Calculate Bank Angle for Airplane Circling Airport

[MJC8719]

As your plane circles an airport, it moves in a horizontal circle of radius 2300 m with a speed of 355 km/h. If the lift of the airplane's wings is perpendicular to the wings, at what angle should the plane be banked so that it doesn't tend to slip sideways

So I understand that the equation for determing the angle for banking is usually:

tan-1 ((v2)/gr)* would give me an angle...

What i do not understand about this problem is what exactly does it mean so that the plan will not turn sideways...do i need to set the above equation equal to something??

 

[hage567]

I think it just means at what angle must the plane bank to keep the radius of the circle constant, at the speed given (so the horizontal component of the lift is the central force keeping the plane in the circle).

 

[m2003]

I would approach this problem by first understanding the concept of banking an airplane. When an airplane is banked, it creates a centripetal force that allows it to turn in a horizontal circle. This force is created by the lift of the wings, which is perpendicular to the wings.

In this scenario, the airplane is moving in a horizontal circle with a radius of 2300 m and a speed of 355 km/h. To determine the angle of banking, we can use the equation you mentioned, tan-1 ((v2)/gr), where v is the speed of the airplane, g is the acceleration due to gravity, and r is the radius of the circle. However, we need to make sure that this angle will prevent the airplane from slipping sideways.

To do this, we need to consider the forces acting on the airplane. The lift force is perpendicular to the wings and creates the centripetal force needed for the airplane to turn. However, there is also a component of the lift force that acts in the direction of the airplane's motion (tangential to the circle). This component is what can cause the airplane to slip sideways.

To prevent this from happening, we need to make sure that the lift force is greater than or equal to the weight of the airplane. This can be achieved by banking the airplane at an angle that creates a greater lift force. We can determine this angle by using the equation:

tan-1 ((v2)/gr) = tan-1 ((355 km/h)^2 / (9.8 m/s^2 * 2300 m))

This gives us an angle of approximately 21.2 degrees. This means that the airplane should be banked at an angle of 21.2 degrees to prevent it from slipping sideways.

Additionally, it is important to note that the angle of banking may need to be adjusted depending on external factors such as wind speed and direction. Pilots are trained to make these adjustments to ensure safe and stable flight.