Dead reckoning and the navigation log

How does a fix become a predicted position?

Dead reckoning carries position forward using velocity and elapsed time.

Begin with position and time

A fix is a position established from observations at a stated time. A dead-reckoning position is propagated from an earlier position using assumed motion: heading and TAS, estimated wind and elapsed time. Under steady conditions on a local plane, north displacement is GS × hours × cos track and east displacement is GS × hours × sin track.

From a reliable fix, track 090° at 180 kt for 20 minutes gives 60 NM east. Near 50°N, a parallel approximation gives longitude change 60/(60 cos 50°) ≈ 1.556°. It is a local approximation; long legs, changing latitude and polar geometry require an appropriate spherical or ellipsoidal method.

Unobserved velocity error accumulates

A constant unrecognised 10 kt crosswind error creates 5 NM lateral error in 30 minutes. A 2° direction error over 100 NM creates about 3.49 NM cross-track displacement. An initial fix error remains as an additional vector; perfect subsequent propagation does not remove it.

A moving cursor is not a new fix merely because it advances smoothly. Identify the last reliable position, its time and the quality of the estimated motion since then. The longer that interval, the more uncertain the prediction can become. Tighter navigation tolerances or greater wind uncertainty call for stronger and more frequent independent checks.

Distinguish along-track from cross-track evidence

If the aircraft reaches a correctly identified checkpoint late but on the intended route, the observation supports a lower along-track GS. It does not identify a lateral correction. If it arrives on time but 3 NM to the right, the timing agreement does not remove the cross-track error. Use the laboratory to vary crosswind error while retaining the same planned GS. The predicted along-track distance can stay correct even while the lateral position becomes unacceptable. This is why a navigation log and a positional cross-check support different parts of the estimate.

What should the navigation log make easy to detect?

A log connects planned values with observations and revisions.

Connect the plan to observations

For each leg, a navigation log connects fixes, tracks, distances, TAS, forecast wind, heading, GS, leg time and ETA with the fuel information required by the operation. At a reliable fix, record actual time and compare it with the prediction. A growing timing discrepancy can reveal an incorrect GS assumption before it becomes a large arrival error.

A 60 NM leg planned at 180 kt takes 20 minutes. If it actually takes 22 minutes between reliable fixes, the implied GS is 163.64 kt. At that speed, a further 90 NM would take 33 minutes. Start the revised ETA from the actual fix time rather than adding a correction to an already stale clock value.

Qualify the observation before revising the plan

A visual feature must be uniquely identified and time-stamped. An ambiguous river bend may provide a poorer fix than a recent, well-founded DR estimate. Compare its shape, orientation, surroundings and expected position with other evidence. Do not force one attractive feature to fit a desired position.

An ETA error alone does not specify which way to turn. Along-track speed, cross-track displacement, station identity and north reference must be assessed separately. Preserve a record of the old assumption and the reason for its revision so that a subsequent discrepancy can be diagnosed rather than explained away.

Use a two-leg update

Suppose the reliable fix at the end of that 22-minute leg is passed at 14:42 UTC. With 90 NM remaining and observed GS 163.64 kt, the new ETA is 15:15 UTC. If a second checkpoint 30 NM ahead is available, predict its crossing near 14:53 UTC. That intermediate prediction tests whether the new GS estimate remains credible. A log is useful because it makes an observable prediction; merely filling every box without comparing actual progress does not improve position assurance.

Can you explain and apply the mechanism?

Four original questions. Work from the stated facts, then compare your reasoning with the explanation.