# The Helicopter

### Model Description

This training aid demonstrates the translational and rotational kinematics of a rigid body in a non-rotational frame. This demonstration should take 10-15 minutes.

### Engineering Principle

Building upon the concept of Rotation About a Fixed Axis (RAFA), the helicopter provides an excellent example to step into general planar motion (GPM) by first demonstrating the hovering helicopter (RAFA) and then demonstrating the helicopter flying (GPM).  Intuitively, this is comfortable and the development of vector equations becomes the tool to describe what the students already know.

$v_b = v_a + v_{b/a}$          $a_b = a_a + a_{b/a}$

$v_b = v_a + \omega \times r_{b/a}$          $a_b = a_a + \alpha \times r_{b/a} - \omega^2 r_{b/a}$

where $\alpha$ = angular acceleration and $\omega$ = angular velocity

### What You Need

Item Quantity Description/Clarification
Toy Helicopter 1 A bigger model is useful here to better see the discussed principles in action.

### How It’s Done

Before Class: Acquire a toy helicopter.

In Class: Helicopter clips start the lesson and the helicopter training aid is utilized to motivate the need for the derivation of the equations.  The example problem for the lesson is then solved.

Additional Application: Helicopter Trivia – American and British helicopter rotors rotate counter clockwise.  Soviet and French rotors rotate clockwise.

As a helicopter travels forward, the velocity of the rotor blades on each side of the aircraft becomes unequal.  This produces an uneven amount of lift and would cause the aircraft to tilt to one side if left uncorrected.  Modern helicopters address this dissymmetry of lift by allowing the blades to flap up on the advancing side and down on the retreating side and hunt forward on the advancing side and lag on the retreating side.

### Cite this work as:

Tom Messervey (2019), "The Helicopter," https://www.handsonmechanics.org/dynamics/597.