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RE: Dual Brake Master Cylinder Conversion-Long Technical Reason

To: <rpalmer@ucsd.edu>
Subject: RE: Dual Brake Master Cylinder Conversion-Long Technical Reason
From: James Barrett <jamesbrt@mindspring.com>
Date: Wed, 07 Feb 2001 21:06:47 -0500
        Consider that the fluid displaced by the first piston
does two things, one it supplies fluid and pressure to the
front brakes.  Second it supplies fluid and pressure to the
second piston in the master cylinder. 

In the following description the "front" piston is the one closest
to the firewall which normally operates the front brakes.  The "rear"
piston is the free floating  one at the far end of the master cylinder
that operates the rear brakes.
        Consider a hypothical example where the area of the
each master cylinder pistons  is 1 square inch.  Also assume that the
area of each brake cylinder ( disk or drum) is 1 square inch.
Assume that each brake cylinder can move 1/4 inch before they
stop. (At the stop point only pressure can change)

( Using the above  values to ease calculations and understanding).

Assume first that one has a single piston master cylinder.
Assume that the master cylinder piston is pushed in 1 inch 
with a force on the cylinder push rod of 100 pounds. This 
provide a fluid displacement of 1 cubic inch and a pressure 
of 100 psi .

With 4 brake cylinders, each cylinder will be displaced
1/4 cubic inch.  As pressure in the master cylinder is 100
psi then each brake cylinder will also have 100 psi (and a
fluid displacement of 1/4 cubic inch).  Therefore the front brake
pair requires 1/2 cubic inch fluid at 100 psi ( 2 X 1/4 cubic inch).
Like-wise the rear pair of brake cylinders require 1/2 cubic inch
at 100 psi ( again 2 X 1/4 cubic inch).  Pressure in a static hydralic
system is constant  no matter where you measure it. i.e every one gets the
100 psi pressure).

Now consider the inline cylinders.  The front cylinder connects to two
front cylinders and also pushes the rear master cylinder piston 
with the brake fluid.
        If the braking is the same as for the single master cylinder 
then 1/2 cubic inch of fluid ( 2 at 1/4 cubic inch) must be supplied at 100 psi
to the front brakes.  Assuming you pushed the same on the dual
inline,  (1 inch at 100 psi), then the rear piston will move 1/2 inch
with 100 psi.  The other end of the rear piston will displace
1/2 cubic inch of fluid at 100 psi ( neglecting some minor friction and
internal return springs).  This 1/2 cubic inch of fluid at 100
psi is exactly what the rear brakes received with the single cylinder.

        Another way to think about the dual inline cylinder is to
assume the rear cylinder is remote from the front cylinder and connected via
a brake line.  The rear cylinder is therefore "free floating" in its own
cylinder.  The only pressure on that cylinder is from the front cylinder.

In the real world, the rear cylinder can not be remote, because the front
cylinder has a push rod that contacts the rear cylinder ONLY when the front
brakes fail and there is no hydralic fluid available to push the rear cylinder.

Now for the side by side cylinders.
        Assume each cylinder also has an area of 1 square inch.
Assume that the bar linking the two cylinders is pushed at exactly
the center.  One cylinder feeds the front brakes and therefore needs 1/2
cubic inch of fluid at 100 psi.  The other cylinder feeds the rear brakes
 and also needs 1/2 cubic inch fluid at 100 psi.
If one were to push the center of the link bar with 100 pounds then the
force is divided by two and 50 pounds is applied to each cylinder.  
The displacement required for each cylinder is 1/2 cubic inch so one only has to
push a distance of 1/2 inch, however the pressure is only 50, so the force
must be doubled to 200 pounds to provide 100 psi at the wheel cylinders.

        Therefore if one uses a dual inline cylinder to replace a single
master cylinder, then the same bore diameter can be used with no increase
in the peddle pressure to stop at the same rate.  To use dual cylinders
side by side with a link bar, if you use the same bore as the single cylinder,
then the peddle force will need to be doubled, but the peddle movement will
be only
1/2 as as far.  For side by side dual cylinders, to keep the same peddle
force then one should use dual cylinders, each with 1/2 the AREA of the single
master cylinder piston.  Area is 3.14 X radii squared. or Pie R^2.

        My dad said pie are round, corn bread are square. %-).

Now you know ( I hope).

At 08:56 PM 2/5/2001 -0800, you wrote:
>Very interesting that the force for two in-line pistons isn't twice that of
>a single piston master cylinder. Why don't the forces just add? Is there
>something internal that makes it work different that two separate master
>cylinders side-by-side? Inquiring minds want to know.
>-----Original Message-----
>From: owner-tigers@autox.team.net [mailto:owner-tigers@autox.team.net]On
>Behalf Of James Barrett
>Sent: Monday, February 05, 2001 5:39 PM
>To: tigers@autox.team.net
>Subject: Dual Brake Master Cylinder Conversion
>        Just replaced my single master cylinder with a
>13/16" dia dual master cylinder removed from a Mustang
>Power Brake Unit.  Had to fabricate a push rod and a
>spacer( presently 3/8" thick).  Had to drill a couple
>of holes in the firewall as the "ears" of the cylinder
>are horizontal, not vertical like the Girling.  Cut one
>"ear" nearest the steering column and redrilled it closer
>to the Master cylinder body.  The total piston travel is
> 1 5/16"( with brake lines disconnected).  This causes
>the peddle to be higher than I perfer.  I may adjust the
>firewall(non stock Tiger) to give me about an inch lower
>peddle before I bottom out on the cylinder and the
>firewall at the same time.  This bottoming out design
>assumes that the front brake lines would have failed.
>        The pressure needed to stop is slightly less than
>the original 7/8" Girling (with no power booster).
>        The Master cylinder is aluminum and the outlets
>are on the passenger side of the cylinder.  I used adapters
>to mate with new 3/16" brake lines.  Used double V flare
>connections.  ( Used my new RIGDID flaring tool that works!).
>    Previously I had  a 7/8" Cast Iron Mustang dual cylinder
>and found that the fittings came off the driver's side
>and interferred with my hand made frame brace.
>         Also at the time I was convienced that a dual
>cylinder would require twice the force to push as a
>single cylinder of the same diameter.  Wrong  and right.
>Inline dual cylinders do not double the needed force.
>(I found it hard to believe myself until I did a lot
>of math and graphics.)
>Side by side single cylinders  do double the force
>required and also push twice the fluid volumn per distance
>pushed compared to the inline cylinder.
>James Barrett Tiger II 351C and others
James Barrett Tiger II 351C and others

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