View Full Version : Summary: Frequency content of cycling

05-24-2005, 06:52 PM
Here's a summary of replies I received to my question about the
frequency content of pedalling. Most people think the highest signal
power is likely to be lower than that for walking - perhaps 2-3 times
the natural frequency, which would be about 4 Hz for a typical cadence
of 80 rpm. Of course, it's always sensible to double-check by doing a
Fourier analysis, and amateurs are likely to have more higher
harmonics than elite cyclists. Thanks to all for your help!

Dear all,

A long time ago, David Winter analysed the frequency content of
natural gait and came to the conclusion that there was very little
signal power after the sixth harmonic (i.e. 6 x stride frequency).
Like many things in motion analysis, Winter's number has become almost
biblical in its widespread use.

I am currently working on a cycling problem, which is not normally my
field (although I am a keen cyclist!). I wonder if anyone has analysed
cycling and can tell me the frequency content of cycling kinematics?

Many thanks,

Dr. Chris Kirtley MD PhD
Associate Professor
Dept. of Biomedical Engineering
Catholic University of America
Washington DC 20064
>From May 9-June 20 2005 I am at STAPS, University of Reims, France

Gait: http://www.univie.ac.at/cga
Radio: http://radiolistener.blogspot.com
Hi Chris

Here is one data set for force and pedal position. This is not the file I
thought I had grabbed from my office so I can send some more interesting
data later. In this data set looks like all the force signal is contained
in the 5 harmonics.

I have data on novice and experienced cyclists that I've been meaning to
work up. The novices have more signal at higher harmonics.

What aspect are you thinking of?


Jim Martin
Dear Chris;

Elite cyclists tend pedal at a frequency of 75-110 rev/min which should
yield you a frequency of 1.25-1.83 hz. If you apply the Nyquist sampling
theorem and double those figures your top sampling frequency should be about
3.66hz. That is what I am figuring from rough calculations.

Hope this helps

Nelson Sierra, M.S.
Dear Chris

I used an approach similar to that reported by Winter to look at the
frequency content of cycling in some preliminary studies for my PhD some
time ago. With a cadence of approximately 1.33 Hz (80rpm), I found 99% of
the signal power within the first 2 or 3 harmonics depending on the marker
point and direction. I chose not to apply a different level of smoothing to
each point and so where I used a Butterworth filter, I used a 4Hz cut off.
As these were preliminary studies they were only based on data from one
subject, but may give you a starting point.

Regards - Martin

Dr Martin Bailey

University of Brighton
Chelsea School
Gaudick Road
BN20 7AS
Dear Chris,
Of course you should take the Word of DW very seriously, but you
should not ignore your own common sense.
My method is to compare the original signal and the signal filtered
at various alternative cut-off frequencies and ask the question: do I
still see the phenomena that interest me?
For walking 6 Hz may be correct for kinematics, but for dynamics
or power curves I am not too sure.
For cycling a low cut-off may be OK, as no fast transients are to be
Further some remarks on inverse dynamics:
1) When the data are collected with a video-based system at 50 Hz
and with a noise level around 1 mm (e.g. VICON), the cut-off can
be little higher than 5 or 6 Hz, because of the noise in the
acceleration. I am in the happy circumstance to have access to an
Optotrak system, and I see things I had never seen before.
2) A chosen cut-off frequency should be applied to all segments.
There are methods in circulation, which calculate an "optimal" cut-
off for each segment, even for x,y and z coordinates separately. I
think this is very unwise.
3) If you filter position and acceleration at (say) 6 Hz, you should
also filter your forceplate data at 6 Hz. Nobody does, but I think it is
a very sensible rule. ("My expensive forceplate measures up to 500
Hz, why should I throw away all these valuable data?")
4) In the landing phase after a jump, we saw a frequency
components in the force signal up to 100 Hz.

All the best Chris, and I hope to see you some time in the near
Yours, At

Hartelijke Groeten,
At Hof

e-mail: a.l.hof@med.rug.nl

Interfacultair centrum voor Bewegingswetenschappen
Rijksuniversiteit Groningen
A. Deusinglaan 1
gebouw 3215 kamer 321
tel: 050 363 2645

postbus 196
9700 AD Groningen
tel: 050 363 2645
Hi Chris,

Maybe this is not the numerical value type of answer you were hoping for,
but why not just do an FFT (fast fourier transform) on
some cycling kinematics if you already have some?

If you want to start from first principles, collect some fresh data.
If your system permits it, bump up the sampling frequency initially:
instead of 64 Hz, maybe use 128 or even 256 Hz.
Paul Guy (who was the technical lab director for Dave Winter back in the
used to say that the FFT etc will effectively down-sample your data to the
next-lowest base-2 number, so may as well collect at a base-2 and not lose

Once you find the max frequencies that you deem to be 'signal',
then you can pick your new sampling frequency (based on Nyquist's 2n+1,
or if you want to examine the data graphically, use about 10n).
We collect gait at 50-60 Hz usually, with the intention of using a low-pass
(6 Hz) dual-pass Butterworth digital filter afterwards.

I hope this helps.



Stephen W. Hill, Ph.D.

Post-Doctoral Fellow
Research, University Centre
Toronto Rehabilitation Institute
550 University Avenue, Room 1209
Toronto, Ontario, Canada
M5G 2A2

Associate Member,
Heart and Stroke Foundation of Ontario Centre for Stroke Recovery,
Sunnybrook Hospital