Rush is right in that the gravity is the force that slows down the
vehicle but not in the way you were thinking.
See, the way that the piezo elements can generate energy is by removing
it from a source, in this case the moving vehicle.
The piezo elements generate energy because a force works on them *and*
because they move (a force without movement by definition does not
generate energy). The movement of the Piezo elements is not
instantaneous, in fact they will generate the most energy when they only
yield slowly to the force, such that the largest possible force over the
largest possible time can act on them.
What does this mean for the movement of the road? Simple, when the
vehicle is entirely on the first piezo element, it is *not yet*
completely compressed, but it continues to be compressed while the
vehicle is already on it. Then when the vehicle reaches halfway, the
piezo element behind him has started to uncompress, but is not yet
halfway uncompressed and the piezo element in front of him is starting
to be compressed, but it is not yet halfway compressed.
The result of this is that the vehicle is driving a longer time on a
ramp upward than on a road that is tilting downward. And that is what is
causing the loss of energy, which is then harvested by the electricity
produced by the piezo elements.
It is quite simple Physics, but you need to take into account the
dynamic system, not the steady-state, because in the steady state that
was described, no energy is generated by the piezo elements (no movement
is no energy).
You can sketch a series of pictures where you assume that the piezo
elements continue compression for 1/4 of the roadway distance between
the piezo elements, the simple way of thinking about this is that they
respond 1/4 distance later than when they would respond instantaneously.
So, when the car is on top of element 1, it is 3/4 compressed while
element 2 is uncompressed
When the car is 1/4 distance down the road, element 1 is fully
compressed while element 2 is still uncompressed, about to start
compression.
When the car is halfway down the road, element 1 is back to 3/4
compression while element 2 is 1/4 compressed
When the car is 3/4 down the road, both elements are halfway compressed
and finally the road is even.
When the car is on top of element 2, element 1 is only 1/4 compressed
and element 2 is 3/4 compressed so for the last 1/4 distance the car has
been able to drive down the ramp, but at this very point it is entering
the next section of roadway that is tilted up because the point where
the car is, is already compressed and the next element is still
uncompressed, so for 3/4 of the distance it will drive up a ramp (which
will "sink" while the car is on it, that is what causes the piezo
elements to generate power)
Hope this clarifies the Physics involved, there *is* a force generate in
the horizontal plane *by* the gravity, due to the tilted road, just like
climbing a hill causes you to lose kinetic energy. In this case, you are
not gaining potential energy like in the case of climbing the hill and
regaining it when you descend, but instead the "hill" is created by the
piezo elements that are generating energy, tapping from the forward
motion of the car.

Cor van de Water 
Chief Scientist 
Proxim Wireless 
  
office +1 408 383 7626                    Skype: cor_van_de_water 
XoIP   +31 87 784 1130                    private: cvandewater.info 

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-----Original Message-----
From: EV [mailto:[email protected]] On Behalf Of via EV
Sent: Friday, August 26, 2016 6:58 PM
To: Rush Dougherty; Electric Vehicle Discussion List
Subject: Re: [EVDL] Piezo-power> 10mi of freeway could charge all the
EVs inBurbank-CA(?)


> I think you've forgotten about a little pesky thing called gravity...
and while
> the distances maybe similar, the energy needed to get the 'vehicle'
back up to
> the same level, the rise, is more than the energy gained on the fall. 

Best check your physics Rush. That same resistance to rising is what
makes objects crash into the ground. While there are losses, gravity
isn't one of them. 
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