Plotting

Every observation must first be translated into the geometric line or circle that contains the aircraft. A fix appears only when independent observations locate a common point at a common time.

Fixing Position

A visual line feature, radio bearing or radar bearing gives a straight position line. DME gives a circular position line centred on the facility. Two independent position lines obtained simultaneously give a fix at their intersection. Three lines usually form a small triangle because each observation contains some error.

Geometry and reliability

Position lines should cross at a strong cut. An angle near 90 degrees gives the clearest intersection. A very acute cut magnifies a small bearing error into a large position error. Choose aids whose lines cross between about 60 and 90 degrees when possible.

Track Made Good

When one heading has been maintained between two timed fixes, the straight line joining them is the track made good. Measure its direction against the correct chart datum and its distance with the local scale.

Two fixes at 1700 and 1730 are 100 NM apart. The elapsed time is 30 minutes, so groundspeed = 100 x 60 / 30 = 200 kt.

VDF and VOR information is referenced at the ground station. That decides which local variation converts the magnetic bearing to the true bearing needed on the chart.

Bearings Measured by a Ground Station

VDF conversion example

A station measures QTE 140 T. The station variation is 10 degrees west. The corresponding QDR is 150 M. Its reciprocal QDM is 330 M. The station variation is used because the direction was measured at the station.

Plotting of VOR Bearings

1. Identify whether the information is a QDR radial or a QDM to the station.
2. If it is QDM, take the reciprocal to obtain the radial.
3. Use the chart's magnetic north reference when it is adequate, or convert the radial to true with variation at the VOR.
4. Place the protractor centre exactly on the VOR and draw the radial in the FROM direction.
5. Label the line with the observation time and datum.

Plotting QDMs and QDRs

When a VOR defines several published airway radials, those radials provide a strong magnetic alignment for the protractor. Otherwise construct magnetic north from the nearest true meridian and the station variation. A short printed magnetic arrow is less accurate than a longer constructed datum.

ADF and airborne weather radar measure direction at the aircraft. Convert the cockpit indication to a true bearing TO the object, then reciprocate it to draw a line FROM the object.

Bearings Measured by Aircraft: ADF or Airborne Weather Radar

An RBI displays relative bearing clockwise from the aircraft nose. An RMI combines the bearing with slaved magnetic heading and normally displays magnetic bearing to the station. Airborne weather radar in map mode gives range and relative bearing to a ground response.

Relative Bearing

1. Convert the aircraft magnetic or compass heading to true using variation at the aircraft and deviation when required.
2. Add relative bearing to true heading to obtain true bearing TO the station or radar response.
3. Subtract 360 degrees if the sum exceeds 359 degrees.
4. Take the reciprocal to obtain the true bearing FROM the object.

Converting a Relative Bearing into a True Bearing

An aircraft heading is 315 M, aircraft variation is 9 degrees west, and an NDB is observed at relative bearing 207. True heading is 306 T. Adding the relative bearing gives 513 degrees, or 153 T TO the NDB. The reciprocal position line plotted FROM the NDB is 333 T.

Magnetic Bearing

If an RMI shows magnetic bearing to the NDB, convert that indication to true with variation at the aircraft, then take the reciprocal for the line from the NDB. Do not use variation at the NDB because the bearing was measured by the aircraft system.

AWR

Add the radar response's relative bearing to true heading, then take the reciprocal and plot from the charted response. Confirm that the selected response is a unique coastline, headland or island. Range gives a second position line, so one radar response can provide both a bearing and a distance fix.

DME supplies distance rather than direction. On the chart it becomes a circle, or the relevant arc of a circle, centred on the DME facility.

Distance Measuring Equipment

DME indicates slant range from the aircraft to the facility. For exact chart plotting, convert it to horizontal plan range when altitude difference is known. Beyond about 10 NM the difference is normally small unless the aircraft is high.

At 6000 ft above the station, vertical separation is about 1 NM. If slant range is 10 NM, plan range is the square root of 100 minus 1, or 9.95 NM. At short range and large height difference the correction matters much more.

Plotting one DME arc

1. Find the facility and confirm its identity.
2. Use the chart's local latitude scale to set the range on dividers.
3. Place the divider point at the DME and draw only the useful arc.
4. Write the range and four-figure UTC time against the arc.

VOR and DME fix

A VOR radial and a co-located DME arc give a direct fix where the radial meets the arc. Confirm that a QDM has been reciprocated before using it as the radial. A VORTAC is treated as co-located VOR and DME for this plotting purpose.

Two-DME ambiguity

Two DME circles normally intersect at two points. Choose the correct intersection from the approximate DR position, the aircraft heading and whether each range is increasing or decreasing. A third line removes the ambiguity.

A running fix combines observations made at different times. The earlier line is moved by the aircraft's estimated ground movement so both lines refer to the later time.

Transferring a position line

1. Plot the first position line and label its time.
2. Calculate distance moved between observations from estimated groundspeed and elapsed time.
3. Transfer every point of the earlier line parallel to itself in the direction of estimated track by that distance.
4. Label the transferred line with both its original time and the time to which it was transferred.
5. Intersect it with the later position line to obtain the running fix at the later time.

At 120 kt, 10 minutes represents 120 x 10 / 60 = 20 NM. Move the first line 20 NM parallel to estimated track before intersecting it with the second line.

Accuracy of a running fix

The result depends on the first observation, the second observation and the estimated movement between them. Heading changes, wind changes, inaccurate groundspeed or a long time interval increase error. A running fix is not as strong as two simultaneous lines of equal quality.

Three imperfect position lines seldom meet at one point. Their three intersections form a triangle called a cocked hat, and its size and shape reveal the internal agreement of the observations.

The Cocked Hat

For three lines of similar reliability, take the most probable position near the centre determined by the triangle's angle bisectors. A small, well-shaped triangle suggests close agreement. A large or elongated triangle warns that at least one observation or correction may be poor.

Most probable position

Error clues

A constant compass or variation error can shift several bearing lines in the same sense. An identification error may produce a grossly misplaced line. Poor cutting angles stretch the cocked hat. Compare the plotted result with the DR position, timing and range trends before accepting it.

A ground plot shows what the aircraft actually did over the Earth. An air plot shows what heading and true airspeed would have produced in still air. Their difference over the same time interval is the wind displacement.

The track plot

Join successive timed ground fixes. The direction of the joining line is track made good, and its length divided by elapsed time gives groundspeed. Label each fix with UTC and each segment with the measured track and groundspeed.

The air plot

From the first ground fix, draw the air vector in the true-heading direction. Its length equals TAS multiplied by elapsed time. The end is the air position for the later time. Use mean heading and TAS when either changed during the interval.

Finding wind velocity from a plot

Over one hour, an aircraft heads 090 T at TAS 180 kt and makes good 090 T at GS 220 kt. The air position is 180 NM east of the start and the ground position is 220 NM east. The 40 NM vector from air position to ground position shows wind 270 T at 40 kt.

Standard time and direction labels

Use four-figure UTC at fixes and on position lines. Write directions as three figures with T, M or C. Show arrowheads on tracks and vectors. A transferred line carries its original time and the time to which it was transferred.

On convergent charts, nearby meridians are not parallel. A radio bearing follows a great-circle path, so the location at which the bearing was measured controls the plotting datum.

Lambert and Polar Stereo Charts: Effects of Convergence

A straight line on a Lambert chart, or on a polar stereographic chart at high latitude, is treated as a great circle for practical plotting. For a route between two positions, measure the straight-line direction at the mid-meridian when a mean rhumb-line track is required. Plot a known heading or track from the nearest meridian to its starting position.

Measuring Tracks

Join the two positions with a fine straight line. On a Lambert or polar chart, measure the line against the meridian at the position where the required track applies. For a mean route track, use the mid-meridian.

Plotting Headings and Tracks

Lay a known heading or track down from the nearest meridian to its starting position. Record the direction in three figures and state whether it is true, magnetic or compass.

Plotting Positions

1. Mark the required longitude on the longitude scales north and south of the position.
2. Join those two marks with a straight-edge to create the local meridian.
3. Use dividers to measure latitude up or down that local meridian from the nearest parallel.
4. Mark the position lightly, check its hemisphere and label it.

Measuring Distances

Where chart scale varies, measure distance with the latitude scale local to the route or position. Do not use longitude graduations as a distance scale.

Plotting on a Lambert Chart

For bearings measured at a ground station, correct with station variation and plot the true bearing from that station. For a bearing measured at the aircraft, draw a line through the ground object parallel to the aircraft's meridian and measure the reciprocal true bearing from this false meridian. This automatically allows for chart convergence.

Plotting of ADF Bearings

When the aircraft and NDB meridians are visibly non-parallel, construct a false meridian through the NDB parallel to the aircraft meridian. Plot the reciprocal true ADF bearing from that false meridian. Over a very small change of longitude the convergence difference may be negligible, but the parallel-meridian construction is the dependable method.

Climb and Descent

A vertical-profile plotting problem makes vertical time equal horizontal time. If an aircraft must lose 23,000 ft over 65 NM at GS 240 kt, horizontal time is 65 x 60 / 240 = 16.25 minutes. Required rate of descent is 23,000 / 16.25, about 1415 ft per minute.

Complete plotting sequence