Why force multiplication is key to how hydraulic systems work

Why force multiplication is key to how hydraulic systems work

What is force multiplication?

Pascal’s law states that pressure set up in a confined body of fluid, acts equally in all directions, and always at right angles to the containing surface. When a pressure is applied to a fluid trapped in a confined space, that pressure acts on each square millimeter of that surface. The force output of a hydraulic actuator is the result of the pressure applied, and the area to which that pressure is applied.

Force = Pressure x Area

If a given pressure is applied to two identical cylinders, then they will have an equal output force.

How does force multiplication work?

When the same pressure is applied to different sized cylinders, then the larger cylinder will have a greater force output. This is because the area which sees the hydraulic pressure is greater.

Hydraulics Force Multiplication Different Sized Cylinders

Different cylinder sizes create different pressures

The cylinder on the right in this example is twice the diameter of the cylinder on the left.

The area of the circle multiplies the force

The area of a circle is calculated by this formula:

Hydraulics Force Multiplication Circle Area Formulas

The area of a circle = Pi x the radius squared

When a given pressure is applied to two different sized areas, the larger area will see a larger force output than the smaller area. This force differential is often significant. For example, while a 200mm diameter circle is twenty times larger than a 10mm circle in diameter, the area differential between the two is 400 to 1. When pressure is applied, the output force increase would also be 400 to 1.

A bottle jack piston uses force multiplication

A hydraulic bottle jack is a perfect example of force multiplication at work.

A reciprocating piston is moved with a hand lever. This piston applies pressure to the fluid, which is then fed through and applied to a larger piston. The output force is magnified due to the area differential of the two pistons, thus making it possible to lift a car by hand. The bottle jack piston moves slowly in relation to the pump piston because of the volume differential between the two chambers.

The weight of a load affects the hydraulic pressure

The hydraulic pressure required to lift a load is dictated by the mass of the load, and the area to which it is applied.

Hydraulics Force Multiplication - Load Induced Pressure Large

The weight of a load changes the hydraulic pressure required

The three cylinders on the left are all lifting the same weight, 20,000kg, (20T). This mass applies a force of 19,600N to the piston area of the cylinder. The hydraulic pressure that is created is called the load induced pressure. i.e. The pressure that is induced in the fluid by the load applied to it. When the same force applied to different cylinder areas, the load induced pressure will be highest in the smallest cylinder.

Load induced pressure vs system pressure

When the pressure applied to a cylinder is greater than the load induced pressure, the cylinder will begin to move forward and lift the load. As the load is lifted, the pressure seen within that area of the circuit is generally that of the load induced pressure, as long as there is no resistance to movement.

As the cylinder mechanically reaches the end of its stroke, the pressure will rise to the maximum allowed within that area of the system. This maximum pressure allowed is limited by valving such as pressure relief valves, pressure reducing valves or similar hydraulic fittings.

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A beginners guide to hydraulics and fluid transmission

A beginners guide to hydraulics and fluid transmission

What does “Hydraulic” mean?

The term “Hydraulic” is derived from ancient Greek. The word “hydraulics” originates from the Greek word hydraulikos which in turn originates from hydraulos meaning water organ which in turn comes from hydor, Greek for water, and aulos, meaning pipe. It’s also defined as “operated by pressure transmitted through a pipe by a liquid, such as water or oil.” [Collins Dictionary]

How do hydraulic machines work?

Generally speaking, a hydraulic machine gains controlled motion through the use of a transmitted fluid. There is a common assumption that a machine operated by a fluid is a hydraulic machine, but this is not always the case. The water wheel above on the left turns with the weight of the water. But it is not a hydraulic machine.

A correct definition of a hydraulic system is one where motion and force output is created by the use of a pressurised fluid. In the case of the water wheel, the fluid is not entrapped, and therefore, pressure cannot be applied to it at any point.

Hydraulics Introduction Blaise Pascal Laws

Blaise Pascal defined The Fundamental Laws of Hydraulics

What is Pascal’s law?

Blaise Pascal was born in 1623 and died in 1662 at the age of 39. Pascal defined the first of two fundamentals of hydraulics – known as Pascal’s Law.

The first fundamental rule of hydraulics

Pascal’s law states that pressure set up in a confined body of fluid, acts equally in all directions, and always at right angles to the containing surface. Hydraulics Introduction Blaise Pascal Laws

The second fundamental rule of hydraulics

A second important fundamental of hydraulics is that a fluid is considered to be virtually incompressible. It will compress in volume about one third of a percent for every 70 Bar or 1000 PSI of applied pressure. In this example, as pressure was manually applied, the plunger would not be able to move down the measuring flask unless the fluid was able to escape. The applied pressure would shatter the glass flask very quickly.

Mechanical Transmission

Motion, force and power can be transmitted through a solid object. In cases of direct force transmission, the output force will be equal to the input force, minus some friction. For example, if the input force is 25 Newtons, the output force will be 25 Newtons minus an amount of friction.

How does fluid transmit force and movement?

Fluid can be used to transmit force and movement. This is possible because the fluid will act as a solid when it is held in a confined space.

Hydraulics Introduction Mechanical vs Fluid

Mechanical vs Fluid Transmission

Due to Pascal’s Law, any pressure that is applied to the fluid at piston 1 will be transmitted to piston 2. If the areas of the pistons are the same, there will be a direct force transmission.

The first advantage of fluid transmission

The first advantage of fluid transmission is that the direction of output force is not confined to the same axis of the input force. In the example above, the output movement and force is at 90 degrees to the direction of input.

The second advantage of fluid transmission

The second advantage of transmitting power through a fluid is that the fluid may be transmitted through a tube, pipe or high pressure hose. This makes it possible for the output force to be directed anywhere, and to be applied from a distance.

Hydraulic Applications for Felling Heads

The forestry equipment shown above is a typical example of a hydraulic application. Hydraulics allows the application of controlled motion and power in limitless directions.

Need more information?

To help you choose the right hydraulic hose and fittings for your project, download our guide with 15 Keys to Selecting the Right Hose.