Thesis - Beaver simulation

To apply these relations, the spectral density functions of the turbulence velocities must be transformed to functions of o, which may be done, because we have assumed that Taylor's hypothesis holds. The transformation between spatial frequency SL and temporal frequency w is given by:

Notice the term 1/V arising in the spectral density function (see ref.[24])!

B.5.2 Filter design for the Dryden spectra.

The Dryden spectra were developed to approximate the von Kiirmiin turbulence spectra by means of rational functions. This makes it possible to use relation (B-15) for the generation of the turbulence velocities from white noise. From the definitions of the Dryden spectra (B-10) to (B-11) and relation (B-16), the following expressions are found:

(B-18)

Solving equations (B-17), (B-18), and (B-19) yields the following candidate frequency response functions:

Appendix C. The Instrument Landing System and the VOR navigation system.

C.1 Introduction.

In this appendix, a short description of the Instrument Landing System (ILS) and the VOR navigation system will be given. First, the ILS system will be described and equations for the nominal ILS guidance signals will be derived. Then expressions for steady-state errors and ILS noise will be given, and finally, the VOR navigation system will be discussed briefly. See refs.[5], [7], and [21], for more details about navigation systems.

C.2 The Instrument Landing System.

C.2.1 Nominal ILS signals.

The Instrument Landing System (ILS) is the standard aid for non-visual approaches to landing, in use throughout the world today. Under certain circumstances, it can provide guidance data of such integrity that fully coupled approaches and landings may be achieved. The system comprises three distinct equipments :

1- the localizer transmitter, which gives guidance in the horizontal plane,

2- the glideslope (or glide path) transmitter, which supplies vertical guidance,

3- two or three marker beacons, situated on the approach line, which give an

indication of the distance to the runway to the approaching aircraft.

Only the localizer and glideslope signals will be considered here. Figures C-1 and C-2 show the basic layout of the ILS system and the approach path. The localizer signal is emitted by a n antenna situated beyond the up-wind end of the runway. Operating on a frequency in the 108.0 to 112 MHz frequency band, it radiates a signal modulated by 90 and 150 Hz tones, in which the 90 Hz predominates to the left hand (to the aircraft) of the approach path, and 150 Hz to the right. Figure C-3 shows the required coverage of the localizer signals.

Glideslope

/

Localizer antenna

Figure C-1. Positions of the ILS system components.

localiser transmitter

Figure C-2. Layout of the approach path.

Figure C-3. Required coverage of localizer signals.

The glideslope antenna is located some 300 m beyond the runway threshold (approximately adjacent to the touch-down point) and about 120 to 150 m from the runway centerline. The frequency of the signal lies in the 328.6 to 335.0 MHz band. The signal is modulated by 90 and 150 Hz tones, in which the 90 Hz is predominant above the desired approach line, and 150 Hz beneath the glide path. Due to the position of the glideslope antenna, the intersection of the localizer reference plane and the glideslope reference cone is actually a hyperbola located a small distance above the idealized straight glide path. This is shown in figure C-4. The required coverage of the glideslope signals is shown in figure C-5.

actual glide path ( hyperbola)

glide path antenna

Figure C-4. Hyperbolic intersection of localizer and glideslope reference planes.

Figure C-5. Required coverage of glideslope signals compared with required coverage of localizer signals.

An ILS installation is said to belong to a certain performance category, according the meteorological conditions under which it is to be used. These conditions are summarized in figure C-6. An ILS installation of category I is intended to provide guidance down to a n altitude of 200 ft, a n installation of category I1 provides guidance down to 100 ft, and a n installation of category I11 should provide guidance down to the runway surface, hence, its signals can be used by automatic landing systems. This means that if the aircraft is making a n approach under cat. I conditions, the pilot should see the runway lights a t a n altitude of 200 ft. If not, the approach must be cancelled I).

Runway visual range (metres)

Category I : Operation down io minima of 200 ft decision hcight and runway visual range of 800 m with a high probability of approach succeu.

Category 2: Operation down to minima below 200 ft decision hcight and runway visual range of &loom, and to as low as I oo ft decision height and runway visual range of qoo m with a high probability of approach succeu.

Operation down to and along the surface of the runway, with external visual reference during the final phase of the landing down to runway visual range minima of 200 m.

Operation to and along the surface of the runway and taxiways with visibility sufficient oniy for visual taxiing comparable to runway

visual range value in the order of 50 m.

Category 3C:Operation to and along the surface of the runway and taxiways without external visual ref'rcncc.

Figure C-6.ILS performance categories.

The localizer and glideslope signals are received on board the approaching aircraft. They are displayed in appropriate form to the pilot, and may be fed directly to a n automatic pilot as well. The nominal ILS signals on board the aircraft are expressed in terms of the currents supplied to the pilot's cockpit instrument. The magnitude of the localizer current il, depends on the angle The (in [rad]) between the localizer reference plane and a vertical plane passing through the localizer antenna, see figure C-8.

The altitude a t which the runway lights should be visible is called the 'decision height'. Some airlines may use larger decision heights than the ones listed in figure C-6.

The localizer current is:

where S, is the sensitivity of the localizer system. According to ref.[2], S, has to satisfy the following equation:

where x, is the distance from the localizer antenna to the runway threshold (measured in [m]), see figure C-2.

For the simulation of ILS-approaches, a new runway reference frame F, = O&FY$F will be introduced. The XF-axis is directed along the runway centerline in the direction of take-off and landing. ZF points downwards, Y, points rightwards as seen from a n approaching aircraft. At t = 0, the position of the aircraft's c.g. coincides with the earth-fixed reference frame, hence: xe = 0 and ye = 0; H = H,. The position of the origin OFof the runway reference frame a t t = 0, is given by the coordinates: xRWand y , , measured relatively to FE, and the altitude of the runway above sea-level, HRW*From figures C-7 and C-8, the following transformations between FE and F, can be deduced:

where xf,y f f and z f are coordinates in the runway reference frame F, ,and qRw is the headlng of the start and landing direction of the runway (vRW= 0 if it

points to the north). The reference frame F, = o,x,~T,z, in figure C-7 is a n intermediate frame of reference, which has the same orientation as FE,but a n origin that has been moved to the projection point of OFon the horizontal plane

and:

r, and d, are positive if the aircraft flies a t the right hand side of the localizer reference plane if it is headed towards the runway.

Figure C-7. Definition of earth-fixedand runway axes, used for approach simulation (here, the aircraft turns right after a missed approach).

Runway 1 yF,

\YE

Figure C-8. Localher geometry and definition of X, ,yE,X, ,and Y,