A commenter on a post regarding the PPL tests had trouble with the following question:

The average wind applicable to a direct flight from Winnipeg (CYWG) to Brandon (CYBR) at 5,500 ft would be
(1) 290°M at 30 kt.
(2) 290°T at 30 kt.
(3) 310°M at 31 kt.
(4) 310°T at 31 kt.

FDCN CWAO 061920
ISSUED 1200Z 07 FEB 2007 FOR USE 6-17Z

	3000	6000	9000	12000	18000	24000
YWG	2825	2728-07	2932-10	2935-15	2939-26	2841-38
YBR	3030	3132-06	3133-10	3135-15	3041-28	2948-40
YYQ	3529	3428-13	3229-14	3130-19	3032-32	2733-42
YYL	3327	3435-10	3338-14	3337-19	3136-31	3038-44

He got as far as interpolating the wind speeds and directions at 4,500 feet by averaging the respective values but did not know how to proceed after that. Here is how I solved it:

The pertinent information is as follows:

Between 6,000’ and 3,000’ there is a difference of 3,000’. The altitude required is 5,500’ which is 2,500’ above 3,000’ (or 500’ below 6,000’ depending how you look at it. For the purposes of this example I will be using the 2,500’). There are two steps to this problem:

1. Find wind speed and direction at the required altitude at the respective airports.
2. Average them to find the the average wind.

Step 1: Finding wind speed and direction at the respective airports

I will show you the calculation for YWG. Follow the same steps to find the values at YBR.

Wind Direction Adjustment = (270 – 280) * 2500 / 3000 = – 8.333…
Wind Speed Adjustment = (28 – 25) * 2500 / 3000 = 2.5

Wind Direction = 280 + –8.333… = 271°
Wind Speed = 25 + 2.5 = 27.5 kt

At YBR the wind direction would be 308° and wind speed would be 32 kt.

Explanation: Finding the wind at non-reported levels is simply a matter of properly interpolating the information you are provided. In this case I used a weighted average to give me the values I needed. One thing to keep in mind with this calculation is that order is important. The order I followed was going from 6,000’ (I took the values here) to 3,000’ (subtracted these values) then back up to 5,500’ (multiplied by the weight, 2,500/3,000 and added to the values at 3,000’).

Another way to think about it is you will be going 2,500 / 3,000 = 83% of the way from 3,000’ to 6,000’ so you add 83% of the difference between measurements at the different altitudes to the values at the lower altitude (or you subtract 17% of the difference from the values at the higher altitude).

Step 2: Average wind

Average wind direction = (308 + 271) / 2 = 289.5
Average wind speed = (32 + 27.5) / 2 = 29.75

With rounding, the applicable wind is from 290 at 30 kts. Keeping in mind that the FD reports directions in degrees TRUE leads to the correct answer being (2) 290°T at 30 kt.

Notice that these calculations assume the change from one altitude to another is linear which may not always be the case.

How would you have solved it? Leave your reply in the comments!