Performance Bikes — March 2018

80 PERFORMANCEBIKES.CO.UK|MARCH2018

BRAKE MOD WISDOM

Conventional master cylinder

On a standard fixed-pivot axial master cylinder, braking strength and efficiency is

compromised by a rider’s brake input force acting at a right-angle to the hydraulic force.

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AT THE CALIPER

Our 348.5lb.in^2 of fluid

pressure is in for another

major boost when it arrives

at the caliper because it is

multiplied by the area of the

pistons (let’s say 5.3in^2 ).

That gives us a whopping

1847.05lb of force.

Input force

Piv

Hydraulic force

C

Piston area = p nC^2 /4

Number of pistons = n

Force at pad = pressure x p

nC^2 /4

Pad Pad

Caliper

BRAKE FLUID

Brake hose

PISTON

effort force is applied to the smaller syringe, it exerts a

load force on the larger one. Again, allowing for the fact

that the fluid doesn’t compress and supposing the tube

(line) doesn’t expand, the pressure created by the force

applied at the smaller syringe (master cylinder) arrives

undiminished at the larger plunger of the syringe

representing our caliper. Because the load force on the

larger plunger is calculated as the effort force at the

smaller syringe multiplied by the area of the large

plunger divided by the smaller one, the load force is

greater than the effort force. Indeed it has been

multiplied through the arcane marvel of hydraulics;

the hydraulic multiplier effect.

Add it up

Just to check we’re on the right track, we’ll test the

theory with a sum. Let’s say the small syringe has a

10mm bore and the larger one a 20mm bore and we

apply a 20Nm force to the former. The area of a circle is

pi times its radius squared (r^2 ), so for the small bore

it’s 3.14 x 52 = 78.5mm^2 and for the large it’s 3.14 x 102

= 314mm^2. Dividing the large by the small we get 4,

which if we then multiply by the effort of force of 20Nm

we find we have a load force of 80Nm bearing on the

larger plunger. Add in a few more pistons of the same

area at the big syringe/caliper end and that’s some

amount of force being applied at the business end.

The distance the pistons travel differs. The smaller

one moves further. This equates to what we refer to as

‘stroke’ at the master cylinder end of a braking system.

Under pressure

Fluid pressure is also a key consideration. This is

calculated by dividing the effort force by the area of the

small plunger (syringe or master cylinder). As hydraulic

systems are closed, this pressure is the same at both