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# Force-based roll centres vs geometrical roll centres2

## Force-based roll centres vs geometrical roll centres

(OP)
I've been noticing more and more mention of a procedure that calculates the roll centre of a vehicle from a force-based perspective, rather than a purely geometrical one.

Circle Track in particular has been running a series of suspension modelling articles, and the author is adamant that the geometric roll centre is NOT the actual centre that the sprung mass rolls around.

There is also supposed to be some benefit to tailoring the roll resistance at each end such that the ultimate roll angle (from a force-based analysis) is the same at both ends - the idea being that you don't want the car fighting itself.

This procedure is supposedly pretty new (last 10 years or so) and came as a result of comparing actual recordings of wheel travel from suspension position sensors to predicted values (for a given amount of roll) from a kinematic analysis.

I have WinGeo3 from Bill Mitchell, and while my suspension position sensors aren't on yet, visually the car does not seem to following the predictions from the software - it looks like the outside is compressing less, and the inside extending more, than would be expected. See http://farnorthracing.com/nats2003/ for examples.

I bought SAE983033 which seems to explain WHY the geometric analysis isn't enough, but it glosses over a lot of steps involved in actually calculating the nonlinear analysis. And if the Circle track article series described it, I missed that issue.

Does anybody have a reference that describes the steps involved in a force-based roll centre analysis in detail?

DG

### RE: Force-based roll centres vs geometrical roll centres

DG,

There likely are not too many (if any) references available in the public domain on how to calculate the roll centers classically. This is because of the inherent non-linearities involved. In the SAE International Technical Paper 983033 Short-Long Arm Suspension System Non-Linearities and Analysis, the author used ANSYS. Most any of the 3-d multi-body solvers that Greg Locock presents in his excellent FAQ Software for suspension analysis (FAQ800-768) will allow for the actual roll center to be determined. ADAMS, DADS, and visualNastran 4D are probably the most used general purpose solvers.

Best regards,

Matthew Ian Loew
"Luck is the residue of design."
Branch Rickey

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

### RE: Force-based roll centres vs geometrical roll centres

No, DG, you didn't miss the issue.  Bob Bolles has been very cagey about discussing the details of his approach, most likely because he offers a software that apparently does the work.  Not only is this info not in the CT series, neither does it show up in his softcover book "Stock Car Setup Secrets".

I've been wondering about much the same things, but can't offer much beyond conjecture that he may be considering roll center migration in the software.  His text spends quite a bit of time discussing that point.  No idea if any force-based approach is included, but I'm thinking that for top-level NASCAR and circle track cars that they'd be using rod ends rather than bushings anyway.  IOW, I think the kinematic model is probably a better approximation in these cases than for suspensions that include compliant bushings (Greg, feel free to slap me upside the head if I'm off base here . . .).

Don't I know you as 'DG2' on another forum?

Norm

### RE: Force-based roll centres vs geometrical roll centres

Norm, why would I do that? You have been on the money so far...

I am a very lazy person. I have a piece of software here that tells me what the driver is feeling (sort of) and what the tyres are doing (sort of). The horrible mathematics that connect those two are left to the computer to sort out. (and if you believe that...)

One of the reasons that I distrust even FBRC is that no one can actually tell me what the sprung body inertial roll axis is in practice - it certainly is NOT the axis about which the sprung body rolls! I am being duplicitous here, I know about principal moments of inertia, so I could work it out - the point is that generally people worry about suspension roll centres yet don't have the faintest idea where their principal axes are (and neither do we, in practice, until just before we launch the car).

ADAMS allows you to plot roll centre migration in Y and Z (and that's another thing, why should the true kinematic roll centre be confined to the axle plane?) for both geometric /AND/ force based roll centres. For real suspensions in real manouevres with stiction and everything else these curves are very spiky.

If you can get hold of the following paper (I don't know if it is available to the public) it discusses FBRCs and gRCs. It is the reason I am so cynical about them.

Institut für Kraftfahrwesen der RWTH Aachen
Prof. Dr.-Ing. H. Wallentowitz
Diplomarbeit / Diploma Thesis
CAE investigation of the influence of suspension characteristics on the vehicle roll behavior for passenger cars
Cand.-Ing. Eggord Thomaschky
Matr.-Nr. 188 587
Betreuer: Dipl.-Ing. Peter Holdmann
November 1995

Eggord was the author, and does not have seemed to have published anything since, sadly.

I admit, roll centres are a nice idea, as a broad brush concept, but the nitty gritty seems to me to be so full of caveats that you might as well go the whole hog and work out the vertical loads at the contact patch, which when all is said and done is what you are really interested in, and the forces on the body.

As to the car fighting itself being a bad thing - I don't quite agree. If the car was not fighting itself then you couldn't get any rear axle steer happening, and rear axle steer is a very useful concept. The ONLY way you have to communicate what the front axle is doing, to the rear axle, is via the rigid body motions of the sprung body, particularly in roll and yaw.

Too many cups of coffee?

Cheers

Greg Locock

### RE: Force-based roll centres vs geometrical roll centres

I was in a bit of a hurry above, and I completely neglected to include my intended mention of said bushings being bonded and capable of some rotational spring constants of their own, thus generating end moments on what kinematics assumes to be frictionless pin connections . . .

Which kind of got me thinking that what you determine statically may not be quite what happens in reality, since suspension motion is, by definition, a dynamic event.

I think that Bob Bolles is primarily looking at avoiding twist over the length of the chassis.  At least that's how the passage(s) in his book that refer to equalizing front and rear roll angles reads to these eyes.  Maybe I'm just coming at this from a different point of view - more of a civil/structural analysis, with a vague idea of mass centroid axis and its offset from some roll axis as a loading basis.  Anyway, it doesn't seem to me like the phrase "the chassis fighting itself" is a particularly good synonym for "chassis twist" or even "net chassis twist over the wheelbase"; consequently it may serve mostly to confuse people not raised on circle track racers.

FYI, and probably the reason that hard discussion of details is at least not readily available.  In the section on "Roll Angle Analysis" (page 23, for those who may have this reference), he notes that "A method has been invented and patented that will accurately predict the front and rear roll angles in a racecar . . . The patent title is "Method of Land Vehicle Suspension Evaluation and Design Through Roll Angle Analysis", U.S. Patent number 5,723,782.

The horrible mathematics that connect those two are left to the computer to sort out. (and if you believe that...)

Actually I do.  Just attempting to write a few spreadsheet applications gives me a hint as to the sheer volume of math that's potentially involved.  And as avoidable as I can make it (I'm kind of lazy too, not to mention entirely capable of occasionally dropping the odd 'minus' sign).

Sounds like the Eggord paper was his doctoral thesis, no?  Now I need to go back to that other thread where 'E' was mentioned, and the FBRC threads that came up on the search . . .

Too many cups of coffee?

Ummm, just what time of day (night?) were you posting that?

Norm

### RE: Force-based roll centres vs geometrical roll centres

I think the circle track article is referring to aligning the roll axis of the front and rear suspension, with the idea that if they are not aligned, something will have to flex for the body to roll.

What actually happens is roll steer, not flex of the body/mounting points.  The end result of front and rear roll axis alignment may be a more predictable car, and that may be the benefit he is seeing.

I think the end result may be good, but the proposed reasoning is flawed.

I know I asked this in another thread that I started, but how do we quantify the effects of lateral roll center movement.  To put it more simply, if two cars have the same vertical roll center location, let's say at the front of the car, but one has the RC on the vehicle centerline, and the other has it displaced 12" towards the inside of the turn, what would be the end result?  How would the weight transfer calculations differ?

Paul Yaw
Yaw Power Products

### RE: Force-based roll centres vs geometrical roll centres

"Yawpower," as the roll axis is displaced, angularly, in the X-Y plane, the effect of front-rear roll stiffness on roll couple distribution diminishes. If the roll axis were aligned with the Y Axis, as an extreme, roll stiffness would have no effect at all. So, I would multiply those terms involving the roll stiffness, in the equations on pages 682 and 683 of Milliken, by the cosine of the angular displacement.

### RE: Force-based roll centres vs geometrical roll centres

As a point of interest, Bill Mitchell's software rolls the car around a point at ground level, rather than the indicated geometric roll center indicated in the graphic.

Dave

### RE: Force-based roll centres vs geometrical roll centres

I've gone thru the equations, looked at Mr. Bolles patent and it appears that he has sucessfully patented the concept of a roll couple distribution of 1.0
Kevin

### RE: Force-based roll centres vs geometrical roll centres

TalonDG - Have you considered the effects of any sources of rising rate in that a given amount of weight transfer will compress the outside by a lesser amount than the inside is extended?  In addition to (perhaps?) progressive rate springs this would also include consideration of the bump stops being encountered.

Norm

### RE: Force-based roll centres vs geometrical roll centres

BTW, here is a link to the US patent by Robert C. Bolles, Jr., Method of land vehicle suspension evaluation and design through roll angle analysis:

http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO2&Se...

Best regards,

Matthew Ian Loew
"Luck is the residue of design."
Branch Rickey

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

### RE: Force-based roll centres vs geometrical roll centres

(OP)
The springs on the car are fixed-rate Hypercoils.

The motion ratio stays pretty much constant in the normal range of suspension motion.

The roll centres move laterally in roll, but on the order of a couple of inches.

And there are no bumpstops - the tire will contact the fender before shock travel is exhausted, and the ride height is set such that there is only light contact with the tire under the harshest bumps (the car cannot roll onto the tire)

My one experiment with Caroll Smith style silastoes was an unmitigated disaster. Instant terminal understeer.

Interesting that Mitchell's software doesn't roll around the roll centre! I wonder why he does that?

DG

### RE: Force-based roll centres vs geometrical roll centres

"Interesting that Mitchell's software doesn't roll around the roll centre! I wonder why he does that?
"

Perhaps because cars DON'T roll around the roll centre.

Or, more accurately, the instantaneous axis of rotation of the sprung mass rarely coincides with the "roll centre".

Cheers

Greg Locock

### RE: Force-based roll centres vs geometrical roll centres

Greg,
You said it in your first post, and you said it in this last post - and I agree - cars usually do not roll around the roll centers. The roll centers are defined by the suspension geometry (and hence the forces by Kennedy's theorem).  Therefore, these are, by definition, force based roll centers. However, when you add an antiroll bar this classical analysis breaks down because the forces are no longer axial on the member that the bar is attached to (Kennedy's theorem no longer applies).  Agree, disagree?
Kevin

### RE: Force-based roll centres vs geometrical roll centres

Greg,
Mitchell's software does not make an attempt to roll the sprung mass around either the force based center or the geometric center, AFAIK.  The software, as I understand it, restrains the lateral center to the vehicle's centerline.  I was under the impression that the software did roll the chassis around the correct geometric height for the RC.  I have seen other people post that the chassis is rolled around a point on centerline and at ground level.  I have never verified this, perhaps others can offer their experiences?

There exists an option to download data from onboard aquisition systems into Mitchell's software so as to actually view the true real world displacements through his software.  Sorry, I have no experience with this option.

I really just wanted to clarify my understanding of Mitchell's quirk.  Sorry to muddy this interesting thread.

### RE: Force-based roll centres vs geometrical roll centres

Kevin,

The two-force member assumption is not really valid for any real automotive suspension. Rarely are the suspension linkages loaded in pure tension and compression. Bushings will introduce moments about the bushing axis (rotational) and off axis (conical). The location of a spring, damper, and/or anti-roll bar on one of the linkages (other than the upright) will also introduce bending loads on the suspension linkages.

The vehicle will roll instantaneously around an axis that has only rotational velocity. The actual calculation of this axis is best left to a non-linear Multi-Body Dynamics analysis. There is no point in trying to use simple kinematics assumptions to determine the instantaneous roll centers and axis for anything other than a first-order simulation.

Best regards,

Matthew Ian Loew
"Luck is the residue of design."
Branch Rickey

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

### RE: Force-based roll centres vs geometrical roll centres

Matthew, I'm 99.7% sure that Kevin is well aware of all that, evil grin.

The things I puzzle over are:

a)in the past people have found GRCs to be a useful concept,  much quoted and discussed.

b) even now GRC heights for front and rear axles for most production cars are in the rough ballpark that tradition has defined (ie 50-150 for the front and 100-200 at the rear)

Now I can cynically explain (b) - if 'everybody' knows that the RCH has to be at such and such a height, then every suspension will be designed that way, EVEN IF an alternative layout might better meet the actual requirements. Or even more cynically - if it doesn't really affect things then it doesn't matter where it ends up.

I don't believe that latter point - Milliken includes some very helpful diagrams of the force build-up in the suspension during a corner, showing how forces in the arms are the quickest way of feeding forces into the body, hence setting up roll(followed by the springs, shocks and then a/r bar, from memory), which can be used to tell the rear suspension where to go, via the paths in the same order.

Cheers

Greg Locock

### RE: Force-based roll centres vs geometrical roll centres

Greg,
I agree with your point about roll center height being bracketed by traditional designs (packaging constraits, etc) - which minimize vehicle performance variability via RCH concept.
Except for development engineers, lay folks and even a lot of auto enthusiast didn't really notice differences in RCH.
In lumped parameter math models, with 1st & 2nd order parameters, the transient (J-turn & Slalom) model's do fit the aquisitioned data fairly well up thru ~ 0.5g's. These models do tend to exhibit a little more damping.  The parameter variability required for a lay person to notice the difference is typically beyond the model error computed from aquisitioned data.
Soooo ... I believe the concept of roll centers is useful, if for nothing else to tell you that the suspension geometry is in the ball park - lest you wind up with a boat :)
ADAMS vs full vehicle NASTRAN model - I'll take NASTRAN
Kevin

### RE: Force-based roll centres vs geometrical roll centres

So what about the argument that roll centers shouldn't move through the ground plane in transient conditions? How does that add into this?

### RE: Force-based roll centres vs geometrical roll centres

I have also been following Mr. Bolles' articles in Circle Track and here are my interpretations of what he has written: Using his method of matching the "front" and "rear" roll angles will magically give you a "balanced" setup b/c the front end of the car will want to roll the exact same amount as the rear... he doesn't really go on to assert that this will reduce/minimize chassis flex, he just states that this is the way to do things, and if you believe him you can go faster.
After reading his patent, I am still just as skeptical about his method as when I read the articles.  Not that I'm saying that his method is any better/worse than any other method of "optimizing" a chassis setup on paper, but I can't seem to find in any of the literature how he is calculating the CG height for a specific end of the vehicle (and if it was encompassed in the figures of his patent, niether of my browsers seem to want to let me see those).  To me, leaving out this detail is a crucial flaw, b/c the method hinges on being able to look at a vehicle as two separate entities (front and rear), but how do you figure out the CG heights for a given end of the vehicle that will give you two sub-systems that are equivalent to the total system?
I am familiar with the method of determining an effective CG height as described in Milliken, however, they ultimately resort back to the standard rigid body (roll axis) equations to determine the equivalent CG height, "h_e," and they do not imply that this "h_e" is a magical equivalent CG height that can be used to calculate axle loads for any combination of roll center and roll stiffness at an axle, rather it is just a more convenient way of representing the roll moment at the axle for the purpose of analyzing the lateral force potential at the axle.
My belief (which I hope is actually just physical reality) is that there is no way to calculate a truly "equivalent" CG height for an axle that applies to all roll center/roll stiffness combinations, otherwise, there would have been all kinds of papers and text books teaching us this method as opposed the the seemingly more laborious roll axis model.
Mr. Bolles is supposed to include "computer examples" in upcoming issues of Circle Track, perhaps he will shed some light on how to determine the equivalent front and/or rear CG height.
If I were you TalonDG, I would stick to the more traditional methods(physically based) of setting up your racecar rather than completely selling yourself on "matching roll angles."  Many of the people that I have spoken with who struggle with the same issue you have (force effects of the roll center) have resorted to keeping track of the jacking force coefficients (F_y/F_z) in each side of the suspension, and virtually, but not quite, forgetting about the roll center all together.  Keeping track of the jacking coefficient is just like turning the front view situation into two separate "anti" situations typically used to describe the side view characteristics (anti-dive, anti-squat, etc).
Looking forward to that next Circle Track,
bhart

### RE: Force-based roll centres vs geometrical roll centres

For those of you that are interested, I just received this as an inclusion to the newsletter that Mark Ortiz (an independant chassis consultant and author of a vehicle dynamics Q&A section in Racecar Engineering magazine) publishes each month.  It seems very applicable to this discussion, however, I did not attend the lecture and have not seen the video, so I am not vouching for its worth.  So far, everything that I've managed to get my hands on that was written by Mr. Ortiz seems to be well thought out and concisely presented, and he has never shyed away from confronting the details.
Should this post be interperted as an advertisement by any of the users of this forum, then I should mention that I am not affiliated with Mark Ortiz in any way.
I would prefer not to publish anybody's contact information on the internet, so if you're interested in the video, a quick Google search should point you toward Mark Ortiz the chassis consultant.

NEW VIDEO

I am pleased to announce that I now have videos available of the presentation I gave at UNC Charlotte this past March. The one-hour lecture is entitled “Minding Your Anti: Understanding Factors in Load Transfer”. It deals with the origins of load transfer and presents a “force-based” or “lateral anti” approach to the notion of roll centers. This is original and very current thinking on the matter, and not to be found elsewhere. Videos are single VHS cassettes, and sell for US$50.00. This price includes shipping to any destination, worldwide. North Carolina residents please add 7½ % ($3.75) sales tax.

### RE: Force-based roll centres vs geometrical roll centres

Fair enough tho I'd argue with "It deals with the origins of load transfer and presents a “force-based” or “lateral anti” approach to the notion of roll centers. This is original and very current thinking on the matter, and not to be found elsewhere."

As I have seen that very idea promulgated here on eng-tips, and that's how I think about it, when I have to, which is not very often.

Cheers

Greg Locock

### RE: Force-based roll centres vs geometrical roll centres

(OP)
I just got back from PRI.

While I was there, I had an opportunity to meet with Mr Mitchell. The latest version of WinGeo3 contains a "Vehicle Dynamics" section that allows one to specify CG location, etc, and then load the car - and then the program will calculate the roll amount and "actual" roll centre etc based on the load.

I also picked up a book written by... the name escapes me for a moment - he used to do seminars for GM, Canadian gentleman - anyway, the book is called "An Introduction to Race Car Engineering, Volume 1 of 5" and it's a couple of inches thick. Good reading, heavily reliant on WinGeo3, lots of examples.

DG

### RE: Force-based roll centres vs geometrical roll centres

DOES THIS MAKE SENSE TO ANYBODY ON HERE?

According to my GRT book you are right about calculating the roll center. Measure the height of the L side of the J-bar from the floor, add it to the height of the pinion mount from the floor and divide the number by 2.

Roll center is half way between the 2 rod ends in a straight line. If you move the bar up on the frame you are actually raising the roll center by 1/2 of what you move it up on the frame. So why does this add tighten the racecar? Raising the rollcenter is suppost to loosen car, right? This can be hard to understand sometimes, so I'll try to explain as easily as possible.
If the panhard bar is flat, most of the side force on the car is pushing straight sideways on the rear end, trying to slide the RR tire. If the bar has alot of angle in it, the car will try to use the bar as a pole vault. Which causes some of the force to push down on the rear end instead of just sideways. This adds traction to the rear tires and tighten racecar. Once you get a certain amount of rake in the panhard bar, the added rake creates more downforce on the rear tires then the slight raising of the roll center takes away. So the car is tighter even with a slightly higher roll center.

Example. Lets say the panhard is perfectly flat. If you raise the bar on the frame 1 inch this will most likely loosen car. Once you keep raising the bar on the frame it will get to a point that the rake will start tightening car. Most cars start with enuff rake that raising on frame will tighten car up, but if you fairly flat it may loosen car.

Body roll is a fuction of the heigth of the roll center in relationship to the heigth of the COG (center of gravity). Let say your rear COG is 16" up from the ground and your rear roll center is 12" up. If you want more roll, you can lower the rollcenter (i.e. panhard bar) down on both sides one inch. Now your at 11" on the rear roll center, the car will roll more. Or you can raise the COG. This is done by moving wieght up (lead, fuel cell, battery, or anything with weight). Rake in the panhard bar mechanically jacks the car as the car is trying to polevault over it.

The shorter the bar the faster the bar will gain angle when the body rolls. This means usually the shorter the bar the less angle needed to do the same job as a longer one. The shorter it is the faster this happens, which can make the car very erratic and hard to be consistant in.

Alot of times you will be using the panhard bar to make the car start getting up so the car will climb the bars for a tighter exit.

Left side pinion mount verse Right side!!!
When the panhard is mounted to the left side of the pinion, the downward force by the bar is closer to the LR tire so it puts more of the weight on the LR then the RR. This causes the car to be slightly looser in but much tighter coming off. The same with the right side mount, its closer to the RR tire (7") that more of the weight is on the RR. This is tighter in and losser off then a left one.

There is no real set rule on panhard bars, but generally :
1. You can use more rake on banked tracks
2. Too much rake on a small tracks (1/4) can create a loose condition off as the car has a loose rollsteer and you are chasing the back end up the racetrack and can't stay on the bottom.
3. The heavier or faster the track the longer ones are "usually" better.
4. Stop and go tracks like left side bar (if you like left bars)
5. Faster momentum tracks like rake but don't need to be as low- keep the rake your using just raise both pinion and frame. This keep most of the bite but keeps the car from rolling so bad and carring the LF.

### RE: Force-based roll centres vs geometrical roll centres

I've been researching and testing this topic very heavily with NASCAR type stock cars.  I've found that a combination of gRC and fRC helpful in both design and prediction of the race car.

When I design new component sizes such as spindle heights, pin angles, pin heights, a-arm lengths, etc., I calculate the gRC but I'm more concerned with the location of the Instant Centers and camber effects.  I then run through some calculation of the forces involved from the wheel through the linkages, especially the lower a-arm.  I found the angle of the lower a-arm where it connects to the frame to be very important in calculating wheel travel and roll more accuratley.  Along with other lateral type anti forces of course.

I also put together a program that has so far been very close for predicting the balance of the race car.  Granted the testing has been limited to one particular type of car but it's based on formulas found in books from Milleken, Gillespie, Rowley, and others.

If anyone is interested it's located at http://www.BrownPerformanceEngineering.com.

I've used Bob Bolles software and found some interesting anomolies.  Bob's software doesn't seem to work well with anti-roll bars larger than 1.25" in diameter.  It also didn't calculate the rear wheel rates accurately for me.  It doesn't show dynamic wheel loads on the tire contact patch.  It also doesn't give any suggestions or ideas for spring/wheel rates - other than balance out the roll angles.  It continually suggested high cross weight values (which didn't seem to really deviate much from car to car) and very high rear roll centers.

The WinGeo software from Mitchell seems to work well it just takes a while to become accustomed to it.  The latest book from Rowley really helps in using the WinGeo software.

This has just been some of my experiances in trying to learn about roll centers and software that supposed to help us - atleast in the circle track racing side of things.

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