# Analyzing applied torque to one of lug nuts instead of wheel center

• karabiner98k
In summary: The torque is distributed uniformly over the surface of the wheel. You would have to add up the force on each individual lug nut to get the net torque.
karabiner98k
We all know that torque consists of force and distance. If we apply torque to the center of a car wheel, the force that the tire exerts to the ground can be calculated by dividing the torque by tire radius but what about applying torque to one of lug nuts which is off center?

In the above picture of my car:

C = Tire radius = 0.289 meter
B = 0.339 meter
A = 0.238 meter

Therefore, B > C > A

If I set my torque wrench to 35 nm and torque the center bolt down, the force would be: 35 / 0.289 = 121 N
What about applying torque to one of lug nuts at the point between B & A?
How do you calculate force if I apply the same 35 nm to it?
35 / 0.339 = 103 N? or 35 / 0.238 = 147 N?
Which one is the answer and why?

Last edited:
Construct a normal to the line of the wrench handle, a normal that passes through the wheel centre. The distance from that normal, along the wrench to your hand, is the effective wrench length when computing torque to the wheel. It may be more or less than the lug nut torque.

Lug nut torque is not my question because I already know the torque which I'm applying to the nut (35 nm). When I apply this amount of torque to the nut, the wheel starts rotating very slowly and the car begins moving forward. So, there is a force that moves it forward and I want to know the magnitude of this force. If the torque was being applied to the center of wheel, the force would be simply obtained by dividing the torque by tire radius but I don't know how to get it in this case since the nut is off-center.

What part of my post do you not understand ?

Constructing the normal. Could you please edit this picture to show the force and the lines?

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• 20220324_170332.jpg
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The picture is too black.

If the nuts are at a radius of r from the centre of the wheel, then the handle of the torque wrench is effectively lengthened or shortened by a maximum of r, depending on the direction of the handle. If the handle passes over the centre of the wheel, the length is reduced by r, so the torque is less. If the handle points away from the wheel centre, then the handle is effectively lengthened by r, so torque is increased.

karabiner98k
I replaced the black picture with a bright one.

Last edited:

hutchphd and karabiner98k
Thanks for your drawing. What about acceleration force that the tire exerts to the ground and causes movement of the car?

karabiner98k said:
What about acceleration force that the tire exerts to the ground and causes movement of the car?
The force applied to the torque wrench handle, Fh, is multiplied by the torque wrench effective length, w, then divided by the wheel radius. That gives the horizontal force applied to the ground; Fg .
Then use F = m a; So, acceleration; a = Fg / m; where m is the mass of the vehicle.

karabiner98k
karabiner98k said:
Lug nut torque is not my question because I already know the torque which I'm applying to the nut (35 nm). When I apply this amount of torque to the nut, the wheel starts rotating very slowly and the car begins moving forward. So, there is a force that moves it forward and I want to know the magnitude of this force. If the torque was being applied to the center of wheel, the force would be simply obtained by dividing the torque by tire radius but I don't know how to get it in this case since the nut is off-center.
You could do a free body diagram of the wheel and a balance of forces and moments about the contact patch.
Those 35 N-m of torque are applied to the whole wheel, not only to the lug nut.

## 1. How does analyzing applied torque to one of the lug nuts instead of the wheel center affect the overall performance of the vehicle?

Analyzing applied torque to one of the lug nuts instead of the wheel center can have a significant impact on the overall performance of the vehicle. This is because the lug nuts are responsible for securing the wheel to the vehicle, and if they are not tightened properly, it can lead to issues such as vibrations, uneven tire wear, and even accidents.

## 2. What are the potential benefits of analyzing applied torque to one of the lug nuts instead of the wheel center?

One potential benefit of analyzing applied torque to one of the lug nuts instead of the wheel center is that it allows for a more precise and accurate measurement of the torque being applied. This can help ensure that the lug nuts are tightened to the correct specifications, which can improve the overall safety and performance of the vehicle.

## 3. Are there any drawbacks to analyzing applied torque to one of the lug nuts instead of the wheel center?

One potential drawback of analyzing applied torque to one of the lug nuts instead of the wheel center is that it may be more time-consuming and require specialized equipment. This can make it more difficult for individuals to perform this analysis on their own, and they may need to seek professional assistance.

## 4. How does the location of the applied torque affect the distribution of forces on the wheel?

The location of the applied torque can have a significant impact on the distribution of forces on the wheel. When torque is applied to the lug nuts, it creates a clamping force that holds the wheel in place. If the torque is applied to one lug nut instead of the center of the wheel, it can cause uneven distribution of forces, which can lead to issues such as wheel wobbling or loosening over time.

## 5. Is analyzing applied torque to one of the lug nuts instead of the wheel center a common practice in the automotive industry?

Yes, analyzing applied torque to one of the lug nuts instead of the wheel center is a common practice in the automotive industry. This is because it allows for a more accurate and consistent measurement of torque, which is crucial for ensuring the safety and performance of vehicles. Many automotive manufacturers and mechanics use specialized equipment to analyze torque on lug nuts during vehicle maintenance and repairs.

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