Roll Centre and Roll Moment

The roll centre positions of your front and rear suspension geometry are key features affecting the lateral load transfer rates of your front and rear axles. Their position and difference in height front to rear can be used to tune the roll stiffness distribution of your car in a similar way that you would adjust the stiffness of your front and rear roll bars to tune understeer and oversteer.

Calculating the roll moment of your car allows you to determine the amount which your car will roll in certain scenarios and will allow you to adjust spring rates and suspension geometry to tune the perfect amount of roll required at each axle for your vehicle.

The roll moment of your car is a direct feature of your roll centre positions and your centre of gravity position and affects how your car handles and can be used to calculate the exact amount of chassis roll experienced in a certain situation. It is then possible to change spring rates, anti-roll bar settings and suspension geometry figures in the below equations and methods to get your ideal amount of roll.

It is also fundamental to have some roll in the chassis from a driving point of view. It is theoretically perfect to have no degrees of roll through a corner if the tyre could provide unlimited grip but it is not realistic. Some roll is required in order to deliver a message to the driver that the car is approaching its limits. The less roll a car has, the less amount of warning there is before the car loses grip.

It is also useful information to have in order to calculate lateral load transfer rates.

Stages to Complete First

Before you continue with this article it is important that you have read and understood the following articles as there are stages below which require figures from these articles based upon your vehicle:

• How to Calculate Your Centre of Gravity Location
• How to Calculate Wheel Rate and Chassis Roll Stiffness
• Lateral Load Transfer

Calculating Roll Centre Position

Calculating the position of your roll centre is fundamental. The most accurate way to calculate your roll centre is to draw a diagram representing the following points of your suspension system:

• Wheel and tyre location
• Upper wishbone, upper arm or MacPherson strut chassis mounting point
• Upper wishbone, upper arm or MacPherson strut hub mounting point
• Lower wishbone, lower arm chassis or subframe mounting point
• Lower wishbone, lower arm hub mounting point

These measurements need carrying out for the front and rear suspension systems.

The technique for double wishbone and Macpherson strut set ups is slightly different for the measurement and locating stages so these are separated below. Many cars have a mixture of both set ups so will need to carry out both techniques. One very common set up is MacPherson strut suspension at the front and double wishbone at the rear (or upper and lower arm at the rear).

How to Measure

First of all place your car on a flat level surface and make sure that all of your tyre pressures are set correctly for how they would be set on track. Now measure the tyre width and height from the front view and draw it on a piece of paper scaled down to suit the size of the drawing. It is important to keep scaling in-tact and applied to all measurements. If you are using CAD software to do the sketch then enter the true values.

Now draw a vertical line in board of the wheel. This should be a distance of half the track width away from the centre of the drawn tyre. This line is in the position of the centre of your car.

Double Wish Bone Measurements

Now the locations of your wishbone or arm mounting points must be measured. It is important to find a reference point for all measurements. The reference point for the height of each point should be the level flat ground that the car is sat on.

The next reference point that can be used to get the horizontal location of the mounting points for each arm at the wheel end is the back of the brake disc. To use this reference point correctly you must know how far the disc is from the centre line of the wheel to locate it on the sketch accurately and the wheel must have zero toe. If your car has toe then use a datum from the chassis or subframe.

The length of each arm can then be measured from the hub mounting point to the chassis mounting point, used alongside the height from the ground which will accurately place the in-board mounting points on the sketch. An example sketch can be seen below showing these points.

MacPherson Strut Measurements

For a MacPherson strut set up the measurement technique is slightly different. The angle of the coilover or damper must be observed. This could be done with a protractor or by measuring the distance of the bottom of the damper from the chassis and the distance from the top of the coilover or damper to the chassis. If you also measure the length of the coilover at ride height you will now be able to draw or calculate the damper angle.  The height of the bottom and top of the damper from the floor must also be measured accurately to locate the damper exactly.

Next the lower arm is measured in a similar way to the wishbone technique. The reference point for the height of each point should be the level flat ground that the car is sat on.

The next reference point that can be used to get the horizontal location of the mounting points for each arm at the wheel end is the back of the brake disc if the wheel has zero toe; if not then use the chassis or subframe as a datum. To use this reference point correctly you must know how far the disc is from the centre line of the wheel to locate it on the sketch accurately.

The length of each arm can then be measured from the hub mounting point to the chassis mounting point, used alongside the height from the ground which will accurately place the in-board mounting points on the sketch. An example sketch can be seen below showing these points.

How to Locate Roll Centre for a Double Wish Bone Set Up

With these measurements accurately drawn and located on your sketch whether it is on paper or on CAD software, some simple lines can now be drawn to uncover the position of your roll centre. First of all draw a line through the upper arm mounting points and extrapolate it out to the other side of the car. Now do the same through the lower arm mounting points until both lines intersect at some point. Where they intersect is the location of the instant centre for that side of the suspension system. Repeat this for the opposite side. These four lines can be seen intersecting in the image below.

Now draw a line starting at the centre of the contact patch of the tyre at the very bottom and ending at the point where the two lines for the suspension attached to that wheel intersect.  Now repeat this for the opposite wheel. Where these two lines intersect displays the location of the roll centre. If your suspension components are symmetrical this point should be in the centre line of your car. However, due to some set ups requiring different ride heights, the roll centre can be slightly off centre. If it is of centre by a large amount this can have bad affects on cornering making the car handle differently in different directions.

How to Locate Roll Centre for A MacPherson Strut Set up

With the points for your MacPherson strut set up accurately plotted out on a piece of paper or preferably in 2d on CAD software, we can draw some lines that will reveal the roll centre. First draw a line through the centre of the coilover or damper from the bottom of the damper through the top mount at the top. Now from the centre point of the top mount, draw a line perpendicular to the damper towards the centre of the car. Repeat this for the other side of the car. These four lines can be seen in the image below:

Now draw a line that passes through the lower arm hub and subframe mounting points and extrapolate the line out until it intersects with the line coming down from the damper top mount. At this point of intersection draw a dot. This is the instant centre for one side.  Repeat this for the other lower arm and draw the line so it intersects with the other damper top mount line. The image below shows the instant centres being located.

Now draw a line from the centre of the tyre contact patch up to the instant centre that relates to suspension components attached to the same wheel. Repeat this for the opposite tyre. Where these two lines intersect is the location of your roll centre. If your suspension components are symmetrical this point should be in the centre line of your car. However, due to some set ups requiring different ride heights, the roll centre can be slightly off centre. If it is of centre by a large amount this can have bad affects on cornering making the car handle differently in different directions.

One of the above measurement and sketching processes now needs repeating for your rear suspension system.

How to Locate Rear Beam Axle Location

If your car has a solid rear beam axle set up then locating the roll centre is a much more simple operation. Due to the wheel being joined by the one single beam, a line can be traced down the centre of it to the centre point. This is where the roll centre for the rear beam axle is located. The diagram below shows the location of the roll centre for a beam axle.

Roll Moment Calculation

Two important points that are required are the roll centre location and the centre of gravity location. This is because when there is a difference between the positions in height of the centre of gravity and the roll centre, a moment arm is generated, otherwise referred to as a lever arm.

Any cornering acceleration or cornering force acting on the car will always act directly on the centre of gravity. Therefore, if there is a distance between the centre of gravity and the roll centre, the chassis will pivot about the roll centre, causing the car to roll.

Using the result from your calculations in the “how to calculate your centre of gravity position” article; insert it on the previous diagram in its correct location from the front view. The position from our example is on the diagram below:

Now measure the vertical distance between the two points and record it for later. It will be referred to in equations as “d”. As the image shows our example has a distance of:

Therefore:

Choosing a Scenario

The next stage in the process is to choose a scenario. If you have ever data logged your car then you will be able to pull the figure directly from that. Only one corner position at one speed needs to be selected. For this example Lodge Corner at Oulton Park Race Circuit has been selected. Around this corner our example car generates 0.8G of lateral acceleration.

If you are unable to use data logging then follow the steps below to calculate the amount of G your car would pull around a selected corner that you have been around before with some memory of the occasion. For this scenario we can say that our example vehicle is travelling around a corner with a radius of 140m at a speed of 74mph or 33.1 m/s. Now using the equation:

Where:

• V = Velocity (m/s)
• r = Radius (m)
• a = Acceleration (m/s2)

Therefore:

To convert our answer into g force we simply divide by 9.81 to get:

Calculation Time

Torque

The first stage is to calculate the amount of torque acting upon the chassis during cornering. For this we need the following figures:

• Total Vehicle Mass in Kg
• Amount of Lateral Acceleration Being Generated in G
• Vertical Distance (d) in Meters
• Gravity = 9.81ms⁻²

These figures can now be inputted into the following equation for torque:

Therefore:

Your Current Set Up

Before designing new spring and anti-roll bar rates it is important to understand what your car already has and what it already does. This way we can tell how the new designed rates will alter the current handling.

The figure for torque and the figure obtained for your chassis stiffness from our “Calculating Wheel Rate and Chassis Roll Stiffness” article can now be used to find the amount of roll generated. The two figures required are:

• Chassis Cornering Torque in Nm
• Chassis Stiffness in Nm/degree

The equation for amount of roll in degrees is:

Therefore:

This tells us that our amount of roll angle through this corner will be 0.69 degrees of roll. These steps of calculation now need repeating to determine the amount of chassis roll at the rear suspension system.

Neutral Roll Axis

Above we have considered the front and rear suspension systems to be independent of each other in order to calculate the roll moment for the front system and the rear system. However, in reality the two are connected by the chassis. We have accounted for this using the chassis stiffness and assuming that the front and rear suspensions work independently of each other to simplify the calculations which is a perfectly fine assumption to make.

However, for three dimensional calculations the Neutral Roll Axis is required to make more complex calculations with. This level of calculation often requires complex computer software to calculate the roll moments three dimensionally about the roll axis.

The image below shows the car diagram from a side view. In line with the front and rear wheels, the roll centres can be seen drawn on at their respective heights as calculated in the above sections. The neutral roll axis is simply a line that connects these two roll centres from the side view. Also shown on the diagram is the centre of gravity location at its height and longitudinal location as calculated in the “centre of gravity” article. The vertical height differences between the NRA and the centre of gravity position as well as the angle of the NRA from horizontal are important values for calculating complex equations for a car moving in three dimensions.

How to Adjust and Tune Roll Centres

Roll centres can be adjusted as a technique of increasing or decreasing the roll stiffness at one end of the car in a similar way that anti-roll bars can also be used to change the front to rear roll stiffness distribution. By doing this the lateral load transfer rate is increased or decreased as the amount of roll at each end is decreased or increased.

For example, if a car is understeering mid corner, one solution would be to either lower the front roll centre or raise the rear roll centre height. Likewise, if the car is experiencing oversteer mid corner, the front roll centre could be raised and the rear roll centre position could be lowered.

For a front wheel drive car, the front roll centre will generally be lower down than the rear roll centre. Also, for a rear wheel drive car the rear roll centre will often be lower than the front roll centre. This gives the driven wheels more roll and therefore more grip through the corner. A four wheel drive car will tend to have roll centres at a similar height front to rear. They will be tuned from this position to distribute more or less roll to the front or rear axles.

Front Wheel Drive

Rear Wheel Drive

When the two roll centres are joined together by a line from the side view (the neutral roll axis) it will either incline towards the rear or decline towards the rear. A car that has an inclining NRA towards the rear, like most front wheel drive cars, will tend to lift a rear wheel during cornering if the angle is steep enough.

If the NRA is declining towards the rear of the car, like in the application of a rear wheel drive car, then the car will tend to lift the inside front wheel during cornering if the angle is steep enough once again. Lifting wheels does also depend on the roll stiffness of the roll bars and coils spring rates as well but as most race cars are stiff enough to lift wheels it proves to be a good visual representation to remember which way the roll centres should be set up on your car.

A lot of motorsport data suggests an ideal range for roll centres to sit within for non-aero vehicles. The reason it applies to non-aero vehicles is because when an aero car is driving, the downforce deflects the suspension geometry in such a way that the roll centres move. Therefore, they are designed in such a way that the ideal roll centre positions are achieved when the car is driving and the aero is effective on the geometry. The ideal roll centre position range that can be used to begin your set up is between 15% and 30% of the height of your centre of gravity height. Some race cars with extreme amounts of lateral grip can move closer to the centre of gravity position but these figures are a good starting point to set your car up to and tune from.

Front Wheel Drive

Rear Wheel Drive

Four Wheel Drive

There a couple of good techniques to adjust the roll centre position of your front and rear axles. One technique is to adjust your ride heights. Adjusting the ride height will alter the angles of the suspension arms. The angle changes will result in movements of the roll centres up and down. This technique is the easiest option but it does also alter the static mass on the wheels which could cause issues if the car is corner weighted to perfection. The other option is to alter the mounting points of your suspension arms to alter the angles of them where they mount to the hub or chassis. With some designs this can be done easily with the use of spacers. On other designs it could require upright or subframe modifications.

The best way to find what angles your arms need to be at to create the ideal roll centres is to draw the front and rear suspension systems in CAD. This way the ride heights and pick up points can all be altered on the computer quickly and easily before you begin working on the car.

How Can This Information Be Used Practically?

With the above information you can now draw the angle of roll on the scale sketch from earlier. Draw a line horizontally out from the roll centre position to the wheel. Then draw a line above and below that line at 0.69 degree angles from the horizontal line until they meet the wheel. The vertical height difference of these points is the amount of roll at the wheel which will be able to allow you to imagine how much roll that is.

Next, you can alter the chassis stiffness figure until an ideal amount of roll is obtained for your set up. When a number works, the “How to Calculate Wheel Rate and Chassis Roll Stiffness” section can be reversed to produce some new anti-roll bar spring rates which you can purchase for your car to reduce the roll to the desired angle.

If you are happy with your suspension stiffness then it is possible to alter the mounting points of suspension arms to change their static angles which will re-locate the roll centre closer to the centre of gravity position. This can be done on the sketch multiple times until an ideal value is obtained which can then be made into a permanent change on the car.