Apples and Oranges.
Windgrins: I've been curious about this quote of 60 to 80 N of noise in a treadmill belt. My wife weighs approximately 45 kilograms. 80N would mean an acceleration of 1.8 meters/s^2, or almost 1/5 of a g orthogonal to the direction of travel of the belt. If this is the noise in the system, am I correct that this would vary from 1/5 g up to 1/5 g down, and every value in between? How could any one walk or run under these conditions? If this was true of the average treadmill, people would be swept off their feet every few minutes at every gym and spa. It would be like running on a small boat deck in an intensely choppy sea. Or have a made an error in my interpretation?
Since the author of the paper did not state how the TM measured was instrumented its a little difficult to state what and how they were measuring the frame. After reading the paper what did become clear was that the high g measurements were high frequency vibrations starting around 45 Hz and plotted as being higher with higher frequency. This frequencies are higher than low "bass" notes on a stereo system (20 Hz considered the threshold of hearing) and the author called it "noise" transients. The expectation is that any high frequency vibration (from a mechanical point of view) would be typically sinusoidal and would be considerably diminished via the elastomeric (rubber) tread and rubber wheels of any device on a TM. The author did state they excited the frame with a hammer (normal practice) to obtain transient response. Basically an impulse has frequency components from dc to infinity and this will normally excite any natural resonant frequency components of the TM frame. The assumption is that the author of the cited paper was placing their transducers on the frame and seeing this "ringing". I was initially surprised at the plot showing the magnitude increasing for higher frequencies but then I read the scale and saw it was the integrated power which shows most of the noise is at higher frequencies than the ones of interest. For their use, the simply low pass filtered the data as they did not consider the high frequency noise as important to their measurements of gait analysis. The use of the word "noise" by the authors indicate that it is uncorrelated and random and not a consistent vibration. In the graph in their paper, a true resonance will appear as a step function in the integral as a lot of energy is contained there. They note their first resonances are near 90 Hz which corresponds to that step but they don't mention anything about the one at about 73 Hz so I'm not sure what that is. Noise can occur from transducer placement, type and nature of the coupling of the transducers, electrical noise in the amplifiers and other ambient noise sources so it is difficult to know what the "mat" of their TM transmitted without more info. They were trying to characterize their noise from the motors, flywheels, etc. to be able to separate it from actual signals from a person walking on the TM.
So to answer your question, the assumption is that the authors measured the values on the steel frame of the TM where their force transducers were and the forces were indeed vibrational in nature of low amplitude in the steel frame and it is not clear how they coupled into their "mat" or belt. In essence, not a whole lot can be gleaned without putting a vibration transducer on the belt itself for our purposes and as you can imagine this is difficult due to the rotating nature of the belt. One could do this "hammer test" on the frame with the non-rotating belt to understand the coupling but this was not done or discussed in this paper.
For our purposes, what is important is that there is a no-slip condition on the wheels. This is ascertained in Video #6 as earlier stated. Any vibrations that don't have the ability to cause any slip can't transport the cart since they don't lose contact with the surface. The hypothesis is a red-herring that isn't consistent with the evidence presented. One of the interesting things to note is that the experiment was not done to ascertain the noted non-slip condition so fraud or trickery would not be normally considered in the subtly of my observation of the smoothly and continuously aliased wheel spokes in video #6. The other interesting observation is that the cart wonders from equilibrium and there is little net tendency to go up or down TM but when the speed is slightly increased it always goes up and when reduced it always goes down TM. This is consistent with carteer's standard theory of operation but not the denier's vibration hypothesis.
On my final note on this, the paper chosen has limited applicability due to the author's intent having little to do with our subject matter, so generalizations from the paper to our topic have to be carefully considered for any meaningful conclusions. There is one generalization the author makes which is meaningful in the discussion session which is in opposition to the fundamental assertion of the deniers about TMs and reference frames (my italics and underline).:
"From a purely mechanical perspective, steady-speed
walking or running on an adequate motorized treadmill
is identical to overground walking and running;
the
only difference is the frame of reference for each
situation (23). Locomotion on a treadmill with inadequate power or momentum (i.e., no flywheel) does
indeed differ from overground locomotion. However,
on
a treadmill with an adequate motor and flywheel,
where the belt speed does not vary, the kinematics (21),
ground-reaction forces (19), and metabolic cost (2) of
locomotion are nearly indistinguishable from overground locomotion. As detailed above, our motor and
flywheel appear to be adequate in maintaining a constant tread speed."
Hopefully this helped but it is difficult to use this "apples" paper to discuss our "oranges". It is clear our opponents are "grasping at straws" and "cherry picking" to try to find some solace while ignoring the 500 lb gorillas in their own citations of papers. They either don't seem to understand the significance of the giant contradictions to their claims in their papers or are just ignoring them.
Regards,
WindGrins
The paper is a bit dry but I include a link so you know what I'm basing my answers about it on.
Here is the link to the paper:
http://jap.physiology.org/content/85/2/764.full.pdf