Tanker Shuttle Math: Does 400 gpm Actually Arrive?
At 09:40, a rural two-story dwelling is burning with no hydrant within 3 miles. The incident commander sets a required fire flow of 400 gpm and orders a tanker shuttle. Tanker 1 carries 2,000 gallons; Tanker 2 carries 1,500 gallons. The fill site loads at 500 gpm, the dump site empties at 1,000 gpm, and each tanker spends 8 minutes in travel per round trip, from the fill site to the dump site and back. Loading, travel, and dumping do not overlap. Assume tankers cycle independently, with no queuing at either site. A third tanker, identical to Tanker 1, is available from a neighboring district 25 minutes away. Two 1¾-inch handlines and one 2½-inch line are currently in service, and the IC must decide within 10 minutes whether to request the additional tanker.
1. Compute the sustained delivery rate of the current two-tanker shuttle and state whether it meets the 400 gpm requirement. Show the per-tanker cycle math.
Read the worked answer
Each tanker delivers one load per cycle, so its average rate is load ÷ cycle time.
Tanker 1 (2,000 gal)
- Fill: 2,000 ÷ 500 gpm = 4 min
- Dump: 2,000 ÷ 1,000 gpm = 2 min
- Travel: 8 min
- Cycle: 4 + 2 + 8 = 14 min
- Rate: 2,000 ÷ 14 = 142.9 gpm
Tanker 2 (1,500 gal)
- Fill: 1,500 ÷ 500 = 3 min
- Dump: 1,500 ÷ 1,000 = 1.5 min
- Cycle: 3 + 1.5 + 8 = 12.5 min
- Rate: 1,500 ÷ 12.5 = 120.0 gpm
Total: 142.9 + 120.0 ≈ 263 gpm
That is about 137 gpm short of the 400 gpm target - roughly a 34% shortfall. The shuttle, as run, cannot support the fire flow the IC has set, regardless of how many lines are laid.
2. What is the minimum number of additional 2,000-gallon tankers needed to reach 400 gpm? Show the inequality and comment on whether the answer is operationally comfortable.
Read the worked answer
Let n = additional 2,000-gal tankers. Each contributes 142.9 gpm.
263 + 142.9n ≥ 400 142.9n ≥ 137 n ≥ 0.96 → n = 1 tanker
Check: 263 + 142.9 = 405.7 gpm, a margin of only about 6 gpm (about 1.4%).
Operational judgment: the arithmetic answer is one, but one is a poor plan.
- The margin is smaller than the rounding and timing error in any real shuttle (a slow dump connection, a traffic pause, a fill site that slows).
- The third tanker is 25 minutes out, and the fire will grow while it travels. Request it now, not when the shortfall is confirmed by the fireground.
- Two 1¾-inch and one 2½-inch line flowing near capacity will expose any shortfall immediately as pressure loss at the panel.
So: request one additional tanker to satisfy the math, and simultaneously look for a better supply - a dump tank to cut dump time, a closer fill site, or a second arriving engine - because a 6 gpm cushion is not a supply.
3. Suppose the fill site's rate drops to 250 gpm. With the one additional tanker in service, does the shuttle still meet 400 gpm? Show the recalculation.
Read the worked answer
Fill time doubles for each tanker; dump time and travel are unchanged.
Tanker 1 and Tanker 3 (2,000 gal each)
- Fill: 2,000 ÷ 250 = 8 min; dump 2 min; travel 8 min
- Cycle: 8 + 2 + 8 = 18 min
- Rate: 2,000 ÷ 18 = 111.1 gpm each
Tanker 2 (1,500 gal)
- Fill: 1,500 ÷ 250 = 6 min; dump 1.5 min; travel 8 min
- Cycle: 6 + 1.5 + 8 = 15.5 min
- Rate: 1,500 ÷ 15.5 = 96.8 gpm
Total: 111.1 + 96.8 + 111.1 ≈ 319 gpm - short of 400 gpm by about 81 gpm.
One more 2,000-gal tanker at 111.1 gpm would bring it to about 430 gpm, and that is the minimum that clears the target.
The lesson: the fill rate, not the tank size, becomes the controlling factor once it slows. The fix is to add tankers, add a second fill site or pumper at the water source, or reduce the demand - not to assume the same shuttle that worked at 500 gpm still works at 250 gpm.