Physics of anti-roll bars

[sosidge]

Can somebody with a bigger brain and more education than me clarify the physics behind our bent wire anti-roll bars.

I'm pretty certain that the straight centre section of the bar is stiffer if of greater diameter and/or shorter length.

But the bit that has me confused is the effect of the mounting position on the arm and the length of the "lever" part of the bar. Is it cancelled out by the mountings being identical on both sides of the car? Or is the effect cumulative on both sides?

[Garry Driffill]

A lighter front sway bar increases front traction off-power, But has less on-power steering.

A heavier front sway bar decreases off-power front traction making the front of the car more predictable when entering a turn but gives more on-power steering.

Going acrross to the rear of the car..

A lighter rear sway bar will increase rear traction but decreases on-power steering.

A heavier rear sway bar increases stability in the middle of a turn and increases on-power steering, Heavier sway bars also make the car more stable on high speed, high traction tracks like astro or carpet..

[sosidge]

A lighter front sway bar increases front traction off-power, But has less on-power steering.

A heavier front sway bar decreases off-power front traction making the front of the car more predictable when entering a turn but gives more on-power steering.

Going acrross to the rear of the car..

A lighter rear sway bar will increase rear traction but decreases on-power steering.

A heavier rear sway bar increases stability in the middle of a turn and increases on-power steering, Heavier sway bars also make the car more stable on high speed, high traction tracks like astro or carpet..

That doesn't explain the physics though... just the effect. I understand the effect, but want to understand the physics too.

[Garry Driffill]

Wouldnt it work as in further out with a kink gives a smoother the transfare?

[glypo]

Vehicle dynamics (suspension) interests me very little. I did however read a book once which had comprehensive physical analysis of roll-bars.

It was either:

Pacejka, Hans B. 2005. Tyre and Vehicle Dynamics. 2nd Ed. Butterworth-Heinemann.

or:

Genta, G. 1997. Motor Vehicle Dynamics. World Scientific Publishing.

[simoncrabb]

My very simplistic view of roll bars in RC is they increase the springing when one side is under compression, but not when both are under compression.

Our wire roll bars are like a torsion bar I guess?

[SlowOne]

I hope this helps...

An anti-roll bar is a spring (more of which later) that connects one side of the suspension to the other. As you raise one side of the suspension, the ARB tries to raise the other side. By doing this, it effectively uses some of the energy from the weight transfer to raise the other side of the suspension, thus keeping the car flatter in the turn.

It is a spring. The energy you put in 'bends' the metal. As the metal resists the bending, it will lift the other side of the suspension. Like all springs, you can adjust its rate - the amount of effort it takes to compress the spring - and that affects how it deals with apportioning the weight transfer across the car. Strictly speaking, an ARB should twist in the centre section (hence the term torsion bar) but in practice the arms also bend, especially in our model cars. The centre part of the arm (connected to the chassis) is connecting two levers, and the ends of the levers are attached to the suspension at the leverage points.

To make an ARB stiffer you can either increase diameter of the bar (I am ignoring 'blade' type ARBs as they aren't used on electric cars, only gas cars) or change the position of the arm acting on the lever. In other words, make the bar thicker, or move the leverage points on the lever up or down.

If you move the leverage point closer to the centre section, you will stiffen the arm which increases the stiffness of the ARB. Moving the leverage point further away has the opposite effect. For all practical purposes, doesn't matter how far apart the pivot points are on the ARB (where they are attached to the chassis) to determine stiffness, but it does matter how far the leverage points are from where the ARB is attached to the chassis.

ARBs are springs. Worse yet, they are undamped springs. For any given energy input, the ARB will give an immediate energy output. There is nothing to control the rate at which the energy is released - it has no damper. That's a bad thing because at the extreme, it will make the car rock across the chassis (from one corner to the other) as anyone who watched Andy Rouse in a Cosworth 500 Touring Car will remember! So, there comes a point where the ARB will interfere with the damping of the suspension, and control of the wheel travel is compromised.

ARBs will also have a role in limiting suspension travel (they're rarely seen on long-travel rally cars, often seen on short travel track cars) and will add weight and complexity.

Although they limit chassis roll, they do this by taking the weight transfer, unloading the inside tyre, and loading the outside tyre. This reduces grip at that end of the car. Also, because they react to one wheel moving up/down, and are connected to the other wheel, they will transfer any motion over bumps from one side to the other, causing the chassis to wobble from side to side over bumpy terrain. :)

[sosidge]

Well thanks for the answers so far. I have been trying to find a clear reason on t'internet why a longer lever arm results in a softer ARB rate. Much is said about the greater leverage of the longer lever, but I still believe the added leverage is cancelled out by the equal size of the lever on the opposite side of the car, my schoolboy physics implies it would have to be.

However the wire ARB levers are not perfect - they flex a lot, and act more like springs. I think this may be the reason for the change in ARB rate, the long lever acts like a softer spring and absorbs a lot of the energy before it can be transferred to the other side of the car, the effect is duplicated on the other side.

I did do an empirical test on the B4 and yes, the bar is stiffer if you shorten the lever length. Wish I knew where the physics was actually happening but I suppose I shall have to either take another degree or just accept the results!

[DCM]

the longer arm, has a lower ratio of torsional twist to the upstroke of the suspension arm.

eg.

Short link, 15mm of suspension travel = 47' of torsional twist (stiff action)
long link, 15mm of suspension tavel = 30' torsions twist (soft action)

Running an ARB can allow for slightly softer springing and damping on your suspension, to cope with a rough track, with the ARB controlling pitch into and out of a corner.

[sosidge]

the longer arm, has a lower ratio of torsional twist to the upstroke of the suspension arm.

eg.

Short link, 15mm of suspension travel = 47' of torsional twist (stiff action)
long link, 15mm of suspension tavel = 30' torsions twist (soft action)

Running an ARB can allow for slightly softer springing and damping on your suspension, to cope with a rough track, with the ARB controlling pitch into and out of a corner.

If we were to assume that the bar was perfect (ie no actual twist, just complete transmission of the forces), 47 degrees or 30 degrees would not matter as the opposite side of the cars suspension would need be lifted by an identical amount, as the linkages are identical on both sides of the car.

If we assume that the levers are perfect but the centre section twists at a uniform rate (say, 50%), the lift on the opposite side would also be constant (certainly as you approach zero the relationship would be linear). An input of 20deg from a short link that lifted the other side 10deg would be effectively the same as a long link, deflecting 10 degrees, and lifting the other side 5deg.

But obviously the levers are not perfect, they flex, and this takes up more of the input energy before it gets transferred to the centre section of the bar, and more again as it is transferred back to the opposite side. The longer the lever, the greater the energy loss. And the softer the effect of the bar.

I'm fairly certain that it is the "spring" nature of the lever rather than the leverage itself that causes the bar to be stiffer with a shorter lever. But in all honesty it is not that relevant now as after 5 minutes with the car I have seen the lever effect in action. I probably shouldn't have bothered posting the thread in the first place!

[Alfonzo]

Surely the length of the lever arm dictates the amount of torsional twist or 'spring' that gets loaded up within the ARB for any given suspension travel. It's the gearing if you like.

Slow one knows what he's talking about. Your comment about the longer lever giving a softer result through its own 'springiness' might be true, given the scaling issues with model car design, although not at all how an ARB is designed to work. It would effectively be the same as modestly increasing the spring rate.

[SlowOne]

Sosidge, you are confusing two things - what you see on your car and the Laws of Mechanics and Physics. I hope this helps...

In a 'proper' ARB, the arms don't bend. In a model car ARB, we use piano wire and, as you say, the arm does bend. Ignore this! Now go through DCM's good explanation and you will see the reason for a softer action from a longer lever.

The wishbone moves a fixed distance. If the lever is a long way from the centre section, it will move teh lever a small amount, and thus twist the centre section a little. Move the lever closer to the centre section and for the same movement of the wishbone, you will twist the centre section a lot. More twist tries harder to lift the other wishbone, thus making the front end 'stiffer'

By the same token, make the bar thicker and you will get more lift on the opposite wishbone, again making the suspension 'sitffer' at that end.

Always remember that an ARB is transferring weight across the chassis, and taking grip away from the end the ARB is attached to. Your first port of call should always be the roll centres, in order to change the roll-rate of one end or the other. ARBs come into their own when one can no longer get the desired result from this approach (most cars have limits as to where the suspension pick-up points can be placed) or when the car needs to have suspension capable of absorbing bumps, yet remain stiff in roll.

HTH :)

[RickRick]

i guess, just to make it aquard it depends on the amount of movmeant, move 5mm up and down and the springiness of the ARB will absorb most of the movmeant, move 50mm, and the "free" movmeant will be absorbed, and transfer plenty of movmeant to the opposite side

[sosidge]

The wishbone moves a fixed distance. If the lever is a long way from the centre section, it will move teh lever a small amount, and thus twist the centre section a little. Move the lever closer to the centre section and for the same movement of the wishbone, you will twist the centre section a lot. More twist tries harder to lift the other wishbone, thus making the front end 'stiffer'


I would absolutely agree with this analysis if the pickup point on the other side of the car remained in a constant position.

However the opposite side of the roll bar mounting is always moved the same, so the levers are mirrored, and the added twist of the bar on the input makes no difference, as added twist is needed on the output to lift the wishbone by the same amount.

The analogy I keep returning to is that of a see-saw, with me and my daughter sat on it. If she is sat on the seat, I need to sit near the pivot to balance (a smaller force having a greater effect due to unequal lever length). However, if my brother (of equal weight in this example) swaps places with her, it doesn't matter how far in or out on the see-saw he sits, if I sit directly opposite, we will always balance (the size of the force is irrelevant if the levers and forces are equal).

If you can explain why the length the output lever in an ARB is irrelevant to the length of the input, I would really appreciate it.

[bigred5765]

imho. longer arm going to the wish bones, more flex (more bow,it bends before it reaches the center section)shorter center section less twist,stiffer action

[Lee]

Maybe i am picking this up wrong, apologies if i am but... you are assuming the "unloaded" wheel is lifting up the same amount of the "loaded" wheel, it doesn't, no matter how much we say ignore the flex, we can't it is always there and to be honest it's not a constant either in my eyes on our very basic roll bars. (nearly but not quite).

If we did have perfectly stiff bars with zero deflection then for me it would make no difference on the length of the arms of the ARB as long as they were mounted at equal points on the wishbones, but as they do flex i think that the further away the wishbone pick up point is on the bar to the central, chassis mounting points then the softer and "less effective/more flex" you will get, i think this is only natural and it is something i play about with from time to time, obviously it is a tiny adjustment but i believe it is noticable.

I hope this helps or maybe just adds fuel to the fire :lol:

[sosidge]

If we did have perfectly stiff bars with zero deflection then for me it would make no difference on the length of the arms of the ARB as long as they were mounted at equal points on the wishbones, but as they do flex i think that the further away the wishbone pick up point is on the bar to the central, chassis mounting points then the softer and "less effective/more flex" you will get

This is the point I am trying to get across although perhaps you have put it more eloquently than I have!

[Fabs]

Right let's put this straight.

Be it with or without taking into account the FLEX on the arms, their lenght ALWAYS make a difference in the stiffness of the ARB.

Look at it this way : for a defined angular movement of one of the wishbones, we have a vertical movement of the connection of the ARB that is constant, let's call it A.

If the projected length of the ARB arm on a plane that is normal to the central section of the ARB is called L, then we have the following relation:

cos α = A/L

Where α is the angle of the ARB arm in the normal plane defined above.

As A goes smaller the cos goes smaller too which means that alpha increases.

What that means is that the centre section will see a higher twist rate if the arm is shorter, which in returns means that the ARB will be stiffer.

Now if we consider our R/C ARBs, then you cannot neglect the bend in the arm and that also has an influence on the twist rate. However as the arm goes shorter it also gets stiffer so it all works in the same direction as in the centre section.

PS: can you tell i'm bored at work ? :woot:

[sosidge]

Right let's put this straight.

Be it with or without taking into account the FLEX on the arms, their lenght ALWAYS make a difference in the stiffness of the ARB.

Look at it this way : for a defined angular movement of one of the wishbones, we have a vertical movement of the connection of the ARB that is constant, let's call it A.

If the projected length of the ARB arm on a plane that is normal to the central section of the ARB is called L, then we have the following relation:

cos α = A/L

Where α is the angle of the ARB arm in the normal plane defined above.

As A goes smaller the cos goes smaller too which means that alpha increases.

What that means is that the centre section will see a higher twist rate if the arm is shorter, which in returns means that the ARB will be stiffer.

Now if we consider our R/C ARBs, then you cannot neglect the bend in the arm and that also has an influence on the twist rate. However as the arm goes shorter it also gets stiffer so it all works in the same direction as in the centre section.

PS: can you tell i'm bored at work ? :woot:

But surely the cosines are equal on both side of the car, so again the increase in torsion on the centre section is cancelled out by the increased amount of lift required on the opposite side of the car? This is assuming that the centre section behaves in a linear fashion and that the lever arms are perfectly solid.

[Fabs]

If both arms were moving the exact amount it wouldn't matter. But that's when the ARB isn't being used.

What we're looking at is the amount of twist for a certain difference in position between the left and right wishbone, and this increases as the ARB arm goes shorter.

You may need to look at things from an energetic point of view. As the ARB twists, it absorbs a part of the input energy, and the other part is being transfered to the wishbone. The amount that is being transfered to the wishbone increases with the twist angle. If the twist rate increases then more energy will be transfered faster to the wishbone, i.e. the ARB is "stiffer".

[Lee]

Steady on Fabs, anyone would think you knew what you were talking about :lol:

I do agree with what you are saying though, people forget that the roll bar absorbs energy, it is not an equal output from the input of the loaded side.

[sosidge]

Yes, I agree with the energy analysis, and also an analysis based on cosines of a difference in position of the input and output of the bars. I think I have mentioned the energy analysis myself already. It's the lever length analysis that I can't agree with.

Doesn't really matter ultimately - I have done an empirical test and seen the results. I have seen a few explanations based on sound science. My mind is at rest.

I only asked the topic in the first place because the .047thou bar (~1.2mm) on the B4 behaves in a much softer way than the 1.2mm bar on the Yokomo, and the 1.2mm bar on the Tamiya.

[Fabs]

I THINK I know what I'm talking about but odds are I'm just talking rubbish :D

[Lee]

What are the visual differences? a 1.2mm bar with 2 bends/kinks will always have more flex than a 4 kink bar as im sure you know as there will be less flex due to there being shorter lengths. (if that makes sense)

[Fabs]

Yes, I agree with the energy analysis, and also an analysis based on cosines of a difference in position of the input and output of the bars. I think I have mentioned the energy analysis myself already. It's the lever length analysis that I can't agree with.

Doesn't really matter ultimately - I have done an empirical test and seen the results. I have seen a few explanations based on sound science. My mind is at rest.

I only asked the topic in the first place because the .047thou bar (~1.2mm) on the B4 behaves in a much softer way than the 1.2mm bar on the Yokomo, and the 1.2mm bar on the Tamiya.

Two different roll bars design may be different for a same diameter for multiple reasons : Pick up points on the arms is an obvious one, but also the length of the central section of the ARB has a big influence as the twist rate / unit length is mainly what we're interested in. And ultimately the length of the ARB arms as we've established that they do indeed bend in our case.

Also don't forget the angle between the ARB arm and the link between it and the wishbone has an influence too.

[sosidge]

What are the visual differences? a 1.2mm bar with 2 bends/kinks will always have more flex than a 4 kink bar as im sure you know as there will be less flex due to there being shorter lengths. (if that makes sense)

The bar on the B4 has a much longer centre section and the lever arms are somewhat longer too. All the bars have only 2 kinks.

So I think there are two things making it softer - the long levers (absorbing energy), and the long centre (behaving like a softer torsion spring).

[blue_pinky]

So I think there are two things making it softer - the long levers (absorbing energy), and the long centre (behaving like a softer torsion spring).

Spot on!!! A* Simple as that!

[Duncs]

Two different roll bars design may be different for a same diameter for multiple reasons : Pick up points on the arms is an obvious one, but also the length of the central section of the ARB has a big influence as the twist rate / unit length is mainly what we're interested in. And ultimately the length of the ARB arms as we've established that they do indeed bend in our case.

Also don't forget the angle between the ARB arm and the link between it and the wishbone has an influence too.

And the material the ARB is made from, of course. Two different grades of steel will behave differently, Young's Modulus IIRC.

[SlowOne]

Great - we all got there in the end! Keep in mind that the basics 'Rules' of ARBs apply no matter what shape or size they are - roll will increase if the material is thinner or more ductile, and if the lever points are further away from the pivot points. The length of the centre section will have an impact, but since that is fixed for any given car, it can be ignored when making tuning changes. Good luck you rock and (anti) rollers! :D :thumbsup: