Why do airplanes bank when they turn?Why do airplanes bank when they turn? How would you compute the banking angle given its speed and radius of the turn? | |
Why do airplanes bank when they turn?Why do airplanes bank when they turn? How would you compute the banking angle given its speed and radius of the turn? | |
There isn't any traction of the wing on the air, like there is for a tire on the road. An aircraft cannot just yaw its wings and turn while keeping the cabin flat in the true sense.
The aerodynamic lift force acting up on the wing acts perpendicular to its plane, and just about entirely perpendicular.
If the aircraft rolls its wings and cabin to the side, then what happens is that the aerodynamic lift will push both upward and inward toward the side to which it is rolled. The inward component of the aerodynamic lift is what accomplishes the force needed to do the turning (because a turning object IS accelerating, and hence needs a force to cause that acceleration). We call such an acceleration...centripetal acceleration. The upward component of the lift, like usually, will balance the force of gravity acting upon the plane.
The derivation for the formula originates from adding up the two forces (force of gravity and aerodynamic lift) as vectors misaligned by angle theta, and then equating this net force to the mass of the aircraft multiplied by centripetal acceleration. Centripetal acceleration is a=v^2/r.
To compute the banking angle based upon aircraft speed (v) and radius (r) of the turn, use the following formula:
theta = arctan(v^2/(r*g))
theta is the banking angle, with zero being true horizontal.
g is Earth's gravitational field. Accept a value of 9.8 Newtons/kilogram for use in this formula, though do realize it might effectively be slightly less when in flight (for reasons to be discussed in a different question).
Preferred unit for v: meters/second
Preferred unit for r: meters
arctan() refers to the inverse tangent trigonometric function. The notation is not always universal, but "arctan()" is my preferred notation, and it is what you can do if you type your evaluation string in to Google Calculator. Warning: Google Calculator uses radians as angle units. To get the answer via Google Calculator, be sure you include the following factor:
*180/Pi
because there are 180 degrees in Pi radians.