Title: How to Calculate the Force Output of an Extending Cylinder
Course: Fluid Power Pneumatics (Sandbox) > Section: Module 6: The Principle of Pneumatic Pressure and Force - 2 Hours

The Key Principles of Pneumatics

Up to this point, we have talked about various components that make up a pneumatic circuit. We have touched somewhat on the theory behind pneumatics and now we are going to dive a little deeper into key principles of pneumatics: pressure, flow, force, and volume. Once you start to understand these principles, it becomes easier to troubleshoot systems when problems arise.

Pressure vs Cylinder Force

If a pneumatic cylinder is extending a load, the pressure of the air is exerted equally to all the surfaces in the cap end of the cylinder (Pascal's Law). However, only on the area of the piston does this pressure exert a force to move the load. The force output of the cylinder rod, therefore, depends on the area of this piston and the pressure in the cap end of the cylinder.

This directly relates to how much a cylinder can lift. The greater the area (or size of the cylinder), the more the cylinder can lift.

Parker Hannifin Corporation. (1980). Industrial Pneumatic Technology. Parker Hannifin Corp. DOI: 1557690154

So, let's look at a cylinder piston. Cylinder pistons are always round.

Parker Hannifin Corporation. (1980). Industrial Pneumatic Technology. Parker Hannifin Corp. DOI: 1557690154

As we stated above, we want to calculate how much a certain cylinder can lift at a given pressure. In order to do that, we must be able to calculate how many square inches there are in a round object.

Formula:

To do this we use the following formulas:

F= P x A

- Force = Pressure x Area. You were introduced to this formula at the beginning of this class.
- Force is measured in lbs (pounds)
- Pressure is measured in psi (pounds per square inch)
- Area is measured in square Inches

Example:

I have 100 psi of air in my system, and I have a 2" diameter piston. I want to know how big of a load my cylinder can lift.

In order to do this, we have to calculate the diameter of the piston into square inches. We use the following formula to do this:

Area of a cylinder in square inches = Diameter^2 x 0.7854 (D^2 x 0.7854)

So, if we have a cylinder that is 2" in diameter, we need to square it (2^2 = 4) and then times that by 0.7854, which would give us 3.14 square inches. We can now put that into our formula (F = P x A).

F = 100 psi x 3.14 square inches

F = 314 lbs

That means our cylinder can lift 314 lbs.

Now, let's say that we change the diameter of the cylinder to 4". How does that affect the system?

D^2 x 0.7854

4^2 x 0.7854

16 x 0.7854 = 12.56 square inches

F = P x A

F= 100 x 12.56

F = 1256 lbs

You can see that as we increase the size of the cylinder, the ability to do more work increases. Just by changing the size of the cylinder 2" in diameter, we went from a lifting capacity of 314 lbs to 1256 lbs. Size does matter in fluid power.

Now use this knowledge to answer the following quiz questions.

Extra Resources

I have also included the following video to help explain how to calculate using the formulas:

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