A word about upgrading sway bars

[Ryan]

This is a thread about swaybar construction.

I see that people are buying solid sway bars as a performance part.

I say this is not the most effective solution.

Let me explain myself, unfortunately this requires a bit of math.

The term for the figure that describes a shapes resistance to deformation is its 'polar moment of inertia', or I in this thread.


The I describes a cross section's ability to resist deformation. The equations were derived long ago by people much smarter than me. Its units are meters to the fourth, which means it is a function of length four times. (length * length * length * length)

The I for a square/rectangle shape is

I = 1/12 * (base)*(height)^3

This is why a ruler is strong when you stand it on edge and try to bend it, but deflects when you lay it on the flat, its resistance to bending is a function of its height cubed (height * height * height)

Say your ruler is 1 metre thick, and 20 metres wide. I used this massive scale so the numbers are nice, otherwise there would be a decimal, then 13 zeros, then the numbers we care about. The scale does not affect the principle.


the I for that ruler on the flat would be 1.6 m^4.
the I for that ruler on edge would be 666.6 m^4, or 416 times as strong in bending, just by standing it up on edge.


Lets apply the same idea to a sway bar.

The I for a hollow tube is

I = pi/4 * ( ( outside radius)^4 - (inside radius)^4 )

I have never cut our sway bar open, but I know it is approximately 20mm in diameter. Lets say it has a 5mm wall thickness, so we can work with nice numbers.

so, plugging it into that equation,

I = 7.36 E-9 ( 0.00000000736)

Lets pretend the wall thickness is now 6mm, a little thicker.

I = 7.65 E-9

Now pretend its 4mm, a little thinner.

I = 6.84 E-9

Now, decreasing the thickness by 1mm lost 7% strength.
increasing it by 1mm gained only 4% strength.

See where I'm going with this?


Lets pretend its solid, so the inner radius is 0.

I = 7.85 E-9

Its now only 107% as strong as before. Note that from before, this means that the inner 0-4mm of radius only account for 3% of the increase, the 4-5mm section accounted for 4%.


Now lets leave the 5mm wall, but make it a 22mm bar.

I = 1.05 E-8

Holy s---, that is 170% as strong as before.

Now, for giggles, lets compare the cross sectional area of the last two profiles.

The area of the stock 20mm bar with 5mm walls is 235 mm^2
The area of the solid 20mm bar would be 314 mm^2
The area of the 22mm bar with a 5mm wall is 267 mm^2.

Now, you should be able to reason that this area, times the length of the bar, times the density of the steel used will yeild the bar's total mass. That is, if you have a greater cross sectional area, the bar will weigh more.

Now, the options.

Uprade 1: stock diameter, solid bar. 107% as strong, 133% as heavy.

Upgrade 2: +2mm in diameter, same 5mm wall. 170% as strong, 113% as heavy.


No brainer, right?

The bottom line, don't buy solid sway bars over hollow sway bars, its a marketing trick. Intuitively everyone should think that a solid bar would be much superior to a hollow one. That is not the case. Buy larger diameter, but still hollow bars.

Stronger materials will also increase its performance.

I am in no way saying that the Whiteline product is not an upgrade. This math proves that by geometry alone, its is approximately a 7% upgrade in stiffness, nevermind the later-mentioned fatigue effects, corrosion, and alloy.

All I want to get across is that for the purpose of a swaybar, making it solid is not as effective as solution as increasing its diameter. Don't get caught in marketing traps.

Ryan.

[onlytrueromeo]

Ryan,

Yes and No.

Whileline is the biggest / best part out there. Yes, you could go with a used 22mm bar for 95% of the strength, but:

A) It's already been used for about 20 years. This leads to metal fatigue.

B) It's not shiny new.

C) It probably does not come packaged and delivered to my door, I have to go rip it off a car.

D) It does not come with new bushings like a whiteline does.

I got my whiteline bar for $119? I believe a couple years ago.

PS. I like getting shiny new things

[Ryan]

I have no idea whats on the market.

If a piece is properly designed, fatique is not a concern for many millions of cycles. I can't comment on this without knowing the grade of steel, and I don't care to find out empirically. Although, I would assume it was accounted for, in a part that is a spring....


The rest is you just falling for the marketing

Which, admittedly, is a huge factor - being shiny and new, but it doesn't make it an effective performance upgrade

[Sleeper6]

Ryan stop being an engineer, your scaring us.

The solid sway bar is simply and upgrade for those looking to reduce a little bit of body roll. Yes it is heavier, however that increase in weight is also at the lowest point on the car so if anything its further helping. Not only that but my money would be that the whiteline unit is of a better alloy as well compared to something that is being mass produced with a budget in mind so that too is going to help in its performance.

Now it may not be the biggest yield per $$$ but I still say its a worthwhile investment. Just take an old classic muscle car out with a modern upgraded sway bar and I ld bet yould change your mind.

[wytbishop]

The I for a hollow tube is

I = pi/4 * ( ( outside radius)^2 - (inside radius)^2 )

piD^2/4 is the area, not I.

Polar Moment of Inertia of a solid cylinder ... I = pi*(R^4)/2 = pi*((D/2)^4)/2 = pi*(D^4)/32

Polar Moment of Inertia of a hollow cylinder ... I = pi* (D^4 - d^4)/ 32

I have never cut our sway bar open, but I know it is approximately 20mm in diameter. Lets say it has a 5mm wall thickness, so we can work with nice numbers.

so, plugging it into that equation,

I = 5.89 E-5 ( 0.0000589)

Lets pretend the wall thickness is now 6mm, a little thicker.

I = 6.59 E-5

Now pretend its 4mm, a little thinner.

I = 5.03 E-5

Not the numbers I get. I'm not sure what you did here but I would recheck my math. I'm not saying you're not right in principle but the affect might not be as pronounced as you think.

[Nd4SpdSe]

(Edit: Sorry Sleeper, didn't want to make it look like I followed you, I had it mostly typed out but was watching American Chopper Live and it just ended, lol)

Sorry Ryan, and this may be slightly off-topic, but this is why I don't line engineers. You come up with numbers to discredit products from a well known company who's been making well known performance parts for a very long time and making claims that their products are a scam. Sorry, that's a big claim and I'm not buying it.

[Mooneggs]

Well if somebody wants to fabricate a 22mm hollow sway bar, I'm more than happy to compare it to my Whiteline when I go racing this year

As far as I know, the MS swaybars (I'm not even sure I know the dimensions and whether they are hollow/solid) are virtually impossible to find and I haven't seen any other companies producing swaybars for our cars... so we kind of only have Whiteline as an option right?

I'm just a simple minded person who doesn't really get/care about complex math so is the Whiteline better than stock or not?

[MrMazda92]

(Edit: Sorry Sleeper, didn't want to make it look like I followed you, I had it mostly typed out but was watching American Chopper Live and it just ended, lol)

Sorry Ryan, and this may be slightly off-topic, but this is why I don't line engineers. You come up with numbers to discredit products from a well known company who's been making well known performance parts for a very long time and making claims that their products are a scam. Sorry, that's a big claim and I'm not buying it.

I took from Ryan's post that there is more potential in a hollow bar than a solid one, and this makes sense to me. Sailboat masts, tube frames for cars, pretty much any highly stressed support you find will be hollow. Does this mean that Whiteline is scamming people? No, but it means that they(like every other company) are in it for profit. It's cheaper for them to manufacture the bars the way they do, so they do it. End of the day, Mark made a good point about them being the only real aftermarket option. Why build it better, when there's no competition?

It's food for thought, although Ryan might want to change his wording on it being a scam... I don't think many of you interpreted it the way I did.

[Ryan]

Thank you Wyt, This is why I'm not edjumakated yet.

I said myself its a function of length to the fourth, and the proceed with calcs squared. Durr.


Its fixed now, I even lightened up the language for you sensitive types.

I don't mean to say the whiteline bar is BAD, or that it is counterproductive, I'm just saying that its not a very effective design, and that you shouldn't draw the conclusion that solid bars are better than hollow ones. That is a natural conclusion, and it is not the case.

The bottom line is money though, and Whiteline is probably doing the best thing, providing a product that is a legit upgrade, and they can actually sell. We all know how cheap/niche our market is.

Yes, the Whiteline is an upgrade, but its not a very effective one. If you autox, I do still suggest you invest in one.

[wytbishop]

My pleasure Ryan. Here's how i see it fwiw. I haven't reread your post yet.

Polar Moment of Inertia of a hollow cylinder ... I = pi* (D^4 - d^4)/ 32

Polar Moment of Inertia of a solid cylinder ... I = pi*(D^4)/32

A 22mm sway bar with a 5mm wall thickness has and ID of 12mm.

I = pi*(.022m4 - .012m4)/32 = 2.096x10-8 m4

A 22mm sway bar which is solid has an ID = 0.
I = pi*(.022m4 - 0)/32 = 2.300x10-8 m4

That’s about 10% greater resistance to torsion.

Area of a cylinder is pi*D2/4. Area of a hollow cylinder is pi*(D2 – d2)/4. If the length and the density of the sway bars in question are equal the weight of the bars is proportionate to their cross-sectional areas. That allows us to say the percent increase in the weights.

Ahollow = pi(.022m2 - .012m2)/4 = 2.67x10-4m2

Asolid = pi(.022m2)/4 = 3.801x10-4m2

So the solid bar has about 42% more weight.

The question is...as it is with any upgrade...what cost are you willing to pay for the added torsional resistance of the solid bar? In this case we're talking about an additional 5lbs or so? And it has been pointed out that the weight is added to the lowest point in the car.

A 10% increase in stiffness in the front sway bar is going to be noticeable. An additional 5lbs...even 10lbs...is not.

No brainer in my opinion.

[Ryan]

The weight is totally negligible for what we do with our cars. If we were building serious race cars (Say, Formula1 or FASE) 10 grams more will get you yelled at.

It was just an interesting thing to point out.

And I follow and agree with your calcs

[Josh]

Typical Engineer... Over Engineering the simple... kidding Ryan

I get what you are saying, but all the formulas and specs you throw up are meaningless without knowing the exact specs and materials they are using for hollow and solid bars.

I have two rear sway bars both produced by Mazda one hollow (standard OE bar) the other solid (Performance bar off of a GTR). Now I don't have the machines to test the metals used, but I have enough smarts to tell you that they are different. If you are going from the thin a$$ed wall hollow bar from Mazda the solid bar of the same size is going to be better performance.

You should see the hollow bars on the RX8 vs the older MX3 - a lot more engineering has gone into them. I cut it in half to see, large diameter, thick walled. I will take a picture of it for you. I think Mazda was listening. The new MS bars are hollow as well. Hollow is better IMO, but I think for most of our purposes the slight stiffness increase from going to a solid bar in our light little cars is worth it.

@ Moon - the MS bars were solid and both 2mm over stock. The fronts rarely sold, one because they are a PITA to change, the other is because "supposedly" they created a lot of understeer, and really only intended for the GS. Personally I have been thinking about getting my own front made out of SOLID spring steel.

[wytbishop]

Ryan made a very good point in his original post. The majority of the stiffness of any member subjected to a torsional load is created by the outermost portion of the material. That is where the most stress is created so that is where the most resistance comes from. In a solid bar the inner portion is really not subjected to much strain. If you consider what I put in my previous post from the reverse perspective, by removing the inner 12mm diameter core of the cylinder you reduce its mass by 42% while reducing the stiffness by only 10%. That's a great deal if weight savigns are a concern.

Hollow is definitely better if you're starting from scratch. But if you're starting with the hollow bar that the factury supplies and you want to get stiffer without having to go through the trouble of bigger mounts and stuff...just make it solid.

[DeadMaker]

I have changed my oem sway bar with whiteline and all i can say i am very happy with the results..BETTER handling and corner..

[Nd4SpdSe]

I don't mean to say the whiteline bar is BAD, or that it is counterproductive, I'm just saying that its not a very effective design, and that you shouldn't draw the conclusion that solid bars are better than hollow ones. That is a natural conclusion, and it is not the case.

The bottom line is money though, and Whiteline is probably doing the best thing, providing a product that is a legit upgrade, and they can actually sell. We all know how cheap/niche our market is.

Yes, the Whiteline is an upgrade, but its not a very effective one. If you autox, I do still suggest you invest in one.

Way better put than calling it a scam

Just wondering tho, maybe they designed it for a reason. Maybe price-point or materials to work with? Maybe making it engineeringly "perfect" would of been too much, too strong, unbalanced or affected the car in a way they didn't like?