Copyright Goodheart-Willcox Co., Inc.
128 Hydraulic Systems for Mobile Equipment
The difference in areas between a piston’s rod end and cap end affects the
cylinder’s output force and output speed. See Figure 6-4. If an equal amount
of pressure, such as 1000 psi (69 bar), was applied to both sides of a differential
cylinder simultaneously, the cylinder would extend. At fi rst glance it might
appear that the cylinder would be statically locked. However, as described by
Pascal’s law (Force = Pressure × Area), the difference in areas causes two dif-
ferent forces.
If the cylinder’s piston was three inches in diameter, the cap side area
would equal 7.07 in2. If the rod’s diameter was 1.5″, the rod would displace
1.77 in2 of area from the center of the ring, leaving only 5.3 in2 of area on the
ring. See Figure 6-5. Notice when 1000 psi is applied to both sides of the cyl-
inder at the same time that the net effective force is a factor of the cylinder’s rod
area, in this case 1.77 in2.
This principle of different areas within a double-acting cylinder will always
result in a stronger extension force than a retraction force for a given system
pressure. This principle is also necessary to understand cylinder regeneration,
which will be explained later in this chapter.
A similar characteristic exists for cylinder speeds. Chapter 2 explained
that, when given a fi xed amount of fl ow, a smaller cylinder area will result in
a faster cylinder speed. A larger cylinder area will result in a slower cylinder
speed. As a result, anytime a differential cylinder is used in a system with a
fi xed amount of fl ow, the cylinder will always retract faster and extend slower.
1000 psi
1000 psi
Piston Area
3 × 3 × 0.7854
7.07 in2
Rod Area 1.5 × 1.5 × 0.7854 1.77 in2
Ring Area 7.07–1.77 5.3 in2
Extension Force 1000 × 7.07 7070 pounds
Retraction Force 1000 × 5.3 5300 pounds
Net Extension Force 7070–5,300 1770 pounds
Figure 6-4. If an equal pressure is applied to both sides of a differential cylinder, the cylinder will extend because the
larger area will generate a larger force.
Figure 6-5. If a differential cylinder has an equal pressure applied to the rod and cap end simultaneously, the cylinder
will extend with a force equal to the rod’s area times the system’s pressure.