09 Instrumentation Gyroscopes
This version applies to: ATPL(A)
Gyroscopes 9
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. Gyroscopes are widely used in aircraft, both in traditional and modern instruments.
Gyro Principles
Rigidity and precession are the two key properties of gyros
What makes a gyroscope? Any spinning mass can act like a gyroscope if it has a high angular momentum. In physics, the angular momentum of a spinning body is its moment of inertia multiplied by the rate of rotation. The moment of inertia itself depends on the mass of the spinning body and how far the mass is located from the spin axis, the greater moments of inertia coming from large masses located way from the centre of rotation. Even something like a bicycle wheel, as it spins quickly and with its mass located at the rim, can show the properties of a gyroscope. This, in fact, is given as an explanation of how bicycles in motion do not fall over, the wheels act as gyroscopes.
In the diagram below a force is applied to the left of a spinning gyroscope, it is precessed through 90° in the direction of rotation and, rather than causing the gyro axis to rotate in the horizontal plane, the axis is tilted in the vertical.
Rigidity When a gyroscope is designed as part of an instrument the same principles apply, the designers look for high rotation speeds and a high moment of inertia, with the mass concentrated at the rim. If this is achieved the spinning gyroscope will have a high angular momentum and tend to hold its position in space unless acted on by an external force. This property is called the rigidity of a gyroscope. As the gyroscope slows down, and angular momentum reduces, it becomes less rigid.
Precession If an external force acts on a spinning gyroscope the force does not act as you might intuitively expect, it acts at 90° in the direction of rotation. This is the second property of gyroscopes, precession.
Instrumentation
Figure 9.1 More rigid gyroscopes will require a greater force to precess them at any given rate.
Power sources The spin rate, and therefore one aspect of the rigidity, is determined by how the gyroscope is powered. Earlier aircraft will have air driven gyros, either using a positive pressure from a small pump or using vacuum pressure from an engine driven pump to suck air through a nozzle into the instrument casing and then drive the gyro. Whether negative or positive pressure systems the result is the same – the gyro is driven by air impinging on small depressions around its rim, much like water acting on a mill wheel.
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More modern aircraft have AC motors driving the gyroscopes. There are several advantages to electrically powering gyros; the spin rate is faster and more predictable, there is less chance of dust getting into the system and the ambient air pressure is no longer a factor, allowing higher operating altitudes.
Classification of Gyroscopes Gyroscopes can be classified by their degrees of freedom, the orientation of the spin axis and/or their use.
Classification by Degrees of Freedom
Gimbals
The first classification is by degrees of freedom where the number of degrees of freedom equates to the number of axes about which gyro displacement can be measured and also, effectively, the number of gimbals. The spin axis is not counted as a degree of freedom because gyro displacement cannot be sensed around that axis.
Gyroscopes are usually suspended in a system of frames, called gimbals, which allow them freedom of movement in a defined number of 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.
The gyro with one gimbal, for instance, has one degree of freedom because (discounting the spin axis) the only movement possible is that the gyro in the gimbal could rotate in its frame as shown below.
At least one gimbal is required for every axis you want to measure around Shown below is a gyroscope rotor suspended in a single gimbal which is free to rotate around the horizontal axis of its supports.
Figure 9.3 The gyro at the top of the next page has two gimbals (don’t count the mounting frame) and therefore it has two degrees of freedom. The first degree of freedom is that the gyro and inner gimbal could be displaced so that the axis pitches away from the horizontal and the second is that the outer gimbal (with the whole inner gimbal and gyro structure inside it) could spin around the vertical.
Figure 9.2
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Figure 9.4 It is worth noting that, by including the spin axis, a gyro rotor mounted in two gimbals and with two degrees of freedom, as above, is free to move in all three planes, yaw, pitch and roll. This idea of ‘planes of movement’ rather than ‘degrees of freedom’ is actually an alternative method of classification, not used by EASA but still present in many aviation textbooks. If you ever encounter this terminology there is always one more ‘plane’ than ‘degree’ because the spin axis is considered as well.
Figure 9.5 a space gyro 11
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Earth gyros are a sub-category of tied gyros where the spin axis is tied by the Earth’s gravity to remain in the Earth vertical. Rate gyros have only one gimbal, one degree of freedom, and sense rate of rotation in only one plane, for instance rate of yaw.
Classification by Spin Axis Orientation Gyros are also classified by reference to the orientation of their spin axis. This is only meaningful if the gyro spin axis is vertical or horizontal and is maintained in its orientation in some way, but with gyros used in aviation this is often the case.
Classification by Use The final form of classification is almost completely unique to aviation, and that is to class gyros by their general use, and there are five such classes: 11
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Figure 9.6 a rate gyro 11
Rate-integrating gyros have one degree of freedom and sense angular displacement.
Space gyros have two degrees of freedom. Also called ‘free gyros’. Tied gyros also have two degrees of freedom but have an external influence controlling the orientation of the spin axis, perhaps tying it to the aircraft horizontal or vertical.
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Gyroscopic Wander
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 can be caused either by the effects of the Earth’s rotation or by transporting the gyro across the earth’s surface.
The rigidity of a gyro system will tend to keep the spin axis fixed in space. We have seen that a force applied to the gyro will cause it to precess. When we look at how gyroscopes are used in aircraft instruments a force is often deliberately applied and that force, precessed, leads to an indication.
Apparent Topple Caused by the Earth’s Rotation
There are, however, forces that are not deliberately applied such as friction, which can cause the gyro axis to precess out of position. When this occurs the gyro is said to wander.
Consider a vertical space gyro standing on the equator. As always the gyro axis will try to maintain its position in space as the earth rotates underneath it.
Drift and Topple Gyro wander can be broken down into two elements for descriptive purposes. ‘Topple’ is when the axis moves out of the vertical (relative to the earth surface) and ‘drift’ is when the axis moves in the horizontal plane.
Figure 9.8 The earth spins at 15º an hour, so the gyro will appear to topple at the same rate. Figure 9.7
Real Wander When gyro imperfections cause the gyro axis to wander, either toppling or drifting or combinations of the two, this is called real wander. A perfect gyro with no external forces acting on it will not suffer from real wander.
Figure 9.9
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After 12 hours it will appear to be erect again, but actually be upside down, and after 24 hours the axis will be back in its previous position. This is known as apparent topple, as the gyro appears to be toppling, but actually isn’t.
The gyro maintains its orientation in space, but to an observer on the Earth, it appears to be drifting clockwise when viewed from above at a rate of 15º an hour.
Apparent topple is at a maximum at the equator. If a vertical gyro is positioned at one of the Earth’s poles the rotation of the earth will produce no apparent topple, as the rotation is straight along the axis of the gyro.
Figure 9.12 Apparent drift is at a maximum at the poles.
Figure 9.10
At the equator the horizontal gyro experiences no apparent drift as the axios is aligned with the meridians and remains aligned as the Earth rotates.
Apparent topple is zero at the poles and at a maximum at the equator.
Apparent Drift Caused by the Earth’s Rotation The vertically aligned gyro at the North Pole is unaffected by the rotation of the Earth. But what would happen if the gyro were placed on its side?
Figure 9.13 We can see that apparent drift is a maximum at the poles and zero at the equator. Apparent drift is at a maximum at the poles and zero at the equator
Figure 9.11 Instrumentation
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A gyro placed somewhere between the poles will experience both apparent drift and apparent topple.
Figure 9.15 Transport wander is zero when moving north/south
Figure 9.14
However when movement east/west is considered transport wander does produce an effect.
An alternative name for apparent topple or drift caused by the Earth’s rotation is ‘astronomic precession’
Consider the same gyro moved to the west, as below. The gyro axis maintains its orientation in space but the direction of north on the earth has changed, basically because north is a point on a sphere.
Transport Wander Apparent drift and topple can also occur if a gyro is aligned to north on one part of the Earth and then moved to another. This is called transport wander.
Transport Wander = Convergency
Although both apparent drift and topple can occur as a gyro is transported, because the only instrument that transport wander affects uses a gyroscope tied to the horizontal the apparent topple element of transport wander does not concern us, we are only interested in the apparent drift. Although the effect is still called transport wander a more precise description of the error that affects us is transport drift.
If you have studied navigation you will recognise this change of north reference as convergency.
Consider a tied gyro with an axis oriented north/ south. Moving it along a meridian will produce no change in the apparent alignment. Transport wander is zero when moving a gyro north or south.
Figure 9.16
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Therefore we can say that the amount of the error caused by transport wander is the amount caused by convergency. You will recall the formula for convergency is: Convergency = change of longitude x sine mean latitude and so Transport wander =
Rate Gyros Rate gyros, as we mentioned earlier, have only one gimbal and therefore sense movement in only one plane. An example might be a rate gyro which is used to sense yaw. In order to do this, the gyro is mounted in its gimbal with the gyro axis oriented horizontally across the aircraft, see below.
change of longitude x sine mean latitude There is a second formula that you might encounter elsewhere that calculates the rate of the error caused by transport wander in degrees per hour from the east/west element of groundspeed but you will not need that in this subject, we are only concerned with the total amount of transport wander, not the rate. Figure 9.17 summarises the major categories of gyroscopic wander: Figure 9.18 The gimbal can pivot around its one degree of freedom and has a restraining springs which resist the pivoting of the gimbal and tend to restore it to the neutral position.
Figure 9.17
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When a yawing force is felt at A the twisting moment in the horizontal plane is precessed to a moment around the longitudinal axis of the gimbal at B, and the gyro and gimbal assembly tend to rotate out of the horizontal.
Figure 9.21 It is worth noting that the rate gyro described above only indicates yaw rate because of its orientation in the aircraft. If orientated differently, rate gyros could also indicate either pitch rate or roll rate. In the diagram above rate gyro A would sense yaw rate around the vertical axis, rate gyro B would sense roll rate around the aircraft’s longitudinal axis and rate gyro C would sense pitch rate about the aircraft’s lateral axis.
Figure 9.19 The rotation is resisted by the springs and the assembly reaches an equilibrium where the spring force balances the precessing force. The needle deflection then effectively indicates a rate of yaw.
Rate Integrating Gyros Whereas a rate gyro indicates a rate of angular displacement a rate integrating gyro detects the rate of displacement and the time it was applied for, effectively indication rotational displacement. There are other instruments that indicate rotational displacement which use simpler gyroscopes, such as the attitude indicator which shows bank and pitch. Rate integrating gyros are used in special cases where extreme accuracy of output over a small angular movement is required, their natural output is in the order of tenths and hundreds of a degree. The construction of an rate integrating gyro is shown in figure 9.22. It is basically a gyro rotor inside a cylinder, which acts as the sole gimbal, which is itself free to rotate inside a second cylinder. The outer cylinder is filled with a viscous fluid.
Figure 9.20 Of course you have to be very careful how you describe any force acting on a gyroscope, because everything precesses. When we said above ‘the spring force balances the precessing force’ what we really meant was ‘the spring force produces a secondary precession equal to and in the same direction as the yaw’ - a phrase you may encounter. 9.8
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Figure 9.22
Figure 9.23
Consider a rotating force applied around the vertical XX’ axis above (equivalent to yaw in the rate gyro we just discussed). The torque around XX’ will precess, and the gyro and the inner cylinder will begin to rotate about the YY’ axis just as the rate gyro did.
Now, when an input is applied to the XX’ axis the rotation of the gimbal is sensed and opposed by a torque motor 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 XX’ axis.
This rotation will be opposed by the viscous 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, in other words an indication of angular displacement.
The rate integrating gyro has one degree of freedom and is used to sense rotational movement about one axis only As the rate integrating gyro has only one gimbal, the inner cylinder, it has one degree of freedom.
The rate integrating gyro as described has one serious problem, which is that the inner cylinder and gyro rotate. As the gyro assembly rotates the orientation of the gyro changes and it ceases to be sensitive to torque around, in this case, the XX’ axis and starts to become sensitive to torque forces about a second axis, in this case the ZZ’. This is called cross-coupling. To overcome cross-coupling issues a more advanced version of the rate integrating gyro is actually used. In this type an angular rotation sensing pickoff is fitted to one end of the inner cylinder or gimbal and a torque motor or ‘torquor’ to the other.
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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.
Ring Laser Gyros The laser gyro, or ring laser gyro (RLG) is relatively new technology and is used mainly in Inertial Reference Systems (IRS).
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 shown in figure 9.25.
The RLG uses a gas discharge laser to generate monochromatic (single colour – 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, either triangular or square. 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.
The distance between the fringe lines is proportional to the frequency difference between the CW and CCW beams, and therefore to input angular rate.
Figure 9.25 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. Figure 9.24
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Frequency Lock
Uses
The RLG has one major problem, that of frequency lock, otherwise known as ‘lock-in’ or ‘laser lock’.
In a strap-down Inertial Reference System 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.
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. Frequency lock is avoided by ‘dither’ 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.
RLGs can be surprisingly small, an arrangement of three RLGs is shown above, the whole assembly is perhaps 6cm across. Apart from the advantage of size, RLGs have a longer life cycle than conventional rate sensing and rate integrating gyros.
Real Wander 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.
Figure 9.26
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