Smithees Race Car Technologies                                             home                                                 racetech@ozebiz.com.au

Dynamic Load Transfer

In car racing our aim is simple - to drive around the race track in the least possible time, maximising the forces associated with acceleration, braking and cornering.  While we do this, the race car is experiencing forces in all directions, which result in weight transfer to and from all four tyres in a very complex manner.  Race drivers attempt to build and let go these weight transfers progressively, so as to maximise tyre grip.

The "dynamic load transfer" results in ever changing vertical loadings on the tyres, which are additive (+ or -) to static load (due to the force of gravity), and aero forces (lift or down force).  The tyres only see total vertical load, wherever it comes from.  So all the variables of our car set up, driver inputs and external effects end up as just the one dynamic vertical load on the tyre.  The variations in tyre load are large and significant any way you look at it - raw numbers or percentage change.  In so far as our springs, anti-roll bars and shocks influence weight transfer at any point in time, it is clear that they work together to produce a single load at each of the tyres..

As race car supension tuners, we are vitally interested in one aspect of dynamic load transfer - the re-distibution of static loads on the tyres, when the car is in motion. 

We could improve the handling performance of our car by changing to a better tyre, taking weight out of the car, optimising the track, or adding serious amounts of aero dynamic downforce.  But these will be fixed pretty much by the race rules or the designer of our car.  So this leaves us the suspension bits to play with, plus whatever aero adjustment we have.

We only consider chassis movements and forces generated by low speed acceleration of the vehicle mass - the accelerations of braking, cornering and power application.  High speed movements of the wheels, where tyres momentarily loose grip, or complete loss of grip when the vehicle is sliding, will tend to nullify the effects we are talking about.  However, suspension development is often focussed on allowing the driver to maintain balance in the face of external upsets - eg rally and speedway often run on very poor surfaces, sometimes road race cars are specially developed to ride the curbs.

Total Weight Transfer (TWT).

Before we start tweaking the suspension adjustments, we need to recognise that not all the weight transfer goes via the springs, shocks and anti-roll bars.  We'll also get a little insight into what roll centres we might run on our race car.

A certain amount of the weight transfer happens almost immediately as the  forces generated by the acceleration of the vehicle mass feed directly through the suspension links to the tyres.  In roll, two such weight transfer are usually considered - unsprung weight transfer and sprung weight transferred directly through the roll centres.  In general, these weight transfers will be minimised in the design.  The greater amount of sprung weight transfer follows, as the accelerative forces feed through the springs, anti-roll bars and shocks (our major area of interest).  Each of the weight transfers can be calculated as follows:-  
Lateral force times lever arm (or moment), divided by the track - all done quite readily within a good suspension program, such as SusProg3D.

Unsprung weight transfer (WTU):  In roll, weight transfer of unsprung weight is seperate for the front and rear suspensions of the race car.  In a good design, it should only be a small component of TWT.  But it is clear that a big change in the proportion of front vs rear unsprung weight will change the balance of the car.

The following weight transfers apply only to the sprung mass of the race car:-

Sprung weight transfer via the roll centres (WTRC):   Again, weight transfer is seperate for front and rear.  It can be varied simply by raising or lowering the roll centre relative to the ground.  So a ride height adjustment to your race car, or a roll centre geometry change is a very valid tuning device.  Particularly for speedway, where higher roll centres can work, and off-set roll centres are used.  For road racing, roll centres as low as possible (considering other key aims of the suspension geometry) might be the best way to go.

Sprung weight transfer via the sprung mass (WTS): We should not attempt to calculate this weight transfer seperately for front and rear.  The chassis is a rigid structure which rolls around an axis between the front and rear roll centres.   So the sprung mass weight transfer is based on a mass whose centre is the centre of gravity of the entire sprung mass, the mean roll centres and mean track.  This weight transfer is resisted by the springs, anti-roll bars and shocks, and forms the basis of the wheel pair stiffness theory we look at below.

So  TWT = (WTU-F + WTU-R) + (WTRC-F +WTRC-R) + WTS
where the F & R suffixes represent weight transfers calculated for front and rear seperately.

Key Point - Sprung Weight Transfer

The two main  methods of transferring sprung weight, via the roll centres or via the springs, exactly counter balance each other. 

High roll centres leave less weight to be transferred via the springs and vice versa.  We want our springs, anti-roll bars and shocks to work, so we can tune the set up.  This means generally low roll centres.  If the roll centre was at ground level, weight transfer directly through the roll centres would be zero, and all the unsprung weight transfer would go through the springs, anti-roll bars and shocks.

I am indebted to Dennis Jansen, a student in vehicle dynamics, for pointing out the effect of roll centre below ground level.  Now, weight transfer via the roll centres is negative.  This means there is a component of weight transfer that actually goes from the outside wheel to the inside wheel.  This weight transfer in reverse would have to help turn in, but of course, the overly low roll centre could have other, less advantageous effects.  In a practical design, a roll centre a little below ground level would reduce the unsprung weight transfer (there would not actually be any negative weight transfer overall), and the weight transfer through the springs would be correspondingly increased.

It's interesting to consider "If I run higher roll centres, couldn't I run softer springs for increased tyre compliance (more grip)?"  The problem is you also get more scrub (track change), which is bad for grip, and adds to wheel rate stiffness in any case.   It's a similar argument for excessive anti-squat or anti-dive.  The wheel base change is not so much of a problem, but the increase in wheel rate (reduced tyre compliance) can be bad.

Why Do We Need to Understand Weight Transfer?

There are many we can improve improve mechanical grip, either overall, or for understeer/oversteer balance. 

If our car had no suspension and no assymetrical set up, we could use tyre technology, temps and pressures, tyre stagger, steering and alignment angles, ride height, track changes,  wheel width and offset changes, front to rear weight distribution, centre of gravity changes, differential characteristics and some others.  We could think mostly about tyre grip.  We wouldn't really need a comprehensive weight transfer theory. 

But if we started to play with static cross weight, or add suspension to our car, our predictions of tyre grip and resulting effect on understeer/ oversteer balance become more difficult. 

At the race track, we are looking at a particular movement of the car.  We make a change to the suspension set up.  Tyre loading, and therefore the grip of the tyres, will change.  We want to know what the changes to tyre loadings are, so we can predict the likely change to understeer/oversteer balance. 

The suspension set up has another very important role - optimising mechanical tyre grip.  We cover the theory briefly in the next section, so that you can appreciate other set up requirements of the car, and differentiate them from weight transfer issues.

Mechanical Tyre Grip Theory

Tyre grip depends on the ability of the tyre rubber to interlock with the grain of the road surface.  The surface of the road causes continuous small movements of the suspension, and variation in load on the tyre.  For maximum grip, we need to minimise this variation.   Grip increases with suspension pressure. We want to push the tyre into the road surface harder & longer.  The suspension pressure results from the sum of the tyre, spring, and anti-roll bar rates and shock loading, and could also be influenced by the torsional stiffness of the car. 

So we have two competing requirements here.  If we run spring rates as soft as possible, the lower suspension frequency (the suspension moves up and down so many times per second) will allow the tyre to be pressed into the road longer.   But harder spring rates will press the tyre into the road harder.  The best solution can be hard to find.  Optimum grip requirements will change with each race car, tyre and road surface.  But the trend is to run softer springs, and reset the shock to maintain the pressure on the tyre. 

The shock must also control the rebound of the suspension very accurately so as to reduce the amplitude in these small displacements of the suspension.   It appears that only an expensive racing shock is precise enough to do this over a race distance.  We discuss this further in the shock theory section, and in a yet to be written tyre theory section.

Describing Chassis and Suspension Movements of the Race Car

When a wheel moves up relative to the chassis platform, we say that wheel is moving in bump. When a wheel moves down relative to the chassis platform we say that wheel is moving in rebound.

The four modes of chassis and/or suspension movement are:-

Heave:  All four wheels move up or down equally.
Pitch:    Front wheels move up as rear wheels moves down, or vice versa.
Roll:     Chassis leans to one side or the other.
Warp:   Diagonal movement.  Front axle tilts one way and rear axle tilts
              the other way. Note that if all four wheels are on a flat surface,
              warp movement is bump and rebound on one diagonal and no
              movement of the wheels on the other diagonal.

Note the freedom of movement of the chassis in the vertical plane.  There is no fixed pivot to precisely control to roll or pitch.  However, the chassis is precisely controlled in the horizontal plane, which is why we get dynamic load transfer.  This will be obvious to Engineers from their first studies in vector mechanics.

Please take the time to be clear about this point.  When weight comes off a wheel the chassis is free to move up, subject to the position the spring will settle at to support the new weight.  Equally, when weight comes onto a wheel, the chassis is free to move down until the spring supports the new weight.  The roll centre moves up and down with the chassis as required  to accomodate the movement of the springs.

This point allows us to develop just about all the important theory relating to weight transfer.

In race car suspension set up, we are interested in all four suspension movements, and some combinations of heave, pitch, roll and warp.  This looks complex, but we can build a viable model to deal with it.  Note again that we only deal with re-distribution of the static weight on the tyres.  Forces from dips, rises and bankings in the road, or from aero downforce can be added later. 

We need concepts to help us describe and understand the modes of movement of the chassis and suspension.  The first is wheel stiffness. 

Key Point - Wheel Stiffness

We will use wheel stiffness to help us describe the comparative amount and speed of weight transfers for the various modes of movement.

When one of the wheels move in bump, it will be resisted by the spring and anti-roll bar.  The resistance force of the the spring and anti-roll bar combined gets greater as the wheel moves further ie the force is position sensitive.  We define this contributor to "stiffness" at that wheel, as the wheel rate.  Tyres have a stiffness rate, and contribute to wheel rate as well.  Softer wheel rate allows more movement of the chassis, stiffer wheel rate restricts movement of the chassis.

Wheel stiffness in rebound is a little more involved.  As weight is transferred away from the wheel, the chassis is free to move upward, subject to the wheel rate.  Softer wheel rate will again allow more movement of the chassis, until all the weight is transferred.  Stiffer wheel rate again restricts chassis movement.  

We'll refer to the total compliance of the suspension when subject to the force of wheel movement as the wheel stiffness.  Other contributors to wheel stiffness are the suspension geometry, and the shock absorbers moving in bump or rebound.

The affect of suspension geometry on wheel stiffness is discussed in the footnote to this page - a side issue for now.  However, the shock absorbers' slow speed stiffness is vitally important in our understanding of weight transfer. In modern race cars, the shock absorbers contribute significantly to wheel stiffness.  This is the reason why we emphasise the role of the spring/anti-roll bar/shock combination throughout this web site.

As we said, wheel rates for springs and roll bars are position sensitive - force increases with compression of the suspension. The car rolls more with increasing corner speed.  This is obvious, but important when you want to add in the effect of slow speed damping of the shocks.  Shocks are velocity sensitive, so will only add or subtract to wheel stiffness, when the suspension is moving.  The shock force is relatively constant for any given velocity - builds fast as the suspension starts to move, and drops away quickly as the suspension stops moving.  In our shock page, we build a model for tuning dynamic load transfer with shocks.

Relative Wheel Pair Stiffness

"Relative stiffness" is our second concept for understanding the distribution of dynamic weight transfer in racing cars.  Wheel pairs transfer weight in proportion to their total wheel stiffness.  ie the combined stiffness of the wheel gaining weight, and the wheel loosing the weight.

Old  "distribution of roll stiffness" theory only deals effectively with the roll mode.  You know.  If we increase the proportion of front roll resistance the car might understeer, and vice versa for oversteer.  But my aim here is to generalise the discussion, so we can predict the effects of set up changes during all modes of chassis movement, in any combination, using any of the devices at our disposal to make the changes. 

If front wheel pair stiffness is greater than rear wheel pair stiffness, we say the car is front stiff.  The idea is to concisely convey how the stiffnesses of wheel pairs compare.

You can see that a car could be relatively stiff in any combination - front stiff, rear stiff, inside or outside stiff (relative to the direction the car is turning), or diagonally stiff either way. 

The springs and anti-roll bars add to wheel pair stiffness in both bump and rebound. 

A softer spring transfers less weight and promotes more movement of the chassis, at that corner, in all four modes of movement.  We are only re-distributing the static weight, so there must be another wheel pair to take up extra weight transfer. 

To highlight the role of the spring in rebound it usefull to think about the weight jackers in a speedway car.  If we have jacked a lot of weight into one of the inside wheels, we could fit a softer spring at that corner, so it would transfer less weight, hold more weight at that corner.  With the car back on the scales, we could even up the static weight a bit.

The anti-roll bar increases wheel stiffness on the inside wheel, but is working in the opposite direction to the spring.  If the anti-roll bar is too stiff relative to the spring, it could limit droop travel, and unload the wheel.   This is why we cannot use too much anti-roll bar on the driven wheels.

It's interesting to think about an asymetrical sway bar set up - shorter lever on one side, longer on the other.  Weight transfer will be the same as for non-asymetrical set up.  But wheel rate will increase on the short lever side (less movement in bump), and decrease on the long lever side (more movement in rebound).

Shock absorbers add to wheel pair stiffness in both bump and rebound.

Unlike springs and anti-roll bars, the shock can have different stiffness in bump and reboundMakes you think about the tuning possibilities, doesn't it?  Shocks are very important in control of the chassis platform and promoting mechanical grip of the tyres. 

Describing the Weight Transfer

We need a way of visualising weight transfer, so that we can see how how set up changes will contribute to understeer or oversteer.  Our goal is to maximise overall grip, and make the vehicle respond predictably to driver inputs.    We talk about understeer or oversteer (tight or loose) in the various phases of corner entry, mid corner and corner exit.  For instance,we could could loosen the car on entry for better turn in, and tighten it on exit, so the driver can get the power on earlier. 

We want to know what is happening to our car during cornering - turning in and trail braking, steady state, and accelerating through the apex and out of the corner.  The driver feels this as handling balance variation.  The car could understeer more as grip deteriorates mid corner (say if carrying a lot of car speed), and oversteer as grip deteriorates on exit (say if driver accelerates earlier and/or harder).

Key Point - Dynamic Wedge

Our key concept in dynamic weight transfer is dynamic wedge.  Positive wedge, or wedge, is defined as greater inside percentage weight at the rear, compared to the front.  That is, the inside rear wheel weight divided by total rear weight, expressed as a percentage, is greater than the equivalent calculation for the front wheels. The rear wheels are more equally loaded than the front wheels.  The car will have greater tendency to understeer.  Negative wedge is the opposite - greater inside percentage at the front compared to the rear.  The car will have greater tendency to oversteer.

We are considering the redistribution of the static wheel loads. So the load on all four wheels always equals the static weight of the vehicle.

For example, if we stiffen the front roll bar and make the car front stiff in roll, the car wedges itself more as it corners harder - more understeer, tighter.  If the car is rear stiff in roll, the car de-wedges itself as it corners harder - more oversteer, looser.  Note the description in dynamic terms.

A usefull quick way to think about wedge is to consider inside weight, at one end of the car or the other. You could say "I have increased inside rear weight" ie wedged the car (moved the set up in the direction of understeer).  Conceptually, it's easy to follow because the increased inside weight at the rear will improve grip at the rear.  American Race Car Engineers talk about increased or decreased weight across the front of the car. This is equally valid.  By definition, if you have increased inside front weight percentage, you must have decreased rear weight percentage.

Dynamic Wedge for Roll, Pitch, Warp and Heave

To determine wedge in roll we compare the the stiffness of front and rear wheel pairs.  Look at the direction the weight is moving - outward or inward relative to the corner.  Weight will be transferred to or from the inside wheels in proportion to wheel pair stiffness.  Compare inside weight percentages.   If the car is front stiff, it will wedge in initial roll, and de-wedge in roll back.  Vice versa for rear stiff.

Consider pitch the same as roll turned through 90 degrees.  Now we look at the relative stiffness of left and right wheel pairs.  For road racing, right and left wheel pairs will generally be equally stiff, so pitch, by itself will not wedge the car. 

But our speedway car could be left stiff or right stiff depending on our requirements.  Look at the direction of the weight transfer. Forward for forward pitch (braking), or rearward for rearward pitch (acceleration).  The stiffer side will transfer the greater weight percentage.  If the car is outside stiff, the car will wedge in forward pitch and de-wedge in rearward pitch.  If the car is inside stiff, the car will de-wedge in forward pitch and wedge in rearward pitch.

If need be, take time to confirm what is happening here.   Try it on a piece of paper.  Road racers too.  We need it for shock tuning.

Warp movements seriously wedge or de-wedge the car. 

On a narrow road course, accelerating out of a tight corner and over the crown of the road, the inside front and outside rear will be receiving load, and wheels on the other diagonal unloading.  Looking at the directions of weight transfer across the car, the car is de-wedging, big oversteer.  To tune for this we would need to reduce wheel stiffness at all four corners.  We would not want to do this, because we have optimised stiffness for the important roll and pitch modes.   So our driver would have to make the best of it.  He could enter the corner a little earlier.  On exit, use the crown to help turn the car before full acceleration.  If there is enough road on the exit, he could try entering the corner very late, get most of the cornering done, accelerate hard off the apex and balance the car on the throttle going over the crown in the road.  With the late turn in, he might leave the door open for an inside pass.  But the car inside could get caught with oversteer going over the crown, leaving our driver a perfect opportunity for a switch back re-passing move. 

Warp movements on a flat surface become pure weight transfer between diagonally opposite wheels.  We can analyse these as a combination of pitch and roll.

Heave movements will not wedge the car.  But combination roll and heave will.

This must be a big part of suspension set up for stadium truck racing, and in rallying. .

Dynamic Wedge in Braking, Cornering and Acceleration - Combination Roll and Pitch.

This is the "guts" of weight transfer as it applies to race car chassis and suspension tuning. 

You can add pitch and roll weight transfers to look at the resulting wedge of the race car.

Click here(wedge example),and see how the driver inputs of braking, cornering and acceleration have a massive affect on wedge, and therefore car balance.  If the discussion has made sense so far, it is definitely worth a look.

Notes:

1. In suspension tuning for weight transfer, we  can look at changes to  springs, anti-roll bars and shocks, height of front and rear roll centres, and possibly anti-dive and anti-squat.  See shock tuning page for shocks.
2.  We must know the directions of weight transfer in the vehicle to make a correct analysis.  So the driver and race engineer must be clear about the movement of the car they are influencing.  If the driver changes his style, the movement might be different.   Any change unrelated to a particular movement will only be guess work.  A change for one movement of the car means changes for other movements of the car, for better or worse.  The set up is an un-ending compromise.
3.  Wheel stiffness affects the speed at which wedge or de-wedge occurs during transitions.  Particularly important for shock tuning.
4.  We can analyse all asymetrical set ups for speedway, and we need the same theory for road racing, to analyse handling transitions.
5.  If we had high level data acquisistion, we could carry out a detailed analysis to optimise the weight transfer in the areas where the driver had problems.
6. We need chassis and suspension components stiff enough and the operation of the suspension smooth, so the intended weight transfers can take place.

Shock Absorbers and Dynamic Wedge.

Dynamic wedge helps us to consider the effects of shock absorber changes.  As indicated earlier in this article, shocks are velocity sensitive ie they only affect wheel stiffness while the suspension is moving.  To affect handling balance, we only consider low speed damping, say around 0 to 2 inches/sec.  The feature of the low speed damping is that it comes on straight away and stays fairly constant (controlled by a port in the shock piston)- not building like the anti-roll bar load.  So playing with low speed damping might have quite a nice effect on transients - eg initial turn in, and feeding the power in for corner exit.  If we make low speed damping more rear stiff, we could de-wedge the car on corner entry, and increase wedge for corner exit.  For a description of this, click here(shock example). 

 
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Footnote:
In pitch, anti-dive and anti-squat suspension geometry add to wheel pair stiffness. 

In roll, any change in track dimension (track variation, or tyre scrub), resulting from the design of the suspension geometry adds to wheel stiffness.  The affect on tyre grip is all bad.  In modern formula race car design, tyre scrub is reduced to a minimum, at the expense of other design criteria, such as optimising camber curves.  In older designs, we live with it.

        

Smithees Race Car Technologies         ABN                                                                                  racetech@ozebiz.com.au