Torque and Force

The relationship between the Center of Gravity and the vehicle’s Roll Center, is a very important concept to grasp. This will help you understand how the forces acting on the vehicle through the corner affects the roll of the vehicle, which will then help you understand how to help tune your suspension because body roll translates into suspension movement.

Here is a basic explanation of torque and force and how they relate.  Let’s say for example that you are trying to loosen a hex nut and you cannot get it to move with the wrench that you are using and the force that you are able to generate with your arms. What you need is more leverage. You can either get a wrench with a longer handle, or you get a piece of pipe to place over the end of the wrench so you can apply force to the end of the handle. Now you are able to move the hex nut using the same amount of force with your arms, or even less force.

Why does this work? By increasing the length of your wrench, you have been able to amplify the same amount of force that you were able to apply to the end of the wrench with your arms, which increased the output of rotational force, or torque, around the hex nut to turn it.

Fig 8 Torque and Force

To be more accurate, the amount of torque is determined by the amount of force applied and the perpendicular distance from the line of force to the Axis of Rotation (center of hex nut). This perpendicular distance is referred to as the Moment Arm or Lever Arm. The longer the Moment Arm, the more torque is applied to our Axis of Rotation (or hex nut), even if the amount of force applied to the wrench is exactly the same.

Let’s look at this in the diagrams below.

Here is how the force and moment arm relate to the torque produced around the axis of rotation.

Fig 9 Moment Arm Relate

Here is an example of how a shorter wrench has a shorter moment arm in Figure 10 below.

When the force is applied to the wrench closer to the Rotational Axis (or nut), the moment arm is shortened, and reduces the magnification rotational force, or torque, around the axis.

Fig 10 Shorter Moment Arm

If the force is exactly perpendicular to the wrench, the moment arm is along the wrench and has the maximum force/torque applied to the nut, or rotational axis.

Fig 11 Max Force

If the force is from the same side but at more of a downward angle, the moment arm moves to the other side of the wrench and begins to shorten as the angle of force increases.

Fig 12 Downward Force

If the line of force passes through both the end of the wrench and the rotational axis, no rotation is possible.

Fig 13 Force Through End

As you can see, the distance between the point of applied force and the rotational axis isn’t the only factor, it’s also the angle of the force acting on the rotational axis.

Let’s tie this into the forces that act on the vehicle. The hex nut, or rotational axis would represent our Roll Center, and the Center of Gravity would be represented by the end of the wrench. The force acting on the Center of Gravity would be the forces created by cornering instead of our arms and hand pushing, or pulling, on the wrench.

Fig 14 Relationship

We haven’t discussed how to determine the Center of Gravity or Roll Center yet, and we will cover that, however for now I want you to grasp the relationship between the two using the examples above with the hex nut and wrench. Based on the example given above, the greater the distance between the Roll Center (hex nut), and the Center of Gravity (end of the wrench), and the length of the Moment Arm, the more affect a force will have on influencing the torque around the Roll Center. This would be why a higher center of gravity creates more force attempting to create more body roll in a vehicle on a flatter track (See Figure 15). For performance it is much more advantageous to have the shortest distance possible between the Roll Center and the Center of Gravity to help reduce the body roll produced from the forces applied during cornering. However, as with everything in motorsports there is a compromise, and you will have to determine what those compromises are, and what suits your driving style best.

Fig 15 High CG vs Low CG

Below, in Figure 16, you can see that the flatter the track, the more important the relationship between the height of your Center of Gravity and the Roll Center. On higher banked tracks, the force from cornering acts at more of downward angle. The flatter the track, the more the cornering forces act laterally against the vehicle’s center of gravity, which increases the torque around the roll center. As you see below, the roll center and the center of gravity are at the same location in both illustrations; however in the picture of the vehicle on the higher banking (picture on left) the length of the moment arm is shorter because of the cornering forces acting at a greater downward angle, which therefore reduces the amount of lateral force against the center of gravity and proportionally reduces the amount of torque around the roll center.

Fig 16 High vs Low Banking


  • Torque and force affect body roll. The more torque around the roll center, the more the body wants to roll.
  • Body roll affects suspension movement.
  • Suspension movement affects camber change.
  • Camber change affects the amount of contact patch your tire has on the track.
  • The amount of tire contact patch affects the traction, and handling through the corner.

© 2016 DJ2 Motorsports LLC

All Rights Reserved.


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