Finding the banking angle?

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You are flying to Chicago for a weekend away from the books. In your last physics class, you learned that the airflow over the wings of the plane creates a lift force, which acts perpendicular to the wings. When the plane is flying level, the upward lift force exactly balances the downward weight force. Since...

Banks in Converse, IN

Answer (1):


When the wings are banked at an angle θ with the horizontal, the lift force F, which is perpendicular to the wings, makes an angle θ with the vertical. Therefore the vertical and horizontal components of the lift are respectively:
F₁ = Fcosθ (vertical)
F₂ = F sinθ (horizontal)
Since the plane is at level flight (constant altitude), F₁ is exactly equal to the weight of the plane:
Fcosθ = mg (1)
F₂ is the centripetal force that cause the circular motion, which is mv²/r, so
F sinθ = mv²/r (2)
From (1) and (2) we get
Fsinθ/Fcosθ = mg*r/mv²
tanθ = gr/v²

To have the numerical value of tanθ, you must either take g = 9.8 m/s² and converse the velocity and radius into SI units, or to know the value of g in miles per hour per hour
According to the standard g is approximately equal to 21.937 mph/s
Conversed to mph/h: g = 21.937 mph/s = 3600*21.937 mph/h = 78973 mph/h
Plugging in the formula, with g = 78973 mph/h, r = 6 mi, v = 450 mph
tanθ = gr/v²
tanθ = 78973*6/450² = 2.33994
θ = 66.86° = 66° 51' 36"