Crosswind component
Wind 25 kt at 40° off the runway heading.
XWC = wind speed × sin(angle)
- Keys
- 25 * 40 sin =
- Screen
- 16.07 kt
Worked examples on the SENASA exam calculator
The formulas you type most in the pilot theory exams, solved key by key on the exam calculator. The results are not typed by hand: they are computed by the same engine we checked against the official calculator, so they are what you will see on the screen. Press «Try it» and the sequence types itself on the calculator.
The data in each example is made up and the factors (27 ft/hPa, 120 ft/°C, 101.3, 3.785…) are the usual ones: always use those your question gives you. This is calculator-handling practice, not a syllabus.
Wind
Headwind component
Same wind: 25 kt at 40°.
HWC = wind speed × cos(angle)
- Keys
- 25 * 40 cos =
- Screen
- 19.15 kt
Wind correction angle (WCA)
Crosswind of 16 kt with a TAS of 120 kt. Division first, then = and finally asin.
sin(WCA) = XWC ÷ TAS
- Keys
- 16 / 120 = asin
- Screen
- 7.6623 °
TRAP: adding the WCA to the track in the same operation
Track 270° plus the WCA above. If asin ends up as the second number of the addition, the calculator glues the numbers together.
Heading = track + WCA
- Keys
- 270 + ( 16 / 120 ) asin =
- Screen
- 2707.6623 · Correct: 277.6623 °. The exam calculator gives this wrong result with no warning.
- Safe way
- 16 / 120 = asin + 270 = → 277.6623 °
Ground speed with a headwind
TAS 120 kt and the earlier 25 kt wind at 40°. The headwind component is subtracted.
GS = TAS − wind speed × cos(angle)
- Keys
- 120 - 25 * 40 cos =
- Screen
- 100.85 kt
Navigation
Flight time in minutes
187 NM at a GS of 142 kt.
minutes = distance ÷ GS × 60
- Keys
- 187 / 142 * 60 =
- Screen
- 79.014084507 min
1 in 60 rule
4 NM off track after 50 NM.
track error = distance off × 60 ÷ distance gone
- Keys
- 4 * 60 / 50 =
- Screen
- 4.8 °
Departure
Change of longitude of 5° at latitude 45°.
departure (NM) = ch. long in minutes × cos(latitude)
- Keys
- 5 * 60 * 45 cos =
- Screen
- 212.13 NM
Convergency
Change of longitude of 20° at mean latitude 50°.
convergency = ch. long × sin(mean latitude)
- Keys
- 20 * 50 sin =
- Screen
- 15.32 °
Distance covered in a given time
35 minutes at a GS of 142 kt.
distance = GS × minutes ÷ 60
- Keys
- 142 * 35 / 60 =
- Screen
- 82.833333333 NM
Conversion angle
The same 20° change of longitude at mean latitude 50°: half the convergency.
CA = ch. long × sin(mean latitude) ÷ 2
- Keys
- 20 * 50 sin / 2 =
- Screen
- 7.66 °
Radius of turn
TAS 150 kt with 25° of bank. The square is done with x^2 and the tangent goes inside the brackets.
radius (ft) = TAS² ÷ (11.26 × tan(bank))
- Keys
- 150 x^2 / ( 11.26 * 25 tan ) =
- Screen
- 4285.275147 ft
Rate of turn
The same 150 kt and 25° of bank.
rate (°/s) = 1091 × tan(bank) ÷ TAS
- Keys
- 1091 * 25 tan / 150 =
- Screen
- 3.3915553333 °/s
Altimetry and atmosphere
Pressure altitude
Elevation 2300 ft and QNH 998 hPa, with 27 ft per hPa (use 30 if your question says so).
PA = elevation + (1013 − QNH) × 27
- Keys
- ( 1013 - 998 ) * 27 + 2300 =
- Screen
- 2705 ft
Density altitude
PA 5000 ft and ISA deviation +15 °C.
DA = PA + 120 × ISA deviation
- Keys
- 5000 + 120 * 15 =
- Screen
- 6800 ft
Local speed of sound (LSS)
Outside air temperature −40 °C. The sign goes AFTER the number, and the root after the =.
LSS = 38.95 × √(temperature in K)
- Keys
- 40 +/- + 273 = √x * 38.95 =
- Screen
- 594.5459465 kt
ISA temperature at an altitude
8000 ft. ISA falls 2 °C per 1000 ft from +15 °C.
ISA = 15 − 2 × (altitude ÷ 1000)
- Keys
- 15 - 2 * 8 =
- Screen
- -1 °C
ISA deviation
OAT of −10 °C at 8000 ft. The sign goes AFTER the 10 and ISA is worked out inside brackets.
deviation = OAT − ISA
- Keys
- 10 +/- - ( 15 - 2 * 8 ) =
- Screen
- -9 °C
Mach number
TAS 450 kt with a local speed of sound of 590 kt.
M = TAS ÷ LSS
- Keys
- 450 / 590 =
- Screen
- 0.7627118644
Performance and fuel
Fuel from US gallons to kg
45 US gal with specific gravity (SG) 0.72.
kg = US gal × 3.785 × SG
- Keys
- 45 * 3.785 * 0.72 =
- Screen
- 122.634 kg
Climb gradient
Rate of climb 900 ft/min at a GS of 110 kt.
gradient % = ROC ÷ (GS × 101.3) × 100
- Keys
- 900 / 110 / 101.3 * 100 =
- Screen
- 8.076819528 %
TRAP: fuel remaining in a single chain
200 kg on board, burn of 12 kg/min for 3.5 min and 15 kg taxi fuel. The calculator groups the subtraction wrongly.
remaining = on board − burn × time − taxi
- Keys
- 200 - 12 * 3.5 - 15 =
- Screen
- 173 · Correct: 143 kg. The exam calculator gives this wrong result with no warning.
- Safe way
- 200 - ( 12 * 3.5 ) - 15 = → 143 kg
Endurance in minutes
180 kg of usable fuel at a burn of 42 kg/h.
minutes = fuel ÷ burn × 60
- Keys
- 180 / 42 * 60 =
- Screen
- 257.14285714 min
Specific range
GS 140 kt at a burn of 42 kg/h.
NM per kg = GS ÷ burn
- Keys
- 140 / 42 =
- Screen
- 3.3333333333 NM/kg
Fuel required with contingency and final reserve
Trip fuel 95 kg, 5 % contingency and 30 min final reserve at 42 kg/h.
total = trip × 1.05 + burn × 0.5
- Keys
- 95 * 1.05 + 42 * 0.5 =
- Screen
- 120.75 kg
Rate of descent for a 3° glide path
GS 120 kt on approach.
ROD (ft/min) = GS × tan(3°) × 101.3
- Keys
- 120 * 3 tan * 101.3 =
- Screen
- 636.9744 ft/min
Mass and balance
Centre of gravity using the memory
Three masses (650, 80 and 120 kg) with arms 2.1, 2.4 and 3.0 m. Each moment is added to memory with M+ and the total is divided by the total mass (850 kg).
CG = total moment ÷ total mass
- Keys
- MC 650 * 2.1 = M+ 80 * 2.4 = M+ 120 * 3 = M+ MR / 850 =
- Screen
- 2.2552941176 m
Centre of gravity as % MAC
CG at 3.25 m, leading edge of the MAC (LEMAC) at 2.9 m and MAC of 1.4 m.
%MAC = (CG − LEMAC) ÷ MAC × 100
- Keys
- ( 3.25 - 2.9 ) / 1.4 * 100 =
- Screen
- 25 %
Mass to shift to move the CG
Total mass 850 kg, the CG must move 0.05 m and the load is shifted 2.1 m.
mass to move = total mass × ΔCG ÷ shift distance
- Keys
- 850 * 0.05 / 2.1 =
- Screen
- 20.238095238 kg
New CG after adding a load
850 kg with CG at 3.25 m; 70 kg are added at arm 4.1 m.
new CG = (M × CG + m × arm) ÷ (M + m)
- Keys
- ( 850 * 3.25 + 70 * 4.1 ) / ( 850 + 70 ) =
- Screen
- 3.314673913 m
Practise until it is automatic
Repeat each sequence on the calculator with the «Study helper» on and, once you can do them without looking, switch to «Exam mode». If you want to know why the two traps fail, they are explained in every quirk of the official calculator.