Radio Navigation — Pilot's Guide

🧰 Quick tools & cheat sheet play with the numbers

Six small calculators for the sums radio navigation asks you to do again and again, and a one-screen list of the numbers worth knowing by heart.

📻 Frequency ⇄ wavelength

Frequency (MHz)

📡 Line-of-sight range

Aircraft height (ft) Station aerial height (ft)

⏱️ Radar timing

Echo time (µs) PRF (pulses per second) Pulse width (µs)

🛬 Glide path check

Glide path angle (°) Distance to touchdown (NM) Ground speed (kt)

📏 DME slant range

DME reading (NM) Height above the station (ft)

🧭 Bearings from the RBI

Magnetic heading (°) Relative bearing of the beacon (°)

📋 Cheat sheet — numbers worth knowing

Idea	Number / rule
⚡ Speed of radio waves	300 000 km/s · 162 000 NM/s
📻 Wavelength and frequency	λ (m) = 300 ÷ f (MHz)
📡 VHF/UHF range (line of sight)	1.23 × (√h₁ + √h₂) NM, heights in ft
🌊 LF/MF surface wave range	sea 3√P · land 2√P (P in W)
⏱️ Radar mile (1 NM out and back)	12.36 µs
🔁 Maximum radar range from PRF	≈ 81 000 ÷ PRF NM
📏 Minimum radar range	150 m per µs of pulse width
🔊 Range vs power	one-way × 4 · radar × 16 to double range
🛬 3° glide path	≈ 300 ft per NM · ROD ≈ 5 × GS
🎯 CDI full scale	VOR 10° · LOC 2.5° · GP 0.7°
📶 DME/N accuracy	±0.25 NM ±1.25 % of range
🛰️ GPS	24 SVs · 20 200 km · 12 h · 55° · L1 1 575.42 MHz

1 Properties of Radio Waves Chapter 1

Every radio aid is built on three numbers — speed, frequency and wavelength — and on one idea: comparing two signals.

🎯 What a radio wave is🎯 Polarization🎯 f, τ and λ🎯 The eight bands🎯 Phase difference

💡 Key idea

Radio waves travel at the speed of light, so frequency and wavelength are two ways of saying the same thing: λ = c / f. Get comfortable with that one formula and half the chapter is done.

From a wire to a wave

A steady (DC) current makes a magnetic field round a wire, at right angles to the current — and nothing more. Make the current alternate fast enough and the field has no time to collapse before the next reversal, so energy is pushed out into space: electromagnetic radiation.

⚡ The wave has an electric (E) field parallel to the aerial and a magnetic (H) field at right angles to it — the two are perpendicular.
🌍 Long before radio, ocean crossings were navigated by astro-navigation. Today satellites have taken navigation back into space, but ground aids are kept as a back-up to GNSS.
📡 Radar (1930s) let ATC identify and separate aircraft, allowing much busier skies.

Polarization

↕️ Linear

Polarization is the plane of the electric field, set by the aerial: a vertical aerial gives vertical polarization. The receiving aerial must lie in the same plane for the best signal.

🌀 Circular

Made, for example, by a helical aerial. The field rotates once per cycle, right- or left-handed. A dipole receives it in any attitude, and radars use it to reject rain: droplets reverse the rotation.

Period, frequency and wavelength

Frequency counts cycles per second; wavelength measures the distance one cycle covers.

f = 1 / τ

τ = 0.25 µs → f = 4 MHz.

λ (m) = 300 / f (MHz)

Frequency must be in MHz. 150 MHz → 2 m; 400 kHz = 0.4 MHz → 750 m.

f (MHz) = 300 / λ (m)

Wavelength must be in metres. 3 cm = 0.03 m → 10 000 MHz = 10 GHz.

⚠️ The unit trap Almost every wrong answer in this chapter comes from a unit slip: kHz entered as MHz, or centimetres as metres. Convert first, then divide.

The eight frequency bands

Band	Frequency	Wavelength	Used for
VLF	3–30 kHz	100–10 km	Nothing in civil aviation
LF	30–300 kHz	10–1 km	NDB / ADF
MF	300–3 000 kHz	1 000–100 m	NDB / ADF, long-range communication
HF	3–30 MHz	100–10 m	Long-range communication
VHF	30–300 MHz	10–1 m	Voice, VDF, VOR, ILS localizer, markers
UHF	300–3 000 MHz	100–10 cm	ILS glide path, DME, SSR, satcom, GNSS, long-range radar
SHF	3–30 GHz	10–1 cm	Radio altimeter, weather radar, MLS, short-range radar
EHF	30–300 GHz	10–1 mm	Nothing in civil aviation

✈️ Memory hook Each band is ten times the one below: the edges always go 3 – 30 – 300 – 3 000. Wavelengths do the same thing backwards.

Phase comparison

VOR and several other aids find direction by comparing the phase of two signals. Rules: both must have the same frequency; one is the reference, the other the variable; and the answer is always positive.

Δφ = reference − variable (+360° if negative)

080° − 200° = −120° → 240°. 300° − 045° = 255°.

2 Radio Propagation Theory Chapter 2

How a signal gets from the aerial to you decides its range, its reliability by night, and what it can be used for.

🎯 Attenuation & inverse square🎯 Surface, space and sky wave🎯 The ionosphere's layers🎯 Skip distance & dead space🎯 HF frequency choice🎯 Super- and sub-refraction

💡 Key idea

Low frequencies hug the ground, middle frequencies bounce off the ionosphere, high frequencies go in straight lines. LF/MF = surface wave, HF = sky wave, VHF and above = line of sight.

Losing signal on the way

📉 Attenuation = absorption (air, water, ground, vegetation — worse with frequency, large above ~1 GHz) + spreading.
🔆 Inverse square law: power ∝ 1 / range². Twice the range, a quarter of the power; to double range, ×4 power.
⚡ Static is worst at low frequencies and negligible at VHF+. The signal-to-noise ratio measures how clean a signal is.
〰️ Fading: the same signal by two paths, moving in and out of phase.
🎯 Range also grows with receiver sensitivity (less internal noise) and directivity (a beam).

The paths a wave can take

Skip distance runs from the transmitter to the first sky wave; dead space is the silent gap after the surface wave dies.

🌊 Surface wave

~20 kHz–50 MHz, useful to ~2 MHz. Bends round the earth by diffraction. Longer range at lower frequency, over sea (good conductor) and with vertical polarization. Rule of thumb at 300 kHz: 3√P sea, 2√P land. Crossing a coast it speeds up over water and bends towards the coast — coastal refraction.

📶 Space wave

Direct + ground-reflected wave. The only path at VHF and above. Range = 1.23 (√h₁ + √h₂), heights in feet. Below the radio horizon, no amount of power helps.

🌌 Sky wave

Refracted back by the ionosphere. Up to ~2 MHz from the E-layer, 2–50 MHz from the F-layers. Nothing above 50 MHz except in abnormal solar conditions.

🧮 Worked example — line of sight

Aircraft at 10 000 ft, station aerial at 400 ft: 1.23 × (100 + 20) = 148 NM.

Station 150 NM away with its aerial at 100 ft — how high must you be? 150 ÷ 1.23 = 122; 122 − 10 = 112; 112² ≈ 12 500 ft.

Common slip: adding the two heights under one square root gives a range far too short.

The ionosphere

From about 60 km up, ultraviolet and shorter solar radiation knocks electrons off atoms. Ionization peaks about 1400 local, is lowest just before sunrise, and is greater in summer and at low latitudes. Solar flares can push it to disruptive levels.

Layer	Average height	Behaviour
D	75 km	Forms at sunrise, gone at sunset. Absorbs LF/MF by day.
E	125 km	Always there. Lower by day, higher at night. Max single hop ≈ 1 350 NM.
F (F1, F2)	225 km	Splits into F1 and F2 at sunrise. F2 rises above 400 km in summer. Max single hop ≈ 2 200 NM.

Change	Critical angle	Skip distance	Dead space
⬆️ More ionization (day)	smaller	shorter	smaller
⬆️ Higher frequency	larger	longer	larger (surface wave shrinks too)
⬆️ Higher layer	—	longer	—

🌅 Dawn and dusk The ionosphere is in transition and "electrically turbulent": HF and ADF are least reliable then. At night the D-layer vanishes, so LF/MF sky waves appear at short range — the root of ADF night effect.

HF communication

📍 MUF: the frequency whose first sky wave lands exactly at the receiver — least loss, but a drop in ionization loses the signal.
✅ OWF ≈ 0.85 × MUF. MUF 20 MHz → OWF 17 MHz.
🌙 Night needs roughly half the daytime frequency; longer range needs a higher frequency.
🌐 Mid-ocean at dawn: towards the daylight side use the higher frequency, towards the dark side about half of it.

Super- and sub-refraction (VHF and above)

⬇️ Super-refraction (+ up to 40 %)

Humidity falling with height, temperature falling slower than standard (inversion), high pressure, warm air over a cool surface. Extreme case: a duct — very long ranges, common where deserts meet the sea.

⬆️ Sub-refraction (− up to 20 %)

Humidity rising with height, steep lapse rate, low pressure, cold air over a warm surface. Rarer.

3 Modulation Chapter 3

A plain carrier tells you nothing. Modulation is how speech, Morse, data and bearing information ride on it.

🎯 Keyed, AM, FM, phase, pulse🎯 Sidebands and bandwidth🎯 Why SSB on HF🎯 Emission designators

💡 Key idea

Whatever you change on the carrier — on/off, amplitude, frequency or phase — names the type of modulation.

Type	What the information changes	Aviation use
🔘 Keyed	Carrier switched on and off (Morse — telegraphy)	Some NDB idents (A1A)
📶 AM	Carrier amplitude	VHF voice (A3E), HF voice as SSB (J3E)
〰️ FM	Carrier frequency: audio amplitude sets deviation, audio frequency sets rate	Not for aviation voice (too wide)
🔄 Phase	Carrier phase — digital PSK: 0° = 0, 180° = 1	GPS (BPSK), MLS (DPSK)
⏱️ Pulse	Short bursts of carrier	Radar, DME, SSR, data

Sidebands

Mixing (heterodyning) a carrier with audio leaves the carrier unchanged and adds sum and difference frequencies — the upper and lower sidebands. Bandwidth = 2 × highest audio frequency. Both sidebands carry all the information, and only about one third of the power carries any.

🧮 Worked example — bandwidth

1 000 kHz carrier, audio up to 3 kHz: occupies 997–1 003 kHz, bandwidth 6 kHz.

✂️ Single sideband (SSB)

Remove the carrier and one sideband. Benefits: twice the channels, better signal-to-noise (less ionospheric distortion and static), less power and lighter equipment. That is why HF voice is SSB.

📻 Why not FM?

FM broadcasting needs about 150 kHz (AM about 9 kHz). Even narrow-band FM (~8 kHz) is wider than the 6 kHz aeronautical VHF channel or the 3 kHz HF channel.

Emission designators

Three symbols: 1 type of modulation of the main carrier, 2 nature of the modulating signal, 3 type of information.

Aid	Designator	Aid	Designator
NDB / ADF	N0NA1A · N0NA2A	VOR	A9W
VHF voice	A3E	ILS	A8W
HF voice	J3E	Marker beacons	A2A
DME	P0N	MLS	N0XG1D

✈️ Decode A3E A = AM double sideband · 3 = one analogue channel · E = telephony. J = single sideband, suppressed carrier.

4 Antennae Chapter 4

The aerial shapes where energy goes. Get its length and shape right and the whole system works better.

🎯 Dipole and Marconi🎯 Feeders and waveguides🎯 Polar diagrams🎯 Directivity & side lobes🎯 Loop, dish, flat plate

💡 Key idea

An aerial works best at a half or quarter of the wavelength — cut slightly short because waves travel more slowly in a conductor.

Half-wave dipole

Fed at the centre; radiates at right angles to its length, nothing off the ends. 3-D pattern: a torus. 100 MHz → λ 3 m → 1.5 m.

Quarter-wave (Marconi)

Stands insulated on a metal surface that acts as the other half. Short and low-drag — the aircraft's blade aerials. 150 MHz → 50 cm.

Frequency	Feeder
LF / MF	Simple wire
HF / VHF	Twin-wire feeder
UHF	Coaxial cable
Upper UHF, SHF, EHF	Waveguide — hollow rectangular tube, about ½ λ wide

Polar diagrams and directivity

A polar diagram joins points of equal signal strength. A beam gains range in one direction — at the cost of side lobes.

🔁 Reflector: about 5 % longer, ¼ λ behind. Directors: shorter, in front. Together: the TV aerial.
👻 Price of directivity: side lobes (TV ghosting; real problems in SSR, ILS and radar).
🛬 ILS localizer: 16 or 24 elements in a line, ½ λ apart, making two narrow lobes.
🧭 ADF loop: zero output when square to the wave; figure-of-eight with two nulls (180° ambiguity).

Radar aerials

Parabolic dish

Waveguide horn at the focus; reflected rays leave parallel and in phase (a plane wavefront). The beam still diverges, and uneven reflection spills energy into side lobes.

Flat plate (slotted, phased array)

Many slots fed from behind. Narrower beam, smaller side lobes, less power, narrower pulse, better resolution. Standard on modern weather radar.

5 Doppler Radar Systems Chapter 5

Relative motion changes the frequency you receive. Measure that change and you know the speed.

🎯 Doppler shift🎯 Janus array🎯 Ground speed and drift

💡 Key idea

Closing → frequency rises. Opening → frequency falls. The shift is proportional to relative speed, not distance. With no relative motion there is no shift.

Δf ≈ 2V / λ (echo)

The shift happens out and back, hence the 2. 150 m/s on 3 cm → 10 kHz.

Forward and aft shifts give ground speed; a difference between left and right beams gives drift.

🛩️ Airborne Doppler uses one slotted waveguide array, beams pointing down: a Janus array of 3 or 4 beams (named after the god who faced both ways).
➡️ No drift: equal and opposite shifts fore and aft. Drift: port and starboard shifts differ.
🧭 Doppler gives ground speed and drift; heading is needed for position (dead reckoning).
🌊 Weak points: poor heading input and lost returns over a calm sea — today Doppler is blended with IRS, VOR/DME or GPS.
📡 The principle is also used in radar, Doppler VOR and some VDF.

6 VHF Direction Finder (VDF) Chapter 6

The simplest bearing service of all: you talk, the ground station finds where your voice comes from.

🎯 QDM, QDR, QTE, QUJ🎯 Bearing classes🎯 Range and errors

💡 Key idea

All the direction-finding kit is on the ground. The aircraft needs only its VHF radio (118–137 MHz, A3E). Auto-triangulation is offered only on 121.5 MHz.

Code	Meaning	Reference
QDM	Heading to steer to the station (no wind)	Magnetic, TO
QDR	Bearing of the aircraft from the station (radial)	Magnetic, FROM
QUJ	Track to the station	True, TO
QTE	Bearing of the aircraft from the station	True, FROM

🧮 Worked example — converting codes

QTE 120°, variation 5°W: QDR = 120 + 5 = 125°, QDM = 305°, QUJ = 300°.

QTE 353°, variation 8°E: QDR = 353 − 8 = 345°, QDM = 165°.

"Variation west, magnetic best; variation east, magnetic least."

Class	Accuracy
A	±2°
B (normally the best offered)	±5°
C	±10°
D	worse than C
Doppler VDF	±0.5°

📡 Range = line of sight (1.23 formula), limited by terrain and power; ducting can extend it.
🏢 Errors: site and propagation error (reflections), aircraft attitude (vertical polarization — fly straight and level), poor accuracy overhead, two aircraft transmitting together.
✅ Uses: track checks, position lines, homing and VDF let-downs. Stations are listed in the AD section of the AIP.

7 Automatic Direction Finder (ADF) Chapter 7

The oldest aid still in daily use: an LF/MF beacon on the ground and a needle that points at it — most of the time.

🎯 Loop, sense, cardioid🎯 NDB frequencies and types🎯 BFO use🎯 RBI and RMI sums🎯 Tracking and drift🎯 Eight errors

💡 Key idea

The ADF measures relative bearing. Add the heading to get the magnetic bearing to the beacon: QDM = MH + RB (minus 360° if needed). The QDR is its reciprocal.

How the needle finds the beacon

The loop gives a figure-of-eight with two sharp nulls — but which one is the beacon?
A sense aerial (circular pattern) is added: the result is a cardioid with one, rather blunt, null that picks the right loop null.
To meet ±5°, the sense polarity is switched about 120 times a second between left and right cardioids, sharpening the null.
In practice the loop is fixed (crossed elements) and a goniometer with a search coil does the turning.

The beacon

📻 NDBs: 190–1 750 kHz (LF/MF), mostly 250–450 kHz, vertically polarized, surface wave.
📍 Locator (L): low power, 10–25 NM, at approaches/with ILS markers. En route NDB: 50 NM or more.
🔕 A cone of silence sits overhead, wider with height.
🧩 Aircraft kit: loop aerial, sense aerial, control unit, receiver, display (RBI or RMI).

Emission	Ident	BFO for tuning	BFO for ident & monitoring
N0NA1A	Keyed (interrupted) carrier	ON	ON
N0NA2A	Amplitude-modulated tone	ON	OFF

✈️ Why a BFO? An unmodulated carrier is silent on a normal receiver. The beat frequency oscillator mixes in an offset to make an audible tone (say 400 or 1 020 Hz).

RBI and RMI sums

RBI

000 fixed to the nose → needle reads relative bearing. Heading 300°, RB 136° → QDM 076°.

RMI

Card driven by magnetic heading → needle head reads QDM, tail reads QDR. ADF bearings use the aircraft's variation when plotted.

Homing, tracking and drift

Situation	Heading	Relative bearing held
Inbound 080°, 20° starboard drift	060°	020°
Inbound 080°, 28° port drift	108°	332°
Outbound 100°, 23° starboard drift	077°	203°
Outbound 090°, 20° port drift	110°	160°

➰ Homing with RB 000° in a crosswind gives a curved track ending into wind.
🔍 Inbound, steady heading: RB increasing = port drift. Turn 30° right to regain; back on track at RB 330°; then allow, say, 10° → hold RB 350°.
🔍 Outbound, steady heading from overhead: RB 190° = 10° starboard drift; 170° = 10° port drift. Regain with a 30° turn until RB 210° or 150°.
🔁 Holds ("stacks") over a beacon are separated by at least 1 000 ft.

Errors — know all eight

Error	Cause	Signs / cure
🌧️ Precipitation static	Rain, ice crystals hitting the airframe	Wandering needle, hiss
⛈️ Thunderstorms	Lightning is a strong LF/MF source	Needle swings to the Cb
🌙 Night effect	Sky wave mixes with surface wave once the D-layer goes; currents in the loop's horizontal members	Fading, hunting needle; from about 70–100 NM; worst at dawn/dusk
📻 Station interference	Crowded LF/MF band, worse at night	Always identify the NDB
⛰️ Mountain effect	Reflection and diffraction	Fly higher
🏖️ Coastal refraction	Wave speeds up over the sea and bends towards the coast	Fix appears closer to the coast. Use coastal NDBs, cross at 90°, fly higher
✈️ Quadrantal error	Airframe bends signals towards the fore-aft axis	Greatest at RB 045/135/225/315; corrected by the maker
↪️ Dip (bank) error	Bank puts currents in the loop's horizontal members	Only when not wings level

⚠️ No failure flag Most ADF indicators have no failure warning. On an NDB approach, monitor the ident continuously and cross-check other aids. At night: identify, avoid the hour around sunrise/sunset, stay inside the (daytime) DOC — based on a 3:1 signal-to-noise ratio.

Range ≈ 3√P (sea) · 2√P (land)

400 W → 60 NM over water. 30 NM over land → 225 W. Doubling range needs 4 × power.

Accuracy ±5°

Within the DOC, by day only, excluding compass error. Lower frequency and N0NA1A give more range; precipitation reduces it.

8 VHF Omni-directional Range (VOR) Chapter 8

The workhorse of airways: a magnetic radial from every beacon, free of static and night effect.

🎯 Phase comparison🎯 Frequencies and idents🎯 DOC and range🎯 Accuracy ±5°🎯 CDI, RMI, HSI🎯 TO/FROM logic

💡 Key idea

The phase difference between the 30 Hz reference and the 30 Hz variable signal is the radial — the aircraft's magnetic bearing from the station, referenced to magnetic north at the VOR.

Conventional VOR

Reference: 30 Hz FM, same phase everywhere. Variable: 30 Hz AM from a limaçon rotating 30 times a second. In phase on magnetic north.

Doppler VOR

Reference AM, variable FM, simulated rotation anti-clockwise so ordinary receivers still read correctly. Far less site error.

Phase difference measured at the aircraft = radial. 227° measured → on the 227° radial, QDM 047°.

Frequencies, identity and monitoring

📻 108–117.95 MHz: 40 channels below 112 MHz shared with ILS (VOR on even decimals: 108.0, 108.05, 108.2…), 120 above 112 MHz every 50 kHz — 160 in all. Emission A9W.
🔤 3-letter Morse at least every 10 s; voice ident and ATIS can share the voice channel. Bearings continue during the ident.
🛑 Monitor removes ident/nav (or switches off) for: bearing shift >1°, signal drop >15 %, monitor failure. No ident = do not use; TST = on test.

Type	What it is
CVOR	Conventional, airways and en route
BVOR	Broadcasts weather between idents
DVOR	Doppler — beats site error
TVOR	Terminal, low power (~50 W)
VOT	Test transmitter: one 360° radial everywhere. Error over ±4° → service the set
VORTAC	VOR with TACAN

Range, DOC and accuracy

📡 200 W en route VOR ≈ 200 NM, but line of sight decides. Terrain causes screening and scalloping.
🛡️ DOC 50/25 = no co-frequency interference within 50 NM up to 25 000 ft, day and night (except super-refraction). Co-channel beacons would ideally be 2 × line-of-sight apart (≈ 389 NM at 25 000 ft) — about 500 NM for planning.
🎯 Site error ±1°, airborne ±3°, total ±5°, plus pilotage near the station where radials converge.
🌀 Cone of ambiguity overhead: needle swings, OFF may flicker, TO/FROM flips. Coverage at least 40° elevation (60–80° in practice).

🧮 Worked example — plotting a radial

Aircraft on the 240° radial; variation 10°W at the VOR, 8°W at the aircraft. Use the VOR's variation: true bearing from the VOR = 230°.

The cockpit displays

CDI (OBS)

5 dots, 2° each, 10° full scale. Shows angle from the selected course; heading has no effect. FROM when the radial you are on is within 90° of the course; TO when more than 90°.

RMI

Head = QDM, tail = radial. Heading is subtracted (differential synchro) then added back by the card, so a heading error moves only the relative picture. Two needles, VOR or ADF. Heavier and costlier.

HSI

Course arrow on a heading card: a plan view. A 2-dot scale is 5° per dot, still 10° full scale.

⚠️ Reverse sensing Inbound: set the inbound course and see TO. Outbound: set the outbound course and see FROM. Fly the course you set (± drift) and the bar always points to the course.

9 Instrument Landing System (ILS) Chapter 9

Two beams — one left-right, one up-down — and a few checkpoints along the way: the most accurate approach aid in everyday use.

🎯 LOC, GP, markers🎯 Frequency pairing🎯 90/150 Hz🎯 Coverage🎯 Categories🎯 Height & ROD sums

💡 Key idea

On centre line and glide path the 90 Hz and 150 Hz modulations are equal: DDM = 0. Whichever tone dominates tells the receiver which way to steer.

The parts

Component	Band / frequency	Where
Localizer	VHF 108–111.975 MHz (odd decimals), 40 ch.	~300 m beyond the upwind end
Glide path	UHF 329.15–335 MHz, paired automatically	~300 m in from threshold, beside the runway
Markers	75 MHz, vertical fan beams	On the approach
Locator / DME	NDB at the OM; DME zero at threshold	Optional

🔗 Pairing: one selection, fewer mistakes, one ident — 2 or 3 letters, usually starting with I.
🚫 Ident removed or continuous tone = maintenance/test: do not use. GP unserviceable: ident stays, ATC warns "localizer only".
📏 Paired DME protected within the localizer area up to 25 000 ft.

Marker	Light	Code / tone	Distance
Outer	🔵 Blue	2 dashes/s · 400 Hz	3.5–6 NM
Middle	🟠 Amber	dot-dash · 1 300 Hz	1 050 m ± 150
Inner	⚪ White	6 dots/s · 3 000 Hz	75–450 m

How the beams work

The same idea twice: two overlapping lobes on one carrier, told apart by their 90 and 150 Hz tones.

↔️ Excess 150 Hz = right of centre → fly left. Excess 90 Hz → fly right.
📐 Glide path 2°–4°, normally 3°. Passes ~50 ft over the threshold (ILS reference datum).
👻 False glide slopes exist above the real one (first at about 2× the angle, 6°). Intercept from below and check height against range.
↩️ Back course: CDI reversed, glide path wrong, no markers — not used in the UK. An HSI reads correctly if the front-course QDM is set.
👁️ PAPIs use a mean eye height, so they can differ slightly from the ILS near the ground.

Coverage and monitoring

Localizer

25 NM within ±10° · 17 NM 10°–35° · 10 NM beyond ±35° (if provided). May be cut to 18 NM / 10 NM where other aids cover.

Glide path

10 NM within ±8° · from 0.45θ to 1.75θ (1.35°–5.25° for 3°); lower edge may be 0.3θ.

Monitor acts on

LOC shift > 35 ft (Cat I), 25 ft (II), 20 ft (III) · GP change > 0.075θ · power drop > 50 %. Then: stop radiating, remove ident, or downgrade.

Reading the needles

Needle	Full scale	Per dot (5-dot)
Localizer	2.5°	0.5°
Glide path	0.7°	≈ 0.14°

⚠️ Go around Half-scale fly-up (2.5 dots, about 0.35° low) is the safe limit; beyond half-scale on either needle, go around at once.

Category	DH	RVR
I	≥ 200 ft	≥ 550 m
II	100 – <200 ft	≥ 300 m
IIIA	< 100 ft or none	≥ 200 m
IIIB	< 50 ft or none	75 – <200 m
IIIC	none	none

Height and rate of descent

Height ≈ angle × NM × 100 ft

3° at 5 NM → 1 500 ft (exact ≈ 1 590 ft). 3.5° at 4 NM → 1 400 ft.

ROD (3°) ≈ 5 × GS

140 kt → 700 ft/min. Other angles: scale by angle ÷ 3 (2.5°, 120 kt → 500 ft/min).

10 Microwave Landing System (MLS) Chapter 10

Designed to fix what ILS cannot do: few channels, one fixed path, and a fussy site.

🎯 ILS drawbacks🎯 MLS numbers🎯 Time-referenced scanning beam

ILS limits

Only 40 channels · fixed narrow beams, one long queue · nothing special for slow aircraft, helicopters or STOL · needs big flat cleared sites · beams bent by vehicles and buildings.

MLS answers

200 channels · SHF 5 031–5 091 MHz · azimuth ±40° · glide slope 0.9°–20° · range 20–30 NM (20 NM UK) · back azimuth ±20° for go-around · built-in DME (DME/P ±100 ft for Cat II/III) · ident M + two letters · aim: Cat III.

💡 Key idea — TRSB

A narrow beam sweeps "to" and then "fro" at a constant rate. The time between the two passes tells the aircraft its angle. Elevation works the same way, up and down. All functions share one frequency by time division multiplexing.

🎛️ The pilot can fly the centre line or select an offset azimuth and any glide slope; curved and segmented approaches need DME/P.
📨 Data words: station ident, system and runway condition, weather. (A flare function was standardised but will not be implemented.)
🖥️ The display looks like ILS but deviation is from the selected path; multi-mode receivers handle ILS, MLS and GNSS.

11 Radar Principles Chapter 11

Send a pulse, time the echo, note where the aerial was pointing. Everything else is detail — but the detail is examined.

🎯 Primary vs secondary🎯 PRF and PRI🎯 Max and min range🎯 Resolution🎯 MTI

💡 Key idea

Echo for range, searchlight for bearing. One radar mile (out and back) takes 12.36 µs.

Primary

Passive echo on one frequency. Weak (double journey), needs high power; no identity.

Secondary

Interrogator and transponder on different frequencies: SSR (transponder in the aircraft), DME (on the ground).

Range (NM) = t (µs) ÷ 12.36

500 µs → 40.5 NM (75 km). Forgetting to halve doubles the answer.

PRI = 1 ÷ PRF

500 pps → 2 000 µs. Max range ≈ PRI ÷ 12.36: 400 pps → 202 NM.

Min range = 150 m × pulse width (µs)

2 µs → 300 m. To see 450 m, pulse ≤ 3 µs. Fly-back (dead) time trims practical range.

Power ∝ range⁴

Double the range → 16 × the power.

Why radar uses VHF and higher

No static or ionospheric effects, narrow beams, short pulses, and small objects reflect short waves well. But rain attenuates short waves: negligible above 10 cm, tropical rain only 10–4 cm, significant below 4 cm. So: surveillance radar 10/23/50 cm; weather radar and PAR 3 cm; surface movement radar 1.75–2 cm.

Resolution and processing

📏 Range resolution = half the pulse length (1 µs → 150 m).
↔️ Azimuth resolution = beamwidth: 2° at 90 NM → 3 NM wide (1-in-60). Narrow beams need big aerials.
⚙️ Rotation speed, pulse width, PRF, focusing and power must be harmonised.
🚶 MTI removes stationary echoes; jittered PRF removes second-trace echoes from beyond maximum range.
🔇 Side-lobe suppression stops side-lobe echoes being shown as main-beam targets.

12 Ground Radar Chapter 12

One principle, tuned four ways — from 300 NM airway coverage to the taxiway outside the tower.

Radar	Range	Wavelength	Pulse	Notes
Area surveillance	200–300 NM	10–50 cm	2–4 µs	PRF 300–400 pps, 5–6 rpm
Terminal area	≤ 75 NM	10/23/50 cm	1–3 µs	3 NM separation within 40 NM, below FL 245 (UK, where approved)
Aerodrome approach	≤ 25 NM	3 or 10 cm	0.5–1 µs	Approach control, vectors to ILS, SRA
Surface movement (ASMI)	2.5–6 NM	≈ 2 cm (15–17 GHz)	0.03 µs	Beam 0.2–1°, 60 rpm, PRF 4 000–20 000

✈️ Spot the radar 60 rpm, a fraction-of-a-degree beam and a PRF of 10 000 can only be a surface movement radar. Its theoretical range: 100 µs ÷ 12.36 ≈ 8 NM.

Long-range radars use long pulses (more energy on target) and a low PRF (time for echoes to come back). A surface movement radar would like an even shorter wavelength, but at EHF rain would wipe it out, so SHF is the compromise. Processing can remove fixed features to leave aircraft and vehicles clearly visible.

13 Airborne Weather Radar Chapter 13

Not a turbulence detector — a rain detector you interpret to stay out of turbulence.

🎯 9 375 MHz and why🎯 Colours and gradients🎯 Tilt🎯 MAP, MAN, WEA, CONT🎯 Cloud height

💡 Key idea

Turbulence lives where the rainfall gradient is steepest — where the colours crowd together — and in hooks, fingers, U-shapes and scalloped edges. Clear air turbulence gives no echo at all.

The set

Transmitter/receiver, antenna stabilised in pitch and roll, indicator, control unit. Shows range and relative bearing; ground ranges are slant ranges.

The frequency

9 375 MHz (λ 3.2 cm) matches large drops and wet hail. Higher: clutter from small drops. Lower: weak returns. 10 cm+ shows little weather. Water or ice on the radome absorbs energy.

The beams

Pencil (3–5°): weather and mapping beyond ~60 NM. Cosecant² fan (85° × 3.5°): mapping ~15–70 NM, power tapered with range for an even picture.

Colour	Rainfall
⬛ Black	< 0.7 mm/h
🟩 Green	0.7–4 mm/h
🟨 Yellow	4–12 mm/h
🟥 Red	> 12 mm/h
🟪 Magenta	turbulence / most intense

Controls

🔌 STBY on the ground until people and buildings are clear — radiation harms people and reflections damage the set. Pre-flight: max up-tilt, quick look, back to standby.
🎚️ Tilt ±15°. More up-tilt for longer range or lower altitude; less for shorter range or higher altitude. Too much up-tilt can miss a storm.
🗺️ MAP: fan beam, manual gain. MAN: pencil beam, manual gain, 70–150 NM. WEA: pencil beam, swept gain (STC/AGC) to about 25 NM so near and far clouds compare fairly. CONT: strongest cores blanked — a thin bright rim round a dark hole means danger.
⏸️ HOLD freezes the picture: hold heading, release after 2–3 minutes, see how the storm moved. TGT alert: contouring cloud 60–160 NM ahead within ±15°.
🟢 A lopsided picture = stabilisation failure. The dish's "height ring" is energy echoed from the ground below.

Mapping and storm height

Calm sea, sand and flat ground return little; coasts, cities and bridges are bright; snow masks features; hill shadow can look like lakes. Heavy rain can hide what lies behind it (shadow area).

Height above aircraft ≈ (tilt − ½ beam) × NM × 100

4° beam, returns vanish at +3° tilt at 50 NM → (3 − 2) × 50 × 100 = 5 000 ft.

Ground range = √(slant² − height²)

36 000 ft ≈ 5.9 NM; slant 10 NM → about 8 NM.

14 Secondary Surveillance Radar (SSR) Chapter 14

The aircraft answers back: identity, altitude and — with Mode S — much more.

🎯 1 030 / 1 090 MHz🎯 Modes A and C🎯 4 096 codes🎯 Special codes🎯 Garble and fruit🎯 Mode S levels

💡 Key idea

Ground asks on 1 030 MHz, aircraft answers on 1 090 MHz. One-way trips need little power, give clutter-free replies and carry identity.

Item	Value
P1–P2 spacing	2 µs (always)
P1–P3: Mode A / Mode C	8 µs / 21 µs
Reply framing pulses	20.3 µs apart, 12 information pulses
Codes	2¹² = 4 096 (0000–7777, no 8 or 9)
IDENT (SPI pulse)	about 20 s
Mode C	1013 hPa datum, 100 ft steps, to 128 000 ft

📟 Mode C ignores the altimeter subscale. FL 70 shows 070 and changes to 071 at 7 050 ft.
✅ Verification: ATC compares with your reported level (to the nearest 100 ft). Tolerance ±300 ft internationally, ±200 ft in the UK; outside it, switch Mode C off or squawk 0000.
📝 Change or switch off codes only when told; read back; select Mode C with Mode A.

Code	Meaning
7700	Emergency (a discrete code already in use may be kept)
7600	Radio failure
7500	Unlawful interference
7000	UK conspicuity, with Mode C
0000	Transponder malfunction

Garbling

Overlapping replies from aircraft close together on nearly the same bearing, within about 1.7 NM in range (20.3 µs ÷ 12.36).

Fruiting

Replies triggered by another interrogator, received by this one.

Mode S — selective addressing

🔢 24-bit address: over 16.7 million, fixed for the aircraft's life.
📶 Altitude in 25 ft steps (controllers still see 100 ft). Data link cuts R/T and code checks.
📨 Interrogations: All Call, Broadcast (no reply), Selective, Intermode. Extra P4: long = A/C/S all-call, short = A/C-only.
✅ Benefits: no synchronous garble, fewer over-interrogation and reflection problems, no code shortage, better STCA.
💬 Comm-A ground→air, Comm-B air→ground, Comm-C extended uplink, Comm-D extended downlink.
🏷️ Levels: 1 basic (no data link) · 2 minimum for international flight · 3 adds extended uplink · 4 adds extended downlink.
📋 Basic DAPs: flight ID, capability, 25 ft altitude, flight status. Enhanced: heading, speeds, roll angle, track angle rate, vertical rate, true track and ground speed.

15 Distance Measuring Equipment (DME) Chapter 15

Secondary radar turned round: the aircraft asks, the ground beacon answers, and the delay is the distance.

🎯 962–1 213 MHz, ±63 MHz🎯 Jitter and pulse pairs🎯 Search and saturation🎯 Pairing and idents🎯 Slant range

💡 Key idea

Slant range = (round-trip time − 50 µs) ÷ 12.36. The beacon always waits 50 µs before replying 63 MHz away from the interrogation.

Ground range = √(slant² − height²). Overhead the DME reads your height in NM; the error matters within about 3 × height.

📻 UHF 962–1 213 MHz, 1 MHz spacing, 252 channels (1–126 X and Y). Emission P0N. Civil pilots tune the paired VOR/ILS frequency; military TACAN users select a channel and get bearing too.
〰️ Pulses 3.5 µs, in pairs (X 12 µs, Y 36 µs) so stray single pulses are ignored. Each aircraft jitters its PRF and only accepts replies matching its own pattern.
🔍 Search at 150 pps for 15 000 pairs, then 60 pps; tracking at about 27 pps. A sweep takes 4–5 s on modern sets.
📛 Beacon sends a constant 2 700 pps; saturated at about 100 aircraft, it lowers gain so the furthest drop out.
🔤 Ident every 30 s, higher tone than the VOR; no range during it, but a 10 s memory holds the reading (also bridges bank shielding).

VOR and DME	Siting	Ident
Associated	Co-located, ≤ 30 m in TMAs or ≤ 600 m elsewhere	Same call sign; VOR 3 times, DME once per 30 s
Not associated, same location	Further apart, serving one place	DME's last letter is Z
Separated	> 6 NM apart	Totally different

🧮 Worked examples — DME

2 520 µs measured → (2 520 − 50) ÷ 12.36 ≈ 200 NM.

ILS DME 1 500 m from the threshold: 5 µs each way → delay 40 µs so it reads zero at the threshold.

FL 300 (≈ 5 NM), DME 13 NM → ground range 12 NM.

Accuracy at 40 NM: 0.25 + 0.5 = ±0.75 NM.

⚠️ Ground speed DME ground speed comes from the rate of change of slant range: it under-reads close in and high up, and reads zero on a DME arc. It is valid only flying straight to or from the station.

16 Area Navigation Systems (RNAV) Chapter 16

Stop flying from beacon to beacon. Fly any track you like, with the computer doing the geometry.

🎯 B-RNAV and P-RNAV🎯 2D, 3D, 4D🎯 Phantom stations🎯 FMS and CDU🎯 Kalman filtering

💡 Key idea

The IRS is accurate in the short term, radio fixes in the long term. The FMC blends them by Kalman filtering, leaning on the IRS early and on DME/DME or GNSS as the flight goes on.

Accuracy

B-RNAV ±5 NM, P-RNAV ±1 NM, both 95 % of the time. P-RNAV is for terminal airspace.

Levels

2D horizontal · 3D + vertical guidance · 4D + time.

Benefits

Shorter routes (time, fuel), more capacity (parallel and bypass routes), reduced separation.

Simple 2D RNAV

Navigation computer + CDU + CDI/HSI. Each waypoint is a radial and distance from a VOR/DME, and the display treats it as a "phantom station". Deviation is shown in NM. Check every waypoint is inside the DOC of its VOR/DME (and the next one's), mind slant range near the station, and type carefully — the computer cannot spot your mistakes. A station near the track gives good along-track accuracy; one abeam the track gives good across-track accuracy.

The FMS

🧠 FMC + AFDS + autothrottle + 2 IRS → 4D navigation (lat, long, altitude, time) and economy performance.
🗂️ Performance database: aircraft data, cost index. Navigation database: aerodromes, navaids, airways, SIDs, STARs, approaches, company routes — updated every 28 days (current + next held).
✋ Crew-only: thrust initiation, take-off, altitude selection, ILS tuning, configuration, landing rollout. IRS-only position is flagged as downgraded.
🌐 Must use WGS-84; execute changes only after crew action; offsets, holds, direct-to, uncertainty estimate, failure warning.

Talking to the CDU

Entry	Format	Example
Lat/long	7 or 15 characters, leading zeros	N05W010 · N0926.3W00504.7
Aerodrome, navaid, airway	up to 5 characters	EGLL · DHD · A23
SID / STAR	up to 7 characters	TURN05
Place bearing/distance	ident + 3/5-digit bearing / distance	TRN250/76 → TRN01
Bearing/bearing	two places and bearings	GOW167.0/TRN090.5 → GOW01

Type in the scratchpad, insert with a line select key. Boxes = must enter; dashes = optional. ACTIVATE lights EXEC, which must be pressed. CLB speed restriction defaults to 250/10 000, descent to 240/10 000; "A" after an altitude means at or above; V/B is the path angle needed for the next constraint.

Several IRSs, two FMCs

⚖️ Two IRSs that disagree cannot say which is wrong — an external reference decides.
🔺 Three IRSs: check for gross errors, average, then Kalman-filter with external fixes.
🧊 Above 84° latitude each FMC decouples to a single IRS: change of longitude depends on sec(latitude), which explodes near the pole.
🖥️ Dual mode cross-checks positions before the EFIS; both FMCs failed → IRS straight to the EFIS, no performance functions.
📉 IRS drifts about 1 NM/h; DME error stays ±0.25 NM ±1.25 % (1.5 NM at 100 NM). After a few hours DME/DME wins.

17 Electronic Flight Information System (EFIS) Chapter 17

The navigation display ties every sensor into one picture — if you can read its colours and symbols.

🎯 Inputs and symbol generators🎯 Four modes🎯 Colour code🎯 Key symbols

Inputs

IRS, FMC, VOR/DME/ILS/ADF, TCAS, weather radar → symbol generators (the heart of EFIS) → left and right displays.

Modes

Full-rose VOR/ILS, expanded VOR/ILS, MAP, PLAN. Weather and TCAS only in expanded and MAP. PLAN is true-north up; the rest are heading-up.

Colour	Meaning
🟥 Red	Warnings, limits
🟧 Amber	Cautions, abnormal sources
🟩 Green	Engaged modes, selected data
⬜ White	Fixed references, current data, armed modes
🟪 Magenta	"Fly to / keep centred": active route, selected heading, ILS deviation pointer
🟦 Cyan	Sky, inactive route, non-active navaids/airports
🟫 Brown	Earth

Precipitation: black 0–1, green 1–4, amber 4–12, red 12–50, magenta above 50 mm/h; turbulence white or magenta.

Symbols worth knowing

🛣️ Active route solid magenta · modification short white dashes · inactive route long cyan dashes. Active waypoint magenta.
➰ Trend vector: path in 30/60/90 s (three segments above 20 NM range).
📐 Vertical deviation ±400 ft (MAP, descent only). T/C, T/D, E/D, S/C in green. Green altitude range arc = where the MCP altitude will be reached.
🧭 Expanded ILS: glide slope hidden if track is > 90° from the localizer course. Full-rose ILS doubles the localizer scale; full-rose VOR shows TO/FROM as a pointer. 2-dot VOR scale = 5° per dot.
📍 Position difference display: each IRS relative to the FMC position. Track-line range marks are half the selected range. Runway centre lines extend 14.2 NM.
🗺️ NAV AID off: tuned navaids green; on: database navaids cyan (high-altitude only at 80 NM+). ARPT off: origin and destination only. Off-route waypoints at 10–40 NM only. Holding pattern: fixed size above 80 NM, to scale within 3 min of the fix.

18 Global Navigation Satellite Systems (GNSS) Chapter 18

Four satellites, four unknowns, and a position good to a few metres — as long as you know how far to trust it.

🎯 GPS segments and orbits🎯 Codes and frequencies🎯 Why four satellites🎯 Error budget🎯 DOP🎯 RAIM, GBAS, SBAS

💡 Key idea

Each satellite gives a pseudo-range — a range still carrying the receiver's clock error. Four of them solve X, Y, Z and time together: a 3-D position plus accurate time.

	GPS (USA)	GLONASS (Russia)	Galileo (EU)
Satellites / planes	24 / 6	24 / 3	30 / 3
Height	≈ 20 200 km	≈ 19 100 km	≈ 23 200 km
Inclination	55°	65°	56°
Period	≈ 12 h	11 h 15 min	≈ 14 h
Earth model	WGS-84	PZ-90	ETRS-89
Satellite identity	own code, common frequency	same code, own frequency	—

GPS in three segments

🛰️ Space: 5–8 satellites in view above the 5° mask angle; atomic clocks (~1 ns). L1 1 575.42 MHz (C/A 1.023 MHz repeating each ms; P 10.23 MHz repeating each 7 days; nav message 50 bps). L2 1 227.6 MHz (P code). Civil users: C/A code (SPS). P becomes encrypted Y code with anti-spoofing.
🏢 Control: master and back-up stations plus monitors; position and clock checked at least every 12 h. Clock errors are broadcast, not reset.
📱 User: multi-channel all-in-view receivers preferred in aviation.
🗓️ GPS time counts from 6 January 1980 in 1 024-week epochs; it is not adjusted for leap seconds.

Frame 30 s · almanac 12.5 min

5 subframes × 6 s. Lost almanac → at least 15 min to first fix; normally about 30 s.

1 ms clock error ≈ 162 NM

Why the receiver solves for its own clock with a fourth satellite (or altitude aiding).

Error budget

Source	Up to	Reduced by
Ionospheric delay (largest)	5 m	Two frequencies (delay ∝ 1/f²), model in message
Ephemeris	2.5 m	12-hourly updates
Satellite clock	1.5 m	Broadcast correction
Multipath	0.6 m	Aerial siting — top of fuselage near the CG
Receiver noise	0.3 m	—
Troposphere	1 ns ≈ 0.3 m	Models, two frequencies

📐 DOP: HDOP horizontal, VDOP vertical, PDOP both, TDOP time, GDOP all. Best geometry: one satellite overhead, three low and 120° apart.
🎯 Specified SPS accuracy (95 %): 13 m horizontal, 22 m vertical, 40 ns. Selective Availability (clock dithering, ~100 m) ended on 1 May 2000.
🌊 The WGS-84 ellipsoid and mean sea level differ by tens of metres — raw GNSS height is not for vertical guidance near the ground.

Integrity and augmentation

ABAS — RAIM

In the receiver. 5 satellites to detect a fault, 6 to exclude it and keep monitoring.

GBAS (local)

Surveyed site at the airport sends corrections by VHF data link; pseudolite for range. Removes ephemeris and clock errors, almost all atmospheric error nearby — not receiver noise or multipath. Potential to Cat III.

SBAS (wide area)

Reference stations → master station → geostationary satellites (35 800 km, 24 h). EGNOS, WAAS, MSAS, GAGAN.

📡 Radio Navigation

🧰 Quick tools & cheat sheet play with the numbers

📻 Frequency ⇄ wavelength

📡 Line-of-sight range

⏱️ Radar timing

🛬 Glide path check

📏 DME slant range

🧭 Bearings from the RBI

📋 Cheat sheet — numbers worth knowing

1 Properties of Radio Waves Chapter 1

From a wire to a wave

Polarization

↕️ Linear

🌀 Circular

Period, frequency and wavelength

The eight frequency bands

Phase comparison

2 Radio Propagation Theory Chapter 2

Losing signal on the way

The paths a wave can take

🌊 Surface wave

📶 Space wave

🌌 Sky wave

The ionosphere

HF communication

Super- and sub-refraction (VHF and above)

⬇️ Super-refraction (+ up to 40 %)

⬆️ Sub-refraction (− up to 20 %)

3 Modulation Chapter 3

Sidebands

✂️ Single sideband (SSB)

📻 Why not FM?

Emission designators

4 Antennae Chapter 4

Half-wave dipole

Quarter-wave (Marconi)

Polar diagrams and directivity

Radar aerials

Parabolic dish

Flat plate (slotted, phased array)

5 Doppler Radar Systems Chapter 5

6 VHF Direction Finder (VDF) Chapter 6

7 Automatic Direction Finder (ADF) Chapter 7

How the needle finds the beacon

The beacon

RBI and RMI sums

RBI

RMI

Homing, tracking and drift

Errors — know all eight

8 VHF Omni-directional Range (VOR) Chapter 8

Conventional VOR

Doppler VOR

Frequencies, identity and monitoring

Range, DOC and accuracy

The cockpit displays

CDI (OBS)

RMI

HSI

9 Instrument Landing System (ILS) Chapter 9

The parts

How the beams work

Coverage and monitoring

Localizer

Glide path

Monitor acts on

Reading the needles

Categories

Height and rate of descent

10 Microwave Landing System (MLS) Chapter 10

ILS limits

MLS answers

11 Radar Principles Chapter 11

Primary

Secondary

Why radar uses VHF and higher

Resolution and processing

12 Ground Radar Chapter 12

13 Airborne Weather Radar Chapter 13

The set