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Aircraft Turning
   
     
   
When an aircraft is flying in a straight line, at constant altitude, the vertical forces acting on it are in equilibrium.   
   
   
   
   
The lift generated by the air flowing past the wings is equal but opposite to the force of gravity (the weight).   
   
   
   
   
     
The pilot decides to turn to the right (from the pilot's point of view) as shown here.   
   
Suppose that the the pilot maintains the same speed.   
   
In order to cause the plane to turn (ie to follow a curved, let's assume approximately circular, path) the plane must be tilted so that a component of the lift force acts horizontally to provide the centripetal force needed to follow the curved path.  
   
     
Now look again at the forces acting on the plane.   
   
If the speed (relative to the air) remains the same, then the lift force is also the same.   
   
However, this lift force now acts in a different direction  
   
If no other action is taken, the plane will lose altitude because the vertical component of the lift force must now be less than the force of gravity  
   
   
   
   
Conclusion: in order to maintain the same height the speed needs to be increased.   
   
Don't worry... pilots are aware of this fact...  
well, most of them...  
well, some of them... maybe  
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