Inertial navigation systems are computer-based self-contained systems that provide aircraft geographic position information in terms of latitude and longitude, together with aircraft speed, heading and tracking information. When provided with a TAS input, the system also produces an output of wind velocity and direction. They require no external information or refer- ence other than the starting location of the aircraft.
The basis of the inertial navigation system lies in measurement of the aircraft's acceleration in a known direction and this is accomplished with the use of accelerometers. These are devices that measure acceleration along a specific axis; normally one measures accelerations and decelerations along the east±west axis and a second measures accelerations and decelerations along the north±south axis. Acceleration may be defined as increase of velocity per unit time and is usually expressed in terms of metres or feet per second per second (m/s2or ft/s2).
If a vehicle, such as an aircraft, accelerates from rest or steady speed at a constant rate over a given period of time, its final velocity and the distance travelled can be calculated from simple formulae:
v u at and s ut 1
2at2
where: v = final velocity u = initial velocity a = acceleration t = time
s = distance travelled
Since aircraft accelerations and decelerations are seldom constant it becomes necessary to integrate each acceleration with respect to time in order to obtain velocity and then to integrate the result of that with time in order to obtain distance travelled. To achieve this, the outputs from the accelerometers are fed to two integrators in series, as shown in Figure 3.1.
In order to determine position from the factors known, speed, distance travelled and start position, it is necessary to know the direction of travel. This is determined by virtue of the two accelerometers being aligned east± west and north±south. Suppose, for example, that the north±south accel- erometer/integrator combination has recorded a distance travelled of 60 nautical miles (nm) and the east±west accelerometer/integrator combination has recorded zero distance travelled. Clearly the aircraft is now 60 nm, or 18 of latitude, north of its previous position. If both the east±west and north± south accelerometers have recorded speed and distance, then the aircraft is at some point at a known distance and in a calculable direction from its start point.
In order for the system to work, the accelerometers must only measure aircraft accelerations and, to do this, they must be maintained earth hor- izontal at all times so that they do not measure the acceleration due to gravity (9.81 m/s2or 32.2 ft/s2).
Accelerometers can be maintained physically horizontal to the earth on a gyro-stabilised platform called an Inertial Navigation System (INS). Alter- natively, the accelerometers can be fixed to the aircraft axes, in which case the accelerations due to gravity and aircraft manoeuvres are removed mathematically from the accelerometer outputs. This system, called a strapdown inertial system, is the basis of an Inertial Reference System (IRS). We shall first study the gyro stabilised platform inertial navigation system.
Accelerometers
Since the accelerometers are the heart of the inertial navigation system it should come as no surprise that they use inertia to measure acceleration. There are a number of different types of accelerometer, but the one most commonly used in aircraft inertial systems is the pendulous force balance type.
If a freely suspended pendulum is subjected to acceleration it will lag, due to inertia, in a direction opposite to that of the acceleration. The accel- erometer incorporates a pendulous mass that is constrained so that it responds only to acceleration or deceleration along its sensitive axis.
accelerometer a v s
1st integrator 2nd integrator
a.dt v.dt
In the example illustrated in Figure 3.2 the pendulous mass is suspended by two light leaf springs between two pick-off transformers. Ferrite arma- tures are attached to the ends of the mass and the transformer primary coils are supplied with low voltage alternating current at a frequency of about 12 kHz. Whilst the accelerometer is not subjected to acceleration, the sus- pended mass is positioned exactly midway between the two transformers. Under this condition the secondary voltage is identical in both transformers and there is consequently no current flow in the secondary circuit.
When the accelerometer is subjected to an acceleration or deceleration along the axis of the pendulous mass, the mass is deflected by inertia, reducing the gap between one armature and its transformer and increasing the gap at the other end. This causes the voltages induced in the transformer secondary windings to be unbalanced, with a resultant current flow between them.
This current flow is amplified and fed back to the force coil surrounding the pendulous mass, creating an electro-magnetic field around the mass. This field reacts with the field produced by the permanent magnets on either side of the mass, to return the mass to its mid, or null, position. The
N N S S pick-off transformer pick-off transformer force coil mass permanent magnet permanent magnet amplifier primary circuit secondary circuit suspension leaf spring a.c. supply armature armature output
secondary current required to achieve this is directly proportional to the acceleration that caused the deflection and it therefore serves as the output signal from the accelerometer.
As previously stated, the purpose of the gyro-stabilised platform is to provide a mounting for the accelerometers that is earth horizontal at all times and that remains aligned with true north. The system uses rate inte- grating gyroscopes to sense platform horizontality and alignment. The platform is mounted on gimbals which are controlled by pick-off signals from the rate integrating gyros. Servo motors drive the gimbals to keep the platform level and aligned irrespective of aircraft maneouvres.