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What Physics? (archive)

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Posted by Bob ///M3 on October 08, 2000 at 17:06:28:

In Reply to: The Physics behind all this. posted by Dan Wang on October 08, 2000 at 15:21:35:

I saw no physics in your post! Maybe I missed it...

The correct way of writing the formula for calculating Spring Rate is: K = d^4G where K is the spring rate, d is the diameter and G is the modulus of elasticity (constant of steel). So ignoring the G factor and calculating the difference in two diameters the formula is K = (d2^4) - (d1^4) / (d1^4) X 100 where d1 represents the original diameter and d2 represents the new diameter.

Your answers are correct but I have been told the front bar diameter in question is 25.4mm not 25.7mm! If the diameter is indeed 25.4mm compared to 26mm the correct answer is 48.7384% increased stiffness and if the diameter is 25.7mm the answer as you stated is 55.891%.

Regardless which diameter is correct for the front, there is a nice hefty increase of either 55.9% or 48.7% increase in stiffness when compared to the OE 23mm bars when using a 25.7mm or 25.4mm bar. And for the rear, there is a hefty 97% increase in stiffness when compared to the OE 20mm bars when using a 23.7mm bar.

The point is, the increased stiffness using either set of swaybars is perfect to reduce body roll and far more than enough increased stiffness for the rear bar to tune out any understeer condition. Either swaybar set will accomplish the desired result nicely. What little difference there is between the two sets of swaybars is totally insignificant in how a car would handle.

Let me say that again another way. What little difference there is in bar diameters (and the resulting stiffness the bars offer) between the two different sets or brands of swaybars in question, there would be no noticeable difference in how the car would handle.

In fact, if someone could hit an imaginary button changing from one aftermarket swaybar set to the other or any combination of just front bar or just rear bar, the driver (professional or otherwise) would never notice anything. Place the car going into a turn, at the apex or coming out of the turn at the absolute razor's edge limit and flip that switch...there would be no notice of a change to the driver.

Whoever is talking the car owner into removing the 25.4mm and 23.7mm swaybars from their car because they didn't measure 26mm and 24mm was ill informed. And for anyone to think this small difference in stiffness would affect handling is also very ill informed.

You seem to be making a point that the one set of swaybars is not the diameter it should be; that of 26mm and 24mm but instead 25.7mm and 23.7mm. I have no idea if this is true but trust you are correct in your measurements. More important, I personally could care less. I'm not siding with a company statements would be the same if the Pope himself was the maker of these swaybars we're discussing! I'm making the point that if the swaybar set is slightly smaller diameter, as you say they are, the swaybars accomplish the purpose of reduced body roll and correcting oversteer very nicely...and you, me or anyone else could not tell any difference between the two!

Bob ///M3

I have a 95 M3.

'95 Stock sways are 22.5mm/19mm
'96-'99 Stock sways are 23mm/20mm
Eibach are 26mm/24mm
UUC are 25.7mm/23.7mm

Formula to figure out increase in stiffness

%-age increase in anti-swaybar stiffness=
4th power
[new diameter]
[old diameter]

Example on my 95 M3 with Eibach sways=
4th power
------ =1.7830491

This example shows an increase in stiffness of 78.30%

Now apply this formula to my 95 M3 if I had UUC's swaybars on my car
4th power
------ =1.7021679

This example shows an increase in stiffness of 70.21%


Example on a '96-'99 M3 with Eibach sways=
4th power
----- =1.6329844

This example shows an increase in stiffness of 63.29%

Now apply this formula to a '96-'99 M3 if we had UUC's swaybars on the car
4th power
------ =1.558910

This example shows an increase in stiffness of 55.89%

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