**Objective**

To calculate the efficiency of energy transfer between battery and flywheel and between flywheel and battery. Refer the characteristics plotted in the data set and observe the current intake(positive) when the flywheel draws energy from the battery and the current output(negative) when the flywheel gives energy to the battery for charging. A similar graph should be obtained and one should be able to observe regenerative braking from the graph.

**Background Theory**

A flywheel is a rotating mass connected to the shaft of an electric motor/generator. Chemical energy is taken from the battery as electrical energy and used to accelerate the rotating mass. Thus; kinetic (mechanical) energy is stored in the flywheel. Then, by using the motor as a generator the kinetic energy in the flywheel can be converted back into electrical energy, and re-stored in the battery as chemical energy.

The energy stored in the flywheel equates to the electrical energy taken from the battery minus the energy lost as heat.

There are two efficiency calculations do be done.

The efficiency of the energy transfer when accelerating the flywheel and

The efficiency of the energy transfer when decelerating the flywheel.

**Electrical Energy Calculation**

The electrical energy taken from the battery is calculated using voltage multiplied by current, multiplied by time in seconds. V x I x t.

The time (t1), in this case, is the time taken for the flywheel to accelerate from 0 rpm to the pre-set value of N rpm.

The time (t2), in this case, is the time taken for the flywheel to decelerate from N rpm to 0 rpm.

The current, in this case, is the current drawn from the battery, measured every 0.5 seconds, over the same time frames (t1 and t2).

The voltage, in this case, is the voltage across the battery, measured every 0.5 seconds, over the same time frames (t1 and t2).

**Flywheel Energy Calculation**

This flywheel has a pre-set maximum speed of ..... rpm. The formula for the kinetic energy of a rotating mass is given by

E = ½ * I * ω^{2},

Where I is the moment of inertia and ω is the angular velocity.

For a thick walled cylinder, such as this flywheel,

I = ½ * m * (r12 + r22),

where

r12 is the inner radius of the cylinder, and

r22 is the outer radius of the cylinder.

Efficiency of energy transfer = Mechanical energy stored in flywheel / Electrical energy taken from (or returned to) the battery x 100%