Calculating Distance with the 60:1 Rule

Definitions

The 60:1 rule is a method that can be used to determine the distance to (or from) a radio navigation station (an ADF or VOR).

Objective(s)

Use the 60:1 rule to determine the distance to a VOR and ADF station.

Description

  1. Basis for the 60:1 rule
  2. Visualizing how the 60:1 rule is used
  3. What information is needed to apply the 60:1 rule
  4. Solving 60:1 rule problems

Instructional aids

None specified

Content

Basis for the 60:1 rule

At 60 NM from a station, you travel 1 NM for every radial (1 degree) that you cross. If you cross 3 radials, you have traveled 3 NM. For this to work, you must maintain a constant heading.

Visualizing how the 60:1 rule is used
  • The 60:1 rule allows you to formulate a proportion-type math problem: “If I was 60 NM from that station and I just crossed 10 radials, I would have traveled 10 NM. I don’t know how far I am from the station, but I do know I crossed 10 radials and I do know how much ground I covered while crossing those radials.”
  • The graphic below (click to view the full-size, animated version) helps you visualize how the 60:1 rule can be used to determine the distance to a station. The first frame shows the 60:1 relationship; the second frame shows the relationship between degrees and distance; and the third frame shows how this can be plugged into a formula.

What information is needed to apply the 60:1 rule
  • Problems that use the 60:1 rule will supply
    • The number of radials crossed, and
    • The distance traveled, or
    • The true airspeed and time to cross the given radials (which is then used to calculate the distance traveled).
  • The heading flown may be given, but is not important (except that a constant heading is maintained).
Solving 60:1 problems

This example is question COM474 from the FAA Commercial Pilot Test Question bank.

While maintaining a magnetic heading of 270 and a true airspeed of 120 knots, the 360 radial of a VOR is crossed at 1237 and the 350 radial is crossed at 1244. The approximate time and distance to this station are…

First, extract the information you need to solve the problem:

While maintaining a magnetic heading of 270 and a true airspeed of 120 knots, the 360 radial of a VOR is crossed at 1237 and the 350 radial is crossed at 1244. The approximate time and distance to this station are…

Write the formula that you will need to solve this problem:

60 NM / 1 degree  =  (??? NM from station)  / ( ??? NM traveled)

You know that you crossed 360-350=10 degrees, and that 1 degree = 1 NM if you are 60 NM from the station:

60 NM  /  10 NM  =  (??? NM from station)  /  (??? NM traveled)

The distance you traveled to cross those 10 radials is calculated from your TAS and the time in minutes

  • At 120 NM / hr, you are traveling (120 NM/hr) x (1 hr/60 min) = 2 NM/min
  • Your distance = (2 NM/min)  x  (1244 – 1237 min) = 14 NM

Your distance formula now becomes:

60 NM / 10 NM  =  (??? NM from station) / (14 NM traveled)

Solve this problem as you would any other algebraic proportion:

(60 x 14) / 10 = 84 NM

Time to the station can be calculated using the V=d/t formula

Real-life advice and experience

  • You either don’t have an ADF or VOR receiver onboard to apply this rule, or you have a GPS that gives you the information you need to know. This is just for CFIs and commercial students to use on the FAA knowledge test.
  • This method works equally well if you are passing ADF radials.
  • This method does not apply for problems where:
    • The relative bearing to an ADF changes 45 degrees (use the isosceles triangle method); or
    • The relative bearing doubles (use the isosceles triangle method); or
    • A course change is involved.
  • This formula isn’t exactly correct, especially if you cross many radials or if I get close to the VOR!!! [see why]

Additional resources

Enter Text

13 thoughts on “Calculating Distance with the 60:1 Rule”

  1. Pingback: The 60:1 Rule |
  2. Yo, Chris, you are correct in theory with the exception of flying a constant heading! Think about this, If you crossed 20 radials flying a constant heading ( no wind for now) you would not be the same distance from the nav aid unless you flew an arc(like a DME arc). Pull out a sectional, go to a VOR, pick a radial and about 60 miles out draw a course line perpendicular to the radial. Then measure the distance along a radial 20 degrees different. Or measure from the nav aid to a point on the line of +20 degree radial. It will be a greater distance.

  3. No surprise here: you are absolutely correct Mike! As you point out, if you start 60 nm from the VOR and fly on a constant heading until you cross 1 radial, you won’t be 60 nm from the VOR anymore…you’ll actually be a little further from it (use the Pythagorean theorem to figure out that you’ll be 60.008 nm). This error grows as you cross more radials–by the time you crossed 20 radials, you would in fact be 63 nm from the VOR.

    If you fly over just a few radials, the difference is pretty small. You can cross 12 radials be within 2% of the correct distance, which isn’t too bad. Over 20 radials (at 60 nm), the difference gets to be >5%. Just from doing a few sample calculations, it looks like most of the time, if you don’t cross too many radials, you can estimate your distance to within +/-5%. One of the problems that I have with the explanation of the 60:1 rule in the Jeppesen book is that they don’t explain the rationale behind it, but instead just slap out some formulas. If that’s all you know, then 1) it’s harder to solve 60:1 problems and 2) you wouldn’t be able to recognize limitations to the method, like this particular one.

    Now the sad reality: this probably won’t ever be more than a test question for most guys, and one that could be memorized (there are only a few of these questions on the knowledge exam). In that case, you aren’t trying to figure out if you’re over airport A or airport B, you’re trying to select between answer A and answer B.

    The 60:1 problems are neat to think through…thanks for raising this important caveat!

  4. Dear Chris, I found the 60:1 rule useful during cross country instruction to stress the importance of flying a desired heading. I tell pilots that are constantly off the desired heading that if they are off course just 5 dgrees in a 120nm flight we can be 10 miles off at the expected time of arrival. Hopefully many would use good navigation enroute to make off course corrections and fly a desired heading. This was especially important on a VFR flight from Miami to Puerto Rico when spending a lot of time over open ocean with NO reference points and trying hard not to mistake the shadows from clouds as islands in the distance.

    1. I added the emphasis in your post Mike. I remember watching a documentary about SR72 pilots. The one quote I remember is that “1 or 2 degrees is the difference between a successful mission and an international incident.”

  5. As to your beginning post about 60:1, most helo pilots will not be at suffient altitude to be 60 miles from a VOR and receive the station. Therefore my mention of flying an equi-distant arc really does not apply as your math showed how small the error would be. 60:1, 30:.5, 15:.25

  6. well the significance of this is in basic navigation…rule of 60 is critical for contact navigation.

    we draw a line and mark 10 or 20 mile increments for the faster ships… with the 5th marks being bigger and labeled. now drawing that line from point to point gives us a count up or down to the target. Thats for ETA…or PNR or PSR’s..3 engine ahead…return…or RTB..combat radius etc…

    In taking off and flying the mag course we see our groundspeed directly looking at the clock and allow ourselves to drift to measure the crosswind. …20 minutes out you ran how many miles? times it by three you got a GS…
    Or correct for drift if you can accurately old a course overland and then measure the crosswind. with a known groundspeed and crosswind based on drift we have a winds aloft calculation. Without groundspeed we turn 45 degrees off and return to course in a double drift and with two DA’s we have winds aloft.

    We also can use this to divert off course and then come up with a return angle having avoided weather or terrain….we had to go 30 south to get around a squall and have 180 to go..hmm

    in using the old pencil line and marks we have a living breathing chart or journey log as it becomes a document to record the flight as we note our start engines…takeoff ..top o climb….top of descent….landing …off times….calculate the runout and bingo… you write it all down…in pencil

    that takes the rule of 60 and makes for a chart that really comes alive for the navigator who can keep a clean and simple cockpit yet have a precision trip.

    by the way make that line from rally point to rally point….not center of the airfield …that way you fly the plane till you get to somewhere away from the field where you can look at a chart and not bury your eyes in the cockpit as you run up on the field….

    GS/ DRIFT/ WINDS ALOFT/ RANGE and ETA in minutes per tick mark/ DIVERSION/ and more…all in rule a 60…

  7. RULE OF 60 it is liberating….that route centerline is not a narrow ribbon to fly….no…rule of 60 means you fly left or right of course…high over a river valley…or along a railroad…or on the deck over a beach..wherever you have to go knowing you will always know if you are left or right of that centerline and how far….

    see each tick serves also as a ruler to use as you lay that pencil along it …a tack and a half right of course….that is 15 miles…..15 miles off course to fly a definite visual route….not bad.

    add to it the 5-8-16 rule for sightings and calculating range to visual sightings and the .5-.7.9 rule for crosswinds and miles per minute into crosswinds or the 36 second rule….and you are dead accurate with NO fancy stuff but a Compass and an airspeed indicator.

    A lost art?

  8. Why not use the formula for the circumference of a circle? 2×3.14(pie)xradius to get the distance?
    All you need to do is figure out what fraction of a circle you’ve travelled in the given time and what distance that fraction is. Then multiply your fraction to get the entire circumference of the circle around the VOR at your location then apply the formula to solve for the radius:
    14 NM to cover 10 degrees = 14 NM x 36 for the entire circumference = 504 NM. 504 NM divided by 2 = 252 NM.
    252 divided by 3 (pie rounded off) = 84 NM
    (If you don’t round off pie you’ll get 82 miles)
    Seems simpler to me…

  9. Guys this is simple trigonometry.
    You know SOHCAHTOA?
    Well this is the TOA part:
    TAN of 1 degree = Opposite/Adjacent = 1/60
    (0.016666)
    Adjacent (in this case 1) = 1/0.016666 =60
    That is why for each radial (1deg) the distance between radials will be 1 mile at 60 miles from the station, or one minute at 60 minutes from the station, independent of speed.
    Since this is formula is unitless it can be used for time or distance likewise.
    I hope this is useful for someone.
    Keep the Sky safe.

Leave a Reply