022A Inst ATPL(A) Ch 3 gyroscopes

03 Instrumentation Gyroscopes

This version applies to: ATPL(A)

Gyroscopes 3

The name gyroscope comes from two Greek words, gyro, a turn and skopein, to see. A gyroscope is, literally, a “turn see-er”, a reference against which you can measure how you have turned in space. To do this a gyroscope must maintain a space reference. This is the property of rigidity in space, the first and most important of the two properties of gyroscopes. momentum, which is moment of inertia times rate of rotation. Moment of inertia is itself determined by rotor mass and the distribution of the mass near to or away from the centre of rotation. Concentration of the mass nearer to the circumference of the rotor, away from the centre, gives a higher moment of inertia.

It is the axis of rotation of the gyroscope that defines its orientation, and measurements of angular change are made against that axis.

Rigidity and precession are the key properties of gyros

To repeat; the greater the moment of inertia, the greater the rigidity and the faster the spin the greater the rigidity. A more rigid system will require a greater force to precess it at any given rate.

Figure 3.1 There is a series of animations in the computer programme to help you with gyro principles The second property of gyroscopes is precession.

A gyroscope will maintain its reference in space unless acted on by an external force. If a force is applied to a gyroscope it will move, and so long as the force remains applied, it will continue to move. It will not, however, move as though the force were acting directly on the gyroscope, but will precess, and act as if the force had been applied at a point 90º in the direction of rotation of the gyroscope.

Gyroscopes are usually suspended in a system of frames, called gimbals, which allow them freedom of movement in up to three planes. A gyro must have at least one gimbal for every axis around which you need to measure movement.

Thus a turn indicator, that measures only movement round the yaw axis, has one gimbal, and an artificial horizon, that measures pitch and roll, has two. An inertial navigation platform, which measures roll, pitch and yaw, has three, and sometimes four. A two gimbal system is the mechanical equivalent of an ordinary universal joint, or Hooke’s joint, and can demonstrate gimbal error. As long as the gimbals are at right angles to each other, a constant angular rotation around the gyro in space gives a constant rate of readout at the outer gimbal, but when they are misaligned this relationship no longer holds. This primarily affects DIs, and is covered later.

At least one gimbal for every axis you want to measure around

Its momentum, mass times velocity, measures the resistance of a body moving in a straight line to being pushed off course. The rigidity of a spinning gyroscope depends on its angular Instrumentation

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Classification of Gyroscopes

The final group is distinct from the other three by having a freedom of movement in the plane of rotation and one more plane, at 90º to the first.

This is called a rate gyro and can be used as a rate of turn indicator. A developed form of rate gyro is a rate-integrating gyro, and both have two planes of freedom.

To classify gyros, we speak of planes of freedom. The gyro itself rotates in one plane, about its spin axis. There are then two other planes that we can use to define the gyro, both of them at right angles to the plane of rotation, and at right angles to each other. Gyros are split into four main categories. The simplest is the free or space gyroscope that is completely free to move in all three planes in relation to its mounting system. Figure 3.2 shows a space gyro.

There exists a second form of classification of gyros by degrees of freedom; effectively the number of axes about which gyro displacement can be measured It does not count the axis of rotation of the gyro as one of these. Thus a two plane of freedom gyro is a single degree of freedom gyro.

Alignment of Gyroscopes Having classified gyros, we must define their orientation in space. This is done by specifying the alignment of the axis of rotation. Thus a vertical gyro has its spin axis in the Earth vertical. A horizontal gyro has its axis in the Earth horizontal, but as earth horizontal is a plane, not a line, this alone does not give sufficient information to fully define the axis. We have to add the azimuth information, and a full definition would be, for example, “a horizontal gyro with its axis aligned with true north”.

Figure 3.2 - Gyro in gimbal frame The next group is of a special form of space gyro called tied gyros. These retain freedom of movement in all three planes but there is now an external influence controlling the direction of the spin axis. An example of this would be the directional indicator (DI), where the spin axis is tied to the horizontal. This will be looked at later on. The third group is an even more specialised type of tied gyro where the spin axis is tied by the Earth’s gravity to remain in the Earth vertical.

This is called an earth gyro, an example would be the artificial horizon. All of these, space, tied and earth gyros, have three planes of freedom.

3.2

Earth vertical is a line, formed at the intersection of all the vertical planes.

Earth horizontal is a plane, made up of all the azimuth lines

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Gyroscopic Wander

friction. A perfect gyro with no external forces acting on it will not suffer from real wander.

The rigidity of a gyro system will tend to keep the spin axis fixed in space. Any movement away from this fixed direction is called wander. Gyro wander can be either drift or topple. These are earth references. Gyro drift occurs when the spin axis turns in the Earth horizontal plane, gyro topple occurs when the axis tilts in any earth vertical plane. Figure 3.3 shows examples of drift and topple. Notice that a gyro with a vertical axis can initially only topple and not drift.

Apparent Wander Having said that perfect gyros do not suffer from real wander there are many occasions when they appear to, always because our orientation in space has changed while the gyro’s orientation has not. This is apparent wander.

Drift and topple are references to earth alignment, not to space

Figure 3.4 Figure 3.4 shows five gyroscopes, A, B, C, D and E and the apparent effect on them as they are carried around on the rotating earth.

Horizontal gyro B, at the equator with its axis aligned to the local meridian shows no apparent drift as it is carried round on the rotating earth.

Horizontal gyro E at the north pole is showing an apparent drift of the full 15º per hour as the Earth rotates under it. The apparent drift, zero at the equator and the full 15º/hr at the poles, is a function of latitude:

Figure 3.3 Drift and topple are references to earth alignment, not to space There is another looser meaning of topple.

Topple is also used to describe what happens when a gyro in a gimbal system meets its mechanical limit stops and precesses rapidly in random directions.

Apparent drift = 15 x Sin(latitude) degrees per hour.

Gyro C, at the equator, which began as a vertical gyro, appears to become a horizontal gyro then becomes a vertical gyro again. It is showing apparent topple at a rate of 15º per hour. Vertical gyro D at the north pole is showing no apparent topple. The apparent topple, zero at the poles and the full 15º/hr at the equator, is also a function of latitude:

Real Wander Whenever the gyro spin axis moves away from its initial defined orientation in space the gyro is said to suffer from real wander. Real wander can either be deliberately induced by applying an external correcting force, as in alignment of tied gyros, or can be caused by imperfections in the gyroscope, unbalanced gimbals or bearing Instrumentation

Apparent topple = 15 x Cos(latitude) degrees per hour. v6.1.6

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Finally, gyro A which begins as a horizontal gyro aligned with the local meridian at an intermediate latitude shows both apparent drift and apparent topple as it is carried around on the rotating earth.

Its apparent drift is 15 x Sin(Lat) and its apparent topple is 15 x Cos(Lat) in degrees per hour.

Transport Wander If a gyro is aligned to north on one part of the Earth and then moved to another, it will be out of alignment because of the convergency between the two points. This is a form of apparent drift called transport wander. Flights north or south will produce no transport drift but will affect the total apparent drift, as the latitude will change.

Flights to the east will increase the total apparent drift (in the northern hemisphere) and those to the west will reduce it.

Figure 3.6

A DI has two degrees of freedom The rigidity of the gyroscope means that it will retain its orientation in space. The aircraft effectively rotates around the outer gimbal as it turns, and indicated heading is read from the scale fixed to the outer gimbal. This is normally round the middle of the gimbal, but drawn in figure 3.6 at the bottom of the gimbal to give a clear view of the internal layout. The reading given on the scale is periodically synchronised with the aircraft magnetic heading, by caging the gyro – holding the axis horizontal - and manually turning the gimbal and scale until the DI reads the correct heading, then uncaging.

Erection is levelling the gyro.

Synchronisation is making the gyro read the correct magnetic heading

Figure 3.5

The Direction Indicator

The DI can be electric or air driven gyro; an engine driven pump partially evacuates the instrument case and atmospheric air is drawn in through the outer gimbal pivot to fine nozzles that blow on buckets on the outside of the rotor. The rotor will turn at 10 000 to 12 000 RPM. Since we wish to measure changes in azimuth, which is change of bearing in the Earth horizontal, the rotor axis should ideally be tied to earth horizontal. This is difficult, so for simplicity it is tied to aircraft horizontal instead, and this is done by some clever design work with the air jets.

The direction indicator (DI) is fitted on older aircraft to supplement the heading information from the magnetic compass. The rigidity of its gyroscope gives steadier heading information than the compass, which is subject to turning and acceleration errors.

The DI uses a tied gyro with two degrees of freedom, rotating about a horizontal axis and mounted in two gimbals, to give freedom in pitch and roll up to about plus or minus 55°.

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Earth’s Rotation We stated in the last chapter that the apparent drift due to the Earth’s rotation is: 15 x sin latitude, in degrees per hour.

The latitude in this case is the latitude of the actual position of the aircraft. If you are dealing with a period of time with an associated latitude change - flight north or south - then you take the mean aircraft latitude for the period.

This is one of the four errors we consider.

Latitude Nut

Figure 3.7

The latitude nut - and in early instruments it is a real nut, screwed in and out to produce the necessary imbalance and drift - is set to produce the opposite error to earth’s rotation. Therefore the error is also 15 x sin latitude in degrees per hour, but in this case the latitude is the figure set on the latitude nut scale. It is not always the same as the aircraft’s actual latitude, as it is set by the maintenance crew, and cannot be re-set in flight. This is the second of the errors we consider.

The air is fed through two nozzles mounted on the outer gimbal, itself tied to aircraft horizontal, which, when the rotor is erect, impinge equally on both sides of the buckets. When the rotor is out of alignment the stream of air strikes the buckets asymmetrically and produces a side force which precesses to re-erect the gyro. As the aircraft banks in a turn, the erection system will try to make the gyro erect to the new position in space of the aircraft horizontal, but this is not significant at the relatively small angles of bank at which this instrument is used. In straight and level flight, the gyro re-erects to what is both earth and aircraft horizontal.

The latitude nut induces a real wander to counter the apparent wander of earth rotation

Errors

Transport Wander

As aircraft instruments are necessarily imperfect friction and imbalances will create real wander.

The better the instrument the less this value will be.

As the gyro is moved from one point on the Earth to another the gyro maintains its orientation in space. The direction of true north, however, changes, and the further you travel in an east/ west sense the greater the change. Transport wander is the apparent loss of alignment caused by east/west travel and its value is simply the convergency between two points.

The DI will be subject to apparent wander, both because of the Earth’s rotation and because of transport wander. In addition to this, we introduce an adjustable correction for earth’s rotation, the latitude nut attached to the inner gimbal, which is an out-of-balance force that produces a real wander equal to and opposite in sign to the Earth’s rotation error - if it is correctly set. We dealt with these in general in the previous section but we must now look at the mathematics of these errors.

Instrumentation

Transport wander (º) = change of longitude x sin mean latitude.

Transport wander in an easterly direction will have a different sign from transport wander in a westerly direction.

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All you have to do to work out total DI error is to take the equation:

Real Wander Although we have noted that the latitude nut does introduce a real wander, this is dealt with elsewhere. Under this heading we consider only gyro imperfections that produce a known rate of wander. We have no way of calculating the value of the wander. If it is to be taken into consideration then it is given to us in degrees per hour, with a positive or negative change of gyro heading. This is the fourth and last error we consider.

Total drift = real wander + earth’s rotation. + latitude nut + transport wander Then fill in the values, as given for real wander, and according to latitude and E/W groundspeed as appropriate for the others, then apply the signs from the table. It works!

Points to Watch Watch out for aircraft flying in one hemisphere with their latitude nuts set for the correct latitude value in the other hemisphere. Remember that mean latitude must be taken for ER and TW, if the aircraft is flying with a north or south track component. Do not use the mean latitude for a latitude nut correction, it only has one set value for the flight and it might be quite different to the latitude at which you are operating.

Remember also that earth rotation and latitude nut corrections are rates, in degrees per hour, whereas transport wander is a value in degrees.

Total DI Error Taking all these errors into account we can say that total drift is made up of: Real wander + earth’s rotation + latitude nut + transport wander We know how to calculate the values to put into the equation, but we have to consider the signs of the different errors. Real wander will be given, with its sign, so we need to have a quick table to work out the others. It is:

Example:

Northern Hemisphere

Southern Hemisphere

Earth’s Rotation

-

+

A perfect DI has its latitude nut set for 60°N. The aircraft starts from 50ºN 003ºW and flies for 3 hours ending up at 42ºN 0045ºE. At the end of the flight, what is the total DI error?

Latitude Nut

+

-

Solution:

Transport Wander East

-

+

Transport Wander West

+

-

(a) This is a perfect DI, so real wander is zero. (b) Earth rotation produces an error of

Figure 3.8 + = - =

anti-clockwise or left hand rotation clockwise or right hand rotation

In this table we can see that the Earth’s rotation will make DIs in the northern hemisphere under read, and that the latitude nut, if correctly set for the northern hemisphere will have the opposite sign, which it is designed to do. Likewise we can see, that as we said earlier, flying west in the northern hemisphere will introduce an error opposite in sign to the Earth’s rotation, cancelling to zero if you are flying west at exactly the same speed as the Earth is rotating.

3.6

15 x sin 46 º/hr, using the mean latitude = 15 x 0.719 = 10.8º º/hr

which, over 3 hours, is 10.8 x 3 = 32º, it is a negative error in the northern hemisphere, -32º. Drifting clockwise/right hand.

(c) The latitude nut error is:

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15 x sin 60 º/hr = 15 x 0.866 = 13.0 º/hr

over 3 hours the LN error is 3 x 13.0 = 39º, it is a positive error in the northern hemisphere, +39º.

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(d) Transport wander is

DI Caging and Checks

In normal use the DI should be caged and realigned in straight and level flight every 10 to 15 minutes and the system should be caged before any violent manoeuvres.

change of longitude x sin mean latitude = 48 x sin 46 = 48 x 0.719 = 35º, negative because the direction of travel has been west to east.

Putting all these together you get: Total Error = 0 – 32º + 39º - 35º = - 28º RH

The Artificial Horizon

A final point to consider is what happens if you fly holding a constant gyro heading or, alternatively, what happens to the gyro indication if you hold a constant earth azimuth?

The artificial horizon is the primary attitude instrument. It uses an earth gyro, that is, a space gyro with its spin axis maintained in the Earth vertical by a gravity device, to indicate pitch and roll. It has three planes of freedom and two gimbals. Simple artificial horizons have the gyroscope assembly behind the instrument face.

More modern equipment is servo driven and uses attitude information from a remote master attitude reference, or from the IRS.

Negative gyro errors make the gyro under read. Keeping a constant gyro heading will therefore make your true heading increase Consider an aircraft pointing due east, on the ground. The gyro is synchronised to read 090º.

As the Earth rotates the aircraft will remain pointing due east, but the gyro will begin to indicate lower values, 085º, 080º and so on.

The artificial horizon could be described as having two degrees of freedom or three planes of freedom

If, therefore you were flying on a true heading of 090º with no drift the same thing would happen – the gyro would under read. The rate of deviation would be modified by transport wander. If you flew holding a steady gyro heading of 090º, because the gyro is under reading the true heading you will be turning away to the right of track in earth terms and your true heading is increasing.

Air Driven Units Figure 3.9 on the following page, shows the construction of a simple air driven artificial horizon (AH). The rotor with its vertical spin axis can be seen, inside the rotor case, which is the inner gimbal, and the outer gimbal which is connected to the instrument case. Air enters through the centre of the gimbal bearings, drives the rotor by impinging on buckets on its outside edge, and exhausts at the bottom of the rotor case. This gyro, in common with most air driven AHs, rotates anti-clockwise when viewed from above.

Gimbal Error The inner and outer gimbals are aligned at 90º to each other when the aircraft is flying straight and level. Under these conditions there is an exact linear relationship between the direction of the gyro axis and the heading readout on the outer gimbal. When the aircraft is banked in a turn the gimbals are no longer in line and as the aircraft turns the heading indication will sometimes lead and sometimes lag the true azimuth. The effect is small at working angles of bank, and as the wings are levelled and the gimbals line up the error disappears. Gimbal error is ignored in the DI.

Instrumentation

Before flight, instrument condition should be checked and it should be checked as operating in the correct sense during turns in the taxy out.

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Figure 3.9 The rotor case/inner gimbal is connected to a guide pin that moves in a slot to move the horizon bar up and down on the instrument face. The bank angle pointer is connected to the outer gimbal, which is free to swivel about the aircraft fore and aft axis.

The key to pitch indication is in the position of the guide pin relative to the horizon bar arm.

Because the arm is pivoted at the forward end of the instrument, as the gyro remains level and the case pitches with the aircraft, the horizon bar is displaced to show the aircraft symbol above it in a climb and below it in a descent. Figure 3.10 shows how this operates.

3.8

Figure 3.10

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will produce an initial roll error, which changes to pitch error as the aircraft turns through 90º. In addition, the pendulous lower part of the gyro will try to line up with the resultant acceleration, but this effect will be precessed through 90°, and will give an initial pitch error that changes to roll error as the turn continues. The combined effect of these is that the gyro axis describes a wobbly circle during a 360° turn, offset a few degrees from its correct position.

Gyro Erection Air driven artificial horizons are made pendulous, with their centre of gravity below the suspension point, so that they settle in their gimbals in a nearly erect position when not working, to reduce erection time on start-up. Once the gyro is rotating, simple pendulosity does not help with erection, and the gyro has its spin axis tied to the Earth vertical by a system of pendulous vanes and air jets which make the gyro precess back to the vertical if it is displaced.

These errors and the correction system only apply to air driven AHs

Pendulosity is only there to help before start. After start it induces unwanted errors

After 90º the error will be nose up and bank under reading, after 180º of turn the bank angle will be correct and the maximum pitch up error exists. After 270º the pitch error has reduced but is still present but now the bank over reads. If the turn were continued onto the original heading the errors would be zero. These AH erection errors are called turning errors, figure 3.12.

At the bottom of the rotor case are four air exhaust vents, each normally half covered by a flap, a pendulous vane, which is hinged at the top.

When the gyro is vertical, air escapes from all four vents equally. When it is displaced from the vertical, one vent will be closed as the pendulous vane covers the vent and another will be opened.

The now unbalanced reaction from the air vents is precessed by 90° in the direction of rotation, to restore the spin axis to the vertical.

Figure 3.12 Some instruments have the vanes adjusted to keep the gyro offset half the expected maximum turning error (typically a 2° to 2½° offset) from the true vertical when erect, to minimise any turning error. This correction system only works for one specified rate of turn, usually rate 1, and one set TAS, typically 250 KT. This system is called compensation tilt.

Figure 3.11

Erection Errors The gyro will be affected by any false indication of the vertical, caused by lateral acceleration in turns or by aircraft acceleration and deceleration.

In a turn the erection system will try to erect the gyro to the resultant acceleration, which in a balanced turn will be the aircraft vertical. This Instrumentation

The pendulous vanes of the erection system are displaced by sustained fore-and aft acceleration, for instance on take-off, when a false nose up indication is given. Acceleration also affects the v6.1.6

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pendulous lower element of the gyro, and this force is precessed through 90° to indicate a bank to the right. These acceleration errors restrict the use of air driven horizons to aeroplanes that do not accelerate particularly quickly, for instance small Cessnas.

The instruments typically are free in pitch through ±60° and in roll through ±110°. Mechanical stops prevent movement outside these limits at which point the gyro will topple. Once the gyro has toppled it will re-erect at the rate of 2° to 4° a minute.

First, they are more rigid, as the electric “squirrel cage” motor can drive the rotor twice as fast, up to 22 500 RPM. Secondly, their erection system is electric, can be made very fast, and can be cut out at will. With a fast erection system, there is no need for the gyro to be pendulous, although some electric AHs retain a small degree of pendulosity.

With little or no pendulosity, if the normal erection system is cut out at certain values of longitudinal acceleration or lateral acceleration, which is the same thing as angle of bank in balanced turns, then turn and acceleration errors are minimised or eliminated.

There are many variations on the basic system, with or without pendulosity, with or without roll and pitch cut-outs operated by angle sensors or mercury switches, and with various crosscoupling systems between roll and pitch erection in turns. A typical basic system, with some options, is described below.

Electrically Driven Artificial Horizons Electrically driven artificial horizons use the same basic principles as the air driven instruments.

Most electric AHs rotate clockwise when viewed from above. The gyro is still tied to the Earth vertical and held in two gimbals. There are, however, some fundamental differences.

Figure 3.13

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Principle of Operation

With a very rigid gyro, control systems can be cut out and the gyro left on its own for long periods

The pendulous vanes of the air driven unit are replaced by mercury tilt switches mounted on the rotor case, the inner gimbal. Any displacement of the gyro axis from earth vertical is sensed by the tilt switches which make and break electrical circuits connected to torque motors on the gimbals, that re-erect the system at about 5° a minute.

Electric AHs usually have complete freedom in roll, but are restricted to about ±85° in pitch. A fast erection button is provided which supplies a higher voltage to the torque motors, and bypasses the cut-outs, to erect the gyro at up to 180° a minute. This facility should only be used on the ground or in straight and level flight.

The pitch switch, here on top of the rotor case, senses pitch errors, and drives the pitch torque motor, on the roll axis. This motor tries to roll the gyro, but precession takes over, and the effect is transferred through 90° to correct pitch errors.

Roll errors are detected by a second mercury switch lying at right angles to the pitch switch, and corrective signals are fed to a roll torque motor on the pitch axis. Errors due to false erection during acceleration are accepted, as acceleration regimes are relatively short, as in a take-off.

Servo Driven Attitude Indicators Modern aircraft take their attitude information from the inertial reference systems (IRS), which are free of turn and acceleration errors, and the instrument is only a remote indicator. This system has the advantage that the attitude signals going to the Captain’s and first officer’s instruments from IRS 1 and IRS 2 can be compared, errors can be detected and, if required, a failed attitude source can be deselected. IRS 3 is the back-up source. In older systems with just two inertial navigation systems (INS) a master attitude reference gyro, which is just a big independent AH, is used as a back up. An independent and self-contained standby AH is always retained, powered directly from the aircraft batteries.

However, aircraft spend a long time in turns. To prevent the gyro erecting to a false datum in an extended turn there is a roll cut-out switch fitted on the roll axis, to disconnect the roll torque motor at bank angles in excess of 10°.

A development of this system dispenses with the roll cut-out switch, but uses a pair of modified mercury switches which provide power to the pitch and roll erection systems under small accelerations, but then disconnect the power supply under larger accelerations or bank. Figure 3.14 elaborates.

Remote artificial horizons, or attitude indicators, can also be provided with expanded scales for pitch movements near the horizontal. This means that very precise attitudes can be set. Bank indications can be at the bottom of the instrument, in which case it is referred to as an earth pointer, or at the top, a sky pointer.

Information from other aircraft systems can also be displayed. This includes ILS information, radio height, airspeed and flight directors. Figure 3.15 shows a relatively modern sky pointing attitude indicator.

Figure 3.14

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Figure 3.15

Figure 3.16

The final development dispenses with the AH altogether, and attitude information from the IRS is sent to the EFIS symbol generator for electronic display.

The turn indicator is primarily there to indicate rate of turn for navigation purposes, but to do this should be kept orientated to earth horizontal.

Because this is difficult to achieve, it is fixed to the aircraft and measures yaw. In a banked turn the aircraft is turning, yawing and pitching so the turn indicator is calibrated to take account of this and display the correct turn rate to the pilot at specified rates.

Rate Gyros The Turn and Slip Indicator The turn and slip indicator is in effect two instruments in one case, one a rate gyro to measure turn and the other an instrument to measure slip or skid. Remember: 11

11

11

11

Yaw is the movement of the aircraft round its own vertical axis.

Turn is the movement about the Earth vertical axis and will result in a change of heading.

An out-of-balance yawing force into the turn is called slip.

An out-of-balance yawing force out of the turn is called skid.

Figure 3.17

A graphic illustration of turn and skid occurs when the aircraft is turned on the ground. It turns, but with no bank applied a force is felt towards the outside of the turn. Thus the aircraft is turning and skidding.

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Principle of Operation The turn indicator is a rate gyro, with two planes of freedom and one gimbal. It may be air driven or electrically driven. The axis of rotation is in the horizontal plane; the direction of rotation has the top of the gyro moving away from the pilot. When the aircraft is turned the change of direction appears as a yaw rate. This is precessed to act on the top or bottom of the gyro, which rotates Instrumentation

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in its single gimbal, pivoted on the aircraft fore and aft axis and compresses or extends a spring. When the spring force balances the precessed force the gyro remains tilted away from the aircraft vertical as the instrument yaws with the aircraft. The gimbal moves a needle that indicates the rate of turn. Do not worry about the derivation, but remember this phrase:

The direction of rotation of the gyro is chosen so that when the aircraft banks into a balanced turn the gyro precesses in the opposite roll sense to keep its axis more or less horizontal and therefore keep it more sensitive to turn rate. If the gyro rotated in the opposite direction it would only work satisfactorily at very low yaw rates and small angles of bank.

The spring force produces a secondary precession equal to and in the same direction as the yaw.

Note this practical reason for choosing the direction of rotation of the gyro If the air or electrical supply fails the instrument will read zero rate of turn, as the gyro will stop.

Any leaks in the system, or reductions in voltage, tend to make the turn indicator under read. The slip indicator is not subject to any errors.

The turn indicator could be described as having one degree of freedom or two planes of freedom The slip indicator is either a ball in a curved liquid filled tube or a damped pendulum free to move in the same axis. In straight balanced flight the force of gravity keeps the ball or pendulum in the central position and no slip or skid is indicated.

Similarly in a balanced turn the combination of gravity and centrifugal force acts through the aircraft vertical and no slip or skid is indicated. If the bank angle is too great or too small the resultant force will not be through the aircraft vertical and the ball is displaced. Figure 3.16 shows some of the indications that might be seen.

Calculation of Rate and Radius of Turn Rates of turn are standardised. A rate one turn is 180° a minute or 3° a second. A rate two turn is twice that, 360° a minute or 6° a second, and a rate three turn is three times as much, 540° a minute or 9° a second.

The angle of bank required to achieve a given rate of turn increases with the TAS. A useful formula to calculate the bank angle in degrees for rate 1 turns is:

Errors The turn indicator is mounted with the gimbal axis on the aircraft fore-and-aft axis, and the gyro axis horizontal. In this position the gyro measures yaw rate. If the gyro was mounted with its axis vertical the instrument would measure pitch rate. It is inherent in the design of the instrument that in any yaw condition the gyro axis will tilt, and the gyro will become sensitive to pitch rate. If the aircraft is then rapidly pitched nose up, as in a loop or recovery from a spiral dive, this pitch input can deflect the gyro to read maximum turn rate. This is called looping error. This pitch rate error also affects the instrument readings in normal turns.

To compensate for this and for the difference between yaw and turn rates the indicators are calibrated to show rates of turn correctly in balanced turns for rate 1, 2 and 3 turns at specific angles of bank and TAS. Although the indicated rate of turn will be incorrect at speeds away from these datums the errors are not significant in normal operation.

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TAS Angle of bank =

10

+7

To calculate the radius of turn in nautical miles use the following:

Radius of turn =

TAS rate of turn x 60 π

Where π is the constant for circles, 3.142, and rate of turn is rate 1,2,3 etc.

Turn Coordinator A turn coordinator is a development of a turn indicator. The gimbal is raised at the front by 30° and the instrument is sensitive to both roll and yaw, and begins to indicate a turn as soon as the roll in begins. As the yaw rate builds up the roll must be reduced to keep the indicator on its datum, so the idea is that a smooth entry to a turn can be achieved using only one instrument.

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turns accurately, and unfortunately can easily be confused with the artificial horizon, particularly by a pilot under stress. It normally carries a warning “no pitch information”.

drag of the liquid that fills the space between the inner and outer cylinders. When the input torque is taken off, the inner cylinder stops rotating, and the angle that it has turned through, measured electrically, is an integral of input rate and time, that is input angle.

The rate integrating gyro has two degrees of freedom but is used to sense movement about one axis only The liquid in the cylinder balances the precessive torque, as described, and allows the inner can to float in order to reduce bearing friction. The viscosity chosen for the liquid fixes gimbal gain.

Sticky liquid equals less gain, thin liquid equals more gain.

Figure 3.18

Rate Integrating Gyros The turn indicator indicates rate of turn. The rate integrating (RI) gyro, on the other hand, indicates the product of both the rate of turn and the time that the rate is held for. The rate gyro indicates rotational speed; the RI gyro indicates rotational distance, or angular displacement, which keeps the alignment fixed. Rate Integrating Gyros are used in Stable Platform Inertial Navigation systems, and in three-axis attitude referencing systems.

The ordinary attitude gyro indicates angular displacement, as bank or pitch for example, so the RI gyro is used in special cases where extreme accuracy of output over a small angular movement is required. RI gyros can be designed so that for a given angular input the output can be ten times as much, and therefore easier to read accurately. This is called gimbal gain.

The construction of an RI gyro is shown in figure 3.18 It is basically a cylinder mounted with another inside it pivoted to revolve about the YY’ axis, and inside that is the gyro, with its spin axis at XX’. Any attempt to rotate the outer cylinder about the ZZ’ axis affects the gyro in the normal way, the torque will precess, and the gyro and the inner cylinder will begin to rotate about the YY’ axis. This rotation will be opposed by the viscous 3.14

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Figure 3.19 Rate integrating gyros have two degrees of freedom and a horizontal spin axis, but are used to sense movement about one axis only.

Rate integrating gyros have one serious problem.

If you look at figure 3.19 and visualise what happens as an input is applied to the ZZ’ axis you will see that as the gyro itself rotates with the inner can two things begin to happen.

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The axis of rotation of the gyro lines up nearer the ZZ’ axis, reducing the sensitivity of the gyro to inputs on the ZZ’ axis, and As the axis of rotation of the gyro changes, the gyro begins to be sensitive to inputs on the XX’ axis. This is called cross-coupling

Instrumentation

Gyroscopes 3

To overcome these problems in INS a more advanced version of the RI gyro is used. In this type the gyro and inner can do not move.

Instead, when an input is applied to the ZZ’ axis the torque on the inner can is sensed and opposed by a torque motor on the inner can YY’ axis, which keeps the alignment fixed. The integral of the electrical current applied to the torque motor to generate this opposing force is then a measure of the angular input on the ZZ’ axis. This feedback sensing technique is the same in principle as that used in the accelerometer and in the servo altimeter.

Laser Gyros

Figure 3.20

The laser gyro, or ring laser gyro (RLG) is relatively new technology and at the present time used mainly in inertial reference systems (IRS).

Nevertheless, RLGs are now meeting the same performance standards as conventional gyros, and will increasingly be used in applications outside IRS. The system described here is based on the Honeywell RLG used in the Boeing 757/767 IRS.

The output system for measuring the angular rotation depends on the generation of interference patterns in the light output. With a semi-transparent mirror and a prism, samples of both the CW and CCW beams are extracted, and transmitted nearly parallel toward a pair of photo diodes.

As in Young’s and Fraunhofer’s experiments

Principle of Operation

When the RLG is rotated about the input axis and the frequencies of the CW and CCW beams differ, the beams will sometimes combine in phase in the nearly parallel output, to increase the intensity, and sometimes combine out of phase to cancel each other out. This will produce a characteristic fringe pattern of light and dark lines.

An enlarged view of this is at figure 3.21.

The Honeywell RLG uses a gas discharge laser to generate monochromatic (single frequency – in the orange/pink band of the visible spectrum) radiation in two directions. Mirrors are used to reflect each beam around an enclosed area, which produces a laser in a ring configuration.

The gas in the laser determines the basic frequency of the light, but it can be changed over a small range of frequencies. A ring of a specific length forms a resonant cavity for the light emission, within which the light will produce peak output at a frequency, or wavelength, that matches the cavity length to a whole number of wavelengths, and any change of path length will change the frequency of the light. Angular rotation around an input axis perpendicular to the ring plane will generate an apparent path length difference between the clockwise (CW) and counter clockwise (CCW) paths and cause the two beams to have a frequency difference proportional to the input rate. This frequency difference can be measured and converted into a digital output signal.

Instrumentation

Figure 3.21

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3.15

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The distance between the fringe lines is proportional to the frequency difference between the CW and CCW beams, and therefore to input angular rate. As rotation continues the whole fringe pattern moves across the output diodes, and the direction of movement and the number of bars that cross any point indicates the input angle change. The photo diodes determine the direction of movement and count the bars, and the RLG, while first sensing angular rate, is giving its final output as angular displacement about its input axis, and is acting as a rate sensing gyro or rate sensor.

The RLG is basically a rate gyro but is constructed to give an output of rate integral

A change in the length of the ring, perhaps by thermal expansion, or any bias in the discharge current on either side of the laser will produce a change in the readout which is equivalent to real wander in a mechanical gyro. Both of these are compensated for, using active control of the discharge current through an error detection and feedback system and by active control of the path length by moving one of the mirrors.

In a strap-down IRS three RLGs are mounted at right angles to each other, and the whole set is then fixed to the aircraft frame. The system then measures all rotations about the three axes, giving a very accurate readout of aircraft attitude with reference to a space datum.

Advantages

Frequency Lock The RLG has one major problem, that of frequency lock, or lock-in. At very low input rates, when the frequencies of the CW and CCW beams are very nearly the same, they shift frequency and lock together, taking the output to zero. This is unacceptable, particularly in an INS, which has to have gyros with a very low threshold of detection. The cure is called dither.

The whole triangular block with the laser system is mechanically rotated backwards and forwards around the input axis. The amplitude of the rotation is very small, but the frequency changes it produces keep the RLG out of the lock-in range.

Since the rotation is first one way and then the other, the sum over time is zero, and the dither does not affect the mean output in any way.

The RLG is not a rotating mass gyro and does not have to rotate to do its job. Dither is there to correct a specific problem

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Real Wander

RLG use relatively low amounts of electrical power compared to mechanical gyroscopes.

They are virtually instant on start-up, needing virtually no time to run up and align. As they are constructed in extremely high grade glass blocks they are resistant to temperature variations. Even so, they may also include a piezo-electric device to physically change the path length of the laser beam to compensate for temperature changes.

The mean time between failure (MTBF) of RLG is claimed by their manufacturers as being in the tens or even hundreds of thousand hours, often far exceeding the design life of the aircraft to which they are fitted.

Fibre Optic Gyros The fibre-optic gyro measures the difference in time of arrival of light pulses around clockwise and counter-clockwise paths of extreme length.

Many kilometres of fibre optic lines are wound in a circle. Rotation of the circle brings about an apparent path length change and the change in arrival times of the pulse trains is a measure of the rate of rotation. This can be manipulated to provide rate integral. The system is rugged, but is not yet accurate enough to supplant RLGs.

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Instrumentation