Alexander Burton, CFI

Pacific Rim Aviation Academy Inc.

Pitt Meadows Regional Airport

393-11465 Baynes Road

Pitt Meadows, BC V3Y 2B4

- Matthew Green –

Last month, we discussed the Line of Position: how to establish one either electronically

or visually and how to use one to facilitate locating ourselves in this complex, sometimes

confusing world.

Learning to establish a Line of Position is an excellent practice and can be very helpful in

pinpointing our position while enroute. Whether we do this visually or with reference of a

navigational aid the same principles apply. We want to determine where we are in

relation to a known, fixed point.

The basic principle of developing a Line of Position is to establish a bearing FROM a

known point using either a visual or electronic reference and extend that line outward

from the reference point. Your position lies along that Line of Position. If we are

comfortable in establishing one Line of Position, establishing two or more should not

present any significant difficulties.

With a Line of Position and a geographic reference or Lines of Position from two or more

reference points or two or more Lines of Position from the same reference point we can

locate our position over the ground, establishing a “fix” or exact position quite easily.

There are a number of techniques we can use to establish a fix, so let’s take a look at

some common ones.

A Line of Position from one reference point, a VOR, NDB or visual reference can be

used in conjunction with any geographic reference, for example a road, railroad track,

power line, coastline, river or lake to establish a fix. We establish the Line of Position,

draw it on our chart and observe where it crosses a geographic reference within our sight

radius to locate ourselves. What could be simpler?

If two NDBs, two VORs, or an NDB and a VOR are available, they can be used together

to develop two Lines of Position, or more if we really want to be precise, which will

locate or “fix” our position fairly precisely. Typically, when using three or more Lines of

Position, we will end up with a small triangle rather than a single point of intersection.

We are located within that triangle (1).

If we have two receivers in the aircraft, a VOR and an ADF, two VORs or two ADFs, we

can establish the two Lines of Position at about the same moment. With only one

receiver, there will be a necessary time lag between each reading, building in an

inevitable error. Normally, this will not be a significant problem at the speeds we fly with

small aircraft. SR-71 pilots, however, should take note.

To generate a fix using more than one navigation aid, develop a Line of Position from

each reference, draw them on your chart, and observe where the lines cross. This is your

position. When flying VFR, if we can locate ourselves within even a two to three mile

radius, visual references should do the rest of the job nicely.

If only one navigation aid is available to us, we can still fix our position accurately. One

method is to use a variation on the 1 in 60 rule: a one degree difference in track over 60

NM results in a difference of 1 NM in position. This basic rule allows us to generate

several, useful relationships (2).

With reference to a single VOR station, for example, we can develop a Line of Position

by determining the radial over which we are flying, turn 80 degrees right or left from the

inbound heading, the reciprocal of the radial, set the OBS to the nearest 10 degree

increment opposite the direction of the turn and note the elapsed time when the CDI

centres (3). The 10 degree bearing change is arbitrary; it just keeps our math problem

simpler.

If we are using an NDB for reference, we establish an initial Line of Position by using the

tail of the needle to indicate the outbound track over which we are flying. Turn to and

maintain a heading 80 degrees right or left of the inbound heading, the reciprocal of our

Line of Position, and note the time it takes us to fly through 10 degrees of heading change

in relation to the station.

We can now calculate distance to the station using the 1 in 60 rule.

We use the formula: distance to the station is equal to our speed times minutes flown

divided by number of degrees between bearings. If we want to be a bit more precise, we

can use seconds flown divided by 60 to obtain our number for minutes. If we are flying at

100 Kts., for example, and it has taken us five minutes, 300 seconds, to cover 10 degrees

of bearing change relative to our reference point, we are 50 NM out from the reference

along our second Line of Position (100 x 5/10 = 50) (4).

To locate ourselves, to “fix our position”, we measure 50 NM out from the station along

our second Line of Position and there we are. The key is to be familiar and comfortable

with the method through practice on the ground before attempting it in the air.

Another method we can use requiring only one point of reference, VOR, NDB, or visual

reference point, is to establish a Line of Position from our reference point, draw the line

on our chart and fly at something close to right angles to that Line of Position for 6

minutes, or some increment of 6. Make certain you maintain constant heading during this

procedure. Then, establish a second Line of Position from the same reference point or

navigation aid. I suggest six minutes for a reason; I want to keep this simple.

We now have two Lines of Position plotted on our chart. We also have our heading and

distance flown, not counting wind. The 6 minutes now comes in very handy to keep the

math in check. At 90 Kts, discounting wind effects, we will fly 9 NM in 6 minutes; at 130

Kts, we will fly 13 NM in 6 minutes (5).

We can now transfer the distance and heading we have flown to our chart starting at our

first Line of Position, perhaps using a pencil or our fingers to represent the distance. That

distance at a particular heading will fit at only one place between the two, diverging

Lines of Position. Our current position is the point where our line of travel touches the

second Line of Position. Try it a couple of times at the comfort of your desk and you will

see how simple it is.

With VOR, ADF or a visual reference we can also use a couple of simple geometric

relationship to determine our distance from a given point: a 45 degree right triangle has

equal sides; the sides of a 30, 60 degree right triangle have a special relationship for

use other right triangle relationships, or even trig functions, but let’s not get too crazy

here.

The NDB or visual reference problem is a littler simpler (less math), so I’ll focus on that.

With reference to the 45 degree triangle relationship, turn the aircraft until the relative

bearing on the ADF or the relative bearing to the visual reference is either 45 or 315

relative bearing of 90 or 270 degrees, a change in bearing of 45 degrees; take the time

The time interval you have recorded will be equal to the time required to fly to the

your position, is speed times time in minutes divided by 60; for example, 12 minutes at

100 Kts is 20 NM (100 x 12/60 = 20) (6). In this example, your position is 20 NM from

the reference point along your second Line of Position.

To make use of the special length relationships of the 30 degree right triangle, establish a

Maintain that heading until achieving a relative bearing of 90 or 270 degrees, a change in

Perhaps a bit simpler method using ADF is to establish a relative bearing of either 90 or

You can do the distance calculation as you would for the 45 degree triangle.

Playing with and practicing navigational techniques both visually and electronically in a

safe and known environment will enable you to make use of these techniques when

venturing into unfamiliar areas. Having a few extra tricks up your sleeve is all to the good

and, of course, it’s pretty cool to learn something new.

Enjoy.

Notes:

1. Ideally, the angle of interception between Lines of Position extending from reference points and your

position will equal 90 degrees. If the reference points are too close together or too far apart, the angle of

interception formed by the Lines of Position will be too steep (acute) or too shallow (oblique) to

determine an accurate “fix” or position. You can easily draw some triangles and see the problem. As the

reference points get closer or farther apart in relation to your position the inevitable error in the bearing

of your Lines of Position is magnified.

2. Distance between bearings/Distance to station = Degrees between bearings/60; Distance between

bearings = speed x minutes flown/60; Distance to station = TAS x minutes flown/Degrees between

bearings; Time to station = 60 x minutes flown between bearings/Degrees between bearings.

3. Using an 80 degree turn averages out the difference in heading between the two radials we will be using.

A 90 degree heading from our first radial tends to emphasize the difference in radial headings and

increases the error factor in the angles. If you draw the problem out you will see what this compromise is

attempting to achieve. However, no need to get overly excited about the differences.

4. Although the formula calls for TAS, at the speeds and altitudes we fly in small VFR aircraft, I wouldn’t

worry too much about the conversions required to obtain TAS. Use your IAS and things will normally

work out within limits you can easily live with.

5. 100 Kts = 100 NM/60 minutes or 10 NM/6 minutes. This works for any speed. Using a larger increment

of 6, for example 12, simply doubles the distance flown: 100 Kts = 200 NM/120 minutes or 20 NM in 12

minutes. For small aircraft flying at around 100 Kts, 6 minutes will normally be a sufficient amount of

time to produce usable results. This method does not, of course, factor in ground speed resulting from the

effects of wind. However, over a reasonably short distance, unless the wind is very strong, we should still

be able to produce quite usable results. Unless we are on a precision bombing mission, we only need to

locate ourselves within a reasonable radius and then revert to visual reference.

6. Distance = 100NM/1 hour x 1 hour/60 minutes x 12 minutes = 20 NM. Or, more simply, use your handydandy

E6B to compute that 12 minutes of flying at 100 Kts = 20 NM.