Re: <MISC> Re:Sport vs. HD Bilstein / Damping and resonance

[Bob Hazelwood <woodyh@xxxxxxxxxxxxx>]

> Knute Ream wrote

> OK, time for a quick explanation of what "damping" means...
>
> In electrical engineering, they refer this as an LC circuit, in which the
> balance between capacitance and inductance results in a damping constant,
> that determines how long the circuit will oscillate after being "twanged"
> at a given frequency.

Almost. An LC circuit actually describes a resonant circuit, which in the lossless
world of physics textbooks would result in constant ringing. If your car did this it
would bounce up and down perpetually once you got this resonance excited. (Hmmm. If
you somehow were able to use this energy to drive a fan which could.... but I
digress.) The "L" or inductance  is analogous to the vibrating mass or unsprung
weight, the "C" or capacitance is the spring. Now if you add an "R" to the equation
you can control the "R" to damp the resonance to whatever degree you would like.
Essentially the shocks are the "R-equivalent" in the equation. The remaining "R" is
the resistance due to friction between the various parts. The arrangement of the three
components in a suspension constitutes the mechanical equivalent of a low-pass filter.
Very high frequency excitation will not move the suspension much, this energy is
absorbed by the tire sidewalls. Low frequencies will move the wheels just fine. The
"crossover" occurs around resonance. The damping determines the abrupness of that
"crossover". The ratio of mass to compliance (inductance to capacitance) esssentially
moves the resonant frequency up or down. More mass and the frequency moves down, more
stiffness and it moves up. More mass implies more energy at resonance requiring more
resistance to optimally damp the resonance. You can start to see here how lowering the
unsprung weight with lighter wheels and tires can have a similar result to stiffening
the springs and shocks.

> (Perfect damping can only occur at one specific
> frequency unless there are "active" components in the circuit to alter the
> capacitance or inductance)

More correctly, _resonance_ will occur at one frequency. Damping can be either
frequency specific or broadband, depending on the circuit (mechanical or electrical).
It is definitely possible to have damping which varies with frequency as well as with
polarity. Damping which is the same regardless of frequency and polarity. Or anything
in-between. Different damping depending on polarity is essentially what is happening
when there are different stiffnesses for jounce and rebound with a given shock
valving.

> Your car is physical as opposed to electrical, but it's the same math.  You
> can easily observe the damping constant by leaning on car whose shocks are
> pretty well shot; you'll push down on the fender, and when you let it go,
> it will bounce up and down in progressively smaller cycles until it
> eventually comes to rest.  This situation is called "underdamped", because
> the oscillation persisted.  Overdamped means that your shocks are too
> stiff, in which case the same test (leaning on the fender) will let the
> fender rise more slowly than the perfectly damped situation, which would be
> no overshoot.
> <snip>

Theoretically correct (except the term optimum damping may be more appropriate than
perfect damping - nothing is perfect in the physical world outside of Hooters). This
may not be exactly what you want for the best ride/handling compromise. I really don't
know. This is the point where I defer to the suspension gurus. It's a great thing to
shoot for in a subwoofer however ;-)

And by the way. Thanks for not calling it "dampening" like so many of my audiophile
friends insist on doing!

Best regards,
Bob Hazelwood
VP Product Management, a/d/s/
'93 525i 5-sp. Sharked, BL/ss'd, H&R Capacitors and Bilstein Resistors, 17 x 8 Borbet
Type M Inductors.
BMW CCA (Boston Chapter)

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