🎛

Instrumentation

Pitot-static systems, gyroscopes, magnetic compass, electronic instruments

Bernoulli / Dynamic Pressure

P_total = P_static + ½ρv²

Total (pitot) pressure equals static plus dynamic pressure. Foundation of airspeed indication.

Example: At MSL (ρ=1.225 kg/m³), v=100 m/s → dynamic pressure = ½ × 1.225 × 10,000 = 6,125 Pa

MemorizePitot-Static

CAS → EAS

EAS = CAS × √(ρ / ρ₀)

ρ₀ = 1.225 kg/m³ (ISA MSL). Corrects CAS for compressibility.

Example: At 10,000 ft, ρ/ρ₀ ≈ 0.738 → EAS = 150 × √0.738 = 150 × 0.859 = 128.9 kts

Airspeed

EAS → TAS

TAS = EAS / √(ρ / ρ₀) = EAS / √σ

σ = density ratio. TAS increases with altitude for same EAS.

Example: FL200, σ ≈ 0.533, EAS 200 kts → TAS = 200 / √0.533 = 274 kts

Airspeed

TAS from IAS — Quick Rule

TAS ≈ IAS + (2% per 1,000 ft) × IAS

Rough approximation valid up to ~20,000 ft.

Example: FL080, IAS 160 kts → TAS ≈ 160 + (8 × 2% × 160) = 185 kts

Rule of Thumb

Mach Number

M = TAS / a
a = √(γRT) [γ=1.4, R=287, T in K]

Speed of sound varies with temperature only — not altitude directly.

Example: T = −20°C = 253 K → a = √(1.4 × 287 × 253) = 319 m/s. TAS 250 m/s → M = 0.784

High Speed

Pressure Altitude

PA = Elevation + (1013.25 − QNH) × 30

Approximately 30 ft per hPa deviation from standard pressure.

Example: Elevation 500 ft, QNH 1003 → PA = 500 + (10.25 × 30) = 808 ft

Altimetry

Density Altitude

DA = PA + 120 × (OAT − T_ISA)

120 ft per °C above ISA. Critical for performance calculations.

Example: PA = 2,000 ft, OAT 25°C, ISA at 2,000 ft = 11°C → DA = 2000 + 120 × 14 = 3,680 ft

ImportantPerformance

Load Factor in Turn

n = 1 / cos φ

φ = bank angle. At 60° bank, n = 2 — lift must double to maintain altitude.

Example: 45° bank → n = 1 / cos 45° = 1.41. 60° → n = 2

Memorize

Rate 1 Turn Radius

R (nm) = TAS (kts) / 63

Rate 1 = 3°/sec = 2 min for 360°. Approximate formula.

Example: TAS 180 kts → R = 180 / 63 = 2.86 nm

Turns

Turn Radius (General)

R = V² / (g × tan φ)

V in m/s, g = 9.81 m/s². Result in metres.

Example: V = 100 m/s, φ = 30° → R = 10,000 / (9.81 × 0.577) = 1,767 m

Turns

Pitot-Static Error Reference

Fault	Cause	Effect on ASI	Effect on Altimeter
Blocked pitot only	Ice, debris	Acts as altimeter — reads high climbing, low descending	Unaffected
Blocked static only	Ice, blockage	Underreads climbing above blockage; overreads descending	Freezes at blocked altitude
Both blocked	Ice	Freezes at speed at time of blockage	Freezes
Static leak (cockpit)	Pressurisation	Overreads at altitude	Overreads

🌐

General Navigation

Great circles, rhumb lines, chart work, wind, speed/time/distance

1 in 60 Rule — Track Error

TEA = (Off Track × 60) / Distance Flown

TEA = Track Error Angle in degrees. Valid for angles under ~20°.

Example: 4 nm off after 120 nm → TEA = (4 × 60) / 120 = 2°

Memorize

1 in 60 Rule — Closing Angle

CA = (Off Track × 60) / Distance To Go

Additional correction to arrive at destination after rejoining track.

Example: 4 nm off, 60 nm to go → CA = (4 × 60) / 60 = 4°. Total correction = TEA + CA

Memorize

Departure Formula

Departure (nm) = ΔLong (min) × cos(Lat)

East-West distance in nautical miles per minute of longitude.

Example: At 50°N, ΔLong 2° = 120' → departure = 120 × cos 50° = 77.2 nm

Charts

Convergency

Convergency = ΔLong × sin(Lat)

Angle between meridians at a given mean latitude.

Example: ΔLong 10°, Lat 50° → convergency = 10 × sin 50° = 7.66°

Charts

Conversion Angle

CA = ½ × ΔLong × sin(Mean Lat)

Difference between great circle and rhumb line bearing at the mid-point.

Example: ΔLong 30°, Mean Lat 40° → CA = 0.5 × 30 × sin 40° = 9.6°

Charts

Time — Speed — Distance

D = S × T
T = D / S
S = D / T

Fundamental triangle. T in hours if S in knots and D in nm.

Example: 300 nm at 150 kts → T = 300 / 150 = 2 hr = 2 h 00 min

Memorize

Wind Correction Angle

WCA = arcsin[(WS × sin WA) / TAS]

WA = angle between wind direction and desired track.

Example: WS 30 kts, WA 60°, TAS 150 kts → sin WCA = (30 × 0.866) / 150 = 0.173 → WCA = 10°

Wind

Great Circle Distance

cos D = sin φ₁ sin φ₂ + cos φ₁ cos φ₂ cos ΔLong
Distance (nm) = D° × 60

φ = latitude, ΔLong = difference in longitude. D in degrees.

Example: 1° of great circle = 60 nm. The equator is 360° × 60 = 21,600 nm

Great Circle

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Meteorology

Atmosphere, pressure, temperature, clouds, lapse rates

ISA Temperature

T = 15°C − 1.98°C × (Alt / 1,000 ft)
[valid up to 36,089 ft / FL360]

Above tropopause (~FL360), temperature is constant at −56.5°C.

Example: FL100 → T = 15 − (10 × 1.98) = 15 − 19.8 = −4.8°C

Memorize

Pressure Lapse Rate

1 hPa ≈ 27 ft (at MSL)
1 hPa ≈ 8 m

Lapse rate increases with altitude — 27 ft/hPa is a MSL approximation.

Example: Airport at 2,700 ft → pressure reduction ≈ 100 hPa from 1013 → QFE ≈ 913 hPa

Pressure

QNH → QFE

QFE = QNH − (Elevation / 27)

Gives pressure at airfield level. Altimeter reads zero on ground with QFE set.

Example: QNH 1015, elevation 540 ft → QFE = 1015 − (540/27) = 1015 − 20 = 995 hPa

Pressure

Cloud Base (Convective)

Cloud Base (ft AGL) = (Temp − Dew Point) × 400

Applies to cumulus/cumulonimbus. Every 1°C spread ≈ 400 ft.

Example: Temp 22°C, dew point 10°C → spread 12°C → base ≈ 4,800 ft AGL

Clouds

Dry Adiabatic Lapse Rate (DALR)

DALR ≈ 3°C per 1,000 ft

Rate unsaturated air cools when rising. If ELR > DALR — absolutely unstable.

Example: Parcel rises 3,000 ft — cools by 9°C before reaching dew point

Stability

Saturated Adiabatic Lapse Rate (SALR)

SALR ≈ 1.5°C per 1,000 ft (variable)

Rate saturated air cools when rising. Lower than DALR due to latent heat release.

Example: Above cloud base, parcel cools more slowly — conditional instability possible

Stability

Freezing Level Estimate

FL_freeze (ft) ≈ Surface Temp (°C) × 300

Rough estimate assuming standard lapse rate from surface.

Example: Surface 15°C → freezing level ≈ 15 × 300 = 4,500 ft

Icing

Lapse Rate Reference

Lapse Rate	Value	Stability Condition
DALR (Dry Adiabatic)	3°C / 1,000 ft	If ELR > DALR → absolutely unstable
SALR (Saturated Adiabatic)	~1.5°C / 1,000 ft	If ELR < SALR → absolutely stable
ISA ELR (Standard)	~2°C / 1,000 ft	Between SALR and DALR → conditionally unstable
Inversion	Temp increases with altitude	Extremely stable — fog, pollution trapping

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Human Performance & Limitations

Physiology, psychology, fatigue, hypoxia, vision

Time of Useful Consciousness

FL100 → Indefinite
FL200 → 5–10 min
FL250 → 3–5 min
FL300 → 1–2 min
FL350 → 30–60 sec
FL400 → 15–20 sec

TUC assumes resting; active pilots have shorter TUC. Rapid decompression reduces TUC further.

Example: At FL350 you have 30–60 seconds to don oxygen before incapacitation

MemorizeCritical

Dark Adaptation

Full adaptation ≈ 30 minutes
Brief bright light resets adaptation

Cones adapt in 5–10 min (colour, high light). Rods take 30 min (monochrome, low light).

Example: Use red cockpit lighting at night — rods are less sensitive to red wavelengths

Vision

Dehydration & Performance

2% body water loss → ~20% performance loss
Drink ≥ 200 ml/hr in flight

Dehydration impairs concentration, reaction time, and decision-making at altitude.

Example: Mild dehydration is common at FL350 due to low cabin humidity (~10–20%)

Physiology

Circadian Rhythm

Body clock period ≈ 24.2 hours
Performance dips: 0300–0500 and 1400–1600 local

Reset by light exposure. Jet lag disruption: ~1 day per time zone crossed.

Example: Most night accidents cluster between 0300–0500 local time

Fatigue

Alcohol Elimination

Elimination ≈ 1 standard drink / hour
EASA rule: 8 hours bottle-to-throttle

Blood alcohol level continues to rise for 30–90 min after drinking.

Example: 4 drinks at midnight → cleared by body ~0400; still within 8-hr rule for 0600 duty

Regulations

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Radio Navigation

VOR, DME, ILS, NDB, GNSS, RNAV, RNP frequencies and principles

ILS Glide Slope Height

Height (ft) = Distance from THR (nm) × 318
[for 3° glide slope]

Useful for cross-checking approach profile. Rule: 3 nm per 1,000 ft.

Example: At 6 nm from threshold → height ≈ 6 × 318 = 1,908 ft. Rounded: 6 nm = ~2,000 ft

ILSMemorize

DME Slant Range Error

Slant Range = √(Ground Distance² + Altitude²)
Error greatest directly overhead

At long range, error is negligible. At high altitude directly overhead, slant range = altitude.

Example: FL100 = 10,000 ft = 1.65 nm directly overhead — DME reads 1.65 nm instead of zero

DME

VHF Line-of-Sight Range

Range (nm) ≈ 1.23 × √(Altitude in ft)

Applies to VOR, ILS, VHF comms. LOS only — no sky wave.

Example: FL200 = 20,000 ft → range ≈ 1.23 × √20,000 = 1.23 × 141 = 174 nm

Range

ADF Relative Bearing → QDM

QDM = HDG + RB
(±360° if result outside 000°–360°)

QDM = magnetic bearing TO the station. RB = relative bearing shown on ADF.

Example: HDG 280°, RB 060° → QDM = 280 + 60 = 340°M TO station

NDB

Navigation Aid Frequency Bands & Key Facts

Nav Aid	Frequency Band	Range	Key Limitation
NDB	LF/MF 190–1750 kHz	Up to ~200 nm	Night effect, thunderstorm interference, coastal refraction
VOR	VHF 108.0–117.95 MHz	Line-of-sight ~200 nm	Site error, scalloping, cone of silence overhead
ILS Localiser	VHF 108.10–111.95 MHz*	~25 nm	Terrain reflections; false courses possible
ILS Glideslope	UHF 329.15–335.00 MHz	~10 nm	False glideslope above true path (false GS at ~6°)
DME	UHF 960–1215 MHz	Line-of-sight ~200 nm	Slant range not ground distance; station saturation (100 users)
GNSS (GPS)	L-band 1176–1575 MHz	Global	Ionospheric delay, multipath, masking, jamming
Marker Beacon	VHF 75 MHz	Fixed short range	OM ~7.2 nm · MM ~1050 m · IM ~300 m from threshold

* ILS localiser frequencies end in odd 10ths (108.10, 108.15, 108.30... not 108.20, 108.40 etc.)

ILS Approach Categories

Category	Decision Height	RVR Minimum
CAT I	≥ 200 ft	≥ 550 m
CAT II	100–200 ft	≥ 300 m
CAT IIIA	< 100 ft	≥ 200 m
CAT IIIB	< 50 ft	75–200 m
CAT IIIC	No DH	No RVR limit

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Aircraft General Knowledge

Electrics, hydraulics, engines, systems

Ohm's Law

V = I × R
I = V / R
R = V / I

V = volts, I = amps, R = ohms. Most aircraft use 28V DC.

Example: 28V system, lamp 4 Ω → I = 28/4 = 7 A

Electrics

Electrical Power

P = V × I (DC)
P = V × I × cos φ (AC)

Power in watts. cos φ = power factor for AC circuits.

Example: 28V × 10 A = 280 W. Battery 24 Ah × 28V = 672 Wh capacity

Electrics

Hydraulic Force

Force = Pressure × Area

Pascal's principle. Typical aircraft hydraulic pressure: 3,000 psi.

Example: 3,000 psi × 2 in² actuator = 6,000 lb force

Hydraulics

Engine Compression Ratio

CR = (V_swept + V_clearance) / V_clearance

Piston engine. Higher CR = more efficiency but risk of detonation.

Example: Swept 500 cc, clearance 50 cc → CR = 550/50 = 11:1

Engines

Bypass Ratio (Turbofan)

BPR = ṁ_fan / ṁ_core

High BPR = more efficient, quieter, lower fuel burn. Modern jets: BPR 8–13.

Example: 100 kg/s fan, 12.5 kg/s core → BPR = 8:1

Engines

Propeller Efficiency

η = (Thrust × TAS) / Shaft Power

Typical max efficiency: 80–85%. Reduces at very high or low speeds.

Example: Thrust 2,000 N, TAS 80 m/s, power 200 kW → η = (2000 × 80) / 200,000 = 0.80 = 80%

Propulsion

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Air Law

ICAO, EASA regulations, VMC minima, altitudes, FTL

VFR Cloud Clearance

1,500 m horizontally from cloud
1,000 ft vertically from cloud
In-flight visibility: 5 km (below FL100)

Class G airspace VFR minima. Different classes vary.

Example: Below FL100, Class G: 5 km visibility, stay 1500 m from cloud horizontally

Memorize

Minimum Safe Altitudes

Congested area: 1,000 ft above highest obstacle within 600 m
Other areas: 500 ft above surface

SERA and ICAO SARPS. Emergency exception exists.

Example: Flying over a city with 200 ft buildings → minimum 200 + 1,000 = 1,200 ft AGL

Safety

Supplemental Oxygen Requirements

Above 10,000 ft for >30 min → crew oxygen
Above 13,000 ft → crew oxygen entire flight
Above 15,000 ft → oxygen for all occupants

EASA thresholds. Pressurised aircraft requirements are different.

Example: Unpressurised at 14,000 ft for 2 hours — crew must use oxygen throughout

Regulations

EU-OPS Flight Time Limits

Max flight time: 100 hr / 28 days
Max duty: 60 hr / 7 days, 190 hr / 28 days
Rest: min 11 hr between duties

EASA ORO.FTL. Operator and authority variations apply.

Example: After 10 hr of flying duty, minimum rest before next duty = 11 hr

FTL

VMC Minima Summary (EASA)

Airspace	Altitude Band	Flight Visibility	Cloud Clearance
A, B, C, D, E	At and above FL100	8 km	1,500 m horizontal / 1,000 ft vertical
A, B, C, D, E	Below FL100	5 km	1,500 m horizontal / 1,000 ft vertical
F, G	At and above FL100	8 km	1,500 m horizontal / 1,000 ft vertical
F, G	Below FL100, above 3,000 ft AMSL	5 km	1,500 m horizontal / 1,000 ft vertical
F, G	At and below 3,000 ft AMSL	5 km	Clear of cloud & in sight of surface

🗺

Flight Planning & Monitoring

Fuel, ETP, PNR, specific range, wind components

Equal Time Point (ETP)

ETP from A = (D × GS_Home) / (GS_Out + GS_Home)

Point where time to return to A = time to continue to B. Also called Critical Point (CP).

Example: D = 1,000 nm, GS out 450 kts, GS home 400 kts → ETP = (1000 × 400) / 850 = 471 nm from A

Memorize

Point of No Return (PNR)

PNR (nm) = (Endurance × GS_Out × GS_Home) / (GS_Out + GS_Home)

Furthest point from which you can return with available fuel.

Example: Endurance 5 hr, GS out 450, GS home 400 → PNR = (5 × 450 × 400) / 850 = 1,059 nm

Memorize

Headwind & Crosswind Component

HW = WS × cos(WA)
XW = WS × sin(WA)

WA = angle between wind direction and runway/track heading.

Example: Wind 30 kts, 60° off track → HW = 30 × 0.5 = 15 kts; XW = 30 × 0.866 = 26 kts

Wind

Specific Range

SR = TAS / Fuel Flow (nm per unit fuel)

Maximising SR gives maximum range. SR decreases with weight.

Example: TAS 450 kts, FF 2,000 kg/hr → SR = 450/2000 = 0.225 nm/kg

Cruise

Fuel Planning (EASA)

Total fuel = Trip + Contingency (5%) + Alternate + Final Reserve (30 min) + Extra

Final reserve = 30 min at holding speed at 1,500 ft ISA above alternate.

Example: Trip 2,000 kg + contingency 100 + alternate 150 + final reserve 200 = 2,450 kg min

FuelRegulations

Endurance

Endurance (hr) = Usable Fuel / Fuel Flow

Maximum endurance at minimum drag speed (V_MD). Range maximised at 1.32 × V_MD.

Example: 5,000 kg usable fuel, FF 1,000 kg/hr → endurance = 5 hours

Fuel

📻

Communications

VHF/HF frequencies, range, channel spacing, emergency

VHF Line-of-Sight Range

Range (nm) ≈ 1.23 × √(Alt in ft)

Combined range of ground station and aircraft: add √(h1) + √(h2) then × 1.23.

Example: Aircraft at 10,000 ft → range ≈ 1.23 × 100 = 123 nm from ground station at MSL

VHF

Emergency Frequencies

121.500 MHz — Civilian guard
243.000 MHz — Military guard
406 MHz — ELT distress

All aircraft should monitor 121.5 MHz when practicable. COSPAS-SARSAT uses 406 MHz.

Example: 121.5 is guarded by ATC and rescue services worldwide

EmergencyMemorize

Aviation Frequency Bands Reference

Service	Frequency Range	Channel Spacing	Notes
VHF Comms	118.000–136.975 MHz	8.33 kHz (Europe) / 25 kHz	Line-of-sight only
HF Comms	2–30 MHz	Variable	Sky wave — long range oceanic
ACARS / SELCAL	VHF / HF / SATCOM	—	Datalink messaging
Transponder	1030 / 1090 MHz	—	Secondary radar; TCAS uses 1090
ELT	406 MHz (digital)	—	Also monitors 121.5 MHz

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Operational Procedures

Approach categories, minima, ETOPS, noise abatement

Aircraft Approach Categories

Cat A: V_ref < 91 kts
Cat B: 91–120 kts
Cat C: 121–140 kts
Cat D: 141–165 kts
Cat E: ≥ 166 kts

V_ref = 1.3 × V_S0 at max landing weight. Category determines applicable minima.

Example: A320 V_ref ~138 kts → Category C aircraft

Memorize

Go-Around Decision

Continue only if: aircraft stable, visual reference established, above DA/MDA, and able to land in touchdown zone

If any criterion not met at DA/MDA — missed approach immediately.

Example: Reach DH 200 ft with no visual contact → go-around immediately, no delay

Critical

ILS Categories — Decision Height & RVR

Category	Decision Height	RVR Minimum	Equipment Required
CAT I	≥ 200 ft	≥ 550 m	Standard ILS
CAT II	100–199 ft	≥ 300 m	Autoland capability, fail-passive
CAT IIIA	< 100 ft	≥ 200 m	Fail-passive autoland
CAT IIIB	< 50 ft (or no DH)	75–200 m	Fail-operational autoland, HUD
CAT IIIC	No DH	No minimum	Fail-operational, runway guidance

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Principles of Flight

Lift, drag, stall, stability, high-lift devices, transonic

Lift Equation

L = C_L × ½ρV² × S

C_L = lift coefficient, ρ = air density, V = TAS, S = wing area. Doubling V → 4× lift.

Example: C_L=0.5, ρ=1.225, V=100 m/s, S=50 m² → L = 0.5 × 6,125 × 50 = 153,125 N

Memorize

Drag Equation

D = C_D × ½ρV² × S
C_D = C_D0 + C_Di

Total drag = profile drag (∝V²) + induced drag (∝1/V²). Minimum at V_MD.

Example: Same conditions, C_D=0.03 → D = 0.03 × 6,125 × 50 = 9,188 N

Drag

Induced Drag Coefficient

C_Di = C_L² / (π × AR × e)
AR = b² / S

e = Oswald efficiency factor (~0.8). Higher AR → lower induced drag. Key for gliders.

Example: C_L=0.5, AR=9, e=0.8 → C_Di = 0.25 / (3.14 × 9 × 0.8) = 0.011

Drag

Stall Speed vs Load Factor

V_S = V_S1 × √n

Stall occurs at critical AoA regardless of speed. Load factor raises effective stall speed.

Example: V_S1 = 50 kts, n = 2 (60° bank) → V_S = 50 × √2 = 70.7 kts

ImportantMemorize

Lift / Drag Ratio

L/D = C_L / C_D
Best glide = max L/D speed (V_MD)

Maximum L/D gives best glide angle. Occurs at minimum total drag (profile = induced).

Example: L/D max 15:1 at 120 kts → for every 15 nm forward, lose 1 nm altitude (6% glide)

Aerodynamics

Climb Gradient

Gradient = (Thrust − Drag) / Weight
ROC (fpm) = (Excess Thrust × TAS) / Weight

Best angle of climb at V_X (excess thrust max). Best rate at V_Y (excess power max).

Example: Excess thrust 10,000 N, weight 200,000 N → gradient = 0.05 = 5%

Climb

Types of Aerodynamic Drag

Drag Type	Also Called	Varies With Speed	Reduced By
Induced drag	Vortex drag / drag due to lift	Decreases with speed (∝ 1/V²)	High aspect ratio, winglets, lower CL
Profile drag	Parasite drag (form + skin friction)	Increases with speed (∝ V²)	Streamlining, smooth surfaces, retracted gear
Wave drag	Compressibility drag	Appears above Mcrit, rises steeply	Swept wings, supercritical aerofoils, area rule
Interference drag	Junction drag	Speed-dependent, geometry-driven	Fairings at wing-fuselage junctions
Total drag	—	Minimum at V_MD (best glide speed)	Optimise between induced and profile drag

📈

Performance

Takeoff, climb, cruise, landing, density altitude effects

Takeoff Distance vs Weight

TODR ∝ W²
10% ↑ weight → ~21% ↑ distance

Relationship is square law because stall speed (and thus V1/VR/V2) also increases with √W.

Example: Scheduled TODR 1,800 m at MTOW. At 10% over → 1,800 × 1.21 = 2,178 m

Takeoff

Density Altitude Effects on Performance

Per 1,000 ft DA increase:
Takeoff distance ↑ ~10%
Rate of climb ↓ ~10%
Engine power ↓ ~3% (non-turbo)

High DA = less dense air = longer takeoff, reduced climb, weaker engines.

Example: DA = 5,000 ft above sea level → takeoff distance ~50% longer than at MSL

Important

Rate of Descent for 3° Approach

ROD (fpm) = GS (kts) × 5

Precise rule: ROD = GS × tan(3°) × 101.3 ≈ GS × 5.3. Use GS × 5 for mental math.

Example: GS 140 kts on ILS → target ROD = 140 × 5 = 700 fpm

Memorize

Top of Descent Planning

Distance to descend (nm) = Altitude to lose (ft) / 300
[for 3° descent at typical jet speeds]

Rule of thumb: 3 nm per 1,000 ft, plus distance to decelerate and configure.

Example: Cruise FL350, land MSL → need 350/3 × 10 = ~117 nm for descent alone

Descent

V-Speed Relationships

V1 ≤ VR ≤ V2
V2 ≥ 1.2 × V_S (CS-25)
V_ref ≥ 1.3 × V_S0

Regulatory minima. V_S0 = stall speed in landing configuration.

Example: V_S0 = 100 kts → V_ref ≥ 130 kts. V_S = 110 kts → V2 ≥ 132 kts

V-SpeedsMemorize

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Mass and Balance

Moment, CG, %MAC, weight shift, index units

Moment

Moment = Weight × Arm

Arm = distance from datum to item. Moment in kg·m or lb·in.

Example: 1,500 kg cargo at arm 8.2 m → moment = 12,300 kg·m

Memorize

Centre of Gravity

CG = Σ(Moment) / Σ(Weight)
CG = Total Moment / Total Weight

Sum all moments and all weights separately, then divide.

Example: Total moment 250,000 kg·m, total weight 50,000 kg → CG = 5.00 m from datum

Memorize

%MAC

%MAC = ((CG − LEMAC) / MAC) × 100

LEMAC = Leading Edge of Mean Aerodynamic Chord. Typical limits 15–35% MAC.

Example: LEMAC at 5.0 m, MAC = 2.5 m, CG = 5.75 m → %MAC = (0.75/2.5) × 100 = 30%

Memorize

Weight Shift Formula

ΔCG = (Weight Moved × Distance Moved) / Total Weight

CG moves in direction weight is moved. Proportional to weight and distance.

Example: Move 200 kg forward 5 m in 8,000 kg aircraft → ΔCG = (200 × 5) / 8,000 = 0.125 m forward

Weight Shift

Loading Added / Removed

New CG = (Old Moment ± Added Moment) / (Old Weight ± Added Weight)

Use + for loading, − for offloading.

Example: Old: 40,000 kg at CG 5.0 m (moment 200,000). Add 500 kg at arm 7.0 m → new CG = (200,000 + 3,500) / 40,500 = 5.025 m

Loading

CG Shift from Fuel Burn

ΔCG = (Fuel Burned × Fuel Arm) / New Total Weight

CG shifts toward or away from fuel arm depending on fuel arm vs. CG position.

Example: Burn 2,000 kg from tanks at arm 5.5 m, new weight 48,000 kg → ΔCG shift = (2,000 × 5.5) / 48,000 = 0.229 m

Fuel

Universal Constants & ISA Values

Standard values used in all ATPL calculations

g = 9.80665 m/s²

R (air) = 287 J/kg·K

γ (air) = 1.4

ρ₀ (ISA MSL) = 1.225 kg/m³

P₀ (ISA MSL) = 1013.25 hPa = 29.92 inHg

T₀ (ISA MSL) = 15°C = 288.15 K

Lapse rate = 1.98°C / 1,000 ft

Tropopause (ISA) = 36,089 ft / FL360

T (tropopause) = −56.5°C = 216.65 K

Speed of sound (ISA MSL) = 661.5 kts = 340.3 m/s

1 NM = 1,852 m = 6,076.1 ft

1 knot = 1.852 km/h = 0.5144 m/s

1 ft = 0.3048 m

1 m = 3.2808 ft

1 kg = 2.2046 lb

1 US gal = 3.785 L

1 Imp gal = 4.546 L

Avgas density ≈ 0.72 kg/L

Jet A density ≈ 0.80 kg/L

π = 3.14159

Unit Conversions

Quick conversion factors for exam and operations

ft → m × 0.3048

m → ft × 3.2808

kg → lb × 2.2046

lb → kg × 0.4536

hPa → inHg × 0.02953

inHg → hPa × 33.864

NM → km × 1.852

km → NM × 0.5400

kts → km/h × 1.852

kts → m/s × 0.5144

°C → K + 273.15

K → °C − 273.15

°C → °F × 9/5 + 32

°F → °C (−32) × 5/9

US gal → L × 3.785

Imp gal → L × 4.546

🧮

Rules of Thumb & Mental Math

Quick approximations for cockpit and exam use

Top of Descent (3°)

Dist to TOD (nm) = Alt to lose (ft) / 300
OR: Alt (ft) / 1,000 × 3 = nm needed

Example: Cruise FL350, field elevation 0 → TOD = 35,000 / 300 = 117 nm from field

DescentMemorize

Rate of Descent (3°)

ROD (fpm) = GS (kts) × 5

Example: GS 150 kts on ILS → target ROD = 750 fpm

DescentMemorize

TAS from IAS

TAS ≈ IAS + 2% per 1,000 ft

Example: FL100, IAS 200 kts → TAS ≈ 200 + 40 = 240 kts

AirspeedMemorize

ILS Height Check

Height (ft) = Distance from THR (nm) × 300
(rough — precise is × 318)

Example: 4 nm from threshold → height ≈ 4 × 300 = 1,200 ft (exact: 1,272 ft)

ApproachMemorize

1 in 60

1 nm off after 60 nm = 1° error

Example: 3 nm off at 90 nm → TEA = 3 × 60 / 90 = 2°

NavigationMemorize

Fuel: gal to kg (Jet A)

kg/hr ≈ US gal/hr × 3.0
(Jet A density ≈ 0.80 kg/L)

Example: 500 US gal/hr → 500 × 3.0 = 1,500 kg/hr

Fuel

💡

Memory Aids & Acronyms

Mnemonics for exams and flight deck

I'M SAFE — Pre-flight Self-check

Illness · Medication · Stress · Alcohol · Fatigue · Emotion

Check each factor before flying. Any concern = do not fly.

Human Perf

PAVE — Risk Assessment

Pilot · Aircraft · enVironment · External Pressures

Systematic risk identification before each flight.

CRM

ARROW — Required Documents

Airworthiness · Registration · Radio licence · Operating limitations · Weight & balance

Documents required on board before flight.

Air Law

DECIDE — Decision Model

Detect · Estimate · Choose · Identify · Do · Evaluate

Structured decision-making cycle for in-flight problem solving.

CRM

5 Hazardous Attitudes

Anti-authority · Impulsivity · Invulnerability · Macho · Resignation

Recognise and counteract each. E.g. "It won't happen to me" = Invulnerability.

Human Perf

TEM Model

Threats → Errors → Undesired Aircraft State → Accident

Threat and Error Management. Each stage can be caught before it progresses.

CRM

★

100 KSA — Competency Models

Knowledge, Skills and Attitudes — EASA competency framework

Situational Awareness (SA) Model

Level 1: Perception (What is happening?)
Level 2: Comprehension (What does it mean?)
Level 3: Projection (What will happen next?)

Endsley's model. Most accidents involve Level 1 or 2 SA failure.

100 KSA

Communication Model

Sender → Encode → Channel → Decode → Receiver → Feedback

Barriers at any stage cause breakdown. Readback = feedback loop in ATC comms.

100 KSA

Crew Coordination Cycle

Brief → Monitor → Challenge → Decision → Review

Standard flow for crew actions on any task or abnormal.

CRM

Error Types

Slip (action error) · Lapse (memory error) · Mistake (planning error) · Violation (intentional)

Reason's model. Slips and lapses are unintentional skill-based errors.

100 KSA