Pilot Rules of Thumb

Pilots carry a small set of approximations that turn awkward trigonometry into mental arithmetic: how far off track an angle puts the aircraft, what rate of descent holds a 3° path, where to start down, how much bank a rate-one turn needs and how much of the wind blows across the runway. Each trades a little accuracy for an answer in seconds, without a calculator and without looking away from the instruments for long.

The rules run through the whole syllabus. EASA PPL, CPL and ATPL papers and the FAA knowledge tests ask for them with the word "approximately", and airline crews use them to check the flight management system, whose answers are only as good as what was typed into it.

Why rules of thumb

A rule of thumb is a gross-error check, not a replacement for the chart, the flight computer or the FMS. Its value is speed and independence. A pilot who expects about 700 ft/min on final notices at once a vertical speed of 1,200 ft/min, and one who expects the top of descent about 100 NM out questions a computed point at 60 NM. Mental estimates also keep the pilot ahead of the airplane when the workload is high or the automation has failed.

Most of the rules rest on three facts:

• A radian is about 57.3°, close to 60°. An angle of 1° subtends about one sixtieth of the distance: the 1-in-60 rule.
• A nautical mile is about 6,076 ft, close enough to 6,000 for mental arithmetic. One degree of path angle is therefore about 100 ft per NM.
• Groundspeed divided by 60 gives nautical miles per minute. At 120 kt the aircraft covers 2 NM a minute; at 90 kt, 1.5 NM.

The 1-in-60 rule

The 1-in-60 rule states that an angle of 1° subtends about 1 NM at a distance of 60 NM. In general, the displacement is about the angle × distance ÷ 60, and the angle is about the displacement × 60 ÷ distance. Its uses are many:

• Track error. Four nautical miles right of track after 30 NM is a track error of 4 × 60 ÷ 30 = 8°. To reach the destination 60 NM further on, a closing angle of 4 × 60 ÷ 60 = 4° is added, so the heading is altered 12° left (see dead reckoning and visual navigation).
• Radio navigation. On a CDI where one dot is 2°, one dot at 45 NM from a VOR is 2 × 45 ÷ 60 = 1.5 NM off the radial. At 100 NM, the edge of an airway 5 NM wide each side is 3° off the centerline, 1.5 dots.
• DME arcs. Each degree of arc is one sixtieth of the radius, so moving from the 090 to the 095 radial on a 15 DME arc covers about 1.25 NM.
• Drift. The maximum drift in degrees is about 60 × wind speed ÷ TAS, and the drift for any wind about 60 × crosswind component ÷ TAS. A 15 kt wind across the track at a TAS of 90 kt gives about 10°. To make good 360° at 100 kt with the wind from 270° at 20 kt, the heading is about 348° (see triangle of velocities).
• Vertical paths. One degree is about 6,000 ÷ 60 = 100 ft per NM, so a 3° path descends roughly 300 ft per NM. A climb gradient of 1% is about 60 ft per NM.

Rate of descent for a 3° glide path

Most ILS glide paths, PAPIs and published descent angles are about 3°. Exactly, a 3° glide path descends about 318 ft per NM, a gradient of 5.2%, or roughly 1 in 19. The rate of descent needed to hold it is the height lost per NM multiplied by the NM flown per minute: about 300 × groundspeed ÷ 60, or five times the groundspeed in knots. Half the groundspeed times ten gives the same answer.

The rule depends on groundspeed, not indicated airspeed. A headwind on final reduces the rate needed, and a tailwind increases it: an airplane approaching at 140 kt with a 20 kt tailwind needs about 850 ft/min, close to the 1,000 ft/min that common stabilized approach criteria allow.

The same arithmetic works for any gradient: the vertical speed in ft/min is about the gradient in percent multiplied by the groundspeed in knots. A departure requiring 300 ft per NM, about 5%, needs 500 ft/min at 100 kt groundspeed; one requiring 350 ft per NM needs 700 ft/min at 120 kt. FAA terminal procedure books print a table that does the conversion.

A height check on final uses the same figure in reverse: about 300 ft of height for each NM to the touchdown point, so a 3° path is 1,500 ft above the runway about 4.7 NM from touchdown. Charts often add a table of distances and altitudes, which takes precedence over any mental estimate (see continuous descent final approach).

Top of descent and descent planning

The top of descent (TOD) is the point at which the descent from cruise must begin. The planning rule is 3 NM for every 1,000 ft to lose, the 3:1 rule: from FL350 to sea level, 35 × 3 = 105 NM. It equals about 333 ft per NM, a little steeper than 3°, and lies within the gradient window of 250 to 350 ft per NM that the FAA's AIM gives for a fuel-efficient descent.

The basic figure then needs two corrections:

• Deceleration. Distance must be added to slow down to the approach speed. For the A320, Airbus guidance gives a mean deceleration of about 10 kt per NM in level flight, with the flaps extended progressively.
• Wind. A tailwind carries the aircraft further for each 1,000 ft lost, so TOD moves further out; a headwind brings it closer. The correction is about the wind component × descent time ÷ 60: a 20-minute descent with a 30 kt tailwind needs about 10 NM more.

In the descent, the same rule checks the profile. Thousands of feet still to lose, multiplied by 3, should roughly equal the track miles to go. With fewer miles than that, the aircraft is high and needs drag or more distance; with more, it is low.

A light airplane usually descends at a chosen rate rather than at idle, and the arithmetic uses time. From FL100 to 2,000 ft at 500 ft/min takes 16 minutes, which at a groundspeed of 120 kt is 32 NM. At 500 ft/min and 120 kt every 1,000 ft takes 4 NM. The commonest error is to plan the descent to sea level instead of to the altitude where it ends: from 9,000 ft to 3,000 ft at 500 ft/min and 150 kt the descent needs 30 NM, not 45 (see climb and descent planning).

Turn radius and rate-one bank angle

A rate-one turn, called a standard rate turn by the FAA, is 3° per second: 180° in one minute and 360° in two. Rate two is twice as fast. The bank angle that produces rate one grows with true airspeed, and two rules estimate it:

• European texts: TAS ÷ 10 + 7.
• The FAA's Instrument Flying Handbook: TAS ÷ 10, plus half of that, which is 15% of the TAS.

Fast aircraft cannot turn at rate one without steep bank, so procedures cap it. ICAO holding procedures use 25° of bank or 3° per second, whichever needs less bank, which means 25° and a slower turn above about 170 kt TAS. The FAA's AIM uses 3° per second, 30° of bank, or 25° with a flight director, again whichever needs the least.

The turn radius of a rate-one turn is about TAS ÷ 200 in nautical miles; the exact divisor is about 190, so a rate-one turn at 360 kt has a radius of about 1.9 NM. At a constant bank angle the radius grows with the square of the true airspeed: double the speed and the turn needs four times the room. For any bank, the radius in feet is about V² ÷ (11.3 × tan φ), with V the TAS in knots, so at 45° it is simply V² ÷ 11.3, about 885 ft at 100 kt. The AIM gives a circling example at 165 kt groundspeed: a radius of 4,194 ft at 30° of bank and 6,654 ft at 20°.

The radius tells a pilot when to start a turn. To roll out on a track 90° from the present one, the turn begins about one radius before reaching it, about 1 NM at 180 kt in a rate-one turn (see turning flight).

Crosswind and headwind estimates

Every wind estimate starts with the angle between the wind and the runway or track, both referenced to the same north; tower winds and runway designators are both magnetic. The crosswind component is the wind speed × the sine of that angle, and the headwind component the wind speed × its cosine.

The clock code turns the sine into a fraction: read the angle as minutes past the hour. Fifteen degrees gives a quarter of the wind, 30° a half, 45° three quarters and 60° or more the whole wind. The headwind component is about nine-tenths of the wind at 30°, seven-tenths at 45° and half at 60°.

On runway 27 with a wind of 240° at 20 kt, the angle is 30°, so the crosswind is 10 kt and the headwind about 17 kt. With 200° at 25 kt the angle is 70°: the clock code says the whole 25 kt is crosswind, the exact figure is about 23 kt, and against a 17 kt limit both answers rule the runway out. A related rule warns about tailwind on takeoff: a tailwind of 10% of the lift-off speed increases the takeoff distance by about 20%, 21% in the FAA's PHAK, while a headwind of the same size shortens it by only about 19% (see wind components and crosswind limits).

Other rules worth knowing

The background to these rules is in density altitude, altimeter settings, altitude and height and aquaplaning.

Limits of the approximations

Every rule above rests on an approximation, and each has a range where it holds:

• Small angles. Because a radian is 57.3°, not 60°, the 1-in-60 rule overstates angles by about 5% even when they are small, and the error grows with the angle: at 20 NM off in 60 NM the rule gives 20°, the true angle 18.4°.
• Descent rates. Five times the groundspeed is about 6% low, and the 3:1 rule is slightly steeper than 3°. Both ignore deceleration and wind until they are added.
• Bank angles. TAS ÷ 10 + 7 overstates the bank at light-aircraft speeds and understates it above about 150 kt; the 15% rule is accurate at low speed and overstates the bank above about 150 kt.
• Crosswind. The clock code overstates the crosswind between 30° and 90° and does not give the headwind, which must come from the cosine.
• Density altitude and TAS. Both rules read high. The exact density altitude at 5,000 ft and ISA +25 is about 7,800 ft, not 8,000; at 10,000 ft in the standard atmosphere TAS is about 16% above CAS, not 20%.

Most errors come from the inputs rather than the rules: indicated airspeed used where groundspeed or TAS belongs, the ISA deviation taken from 15 °C instead of the ISA temperature at the altitude, a true wind applied to a magnetic runway. When a rule of thumb and the system disagree by more than the rule's own error, the pilot finds out why before trusting either.

Library articles are written for study and exam preparation. They do not replace your aircraft's approved documentation, your operator's procedures or the regulations themselves.