CAAS PPL Navigation Study Guide

Navigation in the PPL syllabus is the art and arithmetic of getting from A to B in good time, with fuel to spare, without entering controlled airspace uninvited and without becoming lost. The exam tests the underlying mathematics (mental arithmetic with whole-number approximations) and the conventions (TVMDC, true vs magnetic, charts and their limitations). A confident PPL navigator can plan a flight on paper, monitor it in the cockpit using only a watch, a compass and a chart, and recover gracefully when reality differs from plan.

The single most valuable habit is the track-and-time mindset: at every checkpoint you ask whether you are on track and on time. If yes, continue; if no, decide what to do before the next checkpoint. The mathematics that follow are simply the tools that let you make those decisions in the air.

It helps to see how the topics fit together before drilling into each one. You begin with the shape of the Earth and the latitude/longitude grid, because every position, track and distance is ultimately referenced to that grid. From the grid come the two kinds of line you can draw between two places — the great circle (shortest) and the rhumb line(constant heading) — and the chart projections that try to render them faithfully on flat paper. Direction then needs three references (true, magnetic, compass), distance and speed need consistent units, and the wind turns a planned track into a heading you actually fly. Dead reckoning ties it all together on paper; pilotage and radio aids confirm it in the air. Treat the syllabus as that single chain rather than a list of disconnected facts and the arithmetic stops feeling arbitrary.

A note on what the exam will and will not pin you down on. General principles — airspace and chart conventions, the geometry of great circles, the behaviour of radio waves, the wind triangle, the arithmetic of time and longitude — are fair game and are tested precisely. For the specifics of the current syllabus, the exact paper format and any local regulatory figures, always work from the current CAAS PPL examination requirements rather than memorising a number from an old crib sheet, as those details are revised from time to time.

For PPL navigation the Earth is treated as a sphere. In reality it is an oblate spheroid, very slightly flattened at the poles and bulging at the equator, but the flattening is tiny (the polar and equatorial diameters differ by only about a third of a percent) and for chart work and mental arithmetic the spherical assumption introduces no error you can measure with a pencil. The modern mathematical model that GPS and charts are built on is the WGS-84 datum, an agreed reference ellipsoid; you do not need its parameters, only the awareness that positions on a chart and positions from a GPS share the same datum so they agree.

Position on that globe is fixed by two angles. Latitude is the angle, measured at the centre of the Earth, between the equator and the point, running from 0° at the equator to 90°N or 90°S at the poles. Lines of equal latitude are parallels; they run east–west, are parallel to one another, and shrink in circumference towards the poles. Longitude is the angle east or west of the Prime (Greenwich) Meridian, running from 0° to 180°E or 180°W. Lines of equal longitude are meridians; they run north–south, are all great circles, and converge to meet at both poles.

Two facts from that grid do almost all the arithmetic work in the exam:

• One minute of arc along a meridian equals one nautical mile. Therefore one degree of latitude is 60 nm, and a change of latitude converts straight to distance: flying 300 nm due south from 15°S takes you 5° further south, to 20°S.
• One minute of longitude equals one nautical mile only at the equator. Because meridians converge, the east–west distance for a given change of longitude shrinks with latitude as the cosine of the latitude. This shrinking distance is called departure: departure (nm) = change of longitude (minutes) × cos(latitude).

So 1° of longitude spans 60 nm at the equator, about 30 nm at 60°N (cos 60° = 0.5), and nothing at all at the pole. A clean equator example: a point 720 nm east of Greenwich on the equator lies at 720 ÷ 60 = 12°E. The same 720 nm at 60° latitude would correspond to 24° of longitude, because each degree there is only 30 nm wide. Keeping latitude (always 60 nm per degree) and longitude (60 nm per degree only on the equator) firmly separate is the single most common place candidates trip up.

Between any two points on the globe you can draw two different lines, and understanding the difference underpins both the chart questions and the practical choice of route.

• Great circle — any circle on the sphere whose plane passes through the centre of the Earth (the equator and all meridians are great circles). The shorter arc of the great circle through two points is the shortest distance between them. Its drawback is that, except along the equator or a meridian, it crosses successive meridians at a continuously changing angle, so it is not a constant-heading track.
• Rhumb line (or loxodrome) — a line that crosses every meridian at the same angle, i.e. a track of constant true direction. It is easy to fly because the heading never changes, but except along the equator or a meridian it is longer than the great circle, and it spirals gently towards the pole.

Two geometric rules earn easy marks. First, the great circle always lies on the polar side of the rhumb line between the same two points (nearer the nearer pole); the rhumb line bows towards the equator. Second, on the legs PPL students actually fly the two lines are close together: at low latitudes and over short distances the difference between a great-circle track and a rhumb-line track is negligible, which is why a straight pencil line on the chart is perfectly adequate for a local cross-country. The distinction only grows important over long distances and at high latitudes — a transpolar airliner saves real miles by following the great circle and continually adjusting heading.

A related idea the exam likes is conversion angle: the angle between the great-circle and rhumb-line tracks joining two points. You do not need to compute it, but you should know that it grows with the distance between the points and with latitude, and that it is zero on the equator.

The 1-in-60 rule is the geometric trick that makes mental navigation possible. It states that an angle of 1° at 60 nautical miles subtends 1 nautical mile of distance — and more generally:

Track error angle (degrees) ≈ (cross-track distance × 60) ÷ distance flown

If after flying 30 nm you find yourself 2 nm right of track, your heading error is (2 × 60) ÷ 30 = 4°. To regain the planned track at the next 30 nm checkpoint you must turn left by twice that — 4° to remove the existing error plus 4° more to converge on track over the next leg, a total of 8°. The 1-in-60 rule is also used for the gradient of a glidepath (a 3° glidepath descends roughly 300 ft per nautical mile) and for closing angles on radials.

Use it in the cockpit by pre-computing for common ratios:

• 1 nm off at 60 nm = 1° error.
• 1 nm off at 30 nm = 2°.
• 1 nm off at 15 nm = 4°.
• 1 nm off at 10 nm = 6°.

A heading is the direction in which the aircraft's longitudinal axis is pointing. There are three flavours, each measured against a slightly different reference, and converting between them is a standard exam topic. The conversion mnemonic is TVMDC:

1. True heading — measured against True North, the geographic pole. Charts use True North for plotting.
2. Variation — the angle between True North and Magnetic North at a given point on the Earth's surface. Variation is published on charts (isogonal lines).
3. Magnetic heading — measured against Magnetic North. This is what the compass would read in the absence of nearby ferrous metal.
4. Deviation — the residual error in the compass caused by the aircraft's own magnetic field (engine, radios, electronics). Tabulated on a card in the cockpit.
5. Compass heading — what the magnetic compass actually reads.

The rule for sign is "West is best (add), East is least (subtract)" when going from True to Compass, and the opposite when reversing. So if True heading is 270°, variation is 5° West, and deviation is 2° East:

Magnetic = 270 + 5 = 275°; Compass = 275 − 2 = 273°.

Variation is geographic and changes slowly over years; deviation is aircraft-specific and is set by ground engineers during a "swing". Singapore lies close to a region of small variation, so examiners may also throw in higher-latitude examples where variation reaches double digits.

Dead reckoning (sometimes glossed as "deduced reckoning") is navigating by calculation rather than by external reference. Given a planned True Track, a forecast wind, and an aircraft True Airspeed, you compute a True Heading and a Ground Speed using the wind triangle. The geometry is:

• True Track (TT) — the path over the ground.
• True Airspeed (TAS) — the aircraft's speed through the air mass.
• Wind — direction (where it blows from) and speed.
• True Heading (TH) — the direction the nose points to make good the TT.
• Ground Speed (GS) — speed along the track over the ground.

You compute TH and GS either by plotting on a flight computer (the "whiz wheel" or electronic CX-3) or, in the cockpit, by mental approximation. A rule of thumb: for a 30° wind angle, the crosswind component is half the wind speed (sin 30° = 0.5) and the head/tail component is about 90% of the wind speed (cos 30° ≈ 0.87). For a 60° angle the proportions reverse. Memorise the standard table:

A typical PPL fuel calculation totals four components: taxi, climb, cruise, descent — and adds reserves. Required reserves are jurisdiction-specific; the principle the exam tests is that you should always land with a minimum reserve regardless of plan. As a working guide, a 45-minute final reserve is typical for VFR day operations and is the safe planning minimum in most syllabuses.

A commonly taught monitoring technique is the 1/2/3 fuel check: at the end of the first leg, compare actual fuel burn against plan and project whether you will land with adequate reserve. If not, divert early. A related technique is the Howgozit chart: a plot of fuel remaining against distance flown, with the planned line drawn in advance. Any divergence from the line is immediately visible.

Three numbers should never be guessed: useable fuel (not total fuel — some fuel cannot be drawn from the tanks in normal attitudes), fuel flow at the chosen cruise setting(from the POH, not from instinct), and diversion fuel for the most distant likely alternate. Singapore PPL students often have short legs and few alternates within range, which makes conservative planning especially important.

Charts must project a curved Earth onto a flat sheet, and every projection distorts something. Two projections dominate aviation:

• Mercator — a cylindrical projection, conformal (angles and small shapes preserved). Meridians are parallel vertical lines and parallels are horizontal. Rhumb lines (lines of constant heading) are straight; great-circle tracks (shortest distance between two points on a sphere) are curves. Distance is severely distorted near the poles. Useful at low latitudes where rhumb-line and great-circle tracks are similar.
• Lambert Conformal Conic — a conic projection, also conformal, with meridians as straight lines converging at the pole and parallels as arcs. Great circles are approximately straight lines (the standard Lambert chart is the most common chart for navigation in mid-latitudes); rhumb lines are curves. Used for most aviation charts because tracks plotted as straight lines closely approximate great circles.

Practical implications: on a Lambert chart, measure the true track at the mid-meridian of the leg (the meridian-track angle changes along the line because meridians converge). On a Mercator chart, the angle is constant — a straight line on the chart is a rhumb line. At Singapore latitudes the differences are small but on long-distance flights the choice of chart matters.

The word that ties this together is conformal (or orthomorphic): both standard aviation projections preserve angles over small areas, so a bearing measured on the chart matches the real-world bearing and shapes of small features look right. What neither preserves everywhere is scale — on a Mercator the scale expands towards the poles, which is why Greenland looks vaster than it is, so always measure distance against the latitude scale at the side of the chart at the mid-latitude of your leg, never against the longitude scale across the top.

Finally, learn the chart symbology. Aeronautical charts encode an enormous amount in colour and shape: relief is shown by contours, layer tinting and spot heights, with the highest terrain on the sheet often boxed as a maximum elevation figure; obstacles such as masts carry their height above ground and above mean sea level; aerodromes, controlled airspace boundaries, danger, restricted and prohibited areas, and the positions of radio aids all have standard symbols explained in the chart legend. Part of pre-flight navigation is simply reading those symbols correctly along the intended route, and the exam expects familiarity with the common ones.

PPL navigation introduces radio aids as a backup to dead reckoning. Four are routinely covered:

• VOR (VHF Omnidirectional Range) — a ground station that broadcasts radial information in the 108-117.95 MHz band. The cockpit instrument shows the radial the aircraft is on (relative to the station) and whether the selected radial is to or from the station. VOR is line-of-sight, so range increases with altitude.
• NDB (Non-Directional Beacon) — a ground station that transmits in the LF/MF band (typically 200-535 kHz). The cockpit ADF (Automatic Direction Finder) points to the NDB regardless of aircraft heading. NDBs follow the curvature of the Earth and can be received at longer range than VORs, but are subject to night effect, terrain effect and thunderstorm interference. Less accurate than VOR.
• DME (Distance Measuring Equipment) — an interrogator-transponder system that reports slant range (not ground distance) to a paired ground station. Often co-located with a VOR (VOR/DME or VORTAC). Useful for cross-checking position along a radial.
• GPS — satellite-based, with horizontal accuracy of a few metres in good conditions. PPL students should understand that GPS in aircraft uses RAIM (Receiver Autonomous Integrity Monitoring) to verify satellite geometry and that, for IFR use, a RAIM prediction is part of pre-flight planning. As a VFR primary or backup, GPS is highly reliable but must be cross-checked against the chart and the compass.

A common exam point about VOR: the radial is measured outbound from the station, so a CDI showing you are on the 090 radial means the station is east of you. Reverse-sensing happens when the OBS is set to a course opposite to the direction of flight, and the needle deflections become misleading. Setting the OBS to the desired course solves it.

The fundamental relation is simple: Distance = Speed × Time. The arithmetic is easier if you commit a few conversion factors to memory:

• 1 nautical mile = 1 minute of arc of latitude ≈ 1.852 km ≈ 1.15 statute miles.
• At 60 knots ground speed you cover 1 nautical mile per minute — handy as a reference, even if you cruise faster.
• At 90 knots you cover 1.5 nm per minute.
• At 120 knots you cover 2 nm per minute.

For drift correction, the "rule of one in sixty" gives the heading correction needed once you measure your error. For a quick crosswind correction in the cockpit, apply the wind-angle table from earlier: a 30° crosswind component at 10 knots is roughly 5 knots of crosswind on the aircraft, which at a TAS of 100 knots gives sin−1(5/100) ≈ 3° wind correction angle. With practice this becomes a one-second mental calculation.

A final exam tip: units. Aviation mixes knots (nm/hour) for speed, feet for altitude, and (in some contexts) kilometres for visibility. The PPL exam will sometimes deliberately offer an answer in the wrong units to catch a candidate who didn't check. Read each question twice; check your units when you check your work.

Aviation runs on a single worldwide clock so that a flight crossing time zones never has to ask "whose midday?". That clock is UTC (Coordinated Universal Time), which for all practical navigation purposes is the same as GMT (Greenwich Mean Time): the mean solar time on the Prime Meridian. Flight plans, NOTAMs, weather reports and ATC clocks are all in UTC, and you should think and log in UTC throughout a flight. Singapore Standard Time, for example, is UTC + 8 hours, so a 0100 UTC departure is a 0900 local start.

The clean piece of arithmetic the exam tests links time to longitude. The Earth turns 360° in 24 hours, so it turns 15° in one hour and 1° of longitude in four minutes. From that single ratio you can convert between local mean time and UTC: places to the east see the sun earlier, so their local mean time is ahead of UTC, and places to the west are behind.

• 15° of longitude = 1 hour of time.
• 1° of longitude = 4 minutes of time.
• 15′ (minutes of arc) of longitude = 1 minute of time.

So a location at 30°E is 2 hours ahead of UTC in local mean time; one at 45°W is 3 hours behind. The International Date Line runs roughly along 180° longitude, and crossing it westbound advances the date by one day while crossing eastbound puts it back a day. The other time-related item to know is civil twilight, used to bracket the legal day for VFR flight: morning civil twilight begins, and evening civil twilight ends, when the centre of the sun is 6° below the horizon. Tables in the flight documents give the times; the concept is what the exam tests.

The flight navigation computer — the circular slide rule still universally called the "whiz wheel" — is two instruments printed back to back. You should understand what each side does conceptually even if you sit the exam with an electronic CX-3 or a calculator, because the questions are written around its logic.

• The circular slide-rule side solves any problem that is a ratio or a proportion by lining up two scales. Its headline use is the time–speed–distance triangle: set ground speed against the index and read distance against time anywhere around the wheel. The same side does fuel flow (gallons or litres against time), unit conversions (nm/km/statute miles, litres/gallons, feet/metres), and the airspeed corrections — it has a small window where you set pressure altitude against temperature to convert CAS to TAS, and another for true altitude.
• The wind (slide) side solves the triangle of velocities mechanically. You slide a printed grid behind a rotating compass-rose face, mark the wind down from the centre, set the track under the index, and read off the wind correction angle (drift) and ground speed directly. It replaces drawing the wind triangle to scale with a ruler.

The point of practising on the wheel is not nostalgia: it builds an intuition for which way an answer should move. If you increase TAS, the drift angle should shrink; if a headwind grows, ground speed should fall and time should rise. When you later approximate in the cockpit, that built-in sense of direction stops you applying a correction the wrong way — the most common cause of a confidently wrong answer.

Dead reckoning gets you close; pilotage — navigating by visual reference to features on the ground — confirms exactly where you are. The two techniques work together: DR tells you where to look and roughly when, and pilotage tells you whether the plan is working. Good pilotage is a discipline of choosing and using checkpoints well.

1. Choose unambiguous features. A single isolated lake, a road–railway crossing, a distinctive coastline or a town with a known shape makes a far better checkpoint than "a road" or "a field", of which there are thousands. Linear features such as coastlines, rivers, motorways and railways are especially useful because they give a line to fly along or to catch.
2. Read from map to ground, not ground to map. Decide from the chart what you expect to see and when, then look out and confirm it. Trying to match a random ground feature back to the chart is how pilots talk themselves into being somewhere they are not.
3. Anticipate, then tick off. Note the next checkpoint and its estimated time before you reach it; as it passes, check track and time, revise the estimate for the following point, and move on. This is the track-and-time habit in action.
4. Have a lost procedure. If a checkpoint does not appear on schedule, do not wander. Hold a known heading, note the time, draw your most-probable-position circle from the last certain fix and the time and ground speed flown, look for a large catching feature, and if necessary use radio aids or ask for assistance.

A practical refinement is deliberate offset: when aiming for a point that sits on a long line feature (an airfield beside a coast, say), plan to arrive a few degrees to one known side. When you reach the line you then know unambiguously which way to turn, instead of guessing left or right when the destination fails to appear dead ahead.

The Navigation paper punishes a small set of recurring errors. Recognising them in advance is worth several marks.

• Applying variation or deviation the wrong way. Going from True towards Compass, "West is best, add; East is least, subtract"; reverse it when going the other way. Always write the TVMDC column out vertically rather than doing it in your head — one sign slip flips the answer by twice the variation.
• Confusing wind direction conventions. A reported or forecast wind is the direction it blows from and is normally given in degrees True; an ATC surface wind passed by radio is given in degrees Magnetic. Mixing the two, or treating a "from" direction as a "towards" direction, reverses your drift correction.
• Treating longitude like latitude. One minute of latitude is always one nautical mile; one minute of longitude is one nautical mile only at the equator and shrinks with the cosine of latitude. Forgetting the cosine is the classic departure error.
• Measuring distance on the wrong scale. Always measure against the latitude scale at the side of the chart at the mid-latitude of the leg, never the longitude scale along the top.
• Reversed VOR sensing. Set the OBS to the course you intend to track, the right way round; a course set 180° out gives reverse needle sensing and tempts you to steer away from the track.
• Forgetting slant range. DME reads the straight-line distance to the station, not the distance over the ground. Directly overhead a station at 6,000 ft, the DME reads about 1 nm even though you are right above it; the error matters only close in and high up.
• Ground speed versus airspeed. Time and fuel depend on ground speed; only the wind triangle gives you that from TAS. Planning a leg on TAS alone, ignoring a headwind, is how candidates underestimate time and fuel.
• Ignoring units. Knots, statute miles, kilometres, feet and metres all appear; a question may offer a numerically correct answer in the wrong unit. Convert deliberately and label every figure.

Navigation rewards two quite different kinds of preparation, and the most efficient candidates treat them as two separate jobs.

1. Drill the facts that are pure recall. The chart-property contrasts (Mercator versus Lambert; conformal; where great circles and rhumb lines lie), the radio-aid taxonomy (VOR, NDB/ADF, DME, GNSS and what each measures and its limitations), the TVMDC definitions, and the time/longitude ratio are all memorisation. Build a one-page table for each and test yourself until the answer arrives without re-reading the question.
2. Practise the arithmetic until the rules of thumb are automatic. Sit down with a navigation computer or calculator and run a batch of problems by hand: latitude/longitude-to-distance, TVMDC conversions, CAS-to-TAS, the 1-in-60 rule, wind-triangle drift and ground speed, and time-from-longitude. Repetition turns each into a reflex, which is what you need when the clock is running — in the exam and in the aircraft.

In the exam itself, a few tactics consistently help:

• Estimate before you compute. Round speeds and distances to friendly numbers, get a ballpark answer, and use it to reject the obviously wrong options. Many questions are designed so a good estimate already isolates the correct multiple-choice answer.
• Write the TVMDC column out every single time rather than trusting mental sign-juggling.
• Watch the units in both the question and the answers, and convert deliberately.
• Sanity-check the direction of every correction: a stronger headwind must lower ground speed and raise time; more crosswind must increase drift. If your answer moves the wrong way, you have applied something backwards.
• Manage the clock. The numerical questions take longer than the recall ones, so bank the quick recall marks first, then return to the arithmetic with the time that remains.

Above all, keep linking the theory back to the cockpit. Every formula here exists to answer one of two questions in the air — am I on track? and am I on time? — and a candidate who understands the navigation that way, rather than as isolated sums, finds both the exam and the actual cross-country far easier.

With 121 questions, the Navigation bank is the second-largest in the app and easily the most numerical. Roughly a third of the questions are pure chart theory (Mercator vs Lambert, what conformal means, where great circles and rhumb lines are concave or convex), a third are radio-aid and radar trivia (VOR, NDB/ADF, DME, GPS, SSR Mode A/C/S), and the remaining third are arithmetic (lat/long change for a given distance, TVMDC conversion, ground-speed and wind triangle, civil twilight, longitude-to-time). The clusters below are the most efficient way in.

• Mercator and Lambert chart properties: the largest cluster. On a Mercator, parallels of latitude are straight lines, scale increases away from the equator, and rhumb lines are straight. On a Lambert, parallels are concave to the pole, scale is reasonably constant across the chart, and great circles approximate straight lines while rhumb lines curve concave to the pole. Both projections are conformal/orthomorphic — meaning angles are preserved, not distances or shapes.
• True, magnetic, compass — TVMDC: variation is the angle between True North and Magnetic North; deviation is the residual aircraft-induced error. Isogonals are lines of equal variation. Deviation is set by aircraft design and is largely constant for a given heading; the standard arithmetic question gives you compass plus variation plus deviation and asks for true.
• Latitude, longitude and the size of the Earth: one nautical mile equals one minute of arc along a meridian; one degree of latitude is 60 nm; one minute of longitude varies as the cosine of the latitude. Standard arithmetic: 720 nm east of Greenwich on the equator is 12 degrees of longitude; 300 nm south from 15°S puts you at 20°S.
• Time, longitude and civil twilight: Local Mean Time is referenced to the sun; the International Date Line runs at roughly 180° longitude with the east side one day earlier than the west side; civil twilight is defined as the centre of the sun being 6° or less below the horizon. Time-conversion questions reduce to four minutes per degree of longitude.
• VOR, ADF and DME basics: a VOR radial is the bearing outbound from the station, so a heading of 310° M when crossing the 130 radial means the station is behind and to the left. DME works by SSR principles installed on the ground unit. ADF accuracy is best when the aircraft flies straight and level; NDB serves both terminal and enroute navigation but is being replaced by GPS.
• NDB wave behaviour and interference: NDBs transmit in the LF/MF band using ground waves, are affected by night effect, coastal refraction (minimised by using NDBs close to the coast or where radials cross the coast near perpendicular), and erratic deflection from lightning at any time of day.
• GPS and satellite constellation: 24 operational satellites in orbit at any time excluding spares; four satellites are required for a 3-D fix; civilian receivers are accurate to about 100 m for 95% of the time; ionospheric error is the dominant accuracy degradation; the receiver uses the satellite almanac to choose the best geometry and the RAIM algorithm to drop a failed signal automatically.
• Radar and transponders: primary radar gives bearing and distance from reflected energy; secondary radar requires a transponder reply on a separate frequency, and has a longer range than primary. SSR Mode A shows only the squawk code; Mode C adds pressure altitude (referenced to 1013.25 hPa). SSR-derived speed is ground speed because it is computed from successive position fixes.
• Airspeeds — IAS, CAS, TAS: CAS is IAS corrected for position and instrument error; TAS is CAS corrected for density (altitude and temperature). At about 7,500 ft in ISA the rule of thumb is roughly 2% per 1,000 ft, so a TAS of 170 kt corresponds to a CAS of about 152 kt.
• 1-in-60 corrections and wind triangle arithmetic: travelling half of an 80 nm leg and finding yourself 3 nm right of track requires a 9° heading correction (4.5° to remove the existing error plus 4.5° to converge over the remaining 40 nm). The wind-triangle questions in the bank are sized so that mental approximation gets you to the correct multiple-choice answer.
• VHF range and propagation: VHF lives between 30 and 300 MHz and is line-of-sight, with range roughly 1.23 × √altitude_in_feet in nautical miles (about 100 nm at 8,000 ft); intervening terrain or large bodies of water reduce accuracy of VHF direction-finding.

Because the Navigation bank rewards both memorisation and quick arithmetic, prepare in two phases. First, drill the chart-property table and the radio-aid taxonomy until you can answer Mercator/Lambert and VOR/NDB/DME questions without re-reading the stem. Then sit at a flight computer (CX-3 or whiz-wheel) and run twenty TAS/CAS, 1-in-60 and wind-triangle problems by hand until the mental rules of thumb take over. With those two foundations the longitude-to-time and SSR-mode questions fall into place as bonus marks.