## Winds Aloft Calculation

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:

3000 | 6000 | |

YWG | 2825 | 2728-07 |

YBR | 3030 | 3132-06 |

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:

- Find wind speed and direction at the required altitude at the respective airports.
- 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.