Formulas

Question 1

Rate of turn

Answer 1

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

Question 2

Radius

Answer 2

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

Question 3

Bank angle

Answer 3

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

Question 4

Load factor in turn

Answer 4

• n_T = load factor in turn*
• φ​ = bank angle [x°]*

Question 5

Load factor

Answer 5

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

Question 6

Distance to climb

Answer 6

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

Question 7

Time to climb

Answer 7

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

Question 8

Ground gradient (FPG)

Answer 8

• 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]*

Question 9

Climb gradient alternatives

Answer 9

• 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]*

Question 10

Rate of climb

Answer 10

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]*

Question 11

Climb gradient

Answer 11

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

Question 12

New stall speed with changing mass/weight

Answer 12

• V_{s new} = new stall speed [kt]*
• V_{s old} = old stall speed [kt]*
• W_new = new weight [N] (can be mass [kg])*
• W_old = old weight [N] (can be mass [kg])*

Question 13

New stall speed with changing load factor

Answer 13

• V_s = stall speed [kt]*
• V_s1g = minimum speed where L = W (steady horizontal flight) [kt]*
• n = given load factor*

Question 14

Climb angle ↔ climb gradient

Answer 14

γ = tan^-1 (CG/100%)

CG = tan (γ) • 100%

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

Question 15

Lift formula

Answer 15

L = ½ • ρ • v² • S • C_L

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

Question 16

Circumference/area of a circle

Answer 16

C = 2 • π • r

A = π • r²

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

Question 17

Mach angle

Answer 17

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

Question 18

Mach number

Answer 18

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

Question 19

Local speed of sound

Answer 19

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

Question 20

Mass flow

Answer 20

mass flow = A • ρ • v

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

Question 21

Gas equation

Answer 21

p = ρ • R • T

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

Question 22

1 NM = ? km = ? ft

Answer 22

1 NM = 1.852 km = 6080 ft

Question 23

Runway slope

Answer 23

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

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

Question 24

Departure (GNAV)

Answer 24

dep = chlong • cos(lat°)

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

Question 25

Cross-/head-/tailwind components

Answer 25

**XWC = V_wind • sin(wa)** **HWC or TWC = V_wind • cos(wa)** * XWC = crosswind component* * HWC = headwind component* * TWC = tailwind component* * V_wind = wind speed (wind speed and components same unit)* * wa = wind angle [x°] (_never more than 90°_)*

Question 26

Earth convergence

Answer 26

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

Question 27

Conversion angle

Answer 27

**CA = ½ • EC** * CA = conversion angle [x°]* * EC = earth convergence [x°]*

Question 28

ILS glide path intercept height ## Footnote *(glide angle/gradient)*

Answer 28

**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*

Question 29

Rate of descent (GNAV) ## Footnote *(glide angle/gradient)*

Answer 29

**RoD = θ • 100• (GS/60)** **RoD = glide gradient • GS** * RoD = rate of descent [ft/min]* * θ = glide angle [x°]* * GS = groundspeed*

Question 30

Angle of bank in rate one turn ## Footnote *(rule of thumb)*

Answer 30

**Angle of bank in rate one turn = (TAS ÷ 10) + 7** * Angle of bank [x°]* * TAS = true airspeed [kt]* * Rate One Turn = 3°/s*

Question 31

Brake Horse Power

Answer 31

**BHP = T • RPM • constant** **BHP ~ T • RPM (~ = proportional)** * BHP = Brake Horse Power* * T = Torque [Nm]* * RPM = Revolutions per minute*

Question 32

Engine Pressure Ratio

Answer 32

*EPR = Engine Pressure _Ratio_*

Question 33

Bypass ratio

Answer 33

*see attachment*

Question 34

Jet engine static thrust

Answer 34

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

Question 35

Jet engine total thrust

Answer 35

**Net engine thrust = thrust + static thrust**

Question 36

Jet engine thrust

Answer 36

**T = m • (V_out - V_in)** * T = thrust* * m = mass flow [kg/s]* * V_out = exhaust nozzle gas velocity [m/s]* * V_in = true airspeed [m/s]*

Question 37

Hennings formula

Answer 37

**base of CU = spread • 400** *base of CU = base of cumulus cloud [ft]*

Question 38

True height ## Footnote *(compared to ISA)*

Answer 38

**Δh_true = Δh_ISA • (1 + 0.004 • ΔISA)** * Δh_true = true height [ft]* * Δh_ISA = height in ISA atmosphere [ft]* * ΔISA = ISA deviation [°C]*

Question 39

1 bar = ? hPa = ? PSI

Answer 39

1 bar = 1000 hPa = 14.51 PSI

Question 40

1 kg = ? lb

Answer 40

1 kg = 2.2 lb

Question 41

1 sm = ? km

Answer 41

1 sm = 1.609 km

Question 42

T_°C ⇔ T_°F

Answer 42

T_°F = T_°C • 1.8 + 32 T_°C = (T_°F - 32) ÷ 1.8

Question 43

Total air temperature

Answer 43

**TAT = SAT • (1 + 0.2 + K_r + M²)** * TAT = total air temperature [K]* * SAT = static air temperature [K] (= OAT)* * K_r = recovery factor* * M = Mach number*

Question 44

Under-/overshoot for turning errors ## Footnote *(rule of thumb)*

Answer 44

Under-/overshoot by **(bank angle + lat°) ÷ 2** ## Footnote *(UNOS)*

Question 45

Apparent wander

Answer 45

**apparent wander = 15° • sin(lat°)** *apparent wander in degrees per hour*

Question 46

Transport wander

Answer 46

**transport wander = chlong • sin(mean lat°)** * transport wander in degrees (total)* * chlong = change in longitude [x°]*

Question 47

Capacitance

Answer 47

* 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]*

Question 48

Work and power

Answer 48

P = T • Ω P = T • n P = work done/time * P = power [W]* * T = torque [Nm]* * Ω = angular velocity [radians/s]* * n = RPM*

Question 49

Electromotive force ## Footnote *(thermocouple)*

Answer 49

**E = K • T_h** * E = electromotive force* * K = contstant* * T_h = hot junction temperature*

Question 50

Line of sight

Answer 50

* Line of sight = range of antenna [NM]* * h_transmitter = height of transmitter [ft]* * h_receiver = height of receiver [ft]*

Question 51

Frequency

Answer 51

**f = 1/T** * f = frequency [Hz]* * T = cycle duration [s]*

Question 52

Wavelenght

Answer 52

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

Question 53

Range of NDB ## Footnote *(over land and water)*

Answer 53

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

Question 54

Length of dipole antenna

Answer 54

**l = ½ • λ** * l = length of dipole antenna [m]* * λ = wavelenght [m]*

Question 55

Slant range

Answer 55

* Pythagoras* * make sure to use same unites for all three variables.*

Question 56

PRF

Answer 56

* PRF = pulse repetition frequency [pps] (pulse _PAIRS_ per second)* * range in **[km]***

Question 57

Scale

Answer 57

*use equal units*

Question 58

Chart convergence

Answer 58

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

Question 59

Constant of cone

Answer 59

**cone = sin(P_o)** *P_o = parallel of origin*

Question 60

Load factor in climb/descent

Answer 60

**n = cos(γ)** * n = load factor* * γ = climb/descent angle [x°]*

Question 61

Aquaplaning speed

Answer 61

*p = pressure **[PSI]***

Question 62

Load factor change with gusts (speed change)

Answer 62

* n = load factor in disturbance* * V_new = speed after disturbance* * V_old = speed in straight and level flight*

Question 63

Grid track

Answer 63

**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°]*

Question 64

Grivation

Answer 64

**grivation = convergence + variation**

Question 65

QDM/QUJ

Answer 65

**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°]*

Question 66

Convergence | (grid nav)

Answer 66

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

Question 67

Time conversion (x°/h)

Answer 67

15°/h 1°/ 4 min

Question 68

Specific air range

Answer 68

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

Question 69

1 imp gal = ? US gal = ? l

Answer 69

1 imp gal = 1.2 US gal = 4.55 l

Question 70

1 US gal = ? l

Answer 70

1 US gal = 3.8 l

Question 71

Moment

Answer 71

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

Question 72

Point of equal time

Answer 72

* d = distance to PET* * D = total distance* * GS_R = groundspeed return* * GS_out = groundspeed continuous (outbound)*

Question 73

Point of safe return

Answer 73

* t_out = time to PSR* * safe endurance = time to fly to alternate with holding* * → T/O fuel - min. reserve fuel → convert to time* * GS_R = groundspeed return (with OEI TAS if applicable)* * GS_out = groundspeed continuous (outbound)*

Question 74

Pole pairs

Answer 74

* n = RPM* * f = frequency [Hz]* * P = number of pole _PAIRS_*

Question 75

Density altitude

Answer 75

**DA = PA + ( 120 • ΔISA )** * DA = density altitude* * PA = pressure altitude* * ΔISA = ISA deviation*

Question 76

NM ⇔ NAM

Answer 76

**Cross multiplication** (e.g. GS = NM • TAS ÷ NAM) ## Footnote *see attachement*

Question 77

1 inch = ... cm

Answer 77

1 inch = 2.54 cm