Do you still assert that the rider is producing essentially no
steady power will climbing in place on the treadmill?

--
Joe Riel

On Fri, 27 Dec 2013 04:20:06 +0000, Phil W Lee
wrote:

Joe Riel considered Thu, 26 Dec 2013 09:10:38 -0800
the perfect time to write:

Phil W Lee writes:

Basic physics tells us we need not apply any energy to remain at the
same speed and direction,

Only if there are no external forces. There is one in this case,
gravity.

so whatever force we are having to overcome
must be applied by the mechanism, not by the attitude of the bike.

Any gravitational component of the force the mechanism applies (the
"rollback" force) could be overcome by holding onto a handrail,

Of course. But the cyclist is not allowed to hold onto a handrail.

think it's fairly obvious that the inclination would need to be pretty
extreme before that sapped very much energy.

An easier way to think of this is to consider the situation with the
treadmill tilted but not running. I hope you agree that the cyclist
has to apply a continuous torque to the wheel to remain in one
position.

Yes - unless it's a track bike the brakes should be more than capable
of that task.

That is not the case when the tilt is 0. Applying that
torque, with the treadmill not running, takes zero power.

Pushing the treadmill surface downhill doesn't take any power if it is
being driven by the mechanism anyway.

With the treadmill running, the cyclist has to continue to apply that
same torque. But now, because the treadmill is running, the wheel must
turn to remain in one position (relative to the outside). The power the
cyclist must exert is then the constant torque times the angular
velocity of the wheel.

The only value of the inclination is to stop the cyclist shooting off
the front if he applies more power than is necessary to remain in the
same place. The same could be done with a sprung roller with a scale,
which the rider was required to exert a particular force against (or
indeed a tow rope with a scale behind).

I can't comment on a bicycle on the treadmill but certainly running on
a treadmill is more stressful as you increase the upward tilt. In fact
this is one of the things done during a stress test to increase the
required effort.

Are bicycles so much different?
--
Cheers,

John B.

Frank Krygowski writes:

On Thursday, December 26, 2013 12:10:38 PM UTC-5, JoeRiel wrote:

An easier way to think of this is to consider the situation with the
treadmill tilted but not running. I hope you agree that the cyclist
has to apply a continuous torque to the wheel to remain in one
position. That is not the case when the tilt is 0. Applying that
torque, with the treadmill not running, takes zero power.

With the treadmill running, the cyclist has to continue to apply that
same torque. But now, because the treadmill is running, the wheel must
turn to remain in one position (relative to the outside). The power the
cyclist must exert is then the constant torque times the angular
velocity of the wheel.

Nice explanation.

Thanks, that was about as simple as I can make it. Part of the problem,
I'm guessing, is the somewhat confusing issue of where the power is
going. Certainly not into the mass (of bike and rider), as would be
the case if the climbing was done in vivo rather than in vitro.
The answer, of course, is into the machine (and eventually, to heat).
Exactly where it goes doesn't matter to the cyclist. One explanation
for where the power goes is this.

Assume (reasonably) that the treadmill belt rides on a bed. Let mu be
the coefficient of friction between the bottom of the belt and the bed.
The normal force between the two is W, the weight of rider and bike (as
pointed out elsewhere, this barely changes over the typical slope). So
the friction force from the bike and rider is F = mu*W. With the belt
turning at a linear velocity v, the power dissipated in the friction is
Pf = mu*v*W. The power the rider is putting into the belt is
approximately Pr = s*v*W, where s is the slope of the treadmill. I
suspect that for most treadmills and slopes, mu s, so Pf Pr, and all
the rider's power is being dissipated in the friction between belt and
bed. The electrical motor of the treadmill supplies the rest of the
power.

With that in mind, why must the treadmill be tilted? Phil's belief, to
keep the cyclist from going off the end, is true, but, at least as he
appears to be expressing it, doesn't capture the real effect. It is
tilted because that is the condition required to generate the constant
rearward force on the cyclist that precisely matches the force generated
by a real road at the same slope. The same effect could be mimiced on a
level treadmill by tying a rope to the rear of the frame, hanging it
over a pully and adding a weight w = s*W, where W is the weight of bike
and rider, and s the desired slope. The situation would be slightly
different in that the effective inertia changes, and handling of the
bike would be effected.

I'm curious as to how the treadmill is controlled. A simple design
would be to run it at a constant spped. More interesting would be one
with a feedback loop which detects the position of the rider and adjusts
the speed so that the rider remains centered in the treadmill. This
would allow the cyclist to, say, launch an attack, and then later sit
up, yet not actually ride off the treadmill nor be restrained by the
harness.

--
Joe Riel

On Friday, December 27, 2013 12:14:48 PM UTC-5, JoeRiel wrote:

With that in mind, why must the treadmill be tilted? Phil's belief, to
keep the cyclist from going off the end, is true, but, at least as he
appears to be expressing it, doesn't capture the real effect. It is
tilted because that is the condition required to generate the constant
rearward force on the cyclist that precisely matches the force generated
by a real road at the same slope. The same effect could be mimiced on a
level treadmill by tying a rope to the rear of the frame, hanging it
over a pully and adding a weight w = s*W, where W is the weight of bike
and rider, and s the desired slope. The situation would be slightly
different in that the effective inertia changes, and handling of the
bike would be effected.

Another possible effect would be biomechanical on the cyclist. A level bike with an added drag force, as you describe, would mimic the effect of a headwind pretty well, I think. But on a grade, especially a steep one, the position of the rider's weight vector changes w.r.t. the cranks and handlebars, and the rider's body tilts as well. It may be a minor effect (it's a cosine thing) but I know that when I climb a steep hill, I'm always compelled to reach forward on the bars. And climbing's a lot harder with high, straight bars.

I'm curious as to how the treadmill is controlled. A simple design
would be to run it at a constant spped. More interesting would be one
with a feedback loop which detects the position of the rider and adjusts
the speed so that the rider remains centered in the treadmill. This
would allow the cyclist to, say, launch an attack, and then later sit
up, yet not actually ride off the treadmill nor be restrained by the
harness.

I don't think there's any feedback mechanism (servos, etc.), aside from the normal adjustable speed drive to the motor. The feedback loop is inside the cyclist, so to speak, to maintain his own position. Which again hints at the possibility of unintended influence from the harness.

You're right, it would be interesting to have a treadmill that responded to "attacks." Although I find all indoor cycling to be really, really boring..

- Frank Krygowski

Frank Krygowski writes:

On Friday, December 27, 2013 12:14:48 PM UTC-5, JoeRiel wrote:

With that in mind, why must the treadmill be tilted? Phil's belief, to
keep the cyclist from going off the end, is true, but, at least as he
appears to be expressing it, doesn't capture the real effect. It is
tilted because that is the condition required to generate the constant
rearward force on the cyclist that precisely matches the force generated
by a real road at the same slope. The same effect could be mimiced on a
level treadmill by tying a rope to the rear of the frame, hanging it
over a pully and adding a weight w = s*W, where W is the weight of bike
and rider, and s the desired slope. The situation would be slightly
different in that the effective inertia changes, and handling of the
bike would be effected.

Another possible effect would be biomechanical on the cyclist. A
level bike with an added drag force, as you describe, would mimic the
effect of a headwind pretty well, I think. But on a grade, especially
a steep one, the position of the rider's weight vector changes
w.r.t. the cranks and handlebars, and the rider's body tilts as well.
It may be a minor effect (it's a cosine thing) but I know that when I
climb a steep hill, I'm always compelled to reach forward on the bars.
And climbing's a lot harder with high, straight bars.

Good point, that is certainly significant.

I'm curious as to how the treadmill is controlled. A simple design
would be to run it at a constant spped. More interesting would be one
with a feedback loop which detects the position of the rider and adjusts
the speed so that the rider remains centered in the treadmill. This
would allow the cyclist to, say, launch an attack, and then later sit
up, yet not actually ride off the treadmill nor be restrained by the
harness.

I don't think there's any feedback mechanism (servos, etc.), aside from the normal adjustable speed drive to the motor. The feedback loop is inside the cyclist, so to speak, to maintain his own position. Which again hints at the possibility of unintended influence from the harness.

You're right, it would be interesting to have a treadmill that responded to "attacks." Although I find all indoor cycling to be really, really boring.

It would be a good project for an engineering major.

I agree with you on indoor cycling. My wife will use a trainer
occasionally (a lot, right now, while she's recovering from an ankle
injury) and do so while watching TV. I don't watch TV much, and find
doing so while on a trainer even more annoying than usual. I used one
for a couple weeks when recovering from the broken leg last year; just
set it up in the garage and did intervals.

--
Joe Riel

Phil W Lee writes:

Joe Riel considered Thu, 26 Dec 2013 20:54:57 -0800
the perfect time to write:

Phil W Lee writes:

Joe Riel considered Thu, 26 Dec 2013 09:10:38 -0800
the perfect time to write:

Phil W Lee writes:

Basic physics tells us we need not apply any energy to remain at the
same speed and direction,

Only if there are no external forces. There is one in this case,
gravity.

so whatever force we are having to overcome
must be applied by the mechanism, not by the attitude of the bike.

Any gravitational component of the force the mechanism applies (the
"rollback" force) could be overcome by holding onto a handrail,

Of course. But the cyclist is not allowed to hold onto a handrail.

think it's fairly obvious that the inclination would need to be pretty
extreme before that sapped very much energy.

An easier way to think of this is to consider the situation with the
treadmill tilted but not running. I hope you agree that the cyclist
has to apply a continuous torque to the wheel to remain in one
position.

Yes - unless it's a track bike the brakes should be more than capable
of that task.

That is not the case when the tilt is 0. Applying that
torque, with the treadmill not running, takes zero power.

Pushing the treadmill surface downhill doesn't take any power if it is
being driven by the mechanism anyway.

We aren't talking about riding downhill.

No, we are talking about riding at a fixed altitude, with the "road
surface" being driven downhill by some combination of the treadmill's
mechanism and the back wheel of the bicycle.


With the treadmill running, the cyclist has to continue to apply that
same torque. But now, because the treadmill is running, the wheel must
turn to remain in one position (relative to the outside). The power the
cyclist must exert is then the constant torque times the angular
velocity of the wheel.

The only value of the inclination is to stop the cyclist shooting off
the front if he applies more power than is necessary to remain in the
same place.

Don't you find it strange that they would go to all the expense of
building a tiltable treadmill when tilting it, according to you,
has no effect on the situation, other than to provide some additional
safety not already provided by the harness? Much simpler would be
to put some kind of gate at the end.

Well, that would be more difficult to market on the basis of it
providing a realistic simulation of "uphill" and it is true that the
attitude of the bike changes, so it does provide a slightly more
realistic simulation to the rider.
That is not to say that the tilting makes the same difference to the
power required of the rider as a road of the same gradient would.
The additional power being exerted by the rider has to go somewhere
other than in raising bike + rider to a higher altitude, which must be
accomplished by something within the mechanism of the treadmill.
Now, it could be that it is linked to a scale under the surface and an
input from the degree of tilt, or the degree of tilt and the
additional drag could both be derived from the control settings - we'd
have to know exactly how the treadmill is built to know which.
But the point I'm making is that even if it gives a decent training
simulation, it is highly unlikely to be accurate enough for testing
the precision of the power meter or the subtle effect of adding small
amounts of weight!

As explained in a separate response, the power probably goes into
friction between belt and bed. However, you are wrong in thinking that
this has to be somehow carefully controlled. It occurs automatically.
Drive any treadmill at a constant speed, tilted at the slope of the hill
being simulated, and ride on it, maintaining a constant position by
pedaling (i.e. not by grabbing onto a handrail). The power required by
the rider is precisely what he would experience on the hill at the same
speed, ignoring drag due a headwind (which could easily be generated
with an external fan).

--
Joe Riel

Joe Riel writes:

Phil W Lee writes:

Joe Riel considered Thu, 26 Dec 2013 20:54:57 -0800
the perfect time to write:

Phil W Lee writes:

Joe Riel considered Thu, 26 Dec 2013 09:10:38 -0800
the perfect time to write:

Phil W Lee writes:

Basic physics tells us we need not apply any energy to remain at the
same speed and direction,

Only if there are no external forces. There is one in this case,
gravity.

so whatever force we are having to overcome
must be applied by the mechanism, not by the attitude of the bike.

Any gravitational component of the force the mechanism applies (the
"rollback" force) could be overcome by holding onto a handrail,

Of course. But the cyclist is not allowed to hold onto a handrail.

think it's fairly obvious that the inclination would need to be pretty
extreme before that sapped very much energy.

An easier way to think of this is to consider the situation with the
treadmill tilted but not running. I hope you agree that the cyclist
has to apply a continuous torque to the wheel to remain in one
position.

Yes - unless it's a track bike the brakes should be more than capable
of that task.

That is not the case when the tilt is 0. Applying that
torque, with the treadmill not running, takes zero power.

Pushing the treadmill surface downhill doesn't take any power if it is
being driven by the mechanism anyway.

We aren't talking about riding downhill.

No, we are talking about riding at a fixed altitude, with the "road
surface" being driven downhill by some combination of the treadmill's
mechanism and the back wheel of the bicycle.


With the treadmill running, the cyclist has to continue to apply that
same torque. But now, because the treadmill is running, the wheel must
turn to remain in one position (relative to the outside). The power the
cyclist must exert is then the constant torque times the angular
velocity of the wheel.

The only value of the inclination is to stop the cyclist shooting off
the front if he applies more power than is necessary to remain in the
same place.

Don't you find it strange that they would go to all the expense of
building a tiltable treadmill when tilting it, according to you,
has no effect on the situation, other than to provide some additional
safety not already provided by the harness? Much simpler would be
to put some kind of gate at the end.

Well, that would be more difficult to market on the basis of it
providing a realistic simulation of "uphill" and it is true that the
attitude of the bike changes, so it does provide a slightly more
realistic simulation to the rider.
That is not to say that the tilting makes the same difference to the
power required of the rider as a road of the same gradient would.
The additional power being exerted by the rider has to go somewhere
other than in raising bike + rider to a higher altitude, which must be
accomplished by something within the mechanism of the treadmill.
Now, it could be that it is linked to a scale under the surface and an
input from the degree of tilt, or the degree of tilt and the
additional drag could both be derived from the control settings - we'd
have to know exactly how the treadmill is built to know which.
But the point I'm making is that even if it gives a decent training
simulation, it is highly unlikely to be accurate enough for testing
the precision of the power meter or the subtle effect of adding small
amounts of weight!

As explained in a separate response, the power probably goes into
friction between belt and bed. However, you are wrong in thinking that
this has to be somehow carefully controlled. It occurs automatically.
Drive any treadmill at a constant speed, tilted at the slope of the hill
being simulated, and ride on it, maintaining a constant position by
pedaling (i.e. not by grabbing onto a handrail). The power required by
the rider is precisely what he would experience on the hill at the same
speed, ignoring drag due a headwind (which could easily be generated
with an external fan).

Perhaps it would help to consider a bit of exercise equipment that I
have seen in gyms, the treadwall. This is an endless belt with a set of
hand and foot holds attached to it. The inclination is adjustable, but
vertical is the simplest case. The climber moves upward as he would on
a real wall, but the surface moves downwards as he does so. There is an
adjustable drag, but I don't remember it being very sophisticated.

Suppose an experimenter were to adjust the drag to the maximum while the
climber rose two meters, and then, while the climber stood still,
adjusted the drag to allow the wall to fall two meters. How much work
has the climber done? His potential energy actually rose by 2m*w, and
then fell by the same amount -- work was done, but we don't have to know
exactly how.

Next, imagine the climber moves at an apparent rate of, say, 0.1 m/sec
for 20 seconds, with the drag adjusted so that he does not actually rise
or fall. Surely he has done the same amount of work as before, modulo
tiny changes due to acceleration, after all he has applied the
same force, his weight, and has done so for the same distance.

--

On Fri, 27 Dec 2013 10:34:40 -0800, Joe Riel wrote:


I agree with you on indoor cycling. My wife will use a trainer
occasionally (a lot, right now, while she's recovering from an ankle
injury) and do so while watching TV. I don't watch TV much, and find
doing so while on a trainer even more annoying than usual. I used one
for a couple weeks when recovering from the broken leg last year; just
set it up in the garage and did intervals.

I'm recovering from an injury now, and it's impossible to regain what
one has lost when the roads are un-usable so often. I'd love to work
out indoors -- but know better than to buy a any equipment; it would
take extreme determination to keep going five minutes when the effort
isn't getting me anywhere. I find it very hard to work out *outdoors*
if there is nowhere I want to go; on several occasions I've resorted
to having myself dumped out in the country and left to walk or ride
home.

What I need is a trainer that does something useful. I've heard of
people setting up a stationary bike to run a generator that runs a
television --hard-wiring the television so that it couldn't be watched
without someone on the trainer-- but that wouldn't work for someone
who gets up and leaves the room when the TV is turned on.

A few decades ago, I rode rollers enough to improve my bike-handling.
There was a "fuel crisis" going on, and the temperature in the house
was not suitable for sedentary work. Whenever I got chilled I would
strip, hop onto the rollers, and work hard until my temperature was
back up. This result is not repeatable.

--
joy beeson at comcast dot net
http://joybeeson.home.comcast.net/
The above message is a Usenet post.
I don't recall having given anyone permission to use it on a Web site.

Per Joy Beeson:
What I need is a trainer that does something useful. I've heard of
people setting up a stationary bike to run a generator that runs a
television --hard-wiring the television so that it couldn't be watched
without someone on the trainer-- but that wouldn't work for someone
who gets up and leaves the room when the TV is turned on.

Have you tried music?

During cold weather, I try to spend an hour a day on an elliptical
machine - but I couldn't do it without music.
--
Pete Cresswell