715 Aircraft Naviation

The Mathematics of Aircraft Navigation

Thales

Aeronautical Engineering

   Vg = Va + Vw .

SCENARIO Knowledge of aircraft navigation is vital for safety. One important application is the search and rescue operation. Imagine that some people are stuck on a mountain in bad weather. Fortunately, with a mobile phone, they managed to contact the nearest Mountain Rescue base for help. The Mountain Rescue team needs to send a helicopter to save these people. With the signal received from the people on the mountain, they determine that the bearing from the helipad (point A) to the mountain (point C) is 054° (i.e. approx. north-east). Also the approximate distance is calculated to be 50 km.

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Aircraft Navigation is the art and science of getting from a departure point to a destination in the least possible time without losing your way. If you are a pilot of a rescue helicopter, you need to know the following:  Start point (point of departure)  End point (final destination)      Direction of travel Distance to travel Characteristics of type of aircraft being flown Aircraft cruising speed Aircraft fuel capacity Aircraft weight and balance information Capability of on-board navigation equipment

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Figure-1

Some of this information can be obtained from the aircraft operation handbook. Also, if taken into consideration at the start of the aircraft design they help an aeronautical engineer to develop a better aircraft. VECTORS: A REMINDER A vector quantity has both magnitude and direction. It can be represented geometrically using a line segment with an arrow. The length of the vector represents the magnitude drawn to scale and the arrow indicates the direction. Velocity is an example of a vector quantity. AIR SPEED / GROUND SPEED / WIND SPEED An aircraft's speed can be greatly enhanced or diminished by the wind. This is the reason for the consideration of two speeds: ground speed and air speed. Ground speed is the...