How can a headwind change trip fuel without changing fuel flow?

Same flow, different time

Crabwise's required-fuel calculation starts from distance and ground speed: trip time t = D ÷ GS × 60, then trip fuel = FF × t ÷ 60. A headwind does not change the hourly flow in this model; it lowers ground speed, which lengthens the time, which raises the fuel. Reserve fuel and taxi fuel are added afterwards as separate lines.

Holding the flow and the distance fixed while changing only the ground speed isolates the wind's effect on the trip line.

Worked example

At 100 kt, a 120 NM leg takes 72 minutes and uses 9.6 units at 8 units per hour. At 120 kt the same leg takes 60 minutes and uses 8 units under the same constant-flow assumption.

Trip time for the isolated case (min)

72

Trip fuel before separate components (chosen units)

9.6

Compare two ground speeds

1. Enter the same distance and the same flow for both runs.
2. Use the ground speed from the wind triangle, not the true airspeed.
3. Read flight time and trip fuel for each run.
4. Add your reserve minutes and taxi fuel only after the trip comparison is clear.

A 150 NM leg against and with the wind

At 95 kt the leg takes 150 ÷ 95 × 60 ≈ 94.736842 minutes, and at 9.5 units per hour that is 9.5 × 94.736842 ÷ 60 = 15 units. At 125 kt the same leg takes 72 minutes and 11.4 units. The 30 kt difference in ground speed costs 3.6 units on this leg.

Flight time at 95 kt (min)

94.736842

Trip fuel at 95 kt

15

Flight time at 125 kt (min)

72

Trip fuel at 125 kt

11.4

Adding a 45-minute reserve at the same flow, 9.5 × 45 ÷ 60 = 7.125 units, and 1.5 units of taxi fuel gives a required total of 23.625 units at 95 kt and 20.025 units at 125 kt. The reserve and taxi lines are equal in both runs, so the 3.6-unit gap comes from the trip line alone.

Common mistakes

• Entering TAS as ground speed, which hides the headwind completely.
• Changing the flow and the ground speed in the same comparison.
• Reading the trip fuel line as the total and forgetting reserve and taxi.
• Recomputing the reserve from the trip time instead of from the reserve minutes you chose.

Scope

The comparison holds flow and wind constant over the leg. Climb, descent and changing winds aloft are outside it, and the app's reserve note reminds you that the legal reserve depends on your rules. The FAA navigation chapter below covers the fuel-time relation.

Primary sources and related work

• FAA Pilot’s Handbook: navigation and basic flight calculations