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The Wind Effect

The Eternal Triangle of Velocities

In every aircraft, either a human of a black box must resolve the problem of the wind

Whether a human navigator or a computer, flying from point A to B, does calculations is primarily an exercise in basic geometry. Point A is the departure base, whether it is Amberley, Pearce or Butterworth and Point B is the destination, be it Honolulu, Cocos or somewhere in SE Asia.

The problem is the wind, the moving mass of air that circles the earth. Early aviators found it was the source of power or the unseen force that blew them off course. As aircraft airspeeds increased, the wind became less of a problem, unless aviators encountered the jet stream at high altitudes. Jet streams of 200 knots are not uncommon; exhilarating if a tailwind but a drag if a headwind. Ground speeds of 650K with a tailwind Vs 250K with the same headwind are typical. A headwind will hinder a flight far more than an equivalent tailwind will assist.

Navigators have used "dead reckoning" to steer left or right of the destination so that the wind will blow them back on the desired course or required track. The technique involves solving the triangle of velocities'.

Triangle of Velocities

To arrive at B, the navigator must carry out a number of steps:

  1. Draw the course from A to B (departure & destination) on the chart or graph paper (due north to make it simple)
  2. Again to make things simple, assume the distance A-B is 450 n miles
  3. Now, determine the air speed of the aircraft, eg 150 knots – we do not yet know the time it will take, but in the order of 3 hours
  4. Determine the wind from the weather forecast, eg 30 knots from the south east, ie a bearing of 135 true (not magnetic)
  5. Draw a line from B on bearing of 135 (T) for 3 hours of wind, ie 90 n miles, to point C
  6. Draw a line connecting points A and C – this is the direction to steer the aircraft, ie the heading, 008T in the example
  7. As you steer the aircraft, it will track towards the destination, under the influence of the wind
  8. The wind has two effects – it pushes the aircraft to the left (drift, 8 degrees left in the example) and it increases its speed across the ground, ie the groundspeed
  9. Because of the increased speed, the time taken is less than 3 hours (2:40 or 2.7h)

The process above is not exactly how a professional navigator would do it. He or she would use a circular slide rule/computer and approach the solution a little differently. But, the principles are the same.

There are one or two other calculations involved and the wind rarely remains constant for the duration of the flight. The example shows the general idea of dead reckoning, which is an old approach but still basic to navigation.

Navigators and pilots still have to know the same basic principles – where they are starting (present position), where they are going (destination) and how far to aim off, ie, the heading of the aircraft, so that the wind doesn't send them elsewhere. They have no control over the ground speed (for a constant air speed).

Whether it's a nervous human, a discrete black box or a handheld GPS receiver, the ancient puzzle of the wind triangle must be solved continuously if the aircraft is to arrive at its destination safely and in the shortest time.

Lance J Halvorson