The Patrol That Had to Turn Back
A 1:50,000 map shows your start at grid 4527 and an observation post at 4927. The straight line between them measures 8 cm on the map; a river runs between the two points. A road crosses the river at a bridge at grid 4728, and the road is marked as a metalled track. The direct line crosses a 300 m hill and a patch of thick scrub. Your patrol of six cadets must leave at 14:00 and be back at the school by 18:00. One cadet has a sprained ankle and can walk at about 2 km/h on the road but less on rough ground. Normal road speed for the patrol is 3 km/h; cross-country is 1.5 km/h. Magnetic declination on the map is 2°E for 2019, with annual variation 5'E. Today is 2026. You have a prismatic compass and one map.
1. Calculate the ground distance of the direct route and of the road route via the bridge; which route do you recommend and why?
Read the worked answer
Direct route: 8 cm × 50,000 = 400,000 cm = 4 km. Road route: start 4527 to bridge 4728 is 2 km east and 1 km north, giving √5 = 2.24 km; bridge 4728 to observation post 4927 is 2 km east and 1 km south, giving another 2.24 km; total 4.48 km. The road is only 0.48 km longer, but the direct route crosses a 300 m hill and thick scrub at 1.5 km/h, taking at least 2 hours 40 minutes and probably more with a sprained ankle. The road at 3 km/h takes about 1 hour 30 minutes. Recommend the road via the bridge because the speed advantage outweighs the extra distance and the metalled surface suits the injured cadet. However, at the injured cadet's pace of 2 km/h the road takes about 2 hours 14 minutes one way, which changes the timing decision.
2. Calculate the magnetic bearing for the first leg of the road route, allowing for declination and annual variation.
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First leg is from 4527 to 4728: 2 km east and 1 km north. The grid bearing is tan^-1(2/1) = 63° from north, i.e. about 063°. Declination in 2019 is 2°E; annual variation is 5'E for 7 years, which is 35' east, so total declination in 2026 is 2°35'E. With east declination, magnetic north lies east of grid north, so the magnetic bearing is smaller than the grid bearing: 063° − 2°35' = 060°25', set about 060° on the prismatic compass. Before moving, check the compass and take a back-bearing on a distant object. Do not apply the declination in the wrong direction; adding it would take the patrol south of the bridge.
3. Work out the timings and decide whether the patrol should go, and what turn-back rule you would set.
Read the worked answer
Normal road party: 4.48 km at 3 km/h = about 1 hour 30 minutes, arriving at 15:30. With 20 minutes at the observation post, the return takes another 1 hour 30 minutes, reaching school at 17:20, inside 18:00. With the injured cadet at 2 km/h: 4.48 km takes about 2 hours 14 minutes, arriving at 16:14; the return would reach school at 18:28, after the deadline. Decision: do not take the injured cadet on the full patrol. Leave him at school with a buddy and a charged phone, or reduce the objective to the bridge and return by 16:30. Set a turn-back rule: if the patrol is not at the bridge by 15:00, or not at the observation post by 15:30, turn back; also fix a hard turnaround at 16:00 regardless of position. Report the plan to the ANO.