Ration Endurance in a Snow-Bound Sector
A relief column of 240 soldiers enters a snow-bound sector with ration scaled for 60 days, and no resupply is expected before Day 60. The normal daily ration weighs 1.8 kg per soldier. On the morning of Day 16 - after 15 full days of consumption - 60 soldiers are detached to reopen a road link and carry no ration with them. On the morning of Day 20 the weather breaks, and the column commander calculates that cold-weather consumption from that point onward will be 20 per cent higher per man per day, because of extra hot meals and wastage. Brigade asks for a clear answer on how long the stock will last and whether a helicopter top-up of five days' ration is needed. Each sortie lifts 900 kg and takes 40 minutes for the round trip; the drop window is 3 hours.
1. Ignoring the cold-weather increase, for how many days does the stock last after the detachment, and on what day does it run out?
Read the worked answer
Work in man-days of ration, since that is what the stock actually buys.
- Total stock = 240 men × 60 days = 14,400 man-days.
- Consumed in Days 1–15 = 240 × 15 = 3,600 man-days.
- Remaining on the morning of Day 16 = 14,400 − 3,600 = 10,800 man-days.
- Strength now 180 men, so duration = 10,800 ÷ 180 = 60 days.
So the same stock now stretches 60 days instead of 45: it lasts to the end of Day 75 (Day 15 + 60). Detaching 60 men lengthened endurance by a full third, which is the whole point of reporting in man-days rather than in 'days of ration'.
2. With the 20 per cent increase from Day 20, on what day does the ration actually run out? Show the two phases separately.
Read the worked answer
Split at the day the rate changes.
Phase 1 - Days 16 to 19 (4 days at normal rate) 4 × 180 = 720 man-days consumed. Balance = 10,800 − 720 = 10,080 man-days.
Phase 2 - from Day 20 at 20 per cent higher consumption The 20 per cent applies to what each man eats, so the day cost rises to 180 × 1.2 = 216 man-day equivalents per day. Duration = 10,080 ÷ 216 ≈ 46.67 days.
That is 46 complete days, covering Days 20 to 65, plus about two-thirds of a day - so the stock runs out during Day 66, roughly 9 days short of the Day 75 requirement.
Report to brigade as: 'Endurance Day 66, shortfall 9 days, top-up requested,' not as a single 'about 50 days', so that the shortfall is visible.
3. Is the 3-hour helicopter window enough to lift five days of ration for 180 soldiers at the higher consumption rate? Give the calculation and a recommendation.
Read the worked answer
Weight required per day = 180 men × 1.8 kg × 1.2 = 388.8 kg. Five days = 388.8 × 5 = 1,944 kg.
Sorties: 1,944 ÷ 900 = 2.16, so 3 sorties are needed. Capacity offered = 3 × 900 = 2,700 kg, leaving 756 kg of margin.
Time: 3 × 40 min = 120 minutes, which fits inside the 180-minute window with 60 minutes to spare.
Judgement points before saying 'yes':
- The margin is only one sortie. If one sortie is lost to weather, delivery falls to 1,800 kg - below the 1,944 kg needed. So plan three sorties and treat the third as the buffer, not as surplus.
- 900 kg is a weight limit; ration packs are bulky, so confirm the load is weight-limited, not volume-limited.
- Recommend a request date no later than Day 60, so a failed window can be re-flown before the stock collapses.