No, it is not wrong and the numbers are correct. You don’t even need to read the entire paper, here is the relevant part again:
In the given example, 70 N is approximately 10% of a subject’s body weight which is mg. So a person with a mass of 70 kg has a weight (force) on the treadmill of approximately 700 N and 10% of that is 70 N. That is the same magnitude as the “noise” forces recorded on the treadmill with no subject on the treadmill. In fact, in the vertical direction the noise was 80 N. The readings of 60 N in the horizontal and lateral directions degraded the signal/noise ratio during physiological testing with subjects on the treadmill.
We don’t need to get into the physiology here, only the kinematics of the treadmill itself. What matters in this discussion is that even with a custom-made treadmill with specially machined rollers, significant forces were measured in all three spatial directions.
It is not difficult to imagine that a 60 N force concentrated in the frequency spectrum between 46 to 86 Hertz can have some effects on a 200 gram cart that is loosely coupled to the treadmill belt. In fact, it is nonsensical to think that it would have no effect!
I do not need to prove what the effect is to discount the Galilean transform of the cart on a treadmill to a cart on a road in a wind. I only need to show that these forces are present on the treadmill and they have not been transformed to the situation of the cart on the road. That is more than enough to say that such a transform is incorrect, incomplete and invalid!
No response to this? I think I know why!
Let’s start at the beginning and return to the issue of inertial reference frames.
Quoting from Wikipedia:
http://en.wikipedia.org/wiki/Inertial_frame_of_reference
The weakness of the principle of inertia lies in this, that it involves an argument in a circle: a mass moves without acceleration if it is sufficiently far from other bodies; we know that it is sufficiently far from other bodies only by the fact that it moves without acceleration.
There are several approaches to this issue. One approach is to argue that all real forces drop off with distance from their sources in a known manner, so we have only to be sure that we are far enough away from all sources to ensure that no force is present. A possible issue with this approach is the historically long-lived view that the distant universe might affect matters (Mach's principle). Another approach is to identify all real sources for real forces and account for them. A possible issue with this approach is that we might miss something, or account inappropriately for their influence.
Indeed, that is exactly what is happening when the carteers attempt a Galilean transformation of the cart on a treadmill to a cart on a road in the wind.
As noted and quoted above, there are forces acting on the treadmill belt on the order of 60 N. Considering the cart on the belt has a mass of about 0.2 Kg, exerting a downward force on the belt of about 2 N, and considering the propeller thrust of said cart is on the order of only 1 N, these forces on the belt are roughly
60 times greater than the propeller thrust, and
30 times greater than the weight of the cart on the belt.
Now consider what that implies for a 200 Kg cart on a road in the wind that has a propeller thrust of approximately 100 N. The downward force of the cart on the ground is about 2000 N or 20 times greater than the propeller thrust, while the small cart on the treadmill had a weight to thrust ratio of 2:1. That is a huge difference and in itself must invalidate any conclusions drawn from the cart on the treadmill being applied to the big cart in the wind.
But that is not all that is wrong with the carteer’s “transformation”. They have completely neglected to transform the belt forces on the treadmill to the situation with the cart on the road.
Those forces of 60 x the propeller thrust, and 30 x the cart weight, would
correspond to seismic forces of the ground motion on the order of 60,000 N !
As I stated earlier, the
only correct transform for a cart on a treadmill, that accounts for
all of the real forces present, would be a velocity transform only, that results in a cart that remains on a treadmill, and
nothing to do with a cart on a road in the wind.
This is not a matter of opinion. It is a matter of scientific fact. The transform the carteers are attempting to push off on the unwary is
completely wrong and deserves no further consideration.