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'[OT] Bicycle power output calculation'
2011\05\22@061839 by

Just a thought.

I wonder if there's an easy way to calculate the power output of a human
pedaling on a bicycle. The only idea that comes to mind is some sort of
method to sense the torque applied to the wheels, and then calculate the
power output from there using classical mechanics. How would one go about
sensing the applied torque though? The ideas I'm currently thinking of don't
seem practical for installation in a normal bicycle - such as a pressure
sensor at some point  along the radius of the hub, sensing the arc pressure
and calling that "force at radius" (torque).

Or - how about pressure sensors on the pedals? The applied pedaling force is
directly related to the torque. Human power output can be calculated from
there. But then there's the issue of bogus pressure applied by the body
which doesn't actually go into doing any work (for example, when standing on
the pedals).

Any other ideas
In the vanishingly unlikely event that anything in this idea is novel,
please hereby consider it public domain.

Conclusion: Best of following meanderings seems to be a sprocket in
the top chain run which deflects the usually straight chain run
somewhat and which can move verticlly wrt chain. Sprocket loads a load
cell which allows chain tension to be measured from frame.

c
c
c sss   =====
c sss    =====
c
c
c

c chain
s idler sprocket
||||||||  sliding sprocket mount rod
====   channel/tube for rod to slide in

__________

1. There is no bogus pressure. If you apply a force to the pedals then
power delivered is foot velocity x force.
ir standing on the pedals IS delivering energy and doing work.
IF the pedal falls when you do this you will need to apply energy to
your body to lift it again to repeat the cycle.
Standing on the pedals and eg pulling on the handlebars to increase
force is just transferring energy from one system to another.
Work = force x distance = F x d
Power = work per unit time =  F x d / t
d/t = Velocity V.

Power = F x V

Close enough (a few %) to be useful

kg "force" x RPM x  crank length = Watts.

This works because the various units and magnitudes cancel 'just so'
Easily derived.

2. I haven't tried this, but measuring chain tension would allow you to use

tension x chain velocity = power (!!!)

This is top/drive chain tension.

Chain tension can probably be measured by using a sprung idler on the
top chain arm and telemetering it's position. Movement can be small.
You could use eg a Teflon or UHMWPE "slipper" and a sprint loaded
plunger or an idler pulley or sprocket on a rod in a tube with a load
cell at the base of the tube. Idler sprocket losses can be smallish.

Triangle of forces (Google knows) issues mean you may waant the chain
to angle a moderate amount, which is not how you usually want a top
chain to go.

Strain gauges on the pedal crank would give good torque measurement.
Accessing them from the frame may be annoying. Could use own battery
and an opto of slip rings of local processing on the crank with result
only sent by opto or whatever.

It would be quite easy [tm] to use inductive power transfer from frame
to crank to power the electronics and gauge and any number of ways to

Strain gauges on pedals give a similar result.

Spoke stresses, crank disk stresses, and wheel rim stresses would have
energy input components but a complex mix of forces is liable to be
present.

In all cases there will be losses between source (rider) sink (road)
and measurer. These may be substantial depending on equipment used.

Of all these the idea of an idler with enough bend in the chain to
allow trying to avoid measuring tan (infinity). (Chain tension
required to stop a force applied at 90 from line of chain from
deflecting sideways approaches infinity as deflection approaches zero
(draw a picture).

3. Force sensor integrated into chain with eg RFID data recovery
sounds doable and fun but harder.

Russell McMahon

On 22 May 2011 22:18, V G <x.solarwind.xgmail.com> wrote:
{Quote hidden}

> the pedals)
> Sprocket loads a load cell which allows chain tension to be
> measured from frame

Bicycle power measurement has been discussed before, with the
same conclusion. I remember because it was something I was
interested in at the time and it went on my To Do list. Where it
still is ;-) 'cos I'm still intereste
V G wrote:
> I wonder if there's an easy way to calculate the power output of a
> human pedaling on a bicycle.

Of course.  This has been done, a while ago too.  I wrote some of the code
for the original Tune PowerTap, which was later sold to Graber Products and
then redesigned.

The PowerTap used a special hum that had a strain guage in it to measure
torque.  It also used that signal to infer pedalling cadence.  The hub
transmitted to a pickup using only a few KHz "RF" to a sensor mounted very
close by but on the fixed part of the bike.  The PowerTap also collected
wheel tick and heartrate information.  The wheel tick gave it distance
travelled, from which speed was also calculated.  It didn't do anything
directly with the heart rate other then provide it in the log along with the
other parameters.  Heart rate was just intended for the trainer to look at
along with power, speed, etc.

********************************************************************
Embed Inc, Littleton Massachusetts, http://www.embedinc.com/products
(978) 742-9014.  Gold level PIC consultants since 2000
RussellMc wrote:
> Conclusion: Best of following meanderings seems to be a sprocket in
> the top chain run which deflects the usually straight chain run
> somewhat and which can move verticlly wrt chain. Sprocket loads a load
> cell which allows chain tension to be measured from frame.

Problems with this are that the chain moves laterally when gears are
shifted, and that the speed/force ratio changes as different back gears are
selected.  You need to know what gear you are in (at least in the back) to
do the math.

These are solvable problems, but add to complexity, weight, and finnikiness..
Tune's solution forces you to use their back wheel, but was accepted well
enough by serious and professional cyclists.

********************************************************************
Embed Inc, Littleton Massachusetts, http://www.embedinc.com/products
(978) 742-9014.  Gold level PIC consultants since 2000
At 06:18 AM 5/22/2011, you wrote:
>Just a thought.
>
>I wonder if there's an easy way to calculate the power output of a human
>pedaling on a bicycle. The only idea that comes to mind is some sort of
>method to sense the torque applied to the wheels, and then calculate the
>power output from there using classical mechanics. How would one go about
>sensing the applied torque though? The ideas I'm currently thinking of don't
>seem practical for installation in a normal bicycle - such as a pressure
>sensor at some point  along the radius of the hub, sensing the arc pressure
>and calling that "force at radius" (torque).
>
>Or - how about pressure sensors on the pedals? The applied pedaling force is
>directly related to the torque. Human power output can be calculated from
>there. But then there's the issue of bogus pressure applied by the body
>which doesn't actually go into doing any work (for example, when standing on
>the pedals).

Power = (force * distance) per unit time.

There are a number of commercial products that offer direct power measurement:-
www.westbrookcycles.co.uk/transmission-components-c189/chainsets-c75/sram-2010-s975-srm-power-meter-crankset-p35922
www.powermeters.org.uk/cycling/cycleops-powertap-elite+-mtb-hub-only/104379149/2698/
http://www.powermeters.org.uk/cycling/cycleops-powertap-elite-plus-wheel-system/40926216/1857/

Plus, apparently, some less convincing products that attempt to estimate
opposing forces, which does away with strain gauges and, most likely, accuracy.

Not particularly cheap, but I doubt it's a very big market.

>Best regards,

Spehro Pefhany --"it's the network..."            "The Journey is the reward"
speffinterlog.com             Info for manufacturers: http://www.trexon.com
Embedded software/hardware/analog  Info for designers:  http://www.speff.com

> The PowerTap used a special hum that had a strain guage in it to measure
> torque.

Now that would be an exceedingly clever trick :-)

I assume that the hum measured the force with which the chain tension
pulled the axle forwards.
If so that would be chain force rather than torque per se, with torque
inferred from chain centre to axle radius.

It's not instantly obvious to me
how you'd measure pure torque in a hub. No doubt enough thinking would
suggest a way.

Russel

RussellMc wrote:
> I assume that the hum measured the force with which the chain tension
> pulled the axle forwards.

No, it had a real torque sensor that was based on strain guages.  This is
why the PowerTap product came with its own hub.  The torque sensor was built
into the hub.  Unfortunately this makes it rotating.  That was solved by
having its own battery and wirelessly transmitting to a pickup on the bike
frame close to the hub.

The advantage of this is that it's light and reliable, and is measuring the
right thing at the right place.  Since it's measuring after the gears, gear
selection doesn't matter.

********************************************************************
Embed Inc, Littleton Massachusetts, http://www.embedinc.com/products
(978) 742-9014.  Gold level PIC consultants since 2000

Olin, is the strain gauge measuring torsion, or compression?

Just curious..

2011\05\22@105933 by
At 09:18 AM 5/22/2011, you wrote:
> > The PowerTap used a special hum that had a strain guage in it to measure
> > torque.
>
>Now that would be an exceedingly clever trick :-)
>
>I assume that the hum measured the force with which the chain tension
>pulled the axle forwards.
>If so that would be chain force rather than torque per se, with torque
>inferred from chain centre to axle radius.
>
>It's not instantly obvious to me
>how you'd measure pure torque in a hub. No doubt enough thinking would
>suggest a way.

Obvious way is to split the hub in some way, connect the two halves with a
torsion bar, mount (a) strain gauge(s) on the torsion bar. We only need one
component of the torque vector.

Here's one that uses standard 350 ohm strain gauges:
http://www.futek.com/files/pdf/Product%20Drawings/FSH00322.pdf

If there was a volume market, there would be cheaper ways.

Best regards,

Spehro Pefhany --"it's the network..."            "The Journey is the reward"
speffinterlog.com             Info for manufacturers: http://www.trexon.com
Embedded software/hardware/analog  Info for designers:  http://www.speff.com

> Olin, is the strain gauge measuring torsion, or compression?

I don't know since the mechanical design was done when I started with the
project and I never saw the insides of a hub.  I think I remember someone
mentioning torsion, but I'm not sure.

********************************************************************
Embed Inc, Littleton Massachusetts, http://www.embedinc.com/products
(978) 742-9014.  Gold level PIC consultants since 2000
It's possible to measure power with accelerometers.

VELOCITY=MPH x 5280/3600

FORCE=MASS x (ACCEL+DECEL)     ;  ACCEL & DECEL in < g >

HP=FORCE x VELOCITY/550

DECEL subsumes grade, aero drag, & so on. In principle, a 3-axis
accelerometer & sufficiently whiz-bang DSP could be carried loose

Measuring torque at the hub is much simpler..
There are iPhone apps that claim to use the accelerometers and position awareness of iOS devices to derive power as well as measure the 0-60, 1/4 mile etc times of your car. "Dynolicious" is one example.
The problem is whether they scale down to bicycle + human levels well.

Cheers,          Robin.

On 22 May 2011, at 16:24, "John Gardner" <goflo3gmail.com> wrote:

{Quote hidden}

> -
Actually, the accelerometer-based  gizmo I built measured speed
conventionally (reed switch/magnet), and ACCEL by reading a LTC
1298 which monitored the ADLX02 (? - Long ago...).

The "equations" are snippets of code from the original Basic supervisor
pgm running on a TI-74 calculator, before it morphed into assembler.
It gave plausible results, on the flat, once the noise problems were
managed - I learned a bit about filters, software & hardware...

DECEL I interpolated from a table, constructed with another routine
which measured speed against time - Coasting. I intended to measure
grade with a 2nd accelerometer, but ultimately did'nt - Could'nt get another
one - AD wanted 10K orders, not onesies :)  I was lucky to get one
On Sun, May 22, 2011 at 10:19 AM, Olin Lathrop
<olin_piclistembedinc.com> wrote:
>> Olin, is the strain gauge measuring torsion, or compression?
>
> I don't know since the mechanical design was done when I started with the
> project and I never saw the insides of a hub.  I think I remember someone
> mentioning torsion, but I'm not sure.
>

I took apart a PowerTap to have a look.  It has four gages arranged
around the outside of a torque tube.  (The torque is transmitted from
the right (drive) side to the left, and the wheel is actually driven
from the left side of the bicycle.)  The microprocessor is a
PIC16F690.  I would not be surprised if some of Olin's code is still
running in there.

Modern state-of-the-art is wireless transmission from the power sensor
to the computer on the handlebars via the ANT+ 2.4GHz protocol.
PowerTap was one of the first to adopt this system.

Regards,
Mark
markrages@gmail
-- Mark Rages, Engineer
Midwest Telecine LLC
markragesmidwesttelecine.com
On Sun, May 22, 2011 at 8:06 AM, Olin Lathrop <olin_piclistembedinc.com> wrote:
> RussellMc wrote:
>> Conclusion: Best of following meanderings seems to be a sprocket in
>> the top chain run which deflects the usually straight chain run
>> somewhat and which can move verticlly wrt chain. Sprocket loads a load
>> cell which allows chain tension to be measured from frame.
>
> Problems with this are that the chain moves laterally when gears are
> shifted, and that the speed/force ratio changes as different back gears are
> selected.  You need to know what gear you are in (at least in the back) to
> do the math.
>

Actually, if you know chain tension and chain speed, you have enough
information to determine power.

One of the more technically interesting system's is the Polar chain
tension sensor.   If the distance from front chainring to rear
sprocket is more-or-less fixed and the mass of the chain in that
section is known, it is possible to measure the frequency of the
chain's vibration and calculate the chain tension.  The system places
what is essentially a bass guitar pickup near the top run of chain,
and uses a modified derailler pulley to measure chain speed.  This is
reasonably accurate when set up properly.

(disclaimer: I work for a bicycle power meter company.)  It turn out
that for training purposes, rather good measurement accuracy is
required.  A cyclist may improve only a percent or two from one season
to the next, so a system with 10% uncertainty is not worth much.  So
the market is moving to systems that measure torque directly with
strain gages.  Even Polar is introducing a
strain-gage-on-pedal-spindle system this year.

Regards,
Mark
markrages@gmail
-- Mark Rages, Engineer
Midwest Telecine LLC
markragesmidwesttelecine.com
On Sun, May 22, 2011 at 5:18 AM, V G <x.solarwind.xgmail.com> wrote:
> Just a thought.
>
> I wonder if there's an easy way to calculate the power output of a human
> pedaling on a bicycle. The only idea that comes to mind is some sort of
> method to sense the torque applied to the wheels, and then calculate the
> power output from there using classical mechanics. How would one go about
> sensing the applied torque though? The ideas I'm currently thinking of don't
> seem practical for installation in a normal bicycle - such as a pressure
> sensor at some point  along the radius of the hub, sensing the arc pressure
> and calling that "force at radius" (torque).
>
> Or - how about pressure sensors on the pedals? The applied pedaling force is
> directly related to the torque. Human power output can be calculated from
> there. But then there's the issue of bogus pressure applied by the body
> which doesn't actually go into doing any work (for example, when standing on
> the pedals).
>
> Any other ideas?

The traditional way to measure power is a steep hill and a stopwatch.
If the hill is steep enough, aerodynamics aren't relevant.  Increase
in potential energy is elevation gain * mass.  Divide by time to get
average power.

Regards,
Mark
markrages@gmail
-- Mark Rages, Engineer
Midwest Telecine LLC
markragesmidwesttelecine.com
....The traditional way to measure power...

!  Thanks, Mark
Mark Rages wrote:
> I took apart a PowerTap to have a look.  It has four gages arranged
> around the outside of a torque tube.  (The torque is transmitted from
> the right (drive) side to the left, and the wheel is actually driven
> from the left side of the bicycle.)  The microprocessor is a
> PIC16F690.  I would not be surprised if some of Olin's code is still
> running in there.

That means you have one of the original PowerTaps.  the 16F690 code was
written by another PIC consultant, Dave Hoch.  If you dig around some more
you'll find another processor, a 16F628.  I wrote the code for that one.
The two major things that processor does is interpret the very noisy data
from the heart rate monitor, and upload ride data over a software UART
interface.  The software UART was pretty tricky since the processor is only
running from a 160 kHz crystal and the baud rate is 9600.

I also wrote the original host code to receive the upload data.  It got run
implicitly under the hood by the user-visible apps.

When Graber bought the product line, they redesigned the hardware to use a
MSP430 and used their own engineers in Wisconsin(?).  The original engineers
from the Boston area then no longer had anything to do with the project.
That happened around 10 years ago, so I have no idea what the product looks
like today.

********************************************************************
Embed Inc, Littleton Massachusetts, http://www.embedinc.com/products
(978) 742-9014.  Gold level PIC consultants since 2000
On Sun, May 22, 2011 at 9:17 AM, Spehro Pefhany <speffinterlog.com> wrote:

> There are a number of commercial products that offer direct power
> measurement:-
>
> http://www.westbrookcycles.co.uk/transmission-components-c189/chainsets-c75/sram-2010-s975-srm-power-meter-crankset-p35922
>
> http://www.powermeters.org.uk/cycling/cycleops-powertap-elite+-mtb-hub-only/104379149/2698/
>
> http://www.powermeters.org.uk/cycling/cycleops-powertap-elite-plus-wheel-system/40926216/1857/
>

Unfortunately, these are all very expensive and way out my budget.

I was thinking of something I could make, or buy for a cheap price.
GPS/acceleration sensing would be /very/ inaccurate because the whole point
of this is to measure my performance in wind and things like that.

The torque measuring hub seems to be the best, but it's very expensive :
.... If you're already got wheel ticks and a time base, you can trivially
compute accelleration...

Yep. A 2nd accelerometer being unavailable (to sense grade), that occured
to me, eventually. Duh -  If I was smart I'd be an engineer :)

Per other comments, remember the DECEL lookup table.

I agree that for high accuracy a torque sensor is the simplest approach
On Sun, May 22, 2011 at 6:52 PM, John Gardner <goflo3gmail.com> wrote:

> ... If you're already got wheel ticks and a time base, you can trivially
> compute accelleration...
>
> Yep. A 2nd accelerometer being unavailable (to sense grade), that occured
> to me, eventually. Duh -  If I was smart I'd be an engineer :)
>
> Per other comments, remember the DECEL lookup table.
>
> I agree that for high accuracy a torque sensor is the simplest approach.
>
>
What's the point of getting acceleration? The quite a bit of the power if
not the majority of power goes into battling the drag/friction/wind which
will not affect the acceleration much. As far as I see it, measurement at
some point in the drivetrain is the only way to do it, unless someone else
has any other suggestions
Accelerometers can also sense grade, normally the
most significant environmental variable.

It might be useful to contemplate Prony brakes, and small
water-brake dynamometers - Give you some ideas...

Or not. Suit yourself
On Sun, May 22, 2011 at 4:22 PM, Olin Lathrop <olin_piclistembedinc.com> wrote:
{Quote hidden}

The hub I took apart was one of the more recent ANT+ ones.  It has
only the 16F690 in there, and a traditional diff amp -> ADC
arrangement.  Maybe the handlebar computer uses an MSP430.

Yes, PowerTap is in Wisconsin.  I've met some of their engineers at
trade shows. They seem like sharp guys.

(BTW, interesting live event at quarq.com right now)

Regards,
Mark
markrages@gmail
-- Mark Rages, Engineer
Midwest Telecine LLC
markragesmidwesttelecine.com
Hello PIC.ers,

On Sun, May 22, 2011 at 5:18 AM, V G <x.solarwind.xgmail.com> wrote:
> Just a thought.
>
> I wonder if there's an easy way to calculate the power output of a
> human
> pedaling on a bicycle. The only idea that comes to mind is some sort
> of

...
<snips>
...

{Quote hidden}

Getting accurate power/energy measurement _output_ has been done very well -as

But every time I ride a bike (lots, I've done many races tho' fewer recently)
I cogitate about how to estimate the amoutn of human effort required to produce
that power. An `efficiency' figure if you like.
Solarwind came close to the button with his comment above. Bogus power, where the
rider is applying pressure to both pedals but there is only a net amount going
to the road. The body is still exerting effort on the trailing pedal but nothing
useful mechanical is coming out of it, its actually a double waste.
Both ways it takes calories out of your leg muscles, the sort you wish you still

It would require (I think, comments sought) :
+/- load sensing on each pedal AND (maybe OR)
torque at the rear hub,
hub speed is needed too but trivial.

I'd guess if the rider could be given that information in real-time he'd
soon adjust style to ratchet up his efficiency.

bestos,   John

eMail from John Sanderson's desk.
JS Controls cc. Manufacturer & purveyor of laboratory force testing
apparatus.
PO Box 1887, Boksburg 1460, Rep. of S. Africa
Tel: +27 (0) 11 023 1412
Fax: +27 (0) 86 516 9725
Cell: +27 (0) 82 741 6275
eMail : johnjscontrols.co.za
Web: http://www.jscontrols.co.za
> I cogitate about how to estimate the amoutn of human effort required to
> produce
> that power. An `efficiency' figure if you like.

The various methods for measuring rear hub power indicate deliverd
power but the rider also has to provide for power train losses.
Difference may be small but useful to know.
I noted that one method would be to telemeter pedal force, with one
method being strain gauges on the cranks. Producing mean power from
the delivered pulsating power would be "easy enough" [tm].

Russel
John Gardner wrote:
> Accelerometers can also sense grade, normally the
> most significant environmental variable.

If you hold your head just right and squint a little you can kindof pretend
using accellerometers for this makes sense.  Otherwise it's just a dumb
idea.  The reasons for this have already been elaborated.  It would be a
good to stop trying to force a inappropriate solution onto the problem, and
let the problem dictate the solution instead.

********************************************************************
Embed Inc, Littleton Massachusetts, http://www.embedinc.com/products
(978) 742-9014.  Gold level PIC consultants since 2000
Hello PIC.ers,

----- Original Message ----- From: "RussellMc" <apptechnzgmail.com>

{Quote hidden}

What I'm really interested in is a way to figure how much the human
rider is exerting, in terms of power, related to that reaching
the chain.

It might have to include articulation functions for limbs, to show the
rider how well he/she is using their available muscles. If you exert
at the wrong points in the cycle you would be wasting a lot of
effort, its not a given that all riders automatically know how to
get the most out of their body joules.
That implies strain-gauging the pedals and making (educated) assumptions

Do we get better chemical efficiency from a short sharp impulse than a
long low one, or vice-versa?

Just how much is the rider losing through trailing pedal force, if they
are not consciously `pulling-up' on the trailing foot?

bestos,   John

eMail from John Sanderson's desk.
JS Controls cc. Manufacturer & purveyor of laboratory force testing
apparatus.
PO Box 1887, Boksburg 1460, Rep. of S. Africa
Tel: +27 (0) 11 023 1412
Fax: +27 (0) 86 516 9725
Cell: +27 (0) 82 741 6275
eMail : johnjscontrols.co.za
Web: http://www.jscontrols.co.za
Hello PIC.ers,

----- Original Message ----- From: "RussellMc" <apptechnzgmail.com>

{Quote hidden}

What I'm really interested in is a way to figure how much the human
rider is exerting, in terms of biological power, related to the mechanical power reaching the chain.

It might have to include articulation functions for limbs, to show the
rider how well he/she is using their available muscles. If you exert
at the wrong points in the cycle you would be wasting a lot of
effort, its not a given that all riders automatically know how to
get the most out of their body joules.
That implies strain-gauging the pedals themselves (not the cranks),
sensing the crank position, and making educated assumptions about muscle efficiency.

Do we get better chemical efficiency from a short sharp impulse than a
long low one, or vice-versa?

Just how much is the rider losing through trailing pedal force, if they
are not consciously `pulling-up' on the trailing foot?
And if they _are_ pulling up on the back foot, how much netbeans
does that take out of him?

bestos,   John

eMail from John Sanderson's desk.
JS Controls cc. Manufacturer & purveyor of laboratory force testing
apparatus.
PO Box 1887, Boksburg 1460, Rep. of S. Africa
Tel: +27 (0) 11 023 1412
Fax: +27 (0) 86 516 9725
Cell: +27 (0) 82 741 6275
eMail : johnjscontrols.co.za
Web: http://www.jscontrols.co.za
> If you hold your head just right and squint a little you can kindof pretend
> using accellerometers for this makes sense.  Otherwise it's just a dumb
> idea.  The reasons for this have already been elaborated.  It would be a
> good to stop trying to force a inappropriate solution onto the problem, and
> let the problem dictate the solution instead.

While John is more than capable of succinctly pointing out errors in
people's interpretations of what he has said, you may wish to benefit
from the opportunity to reread his related posts in a less filtered
way.
He previously noted that a system that he 'played with'  used the
accelerometers for only a portion of the overall task, and that it was
based on a TI system. Why TI choose to do what they do is not always
obvious but they seem better than average at not doing things which
are dumb overall.

And, fwiw, the construct "X can do Y" as in "accelerometers can sense
grade", is surely general enough and broad enough to fail to quality
for "trying to force a inappropriate solution onto the problem".
No?
The answer to that may be yes or no regardless of your understanding
and depends in part on one's skill and comfort with double negatives
:-). It would be about impossible to answer that question yes or no
and be understood with certainty. As a substitute, something that
looks ever so vaguely like a wet fish with a very oblique apology
discernible on its scales if held in the waning light of a full moon
(or the light of a waning full moon) may suffice.

Interpretation: When a person with excellent technical skills, overall
good helpfullness coefficient, generally agreeable approach, laconic
sense of humor and too many years of US military  service makes a
general comment on an approach that might be technically feasible,
pulling out one's Pit-Bull imitation is probably inappropriate. Even
without his M79 and at considerable remove he's far better value to
you as a friend than an opponent. Even an M576 load (real or symbolic)

I have several Maverick-missile rate gyros here somewhere. Small and
heavy with real mechanical spinny things inside. Such might be able to
be shoehorned and levered into this application "just for fun"

FWIW - air drag can be reasonably well approximated by

Newtons Drag = 0.65 A. V^2. Cd                MKS units,

A   frontal area
V   velocity
Cd drag coefficient. - About 0.9 sitting up. Maybe halved all tucked in.
(0.65 is~~50% of the mass of a m^3 or air at STP.)

Add an extra V to get power in Watts.
I'd guesstimate that 0.25 to 0.5V^2 Newton per n^2 of frontal area
So                            0.25 to 0.5V^3  Watts.

Sensibility check.
100 mph. ~= 45 m/s
Power = (0.25 to 0.5) x 45^3 att =
= 23 to 46 kW for 1 m^2 at 100 mph
= 30 to 60 HP.

A streamlined motorcycle with rider well tucked in can ton on 30 HP.

Russell
John Sanderson wrote:
> What I'm really interested in is a way to figure how much the human
> rider is exerting, in terms of power, related to that reaching
> the chain.

provide useful insight into the human part of the workings.  The PowerTap,
for example, includes a heart rate monitor.

I think if you truly want to measure power consumed by the body, you will
need a respiration monitor to measure how much O2 is converted to CO2.

> Just how much is the rider losing through trailing pedal force, if
> they are not consciously `pulling-up' on the trailing foot?

I don't know, but it's not immediately obvious whether pulling up on the
trailing foot is better or not.  The weight of the leg needs to be raised
somehow so that it can go down on the next power stroke.  This energy can
come from the downstroke by letting the trailing foot idle, or you can use
different muscles in the trailing foot to do the work.  Actually if the
trailing foot is idling, then the weight of the leading foot ballances it
and the muscle power goes into moving the bike.  For example, pedalling
backwards is very little work since the weight of both legs ballance.

>From my own subjective experience, it feels like more work to deliberately
raise the trailing foot.  It's something I do when I want a burst of power
for a short time, not for long term efficiency.

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On Mon, May 23, 2011 at 2:28 PM, Olin Lathrop <olin_piclistembedinc.com> wrote:
> >From my own subjective experience, it feels like more work to deliberately
> raise the trailing foot.  It's something I do when I want a burst of power
> for a short time, not for long term efficiency.

IIRC studies on pro cyclists show that they don't actively lift the
rear pedal in normal riding. Whilst I wouldn't take everything pro
cyclists do as gospel I'd think something as basic physiological as
this they'd be doing the right thing.

As you say, there is no net effort involved, as the weight of the
front leg is sufficient to raise the rear leg. The muscles used to
raise the leg are smaller and ess efficient than the nice big ones
powering down the front one.

Chris
> If you hold your head just right and squint a little you can kindof pretend
> using accellerometers for this makes sense.

MEMs gyros can also be used in this sort of application but rapid
spinning around that produces coriolis forces ABOVE THEIR RATINGS WILL
RESULT IN COMPLETELY ERRONEOUS OUTPUTS.

Dead fish and tongue in cheek aside.

MEMS overview
Describes several other types as well as micromachined version
http://www.sensorsmag.com/sensors/acceleration-vibration/an-overview-mems-inertial-sensing-technology-970

Consumer apps
http://www.invensense.com/

Getting real
Better than FOGs
http://www.sensonor.com/gyro-products.aspx

ADXR450 - up to 300 degree/second

General operation
http://en.wikipedia.org/wiki/Vibrating_structure_gyroscope

Russell

_gyro _mems _gyroscop
Shhh - Don't tell him...  :
> Shhh - Don't tell him...  :)

What? You still have some M576 loads?

R

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