Torsion Bar Calcs

[jurhip]

I was never really happy with the "spring rate equivalent" for torsion bars so I ran some additional cals. Main reason I was unhappy is that the moment are changes as the suspension moves and result in a "spring rate" change.

Basis is standard torsion calc: theta= TL/GI.
I calculated the following using Will Ferch's values that have been listed before. The below value have units "force/degree."

Force - upward force at control arm lengths (12" ad 18.5" front and rear respectively per W. Ferch, however these were modified to account for the moment are length change at euro spec ride heights, 12mm rear (wheel CL lower than TB CL), 108mm front (wheel CL high than TB CL)).
Degree - degree rotation of the moving torsion bar spline.
G - 11300 ksi (this may not be 100% acccurate, but the relationships will remain the same)

Front: (dia - Force(lbs)/deg)
18.8 - 23.54
20 - 30.15
21 - 36.65
22 - 44.14
23 - 52.73

Rear:
24 - 36.44
25 - 42.90
26 - 50.18
27 - 58.36
28 - 67.50
29 - 77.67
30 - 88.95

Main purpose is that I wanted to maintain my current "balance" F to R compared to stock if I decide to upgrade. I have an 87, so stock, the rear "spring rate" is about 182% greater than the front (actually the torsion bar is about 300% stiffer in torsion, but the greater moment arm in the rear reduces the net rate). A common "street" upgrade I have seen is a 21/27 combo. This yields a rear spring rate about 160% higher than the front, so you would expect additional understeer, all other things being equal. Best combo I found for matching stock balance on 87-89 carrera's is 21/28. This yields a balance difference within 2% of stock. Below are some common combos and the rate difference R/F.

18.8/25 - 182% - OEM spec
20/26 - 166% - understeer
20/27 - 194% - oversteer
21/27 - 159% - understeer
21/28 - 184% - witin 2% of OEM balance
22/28 - 153% - understeer

Granted the balance can be altered via sway bars.

Anyway, I thought I would share those numbers. When I do some future suspension work I am going to confirm all values for a g50 Carrera's and will post additional information as well as all calcs. Soon to come:

- moment arm change with respect to ride height and suspension travel - and its effect on "effective spring rates"
- effect of Bilstein gas shocks on "spring rate" This will have to wait till I have the shocks on-hand.

[jurhip]

Also, I would like to model hollow bars vs. solid so people have more info on hand. Does anyone have inner diameter measurements for these, along with the OD.

Thanks
Justin

[jurhip]

One more thing I forgot to add:

I will eventually modify the front spring rate equivalents to account for the shock camber/caster angle. As shocks don't take side loads, the upward force component on the a-arm will change with suspension travel. Hopefully I will get these values during my rebuild.

[Wil Ferch]

In the end...it's wheel rates that matter....not spring rates anyway....so I respectfully don't see the point.

Setting up a car is so much more difficult than can be predicted from pure calculations anyway....why do you think race teams ( with unlimited engineering and budgets), still tryout various things at race tracks? Because it can't be all empirically determined.

In my early days I fretted over this too but found the wheel rates I posted to be accurate enough to get us real close in the ballpark...after which fine tuning is done with various settings of sway bars and playing with shocks.

[911st]

Very interested.

I have spent a lot of time trying to understand this stuff to and appreciate your efforts.

I wish I had your math ability. It would help a bunch.

Is pounds per deg any more useful than pounds per inch of travel? Neither takes in to account the change in effective wheel spring rate as the lever or arm changes angle relative to force or the ground. If if they did the variance I suspect would be mostly insignificant.

Also, you seem to be accepting that the factory's set up is neutral. Other factors will effect an ideal such as tire stager, camber, and other factors.

Further, most believe Porsche set up its cars in reaction to product liability suits, not to fit an handling ideal. There reaction was to make sure the car understeered. This is reflected in high front spring rate values relative to COG and weight distribution.

Sway bars are a significant part of the spring rate when cornering. Just looking at the torsion bars is only part of the equation. For example, I do not know the numbers but if the front sway bar is half the fronts cornering rate and the rear sway bar is 50% of the rears, doubling the torsion bar rates equally front and rear will change the effective wheel rate balance when cornering.

Additionally, the factory made a significant change if front to rear balance stiffening the rear a bunch. They went from 24.1 to 25mm which was about 15% stiffer I believe. On top of that they went from sway bars of 21/18 to 22/20 which stiffened the rear further. Was the factory right before, after or still overly conservative in the balance to keep the liability lawyers happy.

I do not like just accepting SOP's like use a 21/27 or 22/28. I want to know why they are suggested.

Keep up the good work.

[efhughes3]

Originally Posted by 911st

I do not like just accepting SOP's like use a 21/27 or 22/28. I want to know why they are suggested.

Things get suggested, because they've been proven to work by many. When it comes to T-bars, your going to be in a certain range before you get way out of whack. That is to say, one person may like a little more push and run stiffer fronts. One may like it loose, and run stiffer rears. It often comes down to feel, where the rubber meets the road.

As Wil points out, it isn't all done on paper. I watch too many races (according to my wife); it is all too regular an occurance that teams roll a car off a truck with what they think will work, then they spend the weekend making changes to correct some ill manners.

[911st]

jurhip,

I ran the standard of pounds / inch against your pounds / deg and they seem directly comparable.

For example the difference between 18.8 & 23mm is 227% (250#/110#).

Using you system the difference is also 2.24 times or 227% (52.73d/23.54d)

Thus, I am not sure I see the advantage or difference.

Alway looking for a better way to understand our cars.

My latest interest has been, how do we convert coil over spring rates to wheel rates. I think on a 911 they are about the same for the front. On the rear however I believe the spring rates have about a 15% higher wheel rate than the spring rating.

[Wil Ferch]

I was afraid someone was going to bring up coil springs..and their possible equivalency.

These too have their difficulties in terms of calculatable affect. Think on this for a moment. I can't draw a picture so I will have to use longer text to describe my point. Imagine a 12" steel ruler being the "suspension" arm that has one end ( "O" inches) as a pivot point. If you place the coil spring on this suspension arm such that it is mounted at the 6" point on the ruler ( the other end of the shock...natch....on the car)..... vs putting the SAME spring on the 12" point of the ruler ( where the "wheel" is).....you'd have a much STIFFER spring in terms of WHEEL RATE when mounted at 12" vs if mounted at 6" where a lot more leverage on the coil spring is applied.

Furthermore. if you can "view" the suspension geometry going thru its arc of movement, a constant spring rate "spring" ( X lbs/in).....will tend to act non-linearly in terms of effective "wheel " rate, as the suspension goes thru its range of motion.

Gets complicated guys !!!! ......

If we keep it to torsion bars.....the 21/27 or 22/28 combo is what works well based on many years of feedback. As time went on, people realized that the rear of the car seemed undersprung no matter what you do....and therefore we started seeing 21/28-29.....and 22/29-30 types of arrangements..and no one killed themselves. Let's also remember this.....the whole concept of neutral / understeer / or oversteer is that characteristic when the car is pretty much at the limit of adhesion in a corner. You are at the car's limits. I doubt many of us ( even the self-proclaimed hotdogs) drive even remotely close to the limit...even for DE days.....so a possible slight mismatch won't be easily noticed, not even for fairly aggresive street driving unless you drive like you have a death wish.

[911st]

Wil,

Appreciate your torsion bar calc's of the past. http://tech.rennlist.com/911/pdf/torsionbars.PDF

Are these wheel rates?

I have used them a bunch.

Why dose it have to be difficult to converted coil over spring rates to wheel rates for a 911.

If we keep it simplistic we should have something close enough to be usable.

For the front, the spring rate should most likely be the wheel rate as the wheel moves at the same rate as the bottom of the strut or spring. The A arm is not a lever any longer, just a locating arm.

For the rear, why can we not just arrive at a conversion factor or percentage where we can multiply the spring rate to come up with the wheel rate?


Not sure if this is how we do it but for example, if the wheel is 18.5" from the pivot (a 116" circumference) and the shock is 22.75" from the pivot (a 144" circumference) . Then the shock travels about 19% further than the wheel at any time. If this is so, then would the wheel rate be 19% more than the rated spring rate?

If this is so, we could take any spring rate and multiply is by 119% to arrive at close to the actual wheel rate. Thus, a 500 lb spring would equal about a 595# wheel rate.

Dose that make any sense?

[unclebilly]

You will find that hollow or not makes little difference. The chief factor with torsion bar spring rates is the outside diameter and spring constant.

[David]

I didn't write down the exact dimensions (maybe I posted them) but I think my 31mm hollow bars are 31.5 OD and 15mm ID. They weight a little less than the stock 26mm bars.

[Wil Ferch]

911st:

All my published work on Porsche torsion bars, either on Rennlist or here are wheel rates....for that is all that matters in the end.

I think my concerns for coils are well founded...as the location of the coils has a profound effect on the resulting wheel rate. Or....do I misunderstand?...are you suggesting that the exsiting shock location is the place where the coil goes ( a coil-over-shock) ?...in ALL cases where you're considering using a coil spring?

Otherwise, the location of the coil has to be factored-in. A coil spring mounted closer the inboard pivot has to have a stronger spring ( than one located near the wheel) ,due to the added leverage affect by its location.....and vice versa. I guess it could be done but it would only prove useful to those amongst us who cannot tolerate a "maxed out" TB setup....something like 23 front / 31 or so rear. Others can chime in if there indeed larger TBS available but if so...we're entering an area where the root diameter of the engagement splines are the max diameter and so the resulting rate is more uncertain.

[304065]

Don't forget another important point brought up by Hayden from WEVO-- in the case of the front torsion bars that are attached to the control arm at the forward end, and the torsion bar adjuster at the aft end, you effectively have TWO torsion bars, the first running forward, then the second which is the tubular portion of the control arm, which has its own spring rate.

[jurhip]

Whoa - I have been away for a while and haven't had time to read all the replies.

I have run calculations that take into account moment arm variations as the suspension goes through its range of motion. Through the normal range, the moment arm changes little. I can post these if anyone is interested.

As most have pointed out, the real test is on the road. There are too many variables to calculate accurately (bushing rates/deflection, sway bars, tire spring rates, weight distribution, suspension binding/design "spring" etc).
My original intent was just to provide information on stock TB balance so people have more information to determine where they may want to go with their set-up (i.e. larger TB, but smaller sways or vice-versa).

"Spring rate" differences between solid and hollow TB is non-existent if they are sized properly.

[911st]

Originally Posted by john_cramer

Don't forget another important point brought up by Hayden from WEVO-- in the case of the front torsion bars that are attached to the control arm at the forward end, and the torsion bar adjuster at the aft end, you effectively have TWO torsion bars, the first running forward, then the second which is the tubular portion of the control arm, which has its own spring rate.

I get the idea that the A arm its self is a spring with a torsion bar system. However, for our purpose I do not expect it contributes to the wheel rate in a significant way but I do not know this for sure. For example. If we staged two springs, one 500# and 100 lbs with one on top of the other.

If we impart 500 lbs on them, the 500# will compress 1" and the 100# will compress 5 inches and equalize. Now, what is the effective spring rate? If the 100 spring has not bottomed out, I believe the spring rate will be 100#/inch.

So unless the spring rate of the arm is lower than that of the TB, I do not think it is a significant concern.

Of course, going to a Coil Over system by design mostly takes that variable away.

Just my guess!

[911st]

Wil,

Again, I love you work and have relied heavily on it to help me better understand my how my car functions and to set my rear spring plate angle.

I looked back at you paper and I have a question.

For the front lever arm length you used 12" which was the distance from the A arm pivot to the brake caliper for your calc's.

I am starting to believe that the front lever length should be the distance between the torsion bar CL (center line) and the ball joint CL giving us a shorter lever than used.

Because of the strut design, I am thinking that all forces imparted at the wheel are constrained to a vector that only allows up and down motion in line with the travel of the strut. That puts our force vector right at the ball joint centerline.

If this is true, our lever length may be shorter than believed and our computed rates higher.

Could this be correct?

Dose anyone know distance between the TB CL and the Ball Joint CL?

[304065]

Originally Posted by 911st

I get the idea that the A arm its self is a spring with a torsion bar system. However, for our purpose I do not expect it contributes to the wheel rate in a significant way but I do not know this for sure. For example. If we staged two springs, one 500# and 100 lbs with one on top of the other.

If we impart 500 lbs on them, the 500# will compress 1" and the 100# will compress 5 inches and equalize. Now, what is the effective spring rate? If the 100 spring has not bottomed out, I believe the spring rate will be 100#/inch.

So unless the spring rate of the arm is lower than that of the TB, I do not think it is a significant concern.


Just my guess!

Which is exactly the point: the spring rate of the control arm IS lower than that of the Torsion bar, and has to be taken into account in the wheel rate calculation.

[911st]

John,

I do not truly know but find this interesting.

So from what you are saying, if we accept that the spring rate of the arm is lower than the torsion bars -- would we then have to accept that changing the torsion bar would not have any effect our our effective spring rate?

I believe it you put a 100 pound spring in series with a 200 lb spring, the spring rate is 100 until it bottoms out and goes to infinity. Then the spring rate becomes 200 lbs.

Unless it is a progressive spring and its rate becomes progressive enough to become greater than the other spring. If this is the case, then we would end up with a progressive nature to our front suspension to some degree.

Also, the torsion tube seems to be the main factor in assuming the A arm is a spring. If so, its OD is much larger than the torsion bar's.

However, how significant might this effect be and what is the risk of making a poor decision if we do not take it into effect?

Could we accidentally choose a 400 lb coil over with a conversion when we shoul have gone with a 300lb?

Or, could we increase the front and rear both say 50% in relative stiffness to find out our front is now to soft by a significant amount?

I appreciate the thought and am just truly interested in how this works and understanding it.





Again, interesting.

[Flieger]

The combined spring rate for a series of springs is lower than either individual spring rate. A 500#/in spring and a 100#/in spring will, as you stated deflect a total of 6in for an applied load of 500#. The 500 will deflect 1 inch and the 100 5 inches. So, that means that the total spring rate is 500#/6in = 83.33#/in.

I think that the A-arm will not contribute significantly to wheel rate, at least not as much as lever arm length or torsion bar size. The A cross brace resists torsion so the deflection would be mostly bending of the lever arm. They seem to be quite stout.

[911st]

John,

I am thinking for the Arm's rate to be softer than the torsion bars it would have to give more or twist more than the torsion bar.

Example, if a 23mm front bar twists one deg for every 52# of force as jurhip has concluded, 500 lbs on a front wheel ( 2500 lb 911) we would have the TB twisting almost 10 deg. Do we think the A arm tube or its arm deforms that much? If not it is most likly a much stiffer spring.