# Inertia of Arm

Inertia of Arm is the moment of inertia of the entire arm around its center of gravity.

For an arm with a uniform cross-section along its length, the moment of inertia can be approximated by the formula,

where m is the mass of the arm, and L is the total length of the arm (Length of Long Arm + Length of Short Arm).

For a non-uniform arm, the moment of inertia can be found by breaking the arm up into simple shapes, finding the moment of inertia for each one, and then combining them together using the parallel axis theorem. A list of formulas for the moment of inertia of different shapes can be found here. See the Arm Example Calculations.

Alternatly, using a 3D CAD software package is probably the easiest way to find the inertia of a non-uniform arm.

For best performance, the moment of inertia of the arm should be as small as possible. This is why the arm is tapered on many trebuchets.

Note: When Auto Calculate is checked, the arm is assumed to have a uniform cross-section and the Inertia of Arm will be calculated automatically.

 Units English (feet)English (inches)Metric Length of Short Arm ft Length of Long Arm ft Length of Sling ft Length of Weight ft Height of Pivot ft Uniform arm Mass of Arm lb Inertia of Arm lb·ft² Pivot to Arm CG ft Mass of Weight lb Inertia of Weight lb·ft² Projectile BaseballGolf BallPumpkinCowCustom Mass of Projectile lb Projectile Diameter ft Wind Speed ft/s Release Angle ° Play speed: 1x Link to save this trebuchet

## VirtualTrebuchet 2.0

VirtualTrebuchet is a web based trebuchet simulator that will allow you to quickly evaluate different trebuchet configurations.

1. To begin, enter the parameters of your trebuchet in the input boxes.
2. Next, press the "Simulate" button located under the inputs.
3. Finally, watch your trebuchet go.