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ATPL(A) Commonly used formulas > Formulas > Flashcards

Formulas Flashcards

1
Q

Rate of turn

A
  • RoT = rate of turn [radials/s]*
  • φ​ = bank angle [x°]*
  • g = gravitational force [m/s2]*
  • v = velocity [m/s]*
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2
Q

Radius

A
  • r = radius [m]*
  • v = velocity [m/s]*
  • φ​ = bank angle [x°]*
  • g = gravitational force [m/s2]*
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3
Q

Bank angle

A
  • φ​ = bank angle [x°]*
  • v = velocity [m/s]*
  • r = radius [m]*
  • g = gravitational force [m/s2]*
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4
Q

Load factor in turn

A
  • nT = load factor in turn*
  • φ​ = bank angle [x°]*
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5
Q

Load factor

A
  • n = load factor*
  • L = lift [N]*
  • W = weight [N]*
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6
Q

Distance to climb

A
  • distance to climb [NM]*
  • h = height [ft]*
  • RoC = rate of climb [ft/min]*
  • GS = ground speed [kt]*
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7
Q

Time to climb

A
  • time to climb [s]*
  • h = height [ft]*
  • RoC = rate of climb [ft/min]*
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8
Q

Ground gradient (FPG)

A
  • FPG = flight path gradient or ground gradient [%]*
  • h = height [m]*
  • SAD = still air distance [m] (can be different, as long as h and d have the same unit)*
  • TAS = true airspeed [kt]*
  • GS = ground speed [kt]*
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9
Q

Climb gradient alternatives

A
  • CG = climb gradient [%]*
  • h = height [m]*
  • d = distance [m] (can be different, as long as h and d have the same unit)*
  • RoC = rate of climb [ft/min]*
  • TAS = true airspeed [ft/min]*
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10
Q

Rate of climb

A

RoC = CG • TAS

(completely correct: RoC = CG • TAS • 6000/6080)

  • RoC = rate of climb [ft/min]*
  • CG = climb gradient [%]*
  • TAS = true airspeed [kt]*
  • T = thrust [N]*
  • D = drag [N]*
  • W = weight [N]*
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11
Q

Climb gradient

A
  • CG = climb gradient [%]*
  • T = thrust [N]*
  • D = drag [N]*
  • W = weight [N]*
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12
Q

New stall speed with changing mass/weight

A
  • Vs new = new stall speed [kt]*
  • Vs old = old stall speed [kt]*
  • Wnew = new weight [N] (can be mass [kg])*
  • Wold = old weight [N] (can be mass [kg])*
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13
Q

New stall speed with changing load factor

A
  • Vs = stall speed [kt]*
  • Vs1g = minimum speed where L = W (steady horizontal flight) [kt]*
  • n = given load factor*
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14
Q

Climb angle ↔ climb gradient

A

γ = tan-1 (CG/100%)

CG = tan (γ) • 100%

  • γ = climb angle [x°]*
  • CG = climb gradient [%]*
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15
Q

Lift formula

A

L = ½ • ρ • v2 • S • CL

  • L = lift [N]*
  • ρ = density [kg/m2]*
  • v = true airspeed [m/s]*
  • S = wing surface area [m2]*
  • CL = lift coefficient*
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16
Q

Circumference/area of a circle

A

C = 2 • π • r

A = π • r2

  • C = circumference of circle [m]*
  • A = area of circle [m2]*
  • r = radius [m]*
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17
Q

Mach angle

A
  • μ = Mach angle [x°]*
  • a = local speed of sound [kt]*
  • TAS = true airspeed [kt]*
  • M = Mach number*
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18
Q

Mach number

A
  • M = Mach number*
  • TAS = true airspeed [kt]*
  • a = local speed of sound [kt]*
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19
Q

Local speed of sound

A
  • a = local speed of sound [kt]*
  • T = temperature [K]*
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20
Q

Mass flow

A

mass flow = A • ρ • v

  • A = cross section area [m2]*
  • ρ = density [kg/m2]*
  • v = velocity*
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21
Q

Gas equation

A

p = ρ • R • T

  • p = pressure [N/m2]*
  • ρ = density [kg/m2]*
  • R = gas constant*
  • T = temperature [K]*
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22
Q

1 NM = ? km = ? ft

A

1 NM = 1.852 km = 6080 ft

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23
Q

Runway slope

A

rwy slope = (Δ threshold elevation / distance between thresholds) • 100%

  • rwy slope = runway slope [%]*
  • Δ thld elev and distance between thlds in same unit!*
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24
Q

Departure (GNAV)

A

dep = chlong • cos(lat°)

  • dep = departrue [NM]*
  • chlong = change in longitude [x’ (minutes)]*
  • lat = latitude [x° (degrees)]*
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25
Q

Cross-/head-/tailwind components

A

XWC = Vwind • sin(wa)

HWC or TWC = Vwind • cos(wa)

  • XWC = crosswind component*
  • HWC = headwind component*
  • TWC = tailwind component*
  • Vwind = wind speed (wind speed and components same unit)*
  • wa = wind angle [x°] (never more than 90°)*
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26
Q

Earth convergence

A

EC = chlong • sin(mean lat°)

  • EC = earth convergence [x° (degrees)]*
  • chlong = change in longitude [x° (degrees)]*
  • mean lat = mean latitude [x° (degrees)]*
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27
Q

Conversion angle

A

CA = ½ • EC

  • CA = conversion angle [x°]*
  • EC = earth convergence [x°]*
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28
Q

ILS glide path intercept height

(glide angle/gradient)

A

Intercept height = θ • 100 • dist from thld + height above thld

Intercept height = glide gradient • 60 • dist from thld + height above thld

  • Intercept height [ft]*
  • θ = glide angle [x°]*
  • height above threshold [ft] (usually 50 ft)*
  • thld = threshold*
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29
Q

Rate of descent (GNAV)

(glide angle/gradient)

A

RoD = θ • 100• (GS/60)

RoD = glide gradient • GS

  • RoD = rate of descent [ft/min]*
  • θ = glide angle [x°]*
  • GS = groundspeed*
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30
Q

Angle of bank in rate one turn

(rule of thumb)

A

Angle of bank in rate one turn = (TAS ÷ 10) + 7

  • Angle of bank [x°]*
  • TAS = true airspeed [kt]*
  • Rate One Turn = 3°/s*
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31
Q

Brake Horse Power

A

BHP = T • RPM • constant

BHP ~ T • RPM (~ = proportional)

  • BHP = Brake Horse Power*
  • T = Torque [Nm]*
  • RPM = Revolutions per minute*
32
Q

Engine Pressure Ratio

A

EPR = Engine Pressure Ratio

33
Q

Bypass ratio

A

see attachment

34
Q

Jet engine static thrust

A

T = A • (p<span>nozzle</span> - p0)

  • T = static thrust*
  • A = area of nozzle [m2]*
  • pnozzle = exhaust nozzle static pressure [Pa]*
  • p0 = ambient static pressure [Pa] (so if given in hPa, make sure to convert to Pa)*
35
Q

Jet engine total thrust

A

Net engine thrust = thrust + static thrust

36
Q

Jet engine thrust

A

T = m • (Vout - Vin)

  • T = thrust*
  • m = mass flow [kg/s]*
  • Vout = exhaust nozzle gas velocity [m/s]*
  • Vin = true airspeed [m/s]*
37
Q

Hennings formula

A

base of CU = spread • 400

base of CU = base of cumulus cloud [ft]

38
Q

True height

(compared to ISA)

A

Δhtrue = ΔhISA • (1 + 0.004 • ΔISA)

  • Δhtrue = true height [ft]*
  • ΔhISA = height in ISA atmosphere [ft]*
  • ΔISA = ISA deviation [°C]*
39
Q

1 bar = ? hPa = ? PSI

A

1 bar = 1000 hPa = 14.51 PSI

40
Q

1 kg = ? lb

A

1 kg = 2.2 lb

41
Q

1 sm = ? km

A

1 sm = 1.609 km

42
Q

T°C ⇔ T°F

A

T°F = T°C • 1.8 + 32

T°C = (T°F - 32) ÷ 1.8

43
Q

Total air temperature

A

TAT = SAT • (1 + 0.2 + Kr + M2)

  • TAT = total air temperature [K]*
  • SAT = static air temperature [K] (= OAT)*
  • Kr = recovery factor*
  • M = Mach number*
44
Q

Under-/overshoot for turning errors

(rule of thumb)

A

Under-/overshoot by (bank angle + lat°) ÷ 2

(UNOS)

45
Q

Apparent wander

A

apparent wander = 15° • sin(lat°)

apparent wander in degrees per hour

46
Q

Transport wander

A

transport wander = chlong • sin(mean lat°)

  • transport wander in degrees (total)*
  • chlong = change in longitude [x°]*
47
Q

Capacitance

A
  • C = capacitance [F] (Farads)*
  • q = charge [coulomb]*
  • U = voltage [V]*
  • e = dielectric permittivity [F/m] (Farads per meter)*
  • A = area of plates [m2]*
  • d = distance between plates [m]*
48
Q

Work and power

A

P = T • Ω

P = T • n

P = work done/time

  • P = power [W]*
  • T = torque [Nm]*
  • Ω = angular velocity [radians/s]*
  • n = RPM*
49
Q

Electromotive force

(thermocouple)

A

E = K • Th

  • E = electromotive force*
  • K = contstant*
  • Th = hot junction temperature*
50
Q

Line of sight

A
  • Line of sight = range of antenna [NM]*
  • htransmitter = height of transmitter [ft]*
  • hreceiver = height of receiver [ft]*
51
Q

Frequency

A

f = 1/T

  • f = frequency [Hz]*
  • T = cycle duration [s]*
52
Q

Wavelenght

A

λ = c/f

  • λ = wavelenght [m]*
  • c = speed of light [m/s] (300 000 000 m/s)*
  • f = frequency [Hz]*
53
Q

Range of NDB

(over land and water)

A
  • range [NM]*
  • P = power [W]*
    • over land: if range • 2, power • 4 (22) -*
54
Q

Length of dipole antenna

A

l = ½ • λ

  • l = length of dipole antenna [m]*
  • λ = wavelenght [m]*
55
Q

Slant range

A
  • Pythagoras*
  • make sure to use same unites for all three variables.*
56
Q

PRF

A
  • PRF = pulse repetition frequency [pps] (pulse PAIRS per second)*
  • range in [km]*
57
Q

Scale

A

use equal units

58
Q

Chart convergence

A

CC = chlong • sin(Po)

  • CC = chart convergence [x°]*
  • chlong = change in longitude [x° (degrees)]*
  • Po = parallel of origin*
    • same formula as earth convergence -*
59
Q

Constant of cone

A

cone = sin(Po)

Po = parallel of origin

60
Q

Load factor in climb/descent

A

n = cos(γ)

  • n = load factor*
  • γ = climb/descent angle [x°]*
61
Q

Aquaplaning speed

A

p = pressure [PSI]

62
Q

Load factor change with gusts (speed change)

A
  • n = load factor in disturbance*
  • Vnew = speed after disturbance*
  • Vold = speed in straight and level flight*
63
Q

Grid track

A

GT = TT +/- conv

GT = MT +/- griv

  • GT = grid track [x°]*
  • TT = true track [x°]*
  • MT = magnetic track [x°]*
  • conv = convergence [x°] (west = - , east = +)*
  • griv = grivation [x°]*
64
Q

Grivation

A

grivation = convergence + variation

65
Q

QDM/QUJ

A

QDM = MH + RB

QUJ = TH + RB

  • QDM = magnetic bearing to station [x°]*
  • QUJ = true bearing to station [x°]*
  • MH = magnetic heading [x°]*
  • TH = true heading [x°]*
  • RB = relative bearing [x°]*
66
Q

Convergence

(grid nav)

A

convergence = chlong

chlong = change in longitude from datum meridian to position [x°]

67
Q

Time conversion (x°/h)

A

15°/h

1°/ 4 min

68
Q

Specific air range

A
  • SAR = specific air range [NM]*
  • SFC = specific fuel consumption [kg/h]*
  • TAS = true airspeed [kt]*
69
Q

1 imp gal = ? US gal = ? l

A

1 imp gal = 1.2 US gal = 4.55 l

70
Q

1 US gal = ? l

A

1 US gal = 3.8 l

71
Q

Moment

A

M = F • a

  • M = moment [Nm]*
  • F = force [N]*
  • a = arm [m]*
72
Q

Point of equal time

A
  • d = distance to PET*
  • D = total distance*
  • GSR = groundspeed return*
  • GSout = groundspeed continuous (outbound)*
73
Q

Point of safe return

A
  • tout = time to PSR*
  • safe endurance = time to fly to alternate with holding*
  • → T/O fuel - min. reserve fuel → convert to time*
  • GSR = groundspeed return (with OEI TAS if applicable)*
  • GSout = groundspeed continuous (outbound)*
74
Q

Pole pairs

A
  • n = RPM*
  • f = frequency [Hz]*
  • P = number of pole PAIRS*
75
Q

Density altitude

A

DA = PA + ( 120 • ΔISA )

  • DA = density altitude*
  • PA = pressure altitude*
  • ΔISA = ISA deviation*
76
Q

NM ⇔ NAM

A

Cross multiplication (e.g. GS = NM • TAS ÷ NAM)

see attachement

77
Q

1 inch = … cm

A

1 inch = 2.54 cm

ATPL(A) Commonly used formulas (2 decks)

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