Why is the mean of two ground speeds not necessarily the route average?

Why the route average is weighted by time

Crabwise's time–speed–distance screen solves one of three modes: time t = D ÷ GS × 60, speed GS = D ÷ (t ÷ 60), or distance D = GS × t ÷ 60, with distance in nautical miles, speed in knots and time in minutes. A route average uses the speed mode with the route's total distance and total minutes. Averaging two leg speeds gives each leg equal weight, while the slower leg actually lasts longer and therefore counts for more.

The same total-over-total rule applies whether the legs are equal in distance or in time; only when both legs last the same number of minutes does the plain mean of their speeds match the route value.

Worked example

A route covering 150 NM in 90 minutes averages 100 kt. The mean of leg speeds 120 kt and 90 kt is 105 kt, which does not describe the 30-minute/60-minute route in the companion example.

Average over the defined route interval (kt)

100

Calculate it from totals

1. Solve each leg's time in the time mode from its distance and ground speed.
2. Add the leg distances and, separately, the leg minutes.
3. Switch to the speed mode and enter the total distance with the total minutes.
4. Write down which interval the minutes cover, for example airborne time only.

Equal distances at different speeds

Fly 60 NM at 120 kt and another 60 NM at 80 kt. The first leg takes 60 ÷ 120 × 60 = 30 minutes; the second takes 60 ÷ 80 × 60 = 45 minutes. The route is 120 NM in 75 minutes, so the speed mode returns 120 ÷ (75 ÷ 60) = 96 kt. The plain mean of 120 and 80 is 100 kt, which would understate the route time by 3 minutes.

First-leg time (min)

30

Second-leg time (min)

45

Route average from totals (kt)

96

Unweighted mean of leg speeds (kt)

100

Common mistakes

• Averaging the two speeds shown on a log sheet instead of their distances and times.
• Including a hold or a ground stop in the minutes for one calculation and leaving it out of another.
• Using true airspeed in the speed mode; the route average is a ground-speed quantity.

What the number covers

The average describes only the interval whose distance and minutes you entered. It is not a forecast for the next flight. The navigation chapter of the FAA handbook below uses the same time, speed and distance relations.

Primary sources and related work

• FAA Pilot’s Handbook: navigation and basic flight calculations
• NIST SI conversion factors