Topic Name :
Gyroscope
Group Presenters:
1.
2.
3.
4.
Wahaj Ahmad
Hassan Baber
Mujtaba Abbas
Hassaan Tariq
Overview
Introduction.
Precessional angular motion.
Gyroscopic couple.
Effect of gyroscopic couple on airplane.
Terms used in Naval ships.
Effect of gyroscopic couple during steering, pitching and rolling.
Stability of a four wheel drive moving in a curved path.
Stability of a two wheel vehicle taking a turn.
Applications of gyroscope.
Numerical Problems.
Introduction
By
WahaJ Ahmad
Introduction
Gyroscope : A gyroscope is a device for measuring or maintaining
orientation, based on the principles of conservation of angular
momentum.
Assembly of Gyroscope : A gyroscope has a spinning wheel or
disk(rotor) fixed on an axle, which is free to take any orientation. Over
the disc, gimbals may or may not be assembled.
Introduction
Assembly of Gyroscope :
Introduction
Gyroscope : A gyroscope is a device for measuring or maintaining
orientation, based on the principles of conservation of angular
momentum.
Assembly of Gyroscope : A gyroscope has a spinning wheel or
disk(rotor) fixed on an axle, which is free to take any orientation. Over
the disc, gimbals may or may not be assembled.
Introduction
Gyroscope : A gyroscope is a device for measuring or maintaining
orientation, based on the principles of conservation of angular
momentum.
Assembly of Gyroscope : A gyroscope has a spinning wheel or
disk(rotor) fixed on an axle, which is free to take any orientation. Over
the disc, gimbals may or may not be assembled.
Concept for working of Gyroscope :
Spin the gyro
Apply force
Perpendicular Twist will be
produced
Precessional Angular Motion
Spin axis :
The axis about which the gyro rotates.
Precession axis : The axis about which the perpendicular twisting or tilting force apply.
The angular motion of the axis of spin about the axis of precession is known as
Precessional angular motion
Precessional Angular Motion
The Cause of Precession: - Newton’s 1st Law of Motion.
- Law of Conservation of Angular Momentum.
Precessional Angular Motion
The Cause of Precession: - Newton’s 1st Law of Motion
- Law of Conservation of Angular Momentum.
Precessional Angular Motion
Gyroscopic Action
Precessional Angular Motion
The angular motion of the axis of spin about the axis of precession is known as
Precessional angular motion
A gyroscope is a device for measuring or maintaining orientation, based
on the principles of conservation of angular momentum.
Gyroscopic Couple
By
Hassan Baber
Gyroscopic Couple
A device consisting of a spinning mass, typically a disk or wheel,
mounted on a base so that its axis can turn freely in one or more
directions and thereby maintain its orientation regardless of any
movement of the base.
The turning moment which opposes any change of the inclination
of the axis of rotation of a gyroscope.
Explanation :
Axis & Plane of Spinning
Axis & Plane of Precession
Active gyroscopic couple.
(Axis and Plane)
Reactive gyroscopic couple.
(Axis and Plane).
Gyroscopic Couple
Consider a disc spinning with an angular velocity ω
rad/s about the axis of spin OX, in anticlockwise
direction when seen from the front;
Change in angular momentum;
and rate of change of angular momentum
In the limit when δt→ 0,
Gyroscopic Couple on Airplane
The top and front view of an airplane.
Let engine or propeller rotates in the clockwise direction when
seen from the rear or tail end and the airplane takes a turn to the
left.
When the propeller rotates in anti-clockwise direction & :
The airplane takes a right turn, the gyroscope will raise the nose and dip the tail.
The airplane takes a left turn, the gyroscope will dip the nose and raise the tail.
Explanation :
Let
ω =
m =
k =
I =
Angular velocity of the engine in rad/s,
Mass of the engine and the propeller in kg,
Its radius of gyration in metres,
Mass moment of inertia of the engine and the propeller in
kg-m²= m.k²,
v = Linear velocity of the airplane in m/s,
R = Radius of curvature in metres, and
ωP = Angular velocity of precession =v/R rad/s
∴ Gyroscopic couple acting on the airplane,
C = I.ω.ωP
Gyroscopic Couple on Airplane
Gyroscope In Naval Ships
By
Mujtaba Abbas
Gyroscope In Naval Ships
The fore end of the ship is called bow.
The rear end is known as stern or aft.
The left hand is called port.
The right hand sides of the ship, star-board.
Effect on Naval Ships during
Steering
Rolling
Pitching
Gyroscopic Effect In Naval Ships during
Steering
Steering is the turning of a complete ship in a
curve towards left or right, while it moves forward.
Consider the ship taking a left turn, and rotor
rotates in the clockwise direction.
When the rotor of the ship rotates in the clockwise
direction when viewed from the stern, it will have its
angular Momentum vector in the direction ox as shown
in Fig. (a)
When the ship steers to the right under Similar
conditions as discussed above, the effect of the reactive
gyroscopic couple, as shown in Fig. (b), will be to raise
the stern and lower the bow.
Gyroscopic Effect In Naval Ships during
Rolling
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.
Gyroscopic Effect In Naval Ships during
Pitching
Pitching is the movement of a ship up and down in a vertical plane about
transverse axis.
The transverse axis is the axis of precession.
The pitching of the ship is assumed to take place with the Simple Harmonic Motion.
Stability of a four wheel drive moving in a
curved path
By
Hassaan Tariq
Stability of a four wheel drive moving in a
curved path
Consider the four wheels A, B, C and D of an automobile locomotive
taking a turn towards left as shown in the figure. The wheels A and C
are the inner wheels whereas B and D are the outer wheels. The
C.O.G. of the vehicle lies vertically above the road surface.
Let,
m = mas of the vehicle in kg
W = wieght of the vehicle in N = mg
R = radius of curvature in meters (R > rw)
h = distance of C.O.G vertically above the road surface in meters
x = width of track in meters
Iw = mass of moment of inertia of one wheel in kgm2
ωw = angular velocity of the wheels or velocity of the spin in rad/s
IE = mass moment of inertia of the rotating parts of the engine in kgm^2
ωE = angular velocity of the rotating parts of the engine in rad/s
G
= Gear ratio = ωE / ωw
v = linear velocity of the vehicle in m/s = ωw . rw
rw = radius of the wheel in meters
For effect of the gyroscopic couple, C = ωW.ωP (4 IW ± G.IE)
For effect of the centrifugal couple,
and
Stability of a two wheel vehicle
taking a turn
Consider a two wheel vehicle taking a right turn as shown in the following
figures, let,
m = mas of the vehicle and its rider in kg
W = wieght of the vehicle and its rider in N = mg
R = radius of track or curvature in meters
h = height of C.O.G of the vehicle and the rider
Iw = mass of moment of inertia of one wheel in kgm^2
ωw = angular velocity of the wheels
IE = mass moment of inertia of the rotating parts of the engine in kgm^2
ωE = angular velocity of the rotating parts of the engine in rad/s
G = Gear ratio = ωE / ωw
v = linear velocity of the vehicle in m/s = ωw . rw
rw = radius of the wheel in meters
θ = angle of heel. Its is the inclination of the vehicle
to the vertical for equilibrium.
For effect of the gyroscopic couple,
C1
For effect of the centrifugal couple,
Co
Applications
Gravity Defiance.
Air & Land Vehicles.
Ships, Hovercrafts etc.
Inertial Compass.
Used in toys like Boomerang, Tops, YO-YO etc.
Camera stabilizer while capturing disturbed by wave action.
Vastly used in UAV’s (Unmanned Aerial Vehicle) commonly named as DRONES.
Used in some non-ballistic missiles, particularly cruise missiles etc.
Numerical Problems
An airplane makes a complete half circle of 50m radius, towards left, when flying at 200km
per hour. The rotary engine and the propeller of the plane has a mass of 400kg with a radius of
gyration of 300mm. The engine runs at 2400 rpm. clockwise, when viewed from the rear. Find
the gyroscopic couple on the aircraft and state its effect on it. What will be the effect if the
airplane turns to the right instead to the left?
[Ans. 10kN-m]
The rotor of a turbine installed in a boat with its axis along the longitudinal axis of the boat
makes 1500 r.p.m. clockwise, when viewed from the stern. The rotor has a mass of 150 kg and
a radius of gyration of 300mm. If at an instant, the boat pitches in the longitudinal vertical
plane, so that the bow rises from the horizontal plane with an angular velocity of 1 rad/s,
determine the Torque acting on the boat and the direction in which it tends to turn the boat at
the instant.
[Ans. 10.6kN-m]
Find the angle of inclination with respect to the vertical of a two wheeler negotiating a turn.
Given : a combined mass of the vehicle with its rider 250 kg ; moment of inertia of the engine
flywheel 0.3 kg-m2 ; moment of inertia of each road wheel 1 kg-m2 ; speed of engine flywheel
5 times that of road wheels and in the same direction ; height of centre of gravity of rider with
vehicle 0.6 m ; two wheeler speed 90 km/h ; wheel radius 300 mm ; radius of turn 50 m.
[Ans. Θ =53.94◦]
Gyroscope
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