At 01:33 PM 1/23/99 -0800, Tom Hall wrote:
>At 10:16 AM 1/23/99 -0800, you wrote:
>
> It is important to recognize that the "brake hydraulic system" consists
>of
>both levers and cylinders. There are ratios for both at both ends which
>end up actually transferring or applying the mechanical force applied by
>your foot to the brake friction material. The stock mechanical ratio of
>the brake and clutch pedals are approximately 4.47:1. This means that for
>every 10 lbs you apply with your foot, about 44.7 lbs are applied to the
>piston in the cylinder. The hydraulic ratios take it from there. Remember
>also that essentially no system pressure is produced until the receiving
>cylinders move and the friction material contacts the discs and or drums.
>At this point the system develops a uniform hydraulic pressure (ignoring
>proportioning valves and similar devices). All of these ratios apply all
>the time to the total system dynamics. The booster is simply a device
>which provides linear amplification of the system pressure.
>
> All of these components are potential variables but it is important to
>know the change that will occur with substitution. Bob wanted to raise the
>clutch pedal so that it operated in a narrower range. His chance reduced
>the hydraulic ratio resulting in more slave movement at the price of higher
>pedal pressure. He could have also reduced the distance between the pedal
>pivot and the connection to the master cylinder with the same result, as
>long as the mechanical components stayed within appropriate operating ranges.
>
> Typical brake systems for race car applications are designed with a 6:1
>mechanical ratio so you can see why the stock 4.47 ratio typically
>requires boosting. Changing components is intriguing but it frequently
>alters the total system dynamics such as front rear brake bias so be
>prepared for some unexpected results until you've done some field testing.
>
Tom,
Thanks for pointing out (again) the importance of the mechanical part of
the system. BTW, probably only an engineer would call 4.47 "approximately".
Being a physicist, I'll just round that off to 4.5 thank you. Also, wrt
your statement: "He could have also reduced the distance between the pedal
pivot and the connection to the master cylinder with the same result, as
long as the mechanical components stayed within appropriate operating
ranges." I believe you meant "increased the distance" so as to reduce the
mechanical advantage.
Now, I suppose it would be helpful if we could come up with an easy way to
remember which way the mechanical advantage works in a hydraulic system. It
seems pretty obvious with a mechanical lever. The longer the lever arm, the
farther we have to push, but the easier it is. With the master/slave ratio
its still the farther we have to push, the easier it is, and a smaller
master bore requires more motion to accomplish the same motion of the
slave. So smaller master bore equates to longer lever arm. Now personally,
I think in terms of force times area, which has to be equal at each end,
but maybe that doesn't work for everyone. Or maybe we could think of the
master cylinder as another foot pushing back and the bigger that foot, the
harder he has to push. Anything clicking here Armand?
I think Armand's suggestion of changing the master cylinder, although to a
slightly smaller bore, might be a good alternative to a booster. Or, as Tom
alludes, you could increase the mechanical ratio at the pedal. The downside
to these ideas is that you increase the pedal travel required, so you can
only go so far with this approach; but maybe enough to make it acceptable
(e.g., 6:1)
Have a nice evening,
Bob
Robert L. Palmer
Dept. of AMES, Univ. of Calif., San Diego
rpalmer@ames.ucsd.edu
rpalmer@cts.com
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