GYROSCOPE

CONTENTS

What is a gyroscope?

Properties of a gyroscope

Construing precession

Limitations

In addition to airspeed indicator, the altimeter and the vertical speed indicator, a basic group of flight instruments also comprises instruments which provide direct indication of an aircrafts attitude.

There are three such instruments they are a gyro horizon( artificial horizon)a direction indicatora turn and bank indicator

The three instruments utilize a gyroscopic type of sensing element.

The three degrees of freedom are obtained by mounting the rotor in two concentrically pivoted rings called inner and outer rings. The whole assembly is known as the gimbal system of a free or space gyroscope.

In its normal operating position, all the axes are mutually at right angles to one another and intersect at the centre of gravity of the rotor.

It may be defined as a system containing a heavy metal wheel of rotor, universally mounted so that it has 3 degrees of freedom i) spinning freedom, about an axis perpendicular through its centre (axis of spin XX1) ii) tilting freedom, about a horizontal axis at right angles to the spin axis( axis of tilt YY1); and iii) veering freedom, about a vertical axis perpendicular to both the other axes ( axis of veer ZZ1)

The system will not exhibit gyroscopic properties unless the rotor is spinning; for example, if a weight is suspended on the inner ring, it will merely displace the ring about its axis YY1 because there is no resistance to the weight.

When the rotor is made to spin at high speed, however, the device then becomes a true gyroscope possessing two important fundamental properties gyroscopic inertia or rigidity and precession.

This system will not exhibit gyroscopic properties unless the rotor is spinning

But when it does spin…

Both these properties depend on the principle of conservation of angular momentum, which means that the angular momentum of a body about a given point remains constant unless some force is applied to change it.

Angular momentum is the product of the moment of inertia (I) and angular velocity (ω) of a body referred to a given point- centre of gravity in the case of a gyroscope.

If a weight is now suspended form the inner gimbal ring with the rotor spinning it will be found that the ring will support the weight, thus demonstrating the first fundamental property of rigidity. It will also be found, however that the complete gimbal system will start rotating about the axis ZZ1, such rotation demonstrating the second property of preccession.

Rigidity: The property which resists any force tending to change the plane of rotor rotation. It is dependent on three factors: i) the mass of the rotor, ii) the speed of rotation and iii) the distance at which the mass acts from the centre i.e the radius of gyration.

Precession: the angular change in direction of the plane of rotation under the influence of an applied force. The change in direction takes place not in line with force, but always at a point 90 degrees away in the direction of rotation.

The rate of precession also depends on three factors i) the strength and direction of the applied force ii) the moment of inertia of the rotor and iii) the angular velocity of the rotor.

The greater the force , the greater is the rate of precession, while the greater the moment of inertia and the greater the angular velocity the smaller is the rate of precession.

The axis about which a force is applied is termed the input axis and the one about which precession takes place is termed the output axis.

As shown is shown spinning in a clockwise direction and with a force F applied upwards on the inner ring. This force is transmitted to the rim of the rotor as shown in fig b

Let us assume for a moment that the rotor is broken into segments as shown in fig c. Each segment has motion m in the direction of the rotor rotation, so that when force F is applied there is a tendency for each segment to move in the direction of force. This motion is resisted by rigidity, but the segments will turn about the axis ZZ1 so that their direction of motion is along the resultant of motion m and force F

The other segments will be affected in the same way, in being combined to form the soled mass of rotor it will precess at an angular velocity proportional to the applied force( fig d and fig e).

In the example illustrated in Fig. 5.4 (a), a 'force, F, is shown

applied on the outer ring; this is the same as transmitting the force on the rotor rim at the point shown in diagram (b). As in the previous example this results in the direction of motion changing to the resultant of motion m and force F,. This time, however, the rotor precesses about the axis YY, as indicated at (d) and (e).

In figure 1, the gyroscope is spinning on its axis.In figure 2, a force is applied to try to rotate the spin axis.In figure 3, the gyroscope is reacting to the input force along an axis perpendicular to the input force.

CONSTRUING PRECESSION

YOU CAN DO THIS AT HOME !!!

For use in aircraft, gyroscopes must establish two essential reference datums: a reference against which pitch and roll attitude changes may be detected, and a directional reference against which changes about the vertical axis may be detected. These references are established by gyroscopes having their spin axes arranged vertically and horizontally respectively, as shown in Fig 5 .5

LIMITATIONS OF GYROSCOPE

Apparent Drift Real Drift Transport Wander Gimbal Lock Gimbal Error

The earth rotates about its axis at the rate of 15degrees/hour and in association with gyrodynamics this is termed earth rate (ωe).

When a free gyroscope is positioned at any point on the earth’s surface, it will sense, depending on the latitude at which it is positioned.

Thus to an observer on the earth having no sense of the earths rotation, the gyroscope would appear to veer or drift.

From the fig a, At A the input axis is aligned with the local N-S component of ωe, therefore to an observer at latitude the gimbal system would appear to drift clockwise(opposite to the earths rotation) in a horizontal direction at a rate equal to 15 cosλ

When the input axis is aligned with that of B the drift would be apparent but at the rate equal to 15 degree /hour.

If the input axis is now aligned with the local vertival component the apparent drift would be equal to 15 sin λ.

Real Drift: this results from imperfections in a gyroscope such as bearing friction and gimbal system unbalance. Such imperfections cause unwanted precession which can only be minimized by applying precision engineering techniques to the design and construction.

Control of drift and transport wanderDrift can be controlled by i) calculating corrections

using the earth rate formulae given in the preceding table and applying them as appropriate ii) applying fixed torques which unbalance the gyroscope and cause it to precess at at rate equal and opposite to ωe iii) applying torques having a similar effect to that statedin ii) but which can be varied according to the latitude in which the gyroscope is being used.

Control of transport wander is normally achieved by using gravity sensing devices which automatically detect tilting of the gyroscope spin axis and applying the appropriate corrective torques

Apparent wander, is the apparent movement of the spin axis away from the local vertical. The cause of this apparent movement is the

rotation of the Earth combined with gyroscope rigidity. Wander may also occur when a gyroscope is transported from one point on the Earth to another. This is referred to as transport wander.

Transport wander can be controlled by using gravity sensing devices to automatically detect tilting of the gyroscope's spin axis and to apply corrective torques.

Real drift It results due to imperfections in the

gyroscope such as bearing friction and gimbal imbalance.

Can be minimised by applying precision engineering techniques to design and construction.

Control of drift For a free gyroscope to be used for altitude

references, it must be converted to "earth gyroscope” i.e., the gyroscope’s plane of spin should be maintained relative to earth

Gimbal lock This occurs when the spin axis coincides with

any of the three axis of freedom. If in this case the gyroscope is turned then the forces acting on the gimbal system would cause the system to precess or topple.

Gimbal error This is related to gimbal orientation, it occurs

when the gimbal rings of the gyroscope are not at right angles to each other