Lab Manual | To determine gyroscopic couple on Motorized Gyroscope.

AIM :- To determine gyroscopic couple on Motorized Gyroscope.

APPARATUS USED:- Four wheeler & two wheeler vehicle.

THEORY :- When a body moves along a curved path with a uniform linear velocity, a force in the direction of centripetal acceleration (known as centripetal force) has to be applied externally over the body, so that it moves along the required curved path. This external force applied is known as active force. When a body, itself, is moving with uniform linear velocity along a circular path, it is subjected to the centrifugal force radially outwards. This centrifugal force is called reactive force.

The change in angular momentum is known as active gyroscopic couple(I.ω.ω_p). When the axis of spin itself moves with angular velocity ω_p, the disc is subjected to reactive couple whose magnitude is same (i.e. I.ω.ω_p ) but opposite in direction to that of active couple.

OBSERVATION :-

• Mass of the vehicle (m) = ———— kg.
• Weight of the vehicle (W) = ——— Newtons.
• Radius of the wheels (r_w ) = ———– metres.
• Radius of curvature ( R ) = ———– meters.
• Distance of centre of gravity, vertically above the road surface(h) = ———– metres,
• Width of track (x) = ——————–metres,
• Mass moment of inertia of one of the wheels( I_w ) = —————–kg-m²
• Angular velocity of the wheels or velocity of spin(ω_w) = ————rad/sec
• Mass moment of inertia of the rotating parts of the engine(I_E) = ———- kg-m²
• Angular velocity of the rotating parts of the engine (ω_E) = ————rad/sec
• Gear ratio = ω_E /ω_w
• Linear velocity of the vehicle (ν) = r_w ω_w
• Angle of heal (θ) = ——– rad.

CALCULATION :-

For 4-wheel drive:

• Gyroscopic couple due to 4 wheels, C_w = 4 I_w ω_w ω_p where, (ω_{p =} ν/R)
• Gyroscopic couple due to the rotating parts of the engine, , C_E = I_E ω_E ω_p = I_w.G. ω_w. ω_p
• Net Gyroscopic couple, C = C_w ± C_E

For 2-wheel drive:

• Gyroscopic couple, C₁ = ν (2 I_w ± I_E._.G) cosθ /R. r_w

PRECAUTIONS :-

• When rotating parts of the engine rotate in opposite directions, then negative sign is used.
• When C_E ›C_w, then C will be negative. Thus the reaction will be vertically downwards on the outer wheels and vertically upwards on the inner wheels.
• The gyroscopic couple will act over the vehicle outwards i.e. in the anticlockwise direction when seen from the front of the vehicle. The tendency of this couple is to overturn the vehicle in outward direction.

RESULT :-

• Gyroscopic couple of four wheel drive is = ————–N-m.
• Gyroscopic couple of two wheel drive is = ————–N-m.

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.