AROTA
Navigation
En-route planning in your head
Reciprocal heading
Add 2 to the 1st digit, subtract 2 from the 2nd digit
OR
Subtract 2 from the 1st digit, add 2 to the 2nd digit
This rule of thumb helps us to quickly get the reciprocal of a heading. It is especially useful for non-standard holdings or making 180 degree turns. Headings are in the form of 3 digits (XXX) up to 360 degrees. For smaller headings: + 2 to 1st digit, - 2 from 2nd digit For larger headings: - 2 from 1st digit, + 2 to 2nd digit The 3rd digit always remains the same. Example: A heading of 336 has a reciprocal of 156. To get the first digit, 3 - 2 = 1. To get the second digit, 3 + 2 = 5. The 3rd digit always remains the same. After just a few practice runs, you can get the hang of getting reciprocal headings in a heartbeat.
Perpendicular heading
Subtract 1 from the 1st digit, add 1 to the 2nd digit
OR
Add 1 to the 1st digit, subtract 1 from the 2nd digit
Like the rule above, we can deduce the heading that is perpendicular to our current heading. The condition is that if it is a left perependicular, you will need to subtract - 1 from the first digit, if it is a right perpendicular, you need to add +1 to the first digit. Example: If you are flying at a heading of 220, the left perpendicular is 130 (-1+1), and the right perpendicular is 310 (+1-1). The 3rd digit always remains the same. For headings less than 100, the starting digit would be 0 but the rule still applies. The 1st digit would revert to 3. Example: A 030 heading will have a left perpendicular of 340 (-1+1) This is also true for headings more than 300, the first digit would revert to 0 for right perpendiculars.
Turning errors in a magnetic compass
If you are flying at a latitude of X degrees, you should undershoot/overshoot turns by 15 + X/2 degrees (While turning towards northerly or southerly headings)
This rule of thumb is for the traditional liquid magnetic compass which are usually a standby instrument for most modern aircraft. The magnetic compass has a turning error when an aircraft turns towards a northerly or southerly heading. A good acronym is UNOS, which stands for: Undershoot north, overshoot south (In the northern hemisphere. It is ONUS in the southern hemisphere) Example: The aircraft is flying at a latitude of 45°N. The amount of lead or lag you should make before stopping the turn at your desired heading would be ≈ 15 + 45/2 ≈ 37°. Let's say you started a turn to the south, desired heading of 180°. You should overshoot your target heading by 37°, which means that when you stop turning at 217°, the compass will restabilize after a few seconds and the indicator will point to the desired heading of 180°.
1 in 60 rule for drift angle/error
For an airplane that has travelled 60 NM, a 1NM drift/error off track approximates a 1 degree error in heading
If rule of thumbs in aviation had a father, it would be the 1 in 60 rule Example: An airplane flying a leg of 120 NM finds that after travelling 60 NM, it is 2 NM to the right of track. A correction of 4° to the left (2° to fly parallel to the intended track and another 2° to bring them to their target) will bring the airplane to the destination. *Tip: Convert or round the distance travelled to the nearest 60th. Example 1: 30NM travelled, 4NM off track: 60/30 x 4 = 8° off track. Example 2: 90NM travelled, 7NM off track: 60/90 x 7 = 2/3 x 7° ≈ 5° *The math behind the 1 in 60 rule has a 5% error rate, but practically useful for simplicity
1 in 60 rule for nautical miles per minute
(Speed Number)
Speed | 90 | 120 | 150 | 180 | 210 | 240 | 270 | 300 |
|---|---|---|---|---|---|---|---|---|
Speed number | 1.5 | 2 | 2.5 | 3 | 3.5 | 4 | 4.5 | 5 |
Knowing how far you would fly per minute is good for situational awareness especially during radar vectoring. Example: A ground speed of 180 knots covers 180 NM in 60 mins, so therefore in one min = 180 ÷ 60 = 3NM. Speed number is also handy for other rule of thumbs, such as finding WCA max and descent rates.
1 in 60 rule for climb & descent angle (°)
1 degree of climb/descent over 1NM ≈ 100 ft/NM
For every degree angle the aircraft climbs or descends, it would cover 100ft per NM. According to the 1 in 60 rule: 1 degree of a 60 NM arc is 1 NM. 1NM = 6076 ft Therefore, 1 degree of a 60 NM arc is also 6076 ft Hence we can come to the conclusion that 1 degree of a 1 NM arc is approximately 6076 ÷ 60 ≈ 100ft
1 in 60 rule for climb & descent gradients (%)
1% gradient over 1NM ≈ 60 ft/NM
When converting between degrees and percentages, the simplified formula is: Climb/descent angle (°) ≈ climb/descent gradient (%) x 0.6 or Climb/descent gradient (%) ≈ climb/descent angle (°) ÷ 0.6 *The math behind this is not entirely accurate but practical The real math: Glideslope (%) = Change in vertical (y) axis ÷ change in horizontal (x) axis = rise ÷ run This means for a 1% gradient, for every 100ft you move along the horizontal (x), you will move 1 ft down vertically (y). For a 5% gradient, for every 100ft you move along the horizontal (x), you will move 5 ft down vertically (y), etc. Example: Aircraft expects to climb at a gradient of 4% after take-off, and there is an obstacle 500m past the runway with a height of 8m. Height at 500m horizontal distance = 500 ÷ 0.04 = 20m. If the aircraft climbs with 4% gradient, it will be 20m high after reaching a horizontal distance of 500m, and it can clear the 8m obstacle with a clearance of 12m.
1 in 60 rule for vertical speed
Vertical speed = Angle (°) x Speed number (NM/min) x 100
Vertical speed = Gradient (%) x Speed number (NM/min) x 60
By utilizing both of the previous ROTs as described above, we can deduce the vertical speed required for any descent angle/gradient for any ground speed. Example: If the aircraft is to descend at 4° at a ground speed of 120 knots: The required vertical speed = 4 x (120 ÷ 60) x 100 = 800 FPM A 4° angle gives a 6.7% gradient (4 ÷ 0.6). The required vertical speed = 6.7 x (120 ÷ 60) x 60 ≈ 800 FPM
1 in 60 rule for descent planning
Descent angle = Altitude to lose (In flight levels) ÷ Distance (NM)
Another useful application of the 1 in 60 rule is to quickly find out the gradient of descent before descending towards a navigation point. Example: You are cruising at FL 280 ATC instructs you to descend to 10,000 ft overhead a point 9 NM away. Descent angle = (280 - 100) ÷ 9 = 2 degrees. By descending the aircraft at a profile of 2 degrees, the aircraft will approximately be at 10,000 ft after 9 NM.
Top of Descent (3°): Altitude in feet (ft) or Flight Levels (FL)
Distance to begin descent (NM) = Altitude ÷ 300
Distance to begin descent (NM) = Flight levels ÷ 3
OR
Distance to begin descent (NM) = Altitude in thousands x 3
We can use this ROT to approximate the distance to begin a descent towards a specified point at a specified altitude or flight level for a 3° descent Example: You are cruising at 20,000 ft towards a navigation point. You need to be at 2,000 ft overhead that point. At what distance before that point should you commence a descent? Top of descent = (20,000 - 2,000)/300 = 18,000/300 = 60 NM If you start a descent at approximately 60NM before the navigation point, you will be at 2,000ft once you reach it. It works the same way for flight levels (FL). Example: FL 200 - FL 020 = FL 180 180/3 = 60 Using the other method, (Altitude in thousands x 3) is more or less the same. Altitude to lose in thousands = 18 Top of descent = 18 x 3 = 54 NM Both methods are approximately the same and are practical enough for a 3° descent.
Rate of Descent for a 3° descent gradient
Rate of descent 3° (ROD) = Ground speed x 5
OR
Rate of descent 3° (ROD) = Ground speed ÷ 2 x 10
Descending at 3 degrees is very common, especially because most ILS glideslopes are calibrated as such. Example: If you are descending at 540 knots ground speed, the required ROD for a 3 degree descent = 540 x 3 = 1620 ft/min. Tying it all together: We are expecting to perform an arrival. The expected last enroute way point is 'BANAN'. We are supposed to overfly a VOR 'VTK' at FL220 (maximum). Currently, our aircraft is on cruise flight level FL360 inbound BANAN 50NM at 450KT ground speed. Using the ROTs previously and above, we need to descend (360 - 220)/3 = 47NM before 'VTK'. So we program the aircraft to start a descent 3NM after 'BANAN' (50 - 47). To acheive the descent rate, we simply multiply 450 x 5 to get 2250ft/min. This is a practical example of the ROTs involved in descent planning
Top of Descent (2.5°): Altitude in feet (ft) or Flight Levels (FL)
Distance to begin descent (NM) = Altitude ÷ 250
Distance to begin descent (NM) = Flight levels ÷ 2.5
OR
Distance to begin descent (NM) = Altitude in thousands x 4
We can use this ROT to approximate the distance to begin a descent towards a specified point at a specified altitude or flight level for a 2.5° descent Example: You are cruising at 20,000 ft towards a navigation point. You need to be at 2,000 ft overhead that point. At what distance before that point should you commence a descent? Top of descent = (20,000 - 2,000)/250 = 18,000/250 = 72 NM If you start a descent at approximately 72NM before the navigation point, you will be at 2,000ft once you reach it. It works the same way for flight levels (FL). Example: FL 200 - FL 020 = FL 180 180/2.5 = 72 Using the other method, (Altitude in thousands x 4) is more or less the same. Altitude to lose in thousands = 18 Top of descent = 18 x 4 = 72 NM Both methods are approximately the same and are practical enough for a 2.5° descent.