Your claim is that a transform can ignore irrelevant forces and give the example of laying a grandfather clock on its side. Fair enough, but just HOW do you know vibration foces of 60 N on the treadmill frame, for a cart that has a gravitational force of 2 N on the treadmill belt, are irrelevant?
PPG, As stated earlier and I see Semper beat me to it:
PPG,
It is clear from Video #6 with the single speed aliasing effect throughout the video that the cart does not lose traction. Therefore the vibrations are not an issue that seem to be any sort of cause.
If the wheels break traction, the prop would very quickly change their speed due to the load which would be evidenced in this video as alias speed variations which are not present. The reason this video is so good is that it stays very stable at the lowest WS possible for such a long time.
The thing is, even if we accept that there are mounting forces between the treadmill chassis and the floor of the magnitude you are proposing, there is no explanation of how that will affect acceleration of the belt, nor then how that would affect the cart on the belt,
You've been asked to explain that in light of the evidence that the wheels turn smoothly with no discernible skidding or any behaviour not consistent with the carteers explanation and you have been spectacularly unable to do so.
BTW, what will it have to do with kinematics?
You may also have noticed that I agreed with Humber on one of his points about the paper presented, but not all. The one point in my comments that should be noted is the part about not being able to discern from the description how the tests were performed and if the results were valid in the actual magnitudes of the vibrations. As Humber stated, (and I agree on this) if the Hammer used to excite the frame for an impulse test had no sensor for a calibration mechanism for the energy imparted, The measured magnitudes of the resulting force are not meaningless but they can't be used for magnitude values except relatively. In other words, the frequency spectrum of the resonance of the chassis could be ascertained but not the absolute levels. For the authors purpose, they showed that the resonances were all above their area of interest so they could simply LPF (Low-Pass Filter) the transducer signals and eliminate any high frequency resonance introduced by the motor. (This is ascertained from the Integral of power spectrum diagram). They did have one unexplained resonance at about 73 Hz that I'm surprised was not mentioned but it was of the same magnitude of the mentioned 90 Hz resonance. If you read the paper closely, and you have experience in this, you too can glean this.
Now finally, I've taken great care to answer all your questions in a serious and studied way but I see you have ignored most of mine such as:
The one you did answer-How is it that the earth's surface can act as IRF today at noon when the same point on it will be going at 2000 miles/hour (roughly) in the opposite direction at midnight (12 hours later)? That's quite an acceleration! Almost as if the surface of the earth is on one big giant 8000 mile diameter roller! I guess it can't be an IRF either by your argument.
You responded that the minor forces (correctly) could be ignored as they did not have an impact upon our problem. I agreed so I posed the following:
Suppose if we could we built a TM with the belt going entirely around the world and we run it a 10 mph over the earth's surface. (yes, I know we don't have the engineering and money to do this but that's why we call it a thought experiment.)
Question 1. Since the accelerations are all the same on the TM roller as the earth, can this be a valid platform for this discussion. If not, why not?
Question 2. If it is a valid platform, can a small portion of it be simulated by our TM moving at 10 mph? If not, why not?
The other one you seem to ignore is my statement about "force, power, and energy explanations all have to be consistent. Reason correctly in the simplest and derive the remainder from this and you have your explanation. Your'e idea is to find a model where you can ignore the axial force increase that exists on the prop due to the tail wind, make calculations which supposedly prove your point, and remain entrenched in your view. Most of us know this is where your missing power is but you continue to ignore this. You continue to produce power arguments as if the cart is in a no wind situation and ignore the power input from the wind. And one final time, yes I understand that it doesn't look like wind on the prop at WS but there is definitely a difference operating at WS vs no wind which keeps being ignored in your analysis.
On the vibration topic-Asking about vibrations having an effect is reasonable. Ignoring all the evidence which shows that it is inconsistent with results is not.
Overall,
When the questions get tough and they point out the problems in your argument, you duck them. This is indicative of someone who is emotionally tied to their line of thought and not open to learning.
There's not much point in responding to dramatically tortured counter explanations until you are willing to face up to the fundamentals. When (or if) this occurs, I'll be happy to discuss those with you. But again, I said "discuss", not listen to a one way diatribe of someone who is fighting just to stick to a preordained emotional based conclusion-which is of course "the cart can't work because I think it can't"
Fundamentally, I care that the
physics is correct and
not that I am.
You seem to be in the opposite world. Until this changes, we are worlds apart.
Windgrins