Other Applications of the 1 in 60 Rule

Viewed from the side, a glidepath is the familiar 1 in 60 triangle. Range is the adjacent side and height above the touchdown reference is the opposite side.

The height rule

At 1 NM, the working horizontal distance is 6000 ft. A 1 degree path changes height by about 100 ft over that distance. Therefore a path of Z degrees changes height by about 100Z ft per nautical mile.

Worked examples

On a 3 degree path at 4 NM, height = 3 x 100 x 4 = 1200 ft. On a 5.5 degree path at 3 NM, height = 5.5 x 100 x 3 = 1650 ft.

Unless the problem states an aerodrome elevation or threshold elevation to add, the result is a height above the touchdown reference. If elevation is supplied, add it only when the question asks for altitude.

A descent rate connects the vertical gradient with groundspeed. The aircraft must lose in one minute the height associated with the distance it covers in that minute.

Deriving the five-times rule

At 120 kt groundspeed, the aircraft covers 2 NM each minute. A 3 degree path loses 300 ft per NM, so it must lose 600 ft in that minute. The required rate of descent is 600 ft/min.

The factor five comes from 300 ft per NM divided by 60 minutes per hour. Use groundspeed, not TAS, because the path is defined relative to distance over the ground.

Any other path angle

First find the 3 degree result, then multiply by actual path angle divided by 3. At 100 kt on a 4 degree path, the 3 degree result is 5 x 100 = 500 ft/min. Correcting for angle gives 500 x 4 / 3 = 667 ft/min, normally rounded to about 670 ft/min.

To keep the same flightpath angle, vertical speed must change in the same sense as groundspeed. Faster groundspeed needs a greater magnitude of vertical speed.

Speed-change rule

If groundspeed decreases from 140 kt to 120 kt on a 3 degree path, reduce ROD by 5 x 20 = 100 ft/min. The original ROD was 700 ft/min and the new ROD is 600 ft/min.

For a path other than 3 degrees, multiply the 3 degree change by actual angle divided by 3. A reduction from 120 kt to 110 kt on a 5.5 degree path gives a 3 degree change of 50 ft/min, then 50 x 5.5 / 3 = 92 ft/min. Reduce the ROD by about 92 ft/min.

Climb gradients

The same geometry works upwards. A climb angle of 4 degrees produces approximately 400 ft of height gain per NM. At a groundspeed of 150 kt, the aircraft covers 2.5 NM each minute, so the rate of climb is about 400 x 2.5 = 1000 ft/min.

Two source calculations

A 5.5 degree path at 120 kt needs 5 x 120 x 5.5 / 3 = 1100 ft/min. A 3 degree path at 140 kt needs 5 x 140 = 700 ft/min.

A difference between the required VOR bearing and the bearing shown at a known DME range can be converted into an approximate lateral displacement.

Cross-track distance from angular error

An airway inbound course to a VOR/DME is 271 degrees magnetic. The RMI indicates QDM 266 degrees at 48 NM. The angular difference is 5 degrees. Distance off = 5 x 48 / 60 = 4 NM. The aircraft is right of the centreline.

In another source example, the desired airway is the 300 degree radial and the aircraft is on the 295 degree radial at 85 NM. The 5 degree angular difference gives 5 x 85 / 60 = 7.1 NM, approximately 7 NM from the centreline.

Slant range

DME normally indicates slant range. At long ranges and ordinary en-route heights, slant range is close enough to horizontal range for a rapid 1 in 60 estimate. Near the station at high altitude, the difference can be significant. Use horizontal range if the problem supplies it or requires precise lateral displacement.

ILS angular displacement

The localiser and glidepath are angular guidance systems. At greater range, a given angular deviation represents a larger linear displacement. At 30 NM, a 2 degree lateral angular error represents about 2 x 30 / 60 = 1 NM. At 6 NM the same angle represents about 0.2 NM.

When an aircraft flies at constant heading and observes a bearing change to a station, the distance flown between observations becomes the opposite side of another small-angle triangle.

Distance and Time

First convert groundspeed and elapsed time into distance flown. If the geometry is close to a right angle and the bearing change is small, range to the station is distance flown multiplied by 60, divided by the bearing change.

Oxford worked example

An aircraft tracks at 180 kt. Over 5 minutes it flies 15 NM. The QDM changes through a total of 5 degrees while the aircraft passes abeam. Range = 15 x 60 / 5 = 180 NM.

Flying a heading 90 degrees to the Navigation Aid

The most convenient observation is made near the station's wingtip bearing, with the aircraft track approximately perpendicular to the station. Small bearing increments such as 10 degrees reduce geometric error. Record the time at the first bearing and again after the selected change.

Flying a constant heading

A similar method can be used with an NDB while a constant heading is maintained. The heading itself is less important than keeping it constant. Problems normally provide the bearing change and either distance flown or true airspeed and elapsed time. The rapid formula is least reliable if many radials are crossed, if the track is not close to perpendicular, or if a course change occurs.

The rule can turn almost any small linear displacement into an angle, but the physical meaning of that angle still depends on the reference lines used.

Estimating drift or wind correction

If a reliable fix is 6 NM right of the air position after 60 NM of flight, the angular difference between the air vector and ground vector is about 6 degrees. This is an estimate of drift when the air-position line represents heading and TAS while the ground-position line represents track and groundspeed.

At 180 kt TAS with 5 degrees of drift, the estimated crosswind component is 180 x 5 / 60 = 15 kt. This is a component, not the complete wind. A headwind or tailwind component must be found from the along-track difference between TAS and groundspeed before the wind vector can be completed.

A single off-track fix by itself gives track error, not necessarily drift. Heading information is required before the angle between heading and track can be named drift.

VOR and ILS sensitivity

A short look at PNR and CP

The point of no return, PNR, is the farthest point from which an aircraft can return to base with the planned safe endurance. The critical point, also called the equal-time point or CP, is the point from which time to continue equals time to return. Both depend on outbound and homebound groundspeeds, so wind shifts the points even when total route distance is unchanged.

Chapter 25 derives the full PNR and CP formulae. At this stage, remember that 1 in 60 helps with angular or linear displacement, while PNR and CP are primarily time, distance and relative-speed problems.

These examples bring the chapter's equations together. Write the formula first, then substitute numbers and add the correct unit.

Glidepath height and ROD

Configuration and wind

An aircraft approaches on a 2.5 degree path at 220 kt TAS with a 10 kt headwind. Groundspeed is 210 kt, so ROD = 5 x 210 x 2.5 / 3 = 875 ft/min. If TAS reduces to 190 kt with the same wind, groundspeed becomes 180 kt and ROD becomes 750 ft/min. Reduce the ROD by 125 ft/min.

Radio-aid displacement and range

Additional distance-and-time checks

Flight log including navigation records

Enter revised wind, groundspeed and any associated time or fuel change in the flight log. At each checkpoint or turning point, record actual time over and revise the estimate for the next checkpoint. A correct mental calculation is only useful if the new heading, vertical speed or estimate is captured and acted upon.

Rate of Climb checks

Climbing 8000 ft in 20 minutes requires 400 ft/min. At 180 kt groundspeed, distance covered is 180 x 20 / 60 = 60 NM. A climb of 26,000 ft at 500 ft/min takes 52 minutes; at 248 kt groundspeed the distance covered is approximately 248 x 52 / 60 = 215 NM.

On a 600 NM route, a 30 minute climb at 160 kt covers 80 NM and a 20 minute descent at 180 kt covers 60 NM. The cruise distance is 460 NM. At 250 kt, cruise takes 1 hour 50 minutes, so total flying time is 2 hours 40 minutes.