The 60-1 rule is a rule of thumb that allows pilots to quickly correlate angles and distances. In mathematical terms, the 60-1 rule states that at a radius of 60 units from a center, a change in 1° is equal to a distance of 1 unit. ![[60-1 rule derivation.png]] ## Using Circumference A circle with a radius of 60 has a circumference of 376.991 $ 2\pi60=376.991 $ Dividing this by 360° gives the arc distance of 1° $ \frac{376.991}{360°}=1.047198 $ ## Using the Law of Cosines To calculate the straight-line distance between two points an equal distance from a center, the law of cosines (isosceles case) can be used. At 1° and a radius of 60: $ \sqrt{2(60)^2(1-\cos(1°))}=1.047184 $ ## Using a Right Triangle To find the shortest distance between a point and a radius, a right triangle can be used: $ 60\sin(1°)=1.047144 $ ## In all three cases, **the error is ~4.7%** - not mathematically perfect, but good enough when a quick, rough estimate is required. # Applications ## VOR Distance Off Course The 60-1 rule can be used to estimate distance off course when navigating using VORs: $ \frac{d}{60}*x=error $ where - $d$ is the distance from the station - $x$ is the angular deviation from the desired course (degrees off course) ### Example 15nm away from the VOR, the pilot notices the CDI indicates 2° off course. $ \frac{15}{60}*2°=0.5 $ The aircraft is 0.5nm off course. ## DME Arc Distance The distance flown during a DME arc is a portion of the arc's circumference, so the 60-1 rule can be used to estimate the distance covered during an arc: $ \frac{d}{60}*x=distance $ where - $d$ is the arcing distance - $x$ is the angular arc distance, or degrees of arc (*difference in starting and ending radials*) Put another way, each 60° of arc, the aircraft will cover a distance equal to the arcing distance ### Example ![[KSAF VOR RWY 33.png]] A pilot will be flying the 7 DME arc on the VOR RWY 33 approach at KSAF. $ \frac{7}{60}*(255°-154°)=11.8nm $ The aircraft will cover 11.8nm on the 7 DME arc. ## Turn Lead If a pilot is proficient in [[Estimating Turn Lead]], the 60-1 rule will allow the pilot to covert lead distance to CDI deflection: $ \frac{60}{d}*y=lead $ where - $y$ is the lead distance, in nautical miles - $d$ is the distance from the station - $lead$ is the CDI deflection, in degrees, to lead the turn ### Example In the example at KSAF above, the pilot is flying the approach at approximately 120 KTAS in light winds. There is no lead radial depicted on the approach chart; the pilot estimates a 0.6nm lead to turn 90° upon completing the arc to join the 334° course inbound. $ \frac{60}{7}*0.6=5.1° $ The pilot should lead the turn by ~5°, or half-scale deflection of the CDI. ## Climb/Descent Angle and Gradient A nautical mile is ~6076ft, so a climb or descent angle of 1° corresponds to approximately 100ft/nm. This can be particularly useful in the absence of a published VDP. $ 100x=g $ where - $x$ is the climb or descent angle - $g$ is the climb or descent gradient, in ft/nm ### Example In the example at KSAF above, there is a published vertical descent angle of 3.33°. $ 100*3.33°=333ft/nm $ The pilot should plan to descend approximately 340ft/nm; or 700ft/min, if the groundspeed is approximately 120kts. ### By Kevin Sakson