Route and distance check for a stores trolley
During a night movement exercise at a naval depot, a Tradesman Mate acts as guide for a stores trolley moving from the quarter guard to the pump house. Only metalled roads may be used, because the direct line crosses a magazine enclosure. The route issued is: 300 m north to the main gate; turn right and go 400 m east along the perimeter road; turn left and go 200 m north; turn right and go 300 m east, where the pump house stands. The escort commander makes two statements before signing the movement log: first, that the pump house lies to the north-east of the quarter guard; second, that if a straight road could ever be built to the pump house, the trolley would save about 500 m compared with the present route. A second sailor adds that the return journey can be found simply by writing the same turns in reverse order, and that reversing left into right is unnecessary.
1. Find the total road distance travelled and the straight-line distance and bearing of the pump house from the quarter guard.
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Total road distance = 300 + 400 + 200 + 300 = 1,200 m.
Net displacement. Combine north-south and east-west legs separately:
- North: 300 + 200 = 500 m
- East: 400 + 300 = 700 m
Straight-line distance by Pythagoras = √(500² + 700²) = √(250,000 + 490,000) = √740,000 ≈ 860 m.
Direction. The pump house is 500 m north and 700 m east of the start, so it lies north-east of the quarter guard, closer to east than to north. The commander's first statement is therefore correct.
2. Test both of the commander's claims and the second sailor's claim, and state what you would enter in the movement log.
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Claim 1 (north-east): true, as the displacement shows.
Claim 2 (saving of about 500 m): false. The straight road would be about 860 m against 1,200 m by road, a saving of roughly 340 m, not 500 m. To save 500 m the straight line would have to be 700 m, which the Pythagoras result rules out. The commander has apparently subtracted the 700 m eastward leg instead of using the diagonal.
Sailor's claim (reverse the turns, no inversion): false. Retracing a route requires both reversing the order of the legs and inverting each turn - left becomes right. The saving in thought is small, but a wrong return route at night inside a depot is a real risk.
Log entry: route as issued, 1,200 m one way, pump house bearing north-east at about 860 m line-of-sight, commander's 500 m saving noted as incorrect, return route to be written out leg by leg rather than improvised.
3. Write the correct return route from the pump house to the quarter guard.
Read the worked answer
Reverse the sequence and invert every turn:
- From the pump house, head west 300 m (reverse of the last eastward leg).
- Turn left (original right, inverted) and go south 200 m.
- Turn right (original left, inverted) and go west 400 m.
- Turn left (original right, inverted) and go south 300 m to the main gate and the quarter guard.
Check by coordinates: starting at (700 east, 500 north) the legs give (400, 500) → (400, 300) → (0, 300) → (0, 0), which is the quarter guard. Distance back is the same 1,200 m.