Lab Manual | Gyroscopic Effect

AIM :- To study gyroscopic effects through models.

APPARATUS USED:- Models of Aero plane and ship.

THEORY :- The earliest observation and studies on gyroscopic phenomenon carried out during Newton’s time. These were made in the context of the motion of our planet which in effect in a massive gyroscopic. The credit of the mathematical foundation of the principles of gyroscopic motion goes to Euler who derived at set of dynamic equation relating applied mechanics and moment inertia, angular acceleration and angular velocity in many machines, the rotary components are forced to turn about their axis other than their own axis of rotation and gyroscopic effects are thus setup. The gyroscopes are used in ships to minimize the rolling & pitching effects of water.

Effect of the Gyroscopic Couple on an Aeroplane :-

1. When the aeroplane takes a right turn under similar conditions. The effect of the reactive gyroscopic couple will be to dip the nose and raise the tail of the aeroplane.
2. When the engine or propeller rotates in anticlockwise direction when viewed from the rear or tail end and the aeroplane takes a left turn, then the effect of reactive gyroscopic couple will be to dip the nose and raise the tail of the aeroplane.
3. When the aeroplane takes a right turn under similar conditions as mentioned in note 2 above, the effect of reactive gyroscopic couple will be to raise the nose and dip the tail of the aeroplane.
4. When the engine or propeller rotates in clockwise direction when viewed from the front and the aeroplane takes a left turn, then the effect of reactive gyroscopic couple will be to raise the tail and dip the nose of the aeroplane.
5. When the aeroplane takes a right turn under similar conditions as mentioned in note 4 above, the effect of reactive gyroscopic couple will be to raise the nose and dip the tail of the aeroplane.

The effect of gyroscopic couple on the naval ship in the following three cases :

1- Steering 2- Pitching and 3- Rolling

Effect of the Gyroscopic Couple on a Naval ship during Steering :-

1. When the ship steers to the right under similar conditions as discussed above, the effect of the reactive gyroscopic couple will be to raise the stern and lower the bow.
2. When the rotor rotates in the anticlockwise direction, when viewed from the stern and the ship is steering to the left, then the effect of reactive gyroscopic couple will be to lower the bow and raise the stern.
3. When the ship is steering to the right under similar conditions as discussed in note 2 above, then the effect of reactive gyroscopic couple will be to raise the bow and lower the stern.
4. When the rotor rotates in the clockwise direction when viewed from the bow or fore end and the ship is steering to the left, then the effect of reactive gyroscopic couple will be to raise the stern and lower the bow.
5. When the ship is steering to the right under similar conditions as discussed in note 4 above, then the effect of reactive gyroscopic couple will be to raise the bow and lower the stern.
6. The effect of the reactive gyroscopic couple on a boat propelled by a turbine taking left or right turn is similar as discussed above.

Effect of the Gyroscopic Couple on a Naval ship during Pitching :-

1. The effect of the gyroscopic couple is always given on specific position of the axis of spin, i.e. whether it is pitching downwards or upwards.
2. The pitching of a ship produces forces on the bearings which act horizontally and perpendicular to the motion of the ship.
3. The maximum gyroscopic couple tends to shear the holding-down bolts.
4. The angular acceleration during pitching.

α = d²θ/dt² = -Φ(ω₁)² sin ω₁t (Differentiating dθ/dt with respect to t)

The angular acceleration is maximum, if sin ω₁t = 1

Therefore Maximum angular acceleration during pitching,

α_max = Φ(ω₁)²

Effect of the Gyroscopic Couple on a Naval ship during Rolling:- We know that, for the effect of gyroscopic couple to occur, the axis of precession should always be perpendicular to the axis of spin. If, however, the axis of precession becomes parallel to the axis of spin, there will be no effect of the gyroscopic couple acting on the body of the ship.

In case of rolling of a ship, the axis of precession (i.e. longitudinal axis) is always parallel to the axis of spin for all positions. Hence, there is no effect of the gyroscopic couple acting on the body of a ship.

APPLICATIONS :- The gyroscopic principle is used in an instrument or toy known as gyroscope. The gyroscopes are installed in ships in order to minimize the rolling and pitching effects of waves. They are also used in aeroplanes, monorail cars, gyrocompasses etc.

VIVA – QUESTIONS :-

• Write a short note on gyroscope.
• What do you understand by gyroscopic couple ? Derive a formula for its magnitude.
• Explain the application of gyroscopic principles to aircrafts.
• Discuss the effect of the gyroscopic couple on a two wheeled vehicle when taking a turn.
• When the pitching of a ship is upward, the effect of gyroscopic couple acting on it will be to move the ship towards port side or to move the ship towards star-board.