§ 18

Hydraulic brake: pressure and brake torque

How much more braking torque does a smaller master cylinder give?

Answer: The force from the hand is amplified by the grip's lever arm and becomes pressure in the master cylinder. Pressure is even throughout the system, so the calliper's pistons press the linings against the disc with pressure times piston area. The calculator shows pressure, clamping force and brake torque, and what it means to switch to a different master cylinder, calliper or dual disc. All measurements and friction figures come from manufacturer's data or your own measurements.

Formula

Kraft på hovedcylinderen = håndkraft × grebsudveksling

Tryk p = kraft ÷ (π/4 × hovedcylinder-Ø²). 1 N/mm² = 10 bar

Klemkraft = p × π/4 × stempel-Ø² × stempler på én side

Bremsemoment = 2 × µ × klemkraft × effektiv radius × antal skiver

The ratio between the calibre's piston area per side and the master cylinder's area is the system's hydraulic ratio

Symbols and units in the formula
Symbol	Meaning	Unit
grebskraft_n	Force from hand on grip	N
grebsudveksling	Handle ratio (handle length ÷ distance from pivot to plunger)	—
hovedcyl_mm	Master cylinder piston Ø	mm
stempel_mm	Calibre stamps' Ø	mm
stempler_side	Punches per side in calibre	—
skiver	Number of discs on the wheel	—
mu	Friction coefficient µ (coating data)	—
radius_mm	Effective brake radius (hub centre to centre of lining)	mm
=	Hydraulic pressure	bar
=	Clamping force per calibre	kN
=	Braking moment on the wheel total	Nm

Validity and source

Source: Fysik: p = F ÷ A (Pascals lov) · bremsemoment = 2 × µ × F × r

Does not apply when

Smaller master cylinder gives more braking force for the same hand force, but longer lever travel. Never change master cylinder or bore without checking the manufacturer's recommended combination. Brakes are safety-critical: always test drive and check.

Worked example

The calculator's own default values inserted. The figures are calculated with exactly the formula the tool uses.

Substituted

Force from hand on grip100 N
Handle ratio (handle length ÷ distance from pivot to plunger)5
Master cylinder piston Ø16 mm
Calibre stamps' Ø32 mm
Punches per side in calibre2
Number of discs on the wheel2
Friction coefficient µ (coating data)0.45
Effective brake radius (hub centre to centre of lining)135 mm

Giver

Hydraulic pressure24.9 bar
Clamping force per calibre4.00 kN
Braking moment on the wheel total972 Nm

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Sådan bruger du den

Når en kunde vil have bedre bremser, eller du fejlfinder på en svag bremse, kan du regne kæden igennem fra hånden til skiven: tryk, klemkraft og bremsemoment. Beregneren viser hvad en anden hovedcylinder, en anden kaliber eller en dobbeltskive gør.

Step by step

Tast håndkraften og grebets udveksling.
Tast hovedcylinderens diameter. Det giver trykket.
Tast kaliberens stempler og diameter. Det giver klemkraften.
Tast friktionstal, bremseradius og antal skiver for bremsemomentet.

Typical errors

At regne stemplerne på begge sider med i klemkraften.
At glemme faktor 2 for de to belægninger.
At tro at en mindre hovedcylinder altid er bedre. Vandringen bliver længere.

Examples from everyday life

Motorcykel med dobbeltskive

En motorcykel har 16 mm hovedcylinder og to 4-stempels kalibre med 32 mm stempler. Føreren trækker grebet med 100 N.

Force from hand on grip: 100 N
Handle ratio (handle length ÷ distance from pivot to plunger): 5
Master cylinder piston Ø: 16 mm
Calibre stamps' Ø: 32 mm
Punches per side in calibre: 2 per side (4-piston calliper)
Number of discs on the wheel: 2 discs (double disc front)
Friction coefficient µ (coating data): 0.45
Effective brake radius (hub centre to centre of lining): 135 mm

It means: Trykket er 24.9 bar, hver kaliber klemmer med 4 kN, og forhjulet får 972 Nm bremsemoment.

Mindre hovedcylinder

Kunden vil skifte til en 14 mm hovedcylinder for at få mere bremsekraft.

Force from hand on grip: 100 N
Handle ratio (handle length ÷ distance from pivot to plunger): 5
Master cylinder piston Ø: 14 mm
Calibre stamps' Ø: 32 mm
Punches per side in calibre: 2 per side (4-piston calliper)
Number of discs on the wheel: 2 discs (double disc front)
Friction coefficient µ (coating data): 0.45
Effective brake radius (hub centre to centre of lining): 135 mm

It means: Trykket stiger til 32.5 bar, og bremsemomentet til 1,270 Nm. Grebet skal til gengæld bevæges længere, og producentens anbefalede kombination skal følges.

Hydraulisk skivebremse på en cykel

En MTB har 10 mm hovedcylinder, en 2-stempels kaliber (ét stempel pr. side) med 22 mm stempler og en 180 mm skive (bremseradius ca. 80 mm). Rytteren trækker med 80 N, og grebet har udveksling 4.

Force from hand on grip: 80 N
Handle ratio (handle length ÷ distance from pivot to plunger): 4
Master cylinder piston Ø: 10 mm
Calibre stamps' Ø: 22 mm
Punches per side in calibre: 1 (floating calliper or 2-piston opposed)
Number of discs on the wheel: 1 disc
Friction coefficient µ (coating data): 0.45
Effective brake radius (hub centre to centre of lining): 80 mm

It means: Trykket er 40.7 bar, klemkraften 1.55 kN, og bremsemomentet 112 Nm. En større skive giver mere moment uden større håndkraft.

Rule of thumb

Halveret hovedcylinder-areal giver dobbelt tryk og dobbelt bremsemoment for samme håndkraft.

How to check the answer

Dobbelt håndkraft skal give dobbelt tryk og dobbelt moment.