# How Do You Calculate Bank Angle to Counteract Centrifugal Force in Turns?

• thetexan
In summary, the problem of centrifugal force with an aircraft in a turn can be solved by calculating the necessary lift force and centripetal force using vectors and trigonometry. To be coordinated in a turn, the horizontal component of lift must equal the centrifugal force. The amount of bank needed to counteract the side force in a car or aircraft for a given speed can be determined using the formula Tan(θ)=v2/(rg). The wings will produce the necessary forces to maintain level flight, and the formulae provided by Haruspex can help with this analysis.
thetexan
I want to understand the problem of centrifugal force with an aircraft in a turn.

If I keep the wings level and input a certain amount of left rudder the aircraft skids and throws the turn coordinator ball to the right due to centrifugal force. The solution is to bank the wings until the ball becomes centered.

A similar situation occurs when you take a turn in a car on a level street. If you bank the road enough you will not feel the centfugal force as a side force but instead will experience a greater downward force, or "g"s.

My question is how do I calculate the amount of bank necessary to counter the side force in the car or in an aircraft for a given speed so that the is no apparent side force?

I know that in the case of the aircraft, to be coordinated in a turn, the horizontal component of lift must equal the centrifugal force. So how do I determine the centrifugal force for a given speed?

For example, a level coordinated turn with a bank of 60 degrees produces 2 gs. In a 4000 lb airplane the wings are supporting 8000 lbs, an increase of 4000 lbs. does that mean that there is 4000 lbs of centrifugal force in the opposite direction?

Again, what is the formula for this and how is it calculated? Thanks.

Tex

If traveling at speed v and executing a turn of radius r, the centripetal force you need is mv2/r.
You also still need a vertical force of mg to counter gravity.
If banked at angle θ, your lift force, R, has to provide both:
R cos(θ)=mg
R sin(θ)=mv2/r.
Taking the ratio:
Tan(θ)=v2/(rg)

thetexan said:
I want to understand the problem of centrifugal force with an aircraft in a turn.

If I keep the wings level and input a certain amount of left rudder the aircraft skids and throws the turn coordinator ball to the right due to centrifugal force. The solution is to bank the wings until the ball becomes centered.

A similar situation occurs when you take a turn in a car on a level street. If you bank the road enough you will not feel the centfugal force as a side force but instead will experience a greater downward force, or "g"s.

My question is how do I calculate the amount of bank necessary to counter the side force in the car or in an aircraft for a given speed so that the is no apparent side force?

I know that in the case of the aircraft, to be coordinated in a turn, the horizontal component of lift must equal the centrifugal force. So how do I determine the centrifugal force for a given speed?

For example, a level coordinated turn with a bank of 60 degrees produces 2 gs. In a 4000 lb airplane the wings are supporting 8000 lbs, an increase of 4000 lbs. does that mean that there is 4000 lbs of centrifugal force in the opposite direction?

Again, what is the formula for this and how is it calculated? Thanks.

Tex
To solve this one, you need to use the dreaded Vectors and Trig. The lift force, keeping the plane up, will always be equal to the weight (on a level flight) and the centripetal force will depend on what radius of turn you need for the particular speed. The wings will produce a force which, provides those necessary forces. See this link for some diagrams and explanations which include a banked turn in a plane. It shows you how the formulae that Haruspex provided (above) apply to the situation, with the aid of a diagram.

thetexan said:
I want to understand the problem of centrifugal force with an aircraft in a turn.
If the centrifugal force is a problem, then analyse the scenario in an inertial frame where the centrifugal force doesn't exist.

thetexan said:
So how do I determine the centrifugal force for a given speed?
https://en.wikipedia.org/wiki/Centrifugal_force#Force

## 1. What is centrifugal force?

Centrifugal force is an apparent force that appears to act on objects that are in a circular motion. It is directed away from the center of the circle and is caused by the inertia of the object in motion.

## 2. Is centrifugal force a real force?

No, centrifugal force is not considered a real force. It is a fictitious force that only appears to act on objects in a circular motion due to their inertia.

## 3. How is centrifugal force different from centripetal force?

Centrifugal force and centripetal force are two sides of the same coin. Centrifugal force is the outward apparent force that appears to act on objects in circular motion, while centripetal force is the inward real force that keeps objects moving in a circular path.

## 4. Can centrifugal force be calculated?

Yes, centrifugal force can be calculated using the equation Fc = mω²r, where Fc is the centrifugal force, m is the mass of the object, ω is the angular velocity, and r is the radius of the circular motion.

## 5. What problems can arise from relying on centrifugal force in calculations?

Using centrifugal force in calculations can lead to errors as it is a fictitious force and does not accurately represent the true forces acting on an object. It is important to use centripetal force in calculations to accurately represent the forces at play in circular motion.

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