I am interested in learning about the power producing capacity of
athletes.  What is the maximum power (watts) an athlete can
produce/deliver? and for how long can he/she maintain that power
output?   I would greatly appreciate some examples.

Mammals, including humans, developed ability to expend burts of energy, and 
in the comment dialog it was placed to the range of few kilowats.
Thinking of evolution, hitting, throwing, fencing and jumping may be the activity
which would show what people had actually acomplished.
Nomally sustained activities, we know range from 100 to several hundred watts.

To consider theoretical limits for sustained we would have to turn to study
of Bioenergetics and perhaps look at performance of animals, who after all are
using same type of 'motor' - muscles fuled by APT and producing lactic acid.

You will get into issues such as:


...Intense, sustained movements, such as running a 400 m race (in a
young, healthy adult or youth) are dependent upon, not only the
phophagen system, but largely upon a slower pathway of ATP production,
glycolysis, and to a much smaller extent, the slowest pathway of
producing ATP, oxidative phosphorylation.  As the duration of maximal
effort work is sustained, the absolute power output will decline as
there is a shift in the energy system that is most dominant in
resynthesizing ATP..
http://www.exercisephysiologists.com/Bioenergetics/

Please do note the references at the bottom. 
(Yes, I am giving reference to a book, ather then straight answer,
and I am willing to withdraw the answer, if this is not useful).

To estimate ehat acrually the muscels can sustain, we may turn to
migrating birds. Migratory flighs can last daya and use 130kJ/d
according to this
http://www.princeton.edu/~wikelski/Publications/2003Nature.pdf
That performance is apparently limited by amount of energy stored in fat:

Diet selection and selective metabolism of lipids play important roles
in determining the fatty acid composition of birds which, in turn,
affects energetic performance during intense exercise.

http://www.blackwell-synergy.com/links/doi/10.1111/j.0908-8857.2004.03378.x/abs/

I recall a lecture which put performance of migratory birds at the top of 
what animals can sustain. They had special type of muscles for that,
lrcturer said. It would have to be scaled up by muscle mass of course.
He also said
that humans have these muscles only in the 'vocal cords' :-)

As an example of peak power deliverable by muscles scientist studied
grasshopper jumps:
http://www.st-andrews.ac.uk/~wjh/jumping/legsprng.htm


Some numbers for humans (jumping, swimming ..) afre here:

 HUMAN PHYSICAL PERFORMANCE I. BASIC METABOLISM A. Energy Budget 1 ...

... a) total power expended by cyclist, P , 3 \Theta 10 ... ANAEROBIC EXERCISE A.
 Jumping 1) vertical leap and high jump. a) legs can support about 3 times ...
www.inference.phy.cam.ac.uk/ sanjoy/oom/1997/lecture-notes/body.ps

It also says, efficiency of human motor is about 25% -
that gives you one limit you can rely on:
energy expended per day cannot exceed energy of the foof intake 
 What we can digest (particularly when running and jumping all the time)
is also limited.


Hereare few more books (not all good stuff is on internet yet)
http://www.amazon.com/exec/obidos/tg/sim-explorer/explore-items/-/0781725445/0/101/1/none/purchase/ref=pd_sxp_r0/102-1914899-4442519
http://www.sciencedaily.com/cgi-bin/apf4/amazon_products_feed.cgi?Operation=ItemLookup&ItemId=0781725445


Hope this helps

Hedgie

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Request for Answer Clarification by fdelaflor-ga on 11 Jun 2005 15:30 PDT

Hedgie, thank you very much for your interest in my question. I could
not find a maximum power approximation I am looking for the references
I browsed.  Yet, I could not access your last reference:
www.inference.phy.cam.ac.uk/sanjoy/oom/1997/lecture-notes/body.ps, as
it seems a special PS reader is required.   I have my fingers crossed
that I will find the number I am looking for in this reference. How
can I open this file?  Most of the other references of your answer
address the biochemistry of energy transformation. I liked very much
your reference of William A. Braun work in bioenergetics.

Thanks

---

Clarification of Answer by hedgie-ga on 11 Jun 2005 21:38 PDT

Hi
      That file is in postcript format, 5 pages, 36 kB , and it looks
like it was custom written to answer your question. It has formulas
describing energy
expended while sprinting, vaulting, biking...

I am surprised that your browser has problem with it and you did not
tell me much about what system are you using (winXP, Linux ...)

So as a first try, I would suggest you download it and send it to printer.
Postscript was invented as 'page description language' and is used by almost
all printers. There is also a free reader 'ghostview' described here: 
http://www.cs.wisc.edu/~ghost/

This is 'format' of the file (downloaded)
body.ps:       PostScript document text conforming at level 2.0

Sometimes computer has the reader (or helper application) and just
needs to be told which to use.

What browser do you use? It may help downloading Firefox
http://www.mozilla.org/products/firefox/

If all that fails, do post another RFC -

This aerticle is a 'must read' for you  and to find a way
 to convert it to something readable should not be that hard.
I would need to know if you have acroread (for .pdf), can read .jpg .png ..
and what browser  on what system you use.


Hedgie

---

Clarification of Answer by hedgie-ga on 11 Jun 2005 22:38 PDT

As a test of one of the link, I tried to convert .ps to .pdf 

It worked and converted file is aavailable at

http://www.ps2pdf.com/tgetfile/body.pdf?key=1118554297&name=body.pdf

I do not know how long  it will stay there,
so try it soon.

.pdf requires adobe reader, which as free and available at 

http://www.adobe.com/products/acrobat/readstep2.html

Hedgie

Hedgie,  the references you cited in your answer, opened a different
and unexpected path to my research.  Thank you very much.

To Answere this Question you first need to difine power, and what Work
is, and the relation ship between power and work. and i am presuming
this Athleate is a Runner.

Power= Work done / Time Taken

Work Done = Force X Distance

you can the define force as Mass X Acceleration (Newtons 2nd law)

Now lets Consider a 100m Sprinter of mass 80kg. and asumes he runs in 10 seconds.

The runners Speed, (speed = Distance / Time = 100m/10s = 10m/s )NOTE:
THIS IS AVERAGE SPEED, THERE IS A PHASE AT THE START OF THE RACE WHERE
THE RUNNER WILL BE ACCELERATING.

In order to find the force wee need to know the acceleration. Using
SUVAT equasions of motion we have.

S=100m
U=0m/s
v=10m/s
a=?
t=10s

using         S=ut+(.5)at^2   = S= (.5) at^2 (we lose ut because 0 x 10 =0 )

 therefore 100= (.5)a 10^2  Rearange to find a= 2 ms-2!! 

(Please note: ACCELERATION OF 2MS-2 IS THE AVERAGE ACCELERATION! TO
FIND THE EXACT VALUSE OF THE ACCELERATION INTERGRATION WOULD HAVE TO
BE USED. HOWEVER SINCE THIS IS JUST TO GET SOME FIGERS I WILL NOT
BOTHER WITH THE COMPLEXITY)

Force = Mass x Aceleration. (newtons 2nd law)

      = 80kg x 2ms-2 = 160N

(remember average force = 160N, again intergration would be used to
find exact maxima and minium values)

 Work done = Force x Distance

           = 160 x 100m = 16,000J

Power = Work done / Time taken
      = 16,000J / 10s = 1,600 watts.!!




So there you have it, please remember this answere is a roungh
estimation, however it is faily accurate, If you are intrested to know
how much power a 1500m runner can produce or the work done, somply
follow the last method but entering the figers that are realtied
specfically to the 1500m runner.

If you keen to know the power of a swimmer, then this is a highly
complex process takinging into consederation Fluid mechanics, Hydro
dynamics and viscus drag effects.

However it's more simple to work out power put out for Javlin
throwere, or shott putters, or even long jumpers. Please contact me if
you require such infomation,

I hope this Helps you.


Alex Peacock ( Mechanical Engineering Undergratuate BEng)

Alex, thank you very much for your comment.  Your approach is simple
and produces a good approximation of power. I agree with the physics
logic of your proposed solution.  In your sprinter exercise, the power
produced by the 80 kg athlete would be 1,600 watts or 20 watts per
kilogram of mass for 10 seconds.  I offer a couple of additional
examples from a different sport  (Reference: ?Toward an Understanding
of Power? by Patrick O'Shea, EdD.)

In power-lifting, muscle force is required, but power output, as
measured in watts, is low in comparison to that generated in
Olympic-style lifting. Lets compare the power generated by the world
record lifts made by two former world champions, power-lifter Doyle
Kenady and weightlifter Alex Pisarenko.  Kenady, with a body weight of
140 kilograms, executed a 405-kilogram dead lift. Approximately two
seconds was required for him to lift the bar and weight 0.40 meters
off the floor and stand erect for a total of 794 watts. Pisarenko,
with a body weight of 120 kilograms, executed a 265-kilogram clean. It
took him 0.90 seconds to clean the weight and stand up. The bar and
weight traveled 0.90 meters from the floor for a power of 2,597 watts.
In comparing the power values of the world record lifts made by these
former champions, we see that Pisarenko's 265-kilogram clean generated
21.64 watts per kilogram of body mass, and Kenady's 405-kilogram dead
lift produced only 5.57 watts per kilogram of body mass.

Yet the original question remains unanswered: What is the maximum
power (watts) an athlete can produce/deliver? and for how long can
he/she maintain that power output?  My hypothesis is that the human
body -as a machine- has certain power limit; And most probably, we can
find this limit in the performance of world class athletes. It seems
humans can transform  larger amounts of energy in very short times as
explosive power ? for a fractions of a second.   What is that Peak
Power?

Ok, This is an Interesting concept you have here. I have studied
A-level Physical Education and have a good understanding on what you
are trying to achieve. However Please appriciate I am now Engineering
and i will do the best of my physics knolege to help you. I am sory i
will not be able to come up with an answer to your question, however i
certainitng think there are points for you to think about.

Initially looking at these results you have told me ( 21.64 W/kg and
5.57 W/kg) Initially it looks surprising That the Man who lifts the
heviest weight has the lowest power output. HOWEVER: there are Three
Factors affecting his total avereage power output. (Time period,
Distance lifted, and  mass lifted)

Basic Conceps:

Work Done against gravity:  = Mass x Gravitatinial force x change in
height. (m.g.h)

By putting in the numbers for the txt you have given me. (Takeing
gravity at 10ms^2)

Kennedy :(m.g.h) 450 x 10 x .40 = 1,800J

Pisarenko: (m.g.h) 265 x 10 x .9 = 2,385J

So by doing this calculation elimiates the suspition on why a man who
lifts a heiver weight has a lower power output. and the simple reason
for that is there is a difference in height!!

Pisarenko altho much lights is doing more WORK (against gravity) altho
lifing a lighter weight he is lifing it much higher.

And Remember Power = Work done / Time taken


Kennedy : 1,800/ 2 = 900W



Pisarenko: 2,385 / 0.9 =  2,650J

Therefore, Kennedy is doing less work! and taking longer to do it.
therfore his power rating is less.
Pisarenko: Doing lots of work (against gravity) and also doing it in a
shoter period of time.


In my honest opinon i think it would be scientifically unfair to use
these results to calculate the maximium power output!! both athleates
are doing two different seperate events. This i know does not answer
your question tho. I sorry i am no help there. however i hope my
sujesstions are worth some thought.

Also, to calculate the maximium power output would be a lenghtly
process (i presume) you would need to correlate lots of data and then
find an average and presume this is the maximium power a human can
produce. it will most definitely will be in a POWER even and not long
distance.
I would be interesting to see Kennedy and  Pisarenko to do the exact
same event and see how their time, to lift the mass differs.

Unfortunately i believe you need these varibles to be the same: ( Mass
Lifted, Hight Lifted.) time will not be the same between the two
atleates (maby it will), and the difference in time will be the
deciding factor of the power. then once you know the power, you will
be able to find the power to weight ratio.

I hope this helps you. when you do fimd an answer please do let me
know. i will be interested to here form you.

Alex

One way to get an idea of the answer would be to find results of
athlete testing on ergometers, especially for rowing, which probably
allows the use of the most muscles.

Here is one site that I found:

http://home.hia.no/~stephens/eliteerg.htm

Since I don't know anything about it all, I cannot comment on the information.

You can find many other sites that might also be of interest with a search:

ergometer watts OR joules

Myoarin

fdelaflor-ga 

Thank you , for the tip and for the kind words

Hedgie