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Formula reference

Cheat sheet

74 formulas and rules across 10 topics, each with the variables, the trap the test sets, and a question to try it on. The test center supplies figures and legends, not formulas, so everything here is yours to know.

Practise with the real figure book. The test center hands you FAA-CT-8080-2H, the same legends and figures the questions refer to. It is free from the FAA testing supplements page. Nothing in this sheet may be carried into the room.

Regulations, currency and limitsI. Preflight Preparation — Pilot Qualifications and Airworthiness

Medical certificate duration, 61.23(d)

third class — under 40 on exam date: 60 calendar months  ·  40 or older: 24 calendar months  ·  first class for ATP: 12 months under 40, 6 months at 40 or older  ·  first or second class for commercial: 12 calendar months

Age is fixed at the date of the examination, not the date of the flight. A pilot who was 39 at the exam keeps 60 calendar months even after turning 40.

A first- or second-class medical does not become worthless when its higher privileges lapse: it keeps serving third-class (private pilot) privileges for the full 60 or 24 months.

Expiry is the end of the last day of the Nth month after the month of the exam, so the day of the month never matters.

Try itpilot qualifications 1 · easypilot qualifications 2 · mediumpilot qualifications 3 · easy

BasicMed, 61.23(c)(3) and 61.113(i)

medical education course every 24 calendar months  ·  physician examination every 48 calendar months  ·  7 occupants max, 6 passengers max, 12,500 lb max takeoff weight  ·  not above 18,000 ft MSL, not above 250 KIAS

The two intervals are deliberately swapped in the distractors: the course is the short one (24), the physician exam is the long one (48).

12,500 is a weight in pounds, not an altitude in feet. The altitude limit is 18,000 ft MSL.

Try itpilot qualifications 4 · mediumpilot qualifications 5 · hard

Flight review, 61.56

1 hour of flight training + 1 hour of ground training  ·  required since the beginning of the 24th calendar month before the month of the flight  ·  logbook endorsement required

This is a requirement to act as pilot in command. The private pilot certificate itself never expires.

A practical test or proficiency check passed in the period, or a phase of the WINGS program, substitutes for the review.

Try itpilot qualifications 6 · easy

Passenger currency by day, 61.57(a)

3 takeoffs + 3 landings in the preceding 90 days  ·  sole manipulator of the controls  ·  same category, class and type  ·  tailwheel airplane: all three to a full stop

Touch-and-go landings count for the day rule in a nosewheel airplane. They do not count in a tailwheel airplane, and they never count at night.

90 days is a rolling day count, not calendar months.

Try itpilot qualifications 7 · easypilot qualifications 10 · hard

Passenger currency at night, 61.57(b)

3 takeoffs + 3 landings to a full stop in the preceding 90 days, made between 1 hour after sunset and 1 hour before sunrise

Three different night periods are tested against each other: sunset to sunrise is when position lights are required (91.209), end of evening civil twilight to beginning of morning civil twilight is night for logging (1.1), and 1 hour after sunset to 1 hour before sunrise is night passenger currency.

All three landings must be full stop, not just one.

Try itpilot qualifications 8 · mediumpilot qualifications 9 · medium

VFR fuel reserve, 91.151

fuel = (to the first point of intended landing) + day 30 min  ·  night 45 min, at normal cruising speed  ·  gallons = distancegroundspeed × GPH + reserve × GPH
GPH
fuel consumption in gallons per hour at cruise

Reverse the day and night figures and the answer is always on the list. 45 minutes is also the IFR reserve, which is why it looks plausible for a VFR day flight.

The reserve is fuel beyond the first point of intended landing, computed at normal cruise, not at the approach or reserve power setting.

Try itnavigation 7 · mediumnavigation 8 · medium

Supplemental oxygen, 91.211(a)

above 12,500 up to and including 14,000 ft MSL cabin: flight crew uses oxygen for that part over 30 minutes  ·  above 14,000 ft MSL: flight crew uses it the whole time  ·  above 15,000 ft MSL: each occupant must be provided with it

The 30-minute grace period belongs only to the 12,500 to 14,000 band. Above 14,000 there is no grace period.

Above 15,000 passengers must be provided oxygen, not required to use it. Only the required minimum flight crew must use it.

Every altitude is cabin pressure altitude, which in an unpressurized airplane equals the flight altitude.

Try ithuman factors 2 · easyhuman factors 3 · medium

VFR cruising altitudes, 91.159

more than 3,000 ft above the surface and below 18,000 ft MSL  ·  magnetic course 0° to 179°: odd thousand + 500 (3,500 · 5,500 · 7,500)  ·  180° to 359°: even thousand + 500 (4,500 · 6,500 · 8,500)

The rule keys on magnetic course, not magnetic heading, so the wind correction angle is irrelevant.

It applies only more than 3,000 ft AGL. Below that, any altitude is legal.

Odd or even thousands without the extra 500 ft are the IFR altitudes, and they are always offered.

Try itnavigation 26 · mediumairspace 27 · medium

Speed limits, 91.117

below 10,000 ft MSL: 250 KIAS  ·  at or below 2,500 ft AGL within 4 NM of the primary Class C or D airport: 200 KIAS  ·  underneath Class B or in a VFR corridor through it: 200 KIAS (230 mph)

Inside Class B the limit is the general 250 KIAS. The 200-knot limit is for the airspace underneath it and for VFR corridors through it. 91.117(b) says so explicitly.

The Class C and D 200-knot limit has two qualifiers that must both be met: at or below 2,500 ft above the surface and within 4 NM of the primary airport.

Try itairspace 26 · medium

Minimum safe altitudes, 91.119

anywhere: an altitude allowing an emergency landing without undue hazard if a power unit fails  ·  congested area: 1,000 ft above the highest obstacle within a horizontal radius of 2,000 ft  ·  other than congested: 500 ft above the surface  ·  open water or sparsely populated: no closer than 500 ft to any person, vessel, vehicle or structure

Over a congested area it is 1,000 ft above the highest obstacle, not 1,000 ft AGL, and the radius is 2,000 ft horizontally, not an altitude.

Over open water or sparsely populated areas there is no altitude floor at all, only a 500 ft standoff distance from people and objects.

Inspection and test intervals

annual 12 calendar months  ·  100-hour (for hire or flight instruction for hire) 100 hours in service  ·  altimeter and static system 24 calendar months  ·  transponder 24 calendar months  ·  VOR check 30 days  ·  ELT inspection 12 calendar months

ELT batteries are not on a calendar interval: replace or recharge after more than 1 cumulative hour of transmitter use, or when 50 percent of the useful life has expired.

A calendar month interval runs to the end of the last day of that month, so an annual signed off 12 July is good through 31 July of the next year.

The 100-hour interval applies only to carrying persons for hire or giving flight instruction for hire, never to personal flying.

Try itairworthiness 11 · easyairworthiness 12 · hardairworthiness 14 · mediumairworthiness 15 · mediumairworthiness 17 · mediumairworthiness 18 · hard

NTSB reporting, 830.15

written report on NTSB Form 6120.1/2: within 10 days after an accident  ·  within 7 days if an overdue aircraft is still missing  ·  an incident report only when requested

Immediate notification of the nearest NTSB office by the most expeditious means is the separate 830.5 duty. The 10-day figure is the written report, not the notification.

The 48-hour figure belongs to the report a pilot given priority by ATC files with the facility manager on request under 91.123(d).

Try itairworthiness 28 · mediumairworthiness 27 · medium

VFR weather minimums (91.155)I. Preflight Preparation — Weather Information and Airspace

Class B

3 statute miles flight visibility  ·  clear of clouds

Clear of clouds, because ATC separates everything inside Class B. It is the only controlled airspace with no cloud clearance distances.

3 miles and clear of clouds appears in no other row: pairing 3 miles with the standard 500/1,000/2,000 is the Class C, D and low Class E line.

Try itairspace 1 · easy

Class C, Class D and Class E below 10,000 ft MSL

3 statute miles  ·  500 ft below  ·  1,000 ft above  ·  2,000 ft horizontal

This is the row to memorise first: it covers three classes of airspace and is the reference everything else is measured against.

Class D tops out at 2,500 ft above the airport elevation, so the at-or-above-10,000 row can never apply to it.

Try itairspace 2 · easyairspace 3 · easyairspace 4 · easy

At or above 10,000 ft MSL

5 statute miles  ·  1,000 ft below  ·  1,000 ft above  ·  1 statute mile horizontal

The horizontal clearance changes units: 1 statute mile, not 1,000 feet. Reading 1,000 as the horizontal figure is the built-in trap.

In Class G this row applies only when the airplane is both at or above 10,000 ft MSL and more than 1,200 ft above the surface.

Try itairspace 5 · mediumairspace 6 · hard

Class G, 1,200 ft or less above the surface

day: 1 statute mile, clear of clouds  ·  night: 3 statute miles, 500 below / 1,000 above / 2,000 horizontal

The band is measured above the surface regardless of MSL altitude, so it follows terrain rather than a chart altitude.

Night in this band jumps straight to the full 3 miles and the standard cloud clearances: there is no 1-mile night rule except the traffic-pattern exception of 91.155(b).

Try itairspace 7 · easyairspace 8 · medium

Class G, more than 1,200 ft above the surface but below 10,000 ft MSL

day: 1 statute mile, 500 below / 1,000 above / 2,000 horizontal  ·  night: 3 statute miles, same cloud clearances

1 statute mile survives the climb through 1,200 ft AGL by day, but the cloud clearances do not: clear of clouds is replaced by 500/1,000/2,000.

Read the question for both numbers: height above the surface decides the row, MSL altitude decides whether the 10,000 ft rule takes over.

Try itairspace 9 · medium

Surface areas and special VFR

takeoff, land or enter the pattern in a Class B, C, D or E surface area: 3 statute miles ground visibility (flight visibility if none is reported) and a 1,000 ft ceiling  ·  special VFR: ATC clearance, clear of clouds, 1 statute mile flight visibility

Special VFR must be requested by the pilot; ATC never offers it unprompted, and it is not available at night to a pilot without an instrument rating and an instrument-equipped airplane.

The 1-mile special VFR figure is the visibility the clearance relieves, so it is the wrong answer to any basic-VFR question.

Try itairspace 10 · mediumairspace 28 · hard

Airspace dimensions, entry and equipmentI. Preflight Preparation — Airspace

Class A

18,000 ft MSL up to and including FL 600  ·  plus the airspace over the waters within 12 NM of the coast

The floor is 18,000 feet MSL, a pressure altitude with the altimeter set to 29.92, never 18,000 AGL.

14,500 ft MSL to below 18,000 ft MSL is the default en route Class E layer beneath Class A.

Try itairspace 11 · easy

Class B

surface to 10,000 ft MSL, two or more tailored layers  ·  ATC clearance required before entry  ·  private pilot certificate, or a student, sport or recreational pilot with the required endorsement

You must hear the words cleared into the Class Bravo. Establishing two-way radio contact is not enough, and that is the Class C rule being borrowed.

Weather does not matter: the clearance is required regardless of conditions.

Try itairspace 12 · easyairspace 17 · easyairspace 19 · medium

Class C

5 NM radius core, surface to 4,000 ft above the airport elevation  ·  10 NM radius shelf, 1,200 ft AGL to that same ceiling  ·  20 NM procedural outer area, not charted  ·  two-way radio communications established before entry

Communications are established when the controller answers with your call sign, including November 1234 Alpha, standby. A reply of aircraft calling, standby does not establish them.

The 20 NM outer area is a service, not airspace, and it carries no entry or equipment requirement of its own.

Try itairspace 13 · mediumairspace 18 · hard

Class D

surface to 2,500 ft above the airport elevation  ·  ceiling charted as a boxed figure in hundreds of feet MSL  ·  two-way radio communications established before entry

The height is above the airport elevation, but the charted box is MSL. 4,000 above the airport is the Class C ceiling.

Try itairspace 14 · medium

Class E floors and Class G

fuzzy magenta vignette: Class E from 700 ft AGL  ·  fuzzy blue vignette: Class E from 1,200 ft AGL  ·  magenta dashed line: Class E surface area  ·  Class G otherwise up to 14,500 ft MSL

Magenta is the lower floor (700), blue is the higher one (1,200). Reversing them is the classic chart-reading error.

Above 14,500 ft MSL the airspace is Class E, except airspace less than 1,500 ft above the terrain.

Try itairspace 15 · mediumairspace 16 · hard

Transponder and ADS-B Out airspace

transponder with Mode C, 91.215(b): Class A, Class B, Class C, and within 30 NM of a Class B primary airport from the surface to 10,000 ft MSL  ·  ADS-B Out, 91.225(d): Class B and Class C, and Class E at or above 10,000 ft MSL excluding at and below 2,500 ft AGL

Class D is on neither list. The 30 NM Mode C veil is charted as a solid magenta ring and is often forgotten entirely.

The 10 NM / 4,000 ft figures belong to the Class C shelf, and 20 NM to the Class C outer area; neither is the veil.

Try itairspace 20 · mediumairworthiness 19 · hardairworthiness 20 · hard

Special use airspace and TFRs

prohibited: flight is not allowed  ·  restricted: unusual hazards, entry needs the controlling agency’s permission  ·  MOA: VFR flight permitted, exercise extreme caution  ·  VR/IR route numbers: 4 digits means at or below 1,500 ft AGL, 3 digits means above 1,500 ft AGL

A four-digit military training route number such as VR1207 means the route is flown at or below 1,500 ft AGL; three digits mean some portion is above it.

Controlled firing areas are the special use airspace that is never charted, because activity stops when an aircraft is detected.

A disaster or hazard TFR is issued under 91.137 and normally has a 3 NM radius up to 2,000 ft AGL.

Try itairspace 21 · mediumairspace 22 · mediumairspace 23 · hardairspace 24 · hardairspace 25 · hard

Weight and balanceI. Preflight Preparation — Performance and Limitations

Datum, station and arm

datum: an imaginary vertical plane fixed by the manufacturer  ·  arm: horizontal distance in inches from the datum  ·  station +50 means 50 inches aft  ·  a minus sign means forward of the datum

The datum never moves. The centre of gravity does, with every change of loading.

A station number is an arm in inches, not a moment in pound-inches.

Try itperformance limitations 1 · easyperformance limitations 2 · easy

Moment

moment = weight × arm  ·  50 lb at 100 in = 5,000 lb-in
weight
pounds
arm
inches from the datum, signed

An item forward of the datum has a negative arm and so a negative moment, which is subtracted from the total moments even though its weight is still added to the total weight.

Adding weight and arm instead of multiplying, or dividing them, produces the two wrong answers on offer.

Try itperformance limitations 3 · easyperformance limitations 7 · hard

Centre of gravity

CG = total momenttotal weight = Σ (weight × arm)Σ weight

Convert fuel from gallons to pounds before anything else: 75 gallons of avgas is 450 lb, not 75 lb.

Every item counted in the weight column must also be counted in the moment column. Dropping one moment while keeping its weight is the standard trap.

Try itperformance limitations 6 · hard

Weight shift

ΔCG = weight shifted × distance shiftedtotal weight  ·  new CG = old CG ± ΔCG
distance shifted
the gap between the two stations, not the new station number

Use the distance between the old and new stations. Moving 100 lb from station 30 to station 150 is a 120-inch shift, not a 150-inch one.

Weight moved aft moves the CG aft: add. Weight moved forward: subtract.

Try itperformance limitations 9 · hard

Weight added or removed

ΔCG = weight added × (arm of the weight − old CG)new total weight

The distance is measured from the old CG to the new item, and the divisor is the new total weight, not the old one.

Adding weight aft of the CG always moves the CG aft. Subtracting in that case is the offered error.

Try itperformance limitations 10 · hard

Standard fluid weights

aviation gasoline 6 lb/gal  ·  engine oil 7.5 lb/gal  ·  jet fuel 6.8 lb/gal  ·  water 8.35 lb/gal  ·  1 quart of oil = 1.875 lb

Applying the oil figure to the fuel is the most expensive slip available: fuel quantities are large, so the error compounds.

Oil is often carried at a negative arm, forward of the datum.

Try itperformance limitations 5 · easy

Useful load, payload and zero fuel weight

useful load = max gross weight − basic empty weight  ·  payload = occupants + baggage + cargo  ·  zero fuel weight = loaded weight − usable fuel

Useful load includes usable fuel and drainable oil; payload does not. That is the whole difference between the two definitions.

Zero fuel weight includes every occupant and every bag, so it is never the basic empty weight and never includes fuel.

Try itperformance limitations 4 · mediumperformance limitations 8 · medium

Overload and load factor

structural overload = excess weight × limit load factor  ·  normal category 3.8 G  ·  utility 4.4 G  ·  acrobatic 6.0 G

100 lb over gross in a normal category airplane is a potential 380 lb structural overload, because the structure must carry 3.8 times whatever it supports.

An aft CG outside the approved range costs stability and can make stall and spin recovery impossible; a forward CG outside it costs elevator authority in the flare.

Try itperformance limitations 14 · mediumperformance limitations 11 · mediumperformance limitations 12 · medium

PerformanceI. Preflight Preparation — Performance and Limitations

Pressure altitude

pressure altitude = height above the standard datum plane, read with the altimeter set to 29.92  ·  PA = field elevation + conversion factor  ·  setting above 29.92 gives a negative factor, below 29.92 a positive one

30.10 carries a conversion factor of −165 ft, so a 5,883 ft field has a pressure altitude of 5,718 ft. Adding the factor instead of subtracting it is the offered answer.

Field elevation equals pressure altitude only when the setting happens to be 29.92.

Try itperformance limitations 15 · easyperformance limitations 16 · hard

Density altitude

density altitude = pressure altitude corrected for non-standard temperature  ·  in flight: set 29.92, read pressure altitude, take the OAT, compute  ·  highest when elevation is high, pressure low, temperature high and humidity high

Correcting indicated altitude for pressure gives pressure altitude, which is only the first of the two steps.

Humid air is less dense than dry air, because water vapour is lighter than the air it displaces. High humidity raises density altitude, it does not lower it.

Try itperformance limitations 17 · easyperformance limitations 18 · mediumweather theory 5 · easyweather theory 6 · medium

What high density altitude costs

less power (the engine takes in less air)  ·  less thrust (the propeller bites less air)  ·  less lift (the wing meets less air)  →  longer takeoff and landing rolls, lower rate of climb

The twofold takeoff penalty is a longer ground run and a shallower climb gradient after lift-off, and both matter for obstacle clearance.

True airspeed at lift-off rises with density altitude even though the indicated airspeed is unchanged, which is why the ground roll lengthens.

Try itweather theory 7 · easyperformance limitations 19 · medium

Chart correction notes

short-field takeoff table: decrease 10% per 9 kt of headwind, increase 15% of the ground roll for a dry grass runway  ·  landing table: increase 20% of the total distance over a 50 ft obstacle for dry grass, decrease 10% per 4 kt of headwind

Read the note attached to the table you are using. The takeoff grass note and the landing grass note use different percentages and different base figures.

A headwind decreases distance and a tailwind increases it. Applying the correction with the wrong sign gives an answer that is always on the list.

Try itperformance limitations 20 · mediumperformance limitations 21 · hardperformance limitations 22 · medium

Ground roll against total distance

ground roll = distance to lift-off  ·  total distance = distance to clear a 50 ft obstacle, always the larger figure  ·  compare the total distance with the runway and departure path when obstacles exist

Using the ground roll alone leaves out the horizontal distance flown while climbing to 50 ft. Averaging the two figures has no basis in any chart.

Try itperformance limitations 23 · medium

Vₓ and Vᵧ

VX = most altitude gained in a given distance, used to clear an obstacle  ·  VY = most altitude gained in a given time  ·  with altitude VX increases slightly and VY decreases slightly

The two speeds converge with altitude and meet at the absolute ceiling, where the only remaining climb speed gives zero rate of climb.

Service ceiling is where the best rate of climb falls to 100 fpm; absolute ceiling is where it reaches zero.

Try itslow flight stalls 21 · mediumperformance limitations 24 · mediumperformance limitations 25 · medium

Crosswind and headwind components

crosswind = wind speed × sin θ  ·  headwind = wind speed × cos θ  ·  θ = angle between the wind and the runway  ·  demonstrated crosswind ≥ 0.2 × VS0
θ
wind angle: runway 17 with wind from 140° gives 30°

At 30° the crosswind is half the wind speed; at 45° both components are about 0.7 of it; at 60° the crosswind is about 0.87 and the headwind is half. An angle over 90° gives a tailwind.

The maximum demonstrated crosswind component in the POH is performance information from a certification flight test, not an operating limitation.

A 45 kt power-off stall speed gives a 9 kt certification crosswind: two tenths of the stall speed, not half of it.

Try itperformance limitations 27 · hardperformance limitations 28 · medium

Aerodynamics and V-speedsVII. Slow Flight and Stalls — Principles of Flight

The lift equation

L = CL · ρ · V² · S2
C_L
coefficient of lift for the airfoil, set by angle of attack
ρ
air density in slugs per cubic foot
V
velocity in feet per second
S
wing planform area in square feet

Lift varies with the square of velocity: doubling the speed at a constant angle of attack gives four times the lift, not twice.

Density and wing area enter linearly, velocity enters squared. That asymmetry is what the question is testing.

Try itslow flight stalls 3 · mediumslow flight stalls 1 · easy

Load factor in a level turn

n = 1cos φ  ·  30° → 1.15 G  ·  45° → 1.41 G  ·  60° → 2.0 G  ·  80° → 5.76 G
φ
angle of bank in a coordinated level turn

Load factor does not grow in proportion to bank angle. It climbs at a terrific rate once the bank passes 45° or 50°, and a 90° level turn is impossible.

Weight does not change the load factor for a given bank angle, only the loads the structure must carry.

Try itslow flight stalls 15 · easyflight maneuvers 15 · medium

Stall speed and load factor

VS at n G = VS × √n  ·  50 kt at 4 G stalls at 100 kt  ·  60° bank (2 G) raises stall speed about 40%

Square root, not proportional. Multiplying 50 by 4 gives 200 and is always offered.

Weight raises the stall speed but never changes the critical angle of attack. The wing stalls at the same angle at any weight, bank, altitude or CG.

Try itslow flight stalls 16 · hardslow flight stalls 9 · mediumslow flight stalls 8 · easy

Design manoeuvring speed

VA ≈ 1.7 × VS for older light airplanes  ·  stalling at 1.7 VS gives 1.7² = 2.89 G  ·  VA is lower at lighter weight

Lighter means slower. A lighter airplane stalls at a lower speed, so it must be slowed further for the wing to stall and unload before the limit load is reached. Believing V_A rises as weight falls is the classic error.

V_A protects against one full deflection of one control in one axis in smooth air. It is no protection against repeated or multi-axis inputs at any speed.

Try itslow flight stalls 18 · hardslow flight stalls 17 · hard

Airspeed indicator markings

white arc: VS0 to VFE, the flap operating range  ·  green arc: VS1 to VNO, normal operating range  ·  yellow arc: VNO to VNE, smooth air only  ·  red line: VNE
V_S0
stall speed, landing configuration, gear and flaps down
V_S1
stall speed in a specified (clean) configuration
V_FE
maximum speed with flaps extended
V_NO
maximum structural cruising speed
V_NE
never-exceed speed

The two arcs share no endpoints by accident: the bottom of the white arc is the flaps-down stall, the bottom of the green is the clean stall.

V_NE is the red line at the top of the yellow arc, never the top of the green arc.

Try itslow flight stalls 19 · easyslow flight stalls 20 · easy

Drag and L/D MAX

induced drag falls as airspeed rises  ·  parasite drag rises with the square of airspeed  ·  total drag is least where the two are equal, at L/D MAX

L/D MAX is the best glide speed and the speed for maximum range in a propeller airplane. Maximum endurance comes at the minimum-power speed, which is slower.

Below L/D MAX the airplane is in the region of reversed command, where more power is needed to fly slower.

Try itslow flight stalls 5 · mediumslow flight stalls 6 · hardslow flight stalls 7 · hard

Ground effect

occurs within about one wingspan of the surface  ·  the surface restricts the vertical airflow, cutting upwash, downwash and tip vortices  ·  induced angle of attack and induced drag fall

It is not a cushion of compressed air. The airplane can lift off below its normal flying speed and then sink back on climbing out of ground effect: performance borrowed, then repaid.

Try ittakeoffs landings 23 · mediumtakeoffs landings 24 · easy

Steep turn standards

private pilot ACS: 360° coordinated turn at approximately 45° bank  ·  altitude ±100 ft  ·  airspeed ±10 kt  ·  bank ±5°  ·  rollout heading ±10°

45° is the private pilot standard. 60° is the upper end of the handbook range and belongs to the commercial standard.

Try itflight maneuvers 14 · easyflight maneuvers 16 · medium

WeatherI. Preflight Preparation — Weather Information

The standard atmosphere

sea level pressure 29.92 in Hg (1013.25 hPa)  ·  sea level temperature 15 °C (59 °F)  ·  pressure falls about 1 in Hg per 1,000 ft up to 10,000 ft

15 °C is 59 °F. A choice pairing 29.92 with 15 °F is the same number wearing the wrong unit.

The 1 in Hg per 1,000 ft relationship is what makes an altimeter setting error worth 1,000 ft per inch.

Try itweather theory 1 · easyweather theory 3 · medium

Lapse rates

standard atmospheric: 2 °C (3.5 °F) per 1,000 ft  ·  dry adiabatic: 3 °C (5.4 °F) per 1,000 ft  ·  dewpoint of a rising parcel: 0.5 °C (1 °F) per 1,000 ft

The standard lapse rate describes the atmosphere as a whole; the dry adiabatic rate describes one unsaturated parcel being lifted through it. Swapping 2 and 3 is the trap.

An actual lapse rate steeper than the dry adiabatic rate means the column is unstable.

Try itweather theory 2 · easyweather theory 11 · mediumweather theory 12 · hard

Convective cloud base

base (ft AGL) = T − DP in °F4.4 × 1,000  ·  85 °F and 71 °F: 144.4 = 3.18 → about 3,180 ft AGL
T
surface temperature, °F
DP
surface dewpoint, °F
4.4
convergence rate: 5.4 °F cooling minus 1 °F dewpoint fall, per 1,000 ft

Divide by the convergence rate of 4.4, not by the dry adiabatic rate of 5.4. Both numbers appear in the derivation, and both appear in the answers.

The formula is stated in Fahrenheit. Feeding it Celsius degrees gives a number that is wrong by nearly a factor of two.

Fog seldom forms while the spread is more than 2 °C: a small spread means high relative humidity, nothing about precipitation or stability.

Try itweather theory 10 · hardweather theory 9 · medium

Thunderstorms: ingredients and stages

needs water vapour + unstable air + a lifting action  ·  towering cumulus: updraft only  ·  mature: begins when precipitation reaches the surface, updraft and downdraft together  ·  dissipating: downdraft throughout, moisture supply cut off

The mature stage starts when rain reaches the ground, not when the anvil appears. Hazards peak toward the end of the mature stage.

Stable air and an inversion suppress convection; they are not ingredients.

Try itweather theory 18 · easyweather theory 19 · medium

Thunderstorm avoidance and microbursts

avoid a severe storm or intense radar echo by at least 20 miles  ·  microburst horizontal winds up to 45 kt, so a 90 kt headwind-to-tailwind shear  ·  downdrafts up to 6,000 fpm

The 90-knot figure is the total change across the microburst, twice the 45-knot one-sided surface wind. Quoting 45 is reading only half the crossing.

Severe turbulence can be met 20 miles laterally from a severe storm, in clear air, under the anvil.

Try itweather theory 20 · hardweather theory 21 · medium

Structural icing

needs visible moisture + an outside air temperature below 0 °C  ·  clear ice: large droplets, high liquid water content, warmer than about −10 °C  ·  rime ice: small droplets, low liquid water content, colder than about −15 °C

Almost all icing occurs between 0 and −20 °C, with about half the reports between −8 and −12 °C. Below about −20 °C clouds are mostly ice crystals and produce little icing.

Freezing rain or ice pellets mean warmer than freezing air lies above you. Climbing is the wrong instinct; the warm layer is where the supercooled water came from.

High relative humidity alone is not visible moisture: the water has to be present as droplets.

Try itweather theory 22 · easyweather theory 23 · hardweather theory 24 · hard

AIRMET and SIGMET

AIRMET Sierra: IFR and mountain obscuration  ·  Tango: moderate turbulence, surface winds 30 kt or more, low-level wind shear  ·  Zulu: moderate icing and freezing levels  ·  valid 6 hours (8 in Alaska)

SIGMET: severe icing, severe or extreme turbulence, widespread dust or sand below 3 miles, volcanic ash. Valid 4 hours, or 6 for tropical cyclones and volcanic ash.

Convective SIGMET: embedded or lines of thunderstorms, or hail 3/4 inch or larger. Issued hourly at 55 past the hour, valid 2 hours, and a bulletin reading NONE is still issued when nothing qualifies.

AIRMET covers moderate intensities, SIGMET covers severe ones. Matching severe conditions to a 6-hour life mixes the two products.

Try itweather services 18 · easyweather services 19 · mediumweather services 20 · mediumweather services 21 · hardweather services 22 · hard

IFR conditions and fog

AIRMET Sierra IFR: ceiling below 1,000 ft and/or surface visibility below 3 miles  ·  radiation fog: clear sky, little wind, small spread, over land at night  ·  upslope fog: moist stable air forced up sloping terrain

Radiation fog needs the ground to cool, so it forms over land, not water, and burns off with heating or wind.

Upslope fog, unlike radiation fog, can form in windy conditions and persists as long as the upslope flow lasts.

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Communications, signals and codesIV. Airport Operations

Light gun signals

steady green — on ground: cleared for takeoff  ·  in flight: cleared to land
flashing green — on ground: cleared to taxi  ·  in flight: return for landing
steady red — on ground: stop  ·  in flight: give way and continue circling
flashing red — on ground: taxi clear of the runway  ·  in flight: airport unsafe, do not land
flashing white — on ground: return to the starting point  ·  in flight: not applicable
alternating red and green — exercise extreme caution, both on the ground and in flight

Every colour means something different on the ground than in flight, except alternating red and green. The distractors are always the other half of the same row.

Acknowledge by rocking the ailerons or moving the rudder by day, and by blinking the landing or navigation lights at night.

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Transponder codes

1200 — VFR, regardless of altitude  ·  7500 — unlawful interference (hijack)  ·  7600 — two-way radio failure  ·  7700 — emergency

7500 is never assigned by ATC without the pilot reporting interference first; refuse it in any other situation. A controller will ask you to verify it.

When changing codes, avoid sweeping through the emergency codes: 2700 to 7200 goes by way of 2200, not 7700.

Squawk 7700 and Mode C when a distress condition arises and you cannot immediately reach a facility, then establish communications.

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Frequencies to know

121.5 and 243.0 MHz — distress and urgency  ·  122.9 — MULTICOM, no tower, FSS or UNICOM on the field  ·  122.95 — UNICOM at an airport with a tower or FSS  ·  122.7, 122.8, 123.0 — common UNICOM/CTAF without a tower  ·  108.0 — repair station VOT

122.9 is MULTICOM, for fields with nothing on them. 122.95 is the UNICOM where a tower or FSS exists, and wind and runway information may not be available on it.

121.5 is guarded by direction-finding stations, military towers, most civil towers and radar facilities.

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Pilot-controlled lighting

7 clicks within 5 seconds — highest intensity  ·  5 clicks — medium  ·  3 clicks — lowest  ·  on for 15 minutes from the most recent activation

Key 7 times first even if you want a lower setting: it guarantees the system is active and the lights are on before you step them down.

The lights cannot be keyed off, and generally stay on for the full 15 minutes.

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Self-announce positions on CTAF

inbound: 10 miles out, entering downwind, base, final, and leaving the runway  ·  outbound: before taxiing and before taxiing onto the runway for departure

At a non-towered field in Class G the pattern is left-hand for a powered fixed-wing airplane unless light signals or markings show otherwise.

Enter the pattern on the downwind, abeam the midpoint of the runway, at pattern altitude.

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Human factorsI. Preflight Preparation — Human Factors

The AIM oxygen recommendation

for optimum protection: supplemental oxygen above 10,000 ft cabin altitude by day, and above 5,000 ft at night

These are recommendations, not the regulation. 12,500 / 14,000 / 15,000 are the 91.211 legal thresholds and answer a different question.

The night figure is 5,000 ft because night vision starts to deteriorate at cabin altitudes that low.

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The four hypoxias

hypoxic — not enough oxygen available (altitude)  ·  hypemic — the blood cannot carry it (carbon monoxide, bleeding, anaemia)  ·  stagnant — the blood is not flowing (G loads, shock, cold)  ·  histotoxic — the cells cannot use it (alcohol, drugs, poisons)

Alcohol produces histotoxic hypoxia: the oxygen arrives and the cells cannot use it. Carbon monoxide produces hypemic hypoxia: the oxygen never gets loaded.

Hyperventilation looks like hypoxia but comes from blowing off too much carbon dioxide. On oxygen at altitude with tingling and lightheadedness, check the equipment first, then slow the breathing rate.

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Time to lose corrective action

18,000 ft: 20 to 30 minutes  ·  20,000 ft: 5 to 12 minutes, unconsciousness soon after  ·  performance can deteriorate seriously within 15 minutes at 15,000 ft

The 1-to-2-minute and 30-to-60-second figures belong to 30,000 and 35,000 ft and are far above any private pilot altitude.

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Carbon monoxide

binds to haemoglobin about 200 times more easily than oxygen  ·  the body needs up to 48 hours to clear it

200 times is why trace quantities matter. 20 times would not explain the hazard; 2,000 times is not a figure the handbooks give.

Suspect it whenever the cabin heater is on and a headache, dizziness or drowsiness appears: shut the heater off and open fresh air vents.

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Scuba diving before flight

no controlled ascent required, flight to 8,000 ft or below: wait at least 12 hours  ·  controlled ascent required, or any flight above 8,000 ft: wait at least 24 hours

A flight to a cabin altitude of 6,000 ft after a decompression-stop dive still needs the 24-hour wait: the dive type, not just the altitude, sets the interval.

48 hours is the carbon monoxide clearance time, not a diving interval.

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Alcohol, 91.17

no crewmember duties within 8 hours after consuming any alcoholic beverage  ·  nor with an alcohol concentration of 0.04 or greater  ·  nor while under the influence

0.04 is half the usual highway driving limit, and 0.08 is always offered. 12 hours overstates the interval the regulation sets, though it is a common personal rule.

An alcohol-related motor vehicle action must be reported in writing to the FAA Civil Aviation Security Division within 60 days.

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Night vision

complete dark adaptation: about 30 minutes  ·  moderate adaptation under dim red light: about 20 minutes  ·  view a dim object 5° to 10° off centre  ·  hold each glance only 2 to 3 seconds

Rods do the night seeing and they are absent from the fovea, so staring straight at a dim object puts its image on the one part of the retina that cannot see it.

Dim red cockpit lighting assists adaptation but makes red chart markings disappear; one bright white light destroys the adaptation outright.

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Sources are the ones cited on each linked question: 14 CFR, the Aeronautical Information Manual, and the FAA handbooks.