anti roll bar/sway bar comparison

Malcolm

Supporter
I am sure someone out there is good with the maths of comparing anti roll bars/sway bars. Can you please help?

Currently I run a 20mm solid bar. This is too soft (professional race drivers assessment as well as mine) and I have no way of adjusting it, so it is to be discarded (put on the shelf!) and a replacement fitted.

I have a choice of two tubes in front of me right now. Both are 25mm (1 inch) outside diameter but the wall thicknesses vary. The skinnier one has a wall thickness of 2.6mm and the chunkier one has a wall thickness of 6.25mm. I can't seem to find a wall thickness tube of 4mm (or thereabouts) as a halfway house.

The effective lenght of all three bars is 27 inches, 685mm. The leverage lenght is the same for all bars.

Clearly both the skinny and chunkier tubes will be stiffer than the 20mm solid bar but by how much? In addition how much stiffer is a 25mm solid bar over a 20mm solid bar?

For discussion sake assume all materials are the same grade steel, CDS2.

Can anyone help, please? Thanks.
 

Ron Earp

Admin
Hey Malcolm,

you could go a long way toward not having to get it exactly right by fitting an adjustable bar. Either by holes in the bar, or a block with heim joints that clamp down where you want it. Or, one of the cool lever adjustable like outlined in Tune to Win.

Ron
 

Malcolm

Supporter
Totally agree but club track day loometh and need a working sway bar soon! Also I am a tight a**e and don't really want to splash on an adjustable system like rotating blades, which really is the way to do it in my books.

The bits I mention above are sitting on the garage floor waiting to be fitted so just wanting to make best choice over what is in front of me now.

The math is not based on just the sectionional area differences is it? Diameter has something to do with it too?
 
For torsion, the thicker wall you have will be about 1.5X stiffer then the thin one. The thin one will be about 1.5X stiffer then the smaller diameter solid bar. The thick walled bar will about 2.4 times stiffer then the solid. You seem to have a good, even spread to try. So far, nothing has been said about the strength of the bars.

Stiffness of a round bar in torsion is a function of the diameter to the 4th power and the length (the length of the twisting section). If you want to compare bars in the future, although the full equation involves more, for comparison purposes when the lengths are the same: just calculate the outer diameter to the 4th power minus (-) the inner diameter to the 4th power. (don't subtract the diameters first and then raise to the 4th power - power is not associative - remember? !) For solid bars, just use diameter to the 4th power (inner diameter = 0)

Whether or not either hollow bar will be strong enough, I don't know - it would require some more calculating. I would imagine the thick one will be strong enough, but I don't know how these are being used. Bending as opposed to attaching an arm and then drop link will have an affect. One interesting point to remember about working with materials is that there is a very important difference between stiffness and strength. The same sway bar made out of two different types of steel - one can be low strength, unhardened stuff from a hardware store, the other could be high carbon and heat treated - have virtually the same stiffness. (To be mathematically exact, yes, they will actually differ by a very small marginal amount, but for most purposes they are the same.) Stiffness is spring rate. They will definitely have different strengths. Obviously the higher grade bar that is heat treated will fail at a higher load. Failure doesn't have to be broken either - yielding is typically used as failure. Yielding is when it can't return to its original strength.
 
The diameter has a lot to do with it. The further away the material is from the axes the more rigid it will be.

Angle = (T*L)/(G*J)

T = torque
L = length
G = Shear Modulus
J = polar moment of inertia

As long as T L and G are staying the same we only have to solve for J
For a solid shaft

J = (pie*r^4)/2

For a hollow shaft

J = (pie/2)*(ro^4-ri^4)

So to simplify if your 20mm solid shaft has a stiffness of 1 then…
25mm x 2.6 mm wall =1.5 times stiffer
25mm x 6.25mm wall = 2.3 times stiller
25mm solid = 2.4 times stiffer
 
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To continue, can you explain the effect of arm length mathimatically? On the solid bar, if the arms are attached at a 9 in point verses an 8 inch point? I have an adjustable bar and I was curious how much a 1 or 2 inch movement in or out at the pivot point would equate to.
 
The adjustment on an arm is just a simple lever.

If you are going from 8” to 9” then divide 8 by 9 = 0.888

0.888 times the roll stiffness (from the bar)

Or if you are going from 10” to 5” it would be 10 / 5 = 2

2 times the roll stiffness (from the bar)

This is your force factor between the previous and current positions.
 

Malcolm

Supporter
Late last night I was digging around my suspension books and came across one by Allan Staniforth with formula provided by David Gould. Both guru's in the UK.

1. Angular Rate formula

19700 * (outside dia ^4 - inside dia ^4) / bar length = AR (in in.lbs.per degree)

19700 is a constant derived from the average modulus of sheer for steel. As said above if a solid bar inside diameter is zero so ignore that in above equation.

2. Now to convert to a Linear Rate.

AR / (lever length ^2 * pi /180) = Roll Bar Rate in in.lbs

To measure lever arm length you take the distance perpendicular from the roll bar centre to the drop link centre.

3. Roll Resistance of roll bar.

Roll Bar Rate * (wheel movement * roll bar movement) ^2 * track ^2 * pi / 180 = Roll Bar resistance in in.lbs per degree.

Wheel movement is say 1 inch , so roll bar movement is the amount the drop link pick up point moves up as the wheel moves up 1 inch. Depends where your drop link connects to.

I think these formula are similar to the above and give similar numbers.

Therefore in answer to my own question I am going to fit the 2.6mm wall thickness tube to my car as it is a good step up but I think that the 6mm tube will be too stiff as others use 4mm and seem happy with that.

I did run some calcs for other bar dimensions and found that a 22mm solid bar would give a good result although much heavier than a tube.

Thanks for your input everyone, it has been a good thinking excercise for me. I wonder how it will translate to on track performance? I hope it cures my handling problem!
 

Howard Jones

Supporter
Just to add some shade tree knowledge to the point. I have a GTD with a stock front bar. I wanted to make it adjustable and have the adjustment be in the more effective direction (stiffer). I cut off the flattened tab and about two additional inches from the arms. I then cut a piece of 1" X 1/4" piece of steel drilled 3 holes into it 1" apart, welded them on the end, and located the longest hole (arm length) in the same location minus 1/2" as the original flat tab hole. This has the effect of a reduction in arm length of 1/2", 1.5", and 2.5". It is interesting to note that the center hole seams to be the sweet spot.

I made up some rod end links to replace the rubber things and long bolt.

I also made a adjusable rear bar out of some 5/8 chrome molly with multi hole tabs on it also.
 

Malcolm

Supporter
I did a similar thing to my 20mm front bar. Except I machined up some ali blocks so that they slide up and down the bar but normally have them set in the same old position at the end of the bar.

I have now made the bar and blades and fitted to the car for the rear, just got to fab the drop links out of some ali hex bar.
 

Howard Jones

Supporter
As you can see the front bar has three adjustment points and the stock link has been replaced with my home made one.
 

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Howard Jones

Supporter
The rear is a completely new bar. Different bend to clear some catch cans but same basic diameter and arm length as original. The main difference is its made from chromoly tubing instead of solid material but with the adjustment set to near stock arm length it is pretty much the same effectiveness.

On this one I was going for a range of effectiveness that spanned the stock setting by about 2.5 inches each way.
 

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Howard Jones

Supporter
Lastly if you study the settings you can see that the rear bar is one hole softer and the front is about one hole stiffer than the stock settings. With the additional overall increase in roll stiffness that was added by taking out all the compliance in the links both front and rear by replacing the rubber with rodends, I am pretty happy with the balance.

Just a little push on entry, neutral on corner center, and lightly power on loose on exit.
 
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