Instructor copy

Master answer key

Every question on the site with its answer and explanation, plus the worked values behind the numeric exercises. Answers that the app computes are read from the same data the lessons use, so they cannot drift from what a student sees.

This page is deliberately not linked from the site menu. Its URL is /answers, and it is marked noindex so search engines leave it alone.

Station · Knowledge check

UTM & MGRS

Eight questions, one per station idea, on /knowledge-check.

1. How many UTM zones are there?

  1. A24
  2. B60Answer
  3. C180

Sixty zones of 6° each cover the 360° of longitude. Zone 1 starts at 180°W and numbering runs east to zone 60.

2. How many degrees of longitude wide is a standard UTM zone?

  1. A3°
  2. B6°Answer
  3. C10°

Six degrees. That keeps distortion small inside the zone, because only the central meridian is true to scale.

3. What does UTM measure coordinates in?

  1. ADegrees and minutes
  2. BMetresAnswer
  3. CNautical miles

UTM coordinates are linear distances in metres from the zone's false origin, with eastings to the east and northings to the north.

4. What is the difference between UTM and MGRS?

  1. AThey use different projections of the Earth
  2. BMGRS labels the UTM plane with lettered 100 km squares; the coordinates underneath are still UTMAnswer
  3. CUTM is used in the northern hemisphere and MGRS in the southern

MGRS is a grid-reference system built on top of UTM. Same projection, same metres; MGRS just makes the numbers easier to say and write.

5. How large is one MGRS 100 km square?

  1. A1 km × 1 km
  2. B10 km × 10 km
  3. C100 km × 100 kmAnswer

Each one is 100 km × 100 km and carries a two-letter identifier, such as VR for the square we followed.

6. Which direction do Eastings increase?

  1. AToward the north
  2. BToward the eastAnswer
  3. CToward the west

Eastings increase to the east. They are read first, along the bottom edge of the map.

7. Which direction do Northings increase?

  1. AToward the east
  2. BToward the south
  3. CToward the northAnswer

Northings increase to the north, read up the side of the map, and always after the easting.

8. What does a six-digit grid reference represent?

  1. AA 1 km square
  2. BA 100 m squareAnswer
  3. CA 10 m square

Six digits identify a 100 m square inside a 1 km cell: three digits of easting, then three of northing. Eight digits give 10 m, ten digits give 1 m.

Lesson · Knowledge check

Resection

Seven questions at the foot of /navigation/resection.

1. Which of these is the best landmark for a resection?

  1. AThe relay towerAnswer
  2. BThe edge of a wood
  3. CSomewhere along Otter Creek

A landmark must be a single point you can identify on the ground and on the map. A wood edge or a creek is a line: you cannot tell which point of it you sighted.

2. What is a back bearing?

  1. AThe bearing with the GMA removed
  2. BThe bearing in exactly the opposite direction, 180° differentAnswer
  3. CThe bearing read from the rear scale of the compass

A back bearing differs from the bearing by 180°. If the landmark is on 050° from you, you are on 230° from the landmark.

3. You sight a landmark on a grid bearing of 050°. In which direction is the line plotted from the landmark?

  1. A050°
  2. B140°
  3. C230°Answer

The line is drawn from the landmark back toward you, on the back bearing: 050° + 180° = 230°.

4. Why take bearings to more than one landmark?

  1. AOne bearing gives a line, not a pointAnswer
  2. BThe compass is more accurate the second time
  3. CTo average out the declination

One bearing only tells you that you are somewhere on a line. A second line gives a crossing, and a third checks it.

5. Three lines of position form a small triangle. Where are you most likely to be?

  1. AAt the corner nearest the closest landmark
  2. BInside or very near the triangleAnswer
  3. CAt the landmark that gave the longest line

With small random errors your position is inside or close to the triangle. Its size shows the uncertainty. A large triangle means a mistake: check the landmarks and the arithmetic.

6. A bearing is 2° out and the landmark is 3 km away. About how far is that line of position from your true position?

  1. AAbout 10 m
  2. BAbout 100 mAnswer
  3. CAbout 1 km

The offset is distance × sin(error): 3,000 m × sin 2° is about 105 m. Near landmarks give tighter lines than far ones.

7. Which set of landmarks gives the most reliable fix?

  1. ATwo landmarks 15° apart
  2. BTwo landmarks almost opposite each other, 175° apart
  3. CThree landmarks spread about 60° to 120° apartAnswer

Lines from landmarks 15° or 175° apart cross at a shallow angle, so a small error moves the crossing a long way. Well spread landmarks cross cleanly, and the third line is a check.

Lesson · Knowledge check

Error and relocation

Four questions at the foot of /navigation/error-and-relocation.

1. The ground around you does not match the map at the checkpoint you believe you have reached. What do you do first?

  1. ACarry on to the next checkpoint and check again there
  2. BStop and reassessAnswer
  3. CTurn round and walk back at once

Stop. Walking on, or back, from a position you have not confirmed only adds to the error.

2. You hold a bearing 5° off for two legs of 2 km each. Roughly how far off line are you?

  1. AAbout 35 m
  2. BAbout 175 m
  3. CAbout 350 mAnswer

Each 2 km leg adds 2,000 m × sin 5°, about 175 m. The second leg starts from the first one's error, so the two add up to about 350 m.

3. Every leg has taken you to the right of your checkpoints by a similar angle. What is the most likely cause?

  1. AA grid-magnetic angle that was not appliedAnswer
  2. BA pace count that is too long
  3. CA misidentified hill

The same angular error on every leg points to the compass setting. A distance error moves you along the leg, not to one side.

4. When is retracing to your last known point the better choice?

  1. AAlways
  2. BWhen you cannot get a fix you trustAnswer
  3. CNever: it wastes time

If landmarks are few, the lines cross badly or the ground does not confirm the fix, go back to a point you can be sure of. With a confirmed fix, resume from it.

Compass familiarization

Component identification

The exercise asks for each component by name, in this order: 12 taps. Any part can be flipped to inspect the underside when the screw or the rear scale is asked for.

1.“Tap the magnetic needle”

Answer: the magnetic needle. The magnetised needle. Its red end points to magnetic north.

Turn your body, or the map, until the red end sits inside the orienting arrow.

2.“Tap the rotating bezel”

Answer: the rotating bezel. The graduated ring, marked from 0° to 360° in 2° steps.

Turn it to set or read a bearing at the index line.

3.“Tap the direction-of-travel arrow and index line”

Answer: the direction-of-travel arrow and index line. The arrow on the baseplate that shows where the bearing points, and the line the bezel is read against.

On the map, point it from where you are to where you are going. On the ground, walk where it points once the needle is boxed.

4.“Tap the orienting arrow”

Answer: the orienting arrow. The red outlined arrow on the floor of the housing.

Box the red end of the needle inside it. The direction-of-travel arrow then points along the bearing at the index line.

5.“Tap the baseplate”

Answer: the baseplate. The clear plate everything is mounted on.

Lay a long edge along the line between two points on the map to take a bearing, or use it as a straight edge.

6.“Tap the mirror”

Answer: the mirror. The hinged lid with a mirror inside.

Hold the compass at eye level, sight the object and box the needle in the reflection for a more accurate bearing.

7.“Tap the measurement scales”

Answer: the measurement scales. The rulers along the edges of the baseplate.

Measure the distance between two points on the map, or the last digits of a grid reference inside a square.

8.“Tap the compass housing”

Answer: the compass housing. The liquid-filled capsule that holds the needle.

Turn it until the orienting lines run parallel to the map's grid lines, with their north end to grid north.

9.“Tap the north indicator”

Answer: the north indicator. The luminous mark at the bezel's N.

Check it is toward grid north on the map, not south, before reading a bearing.

10.“Tap the sighting line and notch”

Answer: the sighting line and notch. The line down the mirror and the notch at the top of the lid.

Aim the notch at the object and keep the line running through the pivot in the reflection, so the compass is not skewed.

11.“Tap the declination adjustment screw”

Answer: the declination adjustment screw. The small brass screw on the back of the housing.

Set it to the sheet's grid-magnetic angle. The bezel then reads grid bearings directly, with no arithmetic.

12.“Tap the rear adjustment markings”

Answer: the rear adjustment markings. The declination scale on the back of the housing, marked E and W.

Read it to confirm how many degrees east or west are set before you rely on the compass.

The exercise accepts only the asked component; any other tap names what was tapped and invites another try.12 components in total are described on the lesson page.

Compass familiarization

Bearing conversions

Ten numeric answers at the foot of /navigation/compass-familiarization. The sheet's grid-magnetic angle is 13.4° E.

1. Map margin: 12.2° E (2018), annual change 9′ E. It is 2026. Angle now (east is positive)

13.4°accepts ±0.2°

8 years × 0.15° = 1.2° E, and 12.2° E + 1.2° = 13.4° E.

2. Map margin: 9° E (2010), annual change 6′ E. It is 2020. Declination now (east is positive)

10°accepts ±0.2°

6′ is 0.1° a year, so 10 years adds 1° E: 9° + 1° = 10° E.

3. Map margin: 8° W (2015), annual change 6′ W. It is 2025. Angle now (west is negative)

-9°accepts ±0.2°

6′ is 0.1° a year, so 10 years adds 1° more west: 8° W + 1° = 9° W, that is −9°.

4. Sheet GMA 13.4° E. Grid bearing 075°. Magnetic bearing

062° (61.6°)accepts ±1°

Magnetic = grid − GMA = 075 − 13.4 = 61.6°, set 062°.

5. Sheet GMA 13.4° E. Magnetic bearing 310°. Grid bearing

323° (323.4°)accepts ±1°

Grid = magnetic + GMA = 310 + 13.4 = 323.4°.

6. Sheet GMA 13.4° E. Grid bearing 008°. Magnetic bearing

355° (354.6°)accepts ±1°

008 − 13.4 is below zero, so add 360°: 354.6°.

7. GMA 6° W. Grid bearing 350°. Magnetic bearing

356° (356°)accepts ±1°

West is negative: 350 − (−6) = 356°. A west angle is added going from grid to magnetic.

8. Grid bearing 140°, magnetic bearing 151°. GMA (west is negative)

-11°accepts ±1°

GMA = grid − magnetic = 140 − 151 = −11°, which is 11° W.

9. Forward bearing 047°. Back bearing

227° (227°)accepts ±1°

A back bearing is the forward bearing plus 180°, less 360° if it passes 360: 047 + 180 = 227°.

10. Forward bearing 290°. Back bearing

110° (110°)accepts ±1°

290 + 180 = 470, and 470 − 360 = 110°.

Error and relocation

How far off?

Four numeric answers on /navigation/error-and-relocation.

1. A bearing is 1° off. Metres off line after 1,000 m

17 maccepts ±2m

Offset = distance × sin(error) = 1,000 × sin 1° = 17 m.

2. A bearing is 6° off. Metres off line after 2,400 m

251 maccepts ±15m

2,400 × sin 6° = 251 m.

3. Your pace count runs 10% long on a 3,000 m leg. Metres past the checkpoint

300 maccepts ±5m

10% of 3,000 m is 300 m, along the line of the leg.

4. Three legs of 2,000 m, each walked 4° to the right. Metres off line at the end

420 maccepts ±25m

Each leg adds 2,000 × sin 4° = 140 m, and each starts from the last one's error: about 420 m.

Route cards

Complete the example card

Five answers on /navigation/route-cards, taken from the worked route from Camp Harrow to the relay tower.

1. Leg 1 grid bearing is 102°. Magnetic bearing

089° (89°)accepts ±1°

Magnetic = grid − GMA = 102° − 13.4° = 089°.

2. Leg 2 grid bearing is 061°. Grid back bearing

241° (241.2°)accepts ±1°

Back bearing = 061° + 180° = 241°.

3. Legs 1 to 3 are 2 560 m, 2 283 m and 3 048 m. Running total after leg 3

7890.3 maccepts ±15m

Add the legs in order: 7 890 m.

4. Leg 4 runs from 679 m to 695 m. Height gained

16 maccepts ±1m

695 − 679 = 16 m of climb to the relay tower.

5. Leg 4 magnetic bearing is 333°. Grid bearing

346° (346.4°)accepts ±1°

Grid = magnetic + GMA = 333° + 13.4° = 346°.

Grid reference · Practice

8- and 10-figure references

The practice set on the zone 18 sheet. Mark mode asks the student to find the landmark; read mode asks for the red marker's reference. Both are graded in the landmark's own 10 m or 1 m square.

Landmark8-figure (10 m)10-figure (1 m)
the farmhouse at Miller Farm18T VR 4562 306818T VR 45623 30685
the barn beside Miller Farm18T VR 4570 306418T VR 45705 30642
the survey pillar on Hill 11218T VR 4538 302118T VR 45385 30215
the jetty on Mill Pond18T VR 4536 306518T VR 45362 30655
the lone oak west of Mill Pond18T VR 4486 305118T VR 44865 30512
the hut in Cedar Wood18T VR 4615 304318T VR 46155 30435
the stone bridge where Route 7 crosses the Grey River18T VR 4402 300018T VR 44021 30003

Terrain association

The three built-in scenarios

Each scenario hides one position on the training sheet. The estimate is accepted within the tolerance, and Review reveals the distance and direction of the miss.

1.Scenario 1 · easy · tolerance 300 m

12U WD 063 449

The road runs a few hundred metres south of you, with the buildings of Camp Harrow about 1.4 km along it to the west. The ground climbs to a spot height about 2 km to the east. A road, a camp and a hill in those directions leave only one stretch of the sheet.

2.Scenario 2 · moderate · tolerance 200 m

12U WD 116 485

The high ground of Signal Ridge rises close by to the east-north-east, and the relay tower stands on its own knoll to the north-north-west, at the end of a track that passes just west of you. The road is about 700 m to the south. The tower and the ridge fix the direction; the road and the track fix the distance.

3.Scenario 3 · hard · tolerance 150 m

12U WD 133 439

Mallard Lake lies to the west-south-west and a wood stands to the south-south-east. The ground rises to a spot height about 2 km to the east. There is no road nearby, so the fix comes from the directions of the lake, the wood and the hill, and how far away each one looks.

Error and relocation

Navigation error scenarios

Nine scenarios on /navigation/error-and-relocation. The student is told the ground they can see; the cause below is what actually went wrong. Positions are revealed in the app once they relocate.

1.Drill: Off the bearing

  • The bearing was walked 12° to the right of the one on the route card.

2.Drill: Too far

  • The leg was walked 30% farther than planned, past the junction.

3.Drill: Declination not applied

  • Grid bearings were set on the compass without subtracting the 13.4° E grid-magnetic angle.

4.Drill: Map not oriented

  • The map was turned 20° off the ground when the direction was taken from it.

5.Drill: Wrong leg

  • Leg 3's bearing and distance were walked instead of leg 2's.

6.Drill: Misidentified feature

  • Signal Ridge was taken for the relay tower's hill and walked toward by eye.

7.Beginner: One clear error

  • The bearing was walked 15° to the right.

8.Intermediate: Bearing and distance

  • The bearing was walked 6° to the right.
  • The bearing drifted 5° left and the leg was walked 25% too far.

Sighted bearings can be up to ±2° out.

9.Advanced: Accumulated error

  • 4° right of the bearing.
  • 5° right and 10% too far.
  • 6° right and 15% too far.
  • 8° left of the bearing.

Sighted bearings can be up to ±3° out.

Marked in the app

Exercises with no fixed answer

These are generated from where the student clicks or where the app places the point, so the answer is produced and marked live. Use the notes below to check a student's work by hand.

Grid quiz · station 6, step “quiz”

Right-click marks the smallest square drawn at the current zoom; left-click reveals its reference. Reading right then up gives the easting digits then the northing digits, prefixed with the grid zone and the 100 km square letters. Four figures name 1 km, six 100 m, eight 10 m, ten 1 m.

Take a bearing · /navigation/orienting-and-bearings

The bearing and distance come from the ruler line the student draws. Grid bearing = atan2(Δeasting, Δnorthing); magnetic = grid − GMA; back bearing = grid + 180°. The app also reports whether the compass edge and the bezel are aligned, so the marked answers follow the drawn line.

Resection exercise · /navigation/resection

The position is random and the bearing error is set by the slider before starting. Each sight converts magnetic to grid (+GMA), then to a back bearing (±180°); two lines cross at the fix and the third checks it. The answer, the true position and the miss are shown when the fix is submitted.

Terrain association · custom scenarios

When an instructor builds a scenario in the app, its saved point is the answer. The estimate is accepted within the scenario's tolerance, and Review reports the distance and compass direction of the miss.

Values that depend on the sheet (grid-magnetic angle, landmark references, route legs) are computed when this page renders, so a change to the map or the route updates the key as well.