Dead Reckoning and Visual Navigation

Dead reckoning (DR) is navigation by calculation. From the last known position the pilot works forward with the heading flown, the true airspeed, the wind and the time elapsed, and deduces where the aircraft should now be. Map reading, which the FAA calls pilotage, is navigation by observation: comparing the ground with the chart to confirm or correct that estimate. Neither is enough alone. DR drifts as the wind differs from the forecast, and map reading needs to know roughly where to look. Used together they are the basis of VFR navigation and the fallback when electronic aids fail.

The same arithmetic runs through every level of the syllabus. The 1-in-60 rule, closing angles and revised ETAs appear in EASA PPL, CPL and ATPL navigation papers and the FAA knowledge tests, and airline pilots use them to cross-check the flight management system.

Principles of dead reckoning

A DR position is the sum of two vectors. The air vector is the heading flown at true airspeed for the elapsed time; the wind vector is the wind velocity for the same time. Together they give the ground vector: the track made good (TMG) and the distance flown over the ground. The inputs are the starting position, heading, TAS, wind velocity and time. The geometry is that of the triangle of velocities.

Before flight the planned track, forecast wind and TAS give the heading to steer and the groundspeed, and hence times and fuel for each leg. A quick mental check is the maximum drift, about 60 × wind speed ÷ TAS. At a TAS of 100 kt, a 20 kt wind at right angles gives about 12° of drift, so to make good 360° with the wind from 270° the heading is about 348°.

In flight the plan is checked against reality:

• A groundspeed check times the aircraft between two charted features. Six nautical miles in 4 minutes is 1.5 NM a minute, or 90 kt.
• A revised ETA uses the actual groundspeed. On a 60 NM leg planned at 90 kt, reaching a checkpoint 15 NM along in 12 minutes gives an actual groundspeed of 75 kt, so the remaining 45 NM will take 36 minutes, not 30.
• A fix, a position from an external reference such as a pinpoint, a VOR/DME or GNSS, resets the DR.
• The actual wind can be found from the fix. Flying 090°(T) at 140 kt TAS and making good 097° at 150 kt means a wind of about 334°/20 kt.

DR errors come mostly from the wind, the least certain input, and they grow steadily with the time since the last fix. That growth defines the circle of uncertainty: a circle round the DR position within which the aircraft is probably to be found, larger the longer it has been since the last fix.

Track error and the 1-in-60 rule

The 1-in-60 rule states that an angle of 1° subtends about 1 NM at a range of 60 NM. It follows from the fact that a radian, about 57.3°, is close to 60°, and it is accurate enough for the small angles of navigation.

The track error (TE), or track error angle, is the angle between the planned track and the track made good. It is not the same as drift, which is the angle between heading and track. From a fix:

track error = distance off track × 60 ÷ distance gone

Four nautical miles right of track after 30 NM is a track error of 4 × 60 ÷ 30 = 8° right. The same displacement early in a leg means a large error, which is why it should be corrected rather than ignored. If the fix is timed rather than measured, convert first: 15 minutes at 120 kt is 30 NM.

Correcting by the track error alone turns the aircraft parallel to the planned track, still displaced by the same distance. At 3 NM right after 45 NM the track error is 4°, and a 4° turn left simply stops the divergence.

Closing angle and regaining track

To reach the destination, or any chosen point on the track, a closing angle (CA) is added:

closing angle = distance off track × 60 ÷ distance to go

The alteration of heading is the track error plus the closing angle, made towards the planned track.

At the halfway point the distances gone and to go are equal, so the closing angle equals the track error and the alteration is simply twice the track error. On arriving overhead, the pilot takes out the closing angle and keeps the track-error correction, which allows for the wind actually found.

Double track error method

Sometimes the aim is to regain the planned track itself, for example to rejoin a route agreed with ATC, rather than to fly direct to the end of the leg. The double track error method, or double-track method, does this without measuring distances.

1. Alter heading towards the planned track by twice the track error.
2. Hold the new heading for the same time as has elapsed since the aircraft was last on track. The two legs form an isosceles triangle, so the aircraft arrives back on track.
3. Turn back by one track error. The net change from the original heading is then one track error into wind, which holds the track if the wind is unchanged.

After 30 minutes with a track error of 5° left, the pilot alters heading 10° right for 30 minutes, then turns 5° left, finishing 5° right of the original heading. Returning to the original heading would repeat the error. The method assumes the same wind and groundspeed on the return leg as on the leg that produced the error.

Map reading and pilotage

Map reading relates the chart to what is seen outside. The habits that make it reliable are simple:

• Hold the chart track-up, so that a feature drawn left of the track line appears out of the left window.
• Work from chart to ground. Use the DR position and the time to predict which feature should appear next and where, then look for it. Starting from the ground and searching the chart for something that matches invites the pilot to find what they hope to see.
• Fly accurately. Heading and speed errors defeat both DR and map reading, and the heading indicator must be realigned with the magnetic compass at regular intervals.
• Keep the head up. A pilot who spends four minutes head-down comparing chart and ground can look up to find the aeroplane 20° off heading and 400 ft low: attention given entirely to one task leaves the aircraft unflown. Aviate first, then navigate in short glances.

VFR GNSS receivers are a valuable cross-check but not a substitute. The FAA warns that no design standard of accuracy or integrity applies to a VFR GPS receiver and that it should be used together with other forms of navigation. The pilot who keeps the log and chart going still knows what to do when the screen fails or misleads.

Checkpoints, pinpoints and line features

A good visual checkpoint is distinctive, close to track, large enough to be seen in good time and impossible to confuse with anything nearby: a large lake, a town of unusual shape, a major road or rail junction, an aerodrome or a tall mast. Small villages look alike from the air, minor roads appear too late, and features far abeam are hard to relate to the track. Checkpoints should be close enough together that the next is in sight before the last is lost.

A pinpoint is a fix obtained by identifying a feature directly beneath or very close to the aircraft. It gives position in both directions and is the visual equivalent of a radio fix.

A line feature is a long, continuous feature such as a coastline, river, railway, motorway or power line. Crossing or following one gives a position line, not a fix: the aircraft is somewhere along it. Line features are valuable as catching features: a motorway lying across the track beyond a turning point warns that the turn has been missed, and a river running parallel to the track keeps drift in check. Aiming deliberately to one side of a destination that lies on a line feature removes any doubt about which way to turn on reaching it.

Visual reporting points and VFR waypoints

A visual reporting point, or VFR reporting point (VRP), is a named, easily identified geographical point used by ATC for position reports and for routing VFR traffic into and out of controlled airspace. VRPs are published in the AIP and printed on VFR charts and visual approach charts. In the ICAO style a filled triangle marks a compulsory reporting point and an open triangle an on-request point, reported only when ATC asks. On the French visual approach charts the track for each direction is printed beside the point it leaves, with the distance between points in the middle, and routes are drawn as a solid line when compulsory with radio contact and a dotted line when recommended. See position reports and required reports.

In the United States, VFR waypoints support GNSS-equipped VFR pilots in and around Class B and Class C airspace, special use airspace and mountain passes. Their five-letter identifiers begin with VP and are retrievable from the navigation database; they are not pronounceable and not used in radio calls, except where a waypoint coincides with a visual checkpoint and takes its name. Stand-alone VFR waypoints are charted with a four-point star, and those at visual checkpoints with a magenta flag. They may be used in the route of a VFR flight plan, never an IFR one, should be loaded before take-off, and attract other traffic, so the lookout near them must be sharp.

Uncertainty of position and the lost procedure

Being uncertain of position is not yet being lost, provided the DR information is preserved. The first actions are:

1. Fly the aircraft: hold the present heading and altitude, and note the time.
2. Work out a DR position from the last positive fix, using heading, groundspeed and time.
3. Draw the circle of uncertainty round it and search inside it for large features, above all a line feature that crosses the probable track.
4. Check the heading indicator against the compass; a misaligned indicator is a common cause of the problem.

Turning back or orbiting destroys the DR run, and descending to read signs adds terrain and airspace hazards to a navigation problem. If the position is still in doubt, ask for help early. A VHF direction-finding station can pass a QDM, the magnetic heading to steer in nil wind to reach it, or a QTE, the true bearing of the aircraft from the station, which can be plotted directly as a position line; radar and a transponder can identify the aircraft within seconds. US flight training summarises the procedure as the four Cs: climb, communicate, confess, comply. Climbing, while remaining clear of cloud and controlled airspace, extends VHF range, brings more landmarks into view and adds terrain clearance.

A pilot uncertain of position with limited fuel or daylight is in an urgency situation and should say so with a PAN PAN call on the frequency in use or on 121.5 MHz; MAYDAY is kept for imminent danger requiring immediate assistance. US training material treats squawking 7700 as a last resort, for when the situation has become an emergency. If the fuel or daylight left will not cover the search, a precautionary landing in a chosen field is safer than pressing on until the choice is gone.

Library articles are written for study and exam preparation. They do not replace your aircraft's approved documentation, your operator's procedures or the regulations themselves.