An Airplane Has A Ground Speed Of 350 Km.docx

An airplane has a ground speed of 350 km/hr in the direction due west. If there is a wind blowing northwest at 40 km/hr, calculate the true air speed and heading of the airplane? Airspeed is the speed of the aircraft relative to the wind blowing around it. Ground speed is the speed of the aircraft relative to the ground. There will be higher ground speed and low true airspeed if there is a tailwind. There will be low ground speed and higher airspeed is a headwind. Now, Ground speed = True Airspeed + Windspeed. So, True Airspeed = Ground speed — Wind speed. Aeronautical Calculations of Headwind and Crosswind. Here it is given that the aircraft is moving towards west. Therefore it is heading 270degrees at a Groundspeed of 350 kmph. Now, the wind is blowing from Northwest.It means it is blowing from 315 degrees. The wind is blowing from NW to SE. So, the aircraft has both headwind component as well as cross wind components. So, angle between the wind and aircraft is therefore 315 — 270 = 45 degrees.

It is to be remembered that Headwind = Windspeed * Cos (A). Crosswind = Windspeed * Sin (A). So, here, the headwind will be HW = 40 * Cos 45 = 40 * 0.707 = 28.28 km/h. CW = 40 * Sin 45 = 40* 0.707 =28.28 km/h. True Airspeed (TAS) = 350 — ( — 28.28) = 350+28.28 = 378.28 km/h. Windspeed will be negative as it is a headwind. It will be positive as it is a tailwind.

Due to the 45 degrees of cross wind, the track of the airplane will change to the below calculated Drift Angle. Drift Angle = (Windspeed * Angle between aircraft & wind) / True Airspeed. Drift angle = (40 *45)/378.28 = 4.75 degrees towards the Wind. So, the drift angle will be also 4.75 degrees.

So, the new heading of the aircraft will be 274.75 degrees (West north-West); the true airspeed of the aircraft will be 378.28 km/h. See that the groundspeed is less than the true airspeed. So, it is headwind.