Sway bar formula?

[Eric Howell]

As of now I have a 1.25" solid bar that I like, but I want better tuning options. Been looking at hollow adjustable sway bars but I don't know the formula to figure out the stiffness. Is the formula different for solid vs. hollow?

[Norm Peterson]

For all practical purposes, the stiffness of a solid bar is a function of

[Outside diameter]^4

while that of a tubular bar is

[Outside diameter]^4 - [Inside diameter]^4


There's an approximate formula in Fred Puhn's softcover book "How To Make Your Car Handle". Maybe somebody who has a way of hosting scanned pics can put it up for you. One caution - I think that formula computes the stiffness of the bar from one endlink to the other (as opposed to being from one endlink to the midpoint, which would be twice as stiff, and perhaps more useful).


Norm

[Eric Howell]

Thank you Norm. I have the book some where but I don't remember it having a separate formula for a hollow bar.

I see you are near Philly, what town? I'm from Laurel Springs originally.

[Norm Peterson]

It doesn't, so the simplest way around it is to run the numbers twice (once using OD and once using ID) and take the difference between the results. Or use (OD^4 - ID^4) in place of D^4 in the numerator, as it amounts to the same thing.

Or you can dig out tables of beam formulas and section properties and derive your own formula that works up the result directly.


They used to call this place Delaware Twp (but that was before the water tower was built )


Norm

[Eric Howell]

They used to call this place Delaware Twp (but that was before the water tower was built )


Norm

BTW is that Camden County? If so I know where your at...haha

[CarlC]

Assuming same materials and length, the D^4 - d^4 works for hollow bars. If different materials and end conditions exist then the full formula must be used.

I'll get it tonight. It's a standard torsion formula.

[Norm Peterson]

Torsion in the center section (Puhn's A^2*B term)
Arm bending (the C^3 term in Puhn's formula)

A few other, typically minor considerations
Bending in the center section (more important in tubular bars, and mostly associated with thinnish OE-style front bars)
Shear
Center section overhanging its chassis bushings/bearings (which cannot be precisely at the bend/joint, and may be several inches inboard)

Considering only torsion can easily result in overestimating the stiffness by as much as 20% unless the arms are separate pieces and particularly rigid. Torsion plus arm bending is usually good to within 5% or so.

Bushing and endlink stiffnesses also play a part as yet other springs in series with the bar itself, but that's almost a whole 'nother topic in itself. Mentioned because it's sort of related and does explain why you can always feel the difference after swapping poly-bushed endlinks in for the OE rubber pieces.


Norm

[Eric Howell]

I don't need the exact stiffness, maybe within 10%. I want to base line the current setup and us that as a mid point in the adjustment range of the new setup.

As of now it has poly bushings and end links. With the adjustable bar it will have rod ends for the end links and pillow blocks instead of bushings. The seem like a good alternative to solid mounts in a heavily street driven application IMO.

Can you write the formulas in "stupid" form. I don't understand what "^" represents.

[Norm Peterson]

Can you write the formulas in "stupid" form. I don't understand what "^" represents.

I'm not sure I can do that in this particular situation. The " ^ " character is used to indicate exponent, so " ^3 " means "cubed" and " ^4 " means "raised to the 4th power". So if D is 1.25", D^4 is 2.44 in^4.


87 - Yup.


Norm

[Eric Howell]

OK. That's what I thought but wasn't sure. Thanks.