Less roll means less load transfer. Or not…?

This is a common heard statement in the paddock. Very understandable, but it is a misunderstanding....

But first things first: the terminology! Often the term ‘Weight Transfer’ is being used where the term ‘Load Transfer’ is meant. Here is the difference:

Weight (as defined by Newton) is the gravity by mother earth working on a mass:

Weight[N]=mass[kg]*gravity [m/s²],

or:  Weight = mass * 9.81.

Weight is a force which ALWAYS is directed perpendicular towards the earth, simply by its definition. And when a chassis rolls during cornering, the CG makes a small horizontal displacement towards the outer wheels, which loads the outer wheels and unloads the inner wheels. This is called ‘Weight Transfer’.

Load is a force too, working on a mass, and can have different causes. To name a few:

-        Static load: like the force generated by a spring on its platform nut

-        Aerodynamic force: like the high-speed air working on a wing or undertray

-        Inertia:  Load [N] = mass [kg] * acceleration [m/s²], like under braking or acceleration) or lateral acceleration (during cornering)

Load can be pointing in any direction, but weight is always vertical.

Load Transfer is caused by the fact that the action forces (lateral forces in the four contact patches which sum up to the total centripetal force) and the reaction force (centrifugal force in the CG) are not acting in the same horizontal plane. This causes a ‘couple’ by the centripetal forces and the centrifugal force. This couple is resisted by a counterrotating couple of vertical forces in the tyres which are acting in the opposite direction. These vertical forces are called ‘Load transfer’. So ‘Load Transfer’ and ‘Weight Transfer’ are complete different things, and can both take place at the same moment.

In a GT car or a saloon car, the Weight Transfer might generate some difference in the contact patches indeed, but in sportscars and formula cars, with their low CG and low amounts of roll, the WT is very low. It is up to the engineer to consider them negligible or not.

So, let’s come back to the myth in the title. To understand what I’m going to explain, we’ll do a little ‘thought experiment’: John weighs exactly 1000 N (approx. 101.9 kg), and we place him on a spring with a spring rate of 50 N/mm, on the floor. The spring will deflect 1000/50 = 20 mm, and the load by the spring on the floor will be 1000N. Now we replace the spring by a spring with a softer spring rate of 25 N/mm. The spring now deflects 1000/25 = 40 mm, which means a larger deflection, but the load on the floor remains 1000N!

Conclusion: both springs show different deflections, but the final load on the floor remains 1000N… This simple example is applicable on cars too: the roll moment is the action, and the elastic roll resistance by the main springs plus anti-roll bar is the reaction.

The Roll Moment = sprung mass a_y  roll arm is the action. The roll resistance – which is the reaction - dictates the amount of roll. However, the increased roll angle in itself does not generate more load transfer or vice versa!

Conclusion: softer springs generate:

-        More roll

-        More weight transfer

-        But equal load transfer!

You see, the problem starts when the terms Load Transfer and Weight Transfer are being mixed up. Let’s look at it in a mathematical way:

Load Transfer =

a_y* total mass*Height CG_{mass tot} 

track     

There is no spring rate part of this equation, which in itself shows that the load transfer is independent from the spring rate and hence independent from the roll angle.            

But everybody knows that more roll does change the handling of the car indeed, raising the question what is causing the change?

Well, quite a lot! Here are a few:

-       Roll causes Weight Transfer (as explained above). Although small, it might become tangible at Saloon cars and GT’s.

-       Roll causes camber change in an undesirable direction on all four wheels, resulting in less lateral forces: the outer wheel get less negative camber, or maybe even positive camber.

-       Roll reduces the aerodynamic effectiveness from the undertray. Especially in formula cars and sportscars this is highly undesirable.

-       Roll causes the anti-roll bar to twist more. In itself not such a big problem, but imho the %-contribution of the ARB to the roll resistance should remain limited, otherwise the construction of the ARB could become overloaded.

So there are enough arguments why you would like to reduce roll. This doesn’t take away the fact that we also would like to reduce the LT, mainly to make better use of the tyres: the smaller the LT is, the better – due to the non-linear character of tyres - the inner tyre will contribute to producing lateral forces.

The role of the Anti-Roll Bar (ARB) is – what’s in a name? -  to reducing roll. It does this by generating resistance against the Roll Moment by transferring load from the inner tyre to the outer tyre. If you don’t like this, there is only one remedy: dismantle the ARB. This is why during rain the ARB’s sometimes are decoupled to make the inner tyres work harder.

So far I have described the situation on one axis, or in a 2D model. However, a car is a 3D model with interaction between the two axes. To understand this, let’s look at a complete car which is fully symmetrical. (This means that the CG is exactly in the middle (l_front = l_rear), meaning % static load front = 50%, track _front = track _rear, spring rates of all four springs are equal, spring rate of anti-roll bar _front = anti roll bar _rear, and the chassis is 100% torsional stiff. You will never find such a car, consider this as just an academic exercise)

At a given Roll Moment this car will react with a certain roll resistance, resulting in a roll-angle, load transfer, and weight transfer. Decreasing the spring rates of the main springs and/or anti-roll bars at equal magnitudes front and rear, does not change the action (roll moment), but the change is in the reactions:

-        More roll

-        More weight transfer

-        Equal load transfer

As described above, the formula for load transfer does not contain any variable for neither roll angle nor spring rates.

But in reality a car is not symmetrical as above, which makes the case more interesting. The load transfer is the sum of three elements:

-        the elastic load transfer (Roll Moment / track) by the sprung mass

-        the geometric load transfer by the sprung mass

-        the load transfer by the unsprung mass

If we consider a_y unchanged, an increased spring rate at the front axis only means that the front will contribute more to the roll resistance, such that the rear axis is contributing less, simply because the total load transfer remains equal. Playing around with spring rates front and rear will change the elastic roll resistance per axis, which in its turn changes the roll angle. The roll angle is the result of the load transfer, not the cause.

As we know the positions of the Roll Centre’s are dynamic. But whatever their positions are, in the end when all forces and moments are being added, you end up with a total roll resistance which is equal to the total load transfer. In a future blog I will elaborate more on this topic.

In conclusion: the statement ‘Less roll means less load transfer’ in the heading is not true. Roll is the result of the roll moment, not the cause.

If you want to verify abovementioned statement, just program the template I have given in Chapter 11 of our book ‘Race car Handling Optimization’ in i.e. an MS-Excel sheet, and play around with the variables.

This is Blog nr 2 in a series of blogs concerning vehicle dynamics of race cars by Ton Serné.

They are based on the book ‘Race Car Handling Optimization’ 2^nd ed. (ISBN 978-3-658-47190-3), see www.handlingracingcars.com .