Is time lost fighting a headwind gained back when riding a tailwind?

As Wolfgang Langewiesche wrote in chapter 6 in “Stick And Rudder” - And then, there is the wind.

This is why it is important to understand that fuel is time in your tanks, and that you know how much time a flight will take. When planning a flight, it is your groundspeed (derived from your airspeed and wind) that will tell you how long, in time, you will need to complete the flight.

Not assuming time to climb, just cruising, lets look at a really simple example to demonstrate:

Airspeed 100 knots, no wind, so groundspeed is 100 knots.

A 150-mile flight eastbound will take 1.5 hours, and the return trip westbound will take 1.5 hours. 3.0 hours round trip.

Now, let’s plan with a 50 knot west wind. Airspeed 100 knots, so groundspeed eastbound is 150 knots and groundspeed westbound is 50 knots.

Most will say it doesn’t matter as the extra time on the westbound leg will be cancelled out by the lesser time on the eastbound leg and it will still take 3.0 hours for the round trip flight.

But not so fast!

Using any E6B, eastbound at 150 knots will take 1.0 hour; westbound at 50 knots will take 3.0 hours. 4.0 hours round trip. One full hour longer than the no wind flight.

If your aircraft has 3.5 hours of fuel on board, you can make the no wind flight, but not the flight with wind. Same distance for each, but a marked difference in the time to complete each.

Time lost fighting a headwind is not gained back riding a tailwind.

1 Replies

Here's a little math to prove it. If you remember that the denominators must be the same to add fractions, that's the key. Suppose D = distance, TT = total time, AS = air speed, WS = wind speed. Then the equation for a direct headwind and tail wind is TT = D/(AS - WS) + D/(AS + WS) = 150/(100 - 50) + 150/(100 + 50) = 150/50 + 150/150 = 450/150 + 150/150 = 600/150 = 4. With WS = 0 the equation becomes TT = 150/100 + 150/100 = 300/100 = 3. This is a rational function which graphs as a hyperbola and is therefore non-linear. As wind speed increases, the trip becomes much longer.