Thoughts about PHB relocation

[Norm Peterson]

To Grant - sorry, but I never got any notice that the other thread had gone anywhere, and I'm now finding it locked. Hence this new one.

But first, a note about "roll center". It is not a point about which the chassis actually rolls, and certainly not in any SAE definition. What a roll center is, is a point at which a lateral force can be applied to the sprung mass without producing roll.

What that means is if a lateral force - meaning horizontal - is applied at any other height than that of the roll center, you will get some roll. The amount of which depends on (a) the magnitude of the lateral force, (b) the distance from the vertical point of application of that force, and (c) the total amount of elastic suspension roll stiffness present.

(a) is sprung mass times your cornering g's, (b) is the difference in elevation between the sprung mass CG and that of the geometric roll centers (both of them), and (c) is your springs, sta-bars, and during transients, dampers.

Since (b) depends on both geo-RCs, vertically relocating one of them will affect the amount of roll, assuming that (a) and (c) are held constant. And greater vertical separation between the CG and the geo-RCs means more roll. Has to.

In the other thread, I think that roll was getting confused with total lateral load transfer. I'm now talking about just the total load transfer here, not its front:rear distribution. Total lateral load transfer is what stays constant when you vertically relocate a geometric roll center, not the amount of roll.

I think it's best to keep in mind that vehicle dynamic effects are force-based (inertial forces due to acceleration, braking, and cornering maneuvers), and that displacement effects (roll, squat, nose-dive, etc.) are only visible indications that load transfer is happening. IOW, roll does not cause "lateral weight transfer", it's the other way around.

Total lateral load transfer (TLLT) has to be equal to (d) total car mass (sprung + unsprung) times (e) the height of the car's total-mass CG height (not the same as (b) above). There are three components that comprise TLLT, those being geometric lateral load transfer (load from the sprung mass transferred through the roll centers, no roll happening from this effect), elastic load transfer (load from the sprung mass transferred through the springs, bars, and dampers, where the roll comes from), and load transfer coming from the unsprung masses (no roll from this, perhaps with an asterisk).

At the point where lowering the rear roll center is on your mind, you're faced with a few choices. Whether to hold the amount of roll constant (outside front wheel camber), whether to hold the current total lateral load transfer distribution constant TLLTD, or allow those to vary for some other purpose.


And just when you think you've got this whole geometry-based roll center thing straightened out, try mentally letting the car roll a bit and watch what happens to your geometric constructions. You may find that this geometrically-defined roll center approach that most of us use isn't adequate to explain what's really going on (convergence points no longer converge, and those geometrically-defined RCs at rest are no longer definable geometrically).


Norm

 

[Grant 302]

To Grant - sorry, but I never got any notice that the other thread had gone anywhere, and I'm now finding it locked. Hence this new one.

Thanks Norm. There is no need for you to apologize. I wanted to discuss this back on 4/16 when I separated the thread, but just didn’t get around to it.

But first, a note about "roll center". It is not a point about which the chassis actually rolls, and certainly not in any SAE definition. What a roll center is, is a point at which a lateral force can be applied to the sprung mass without producing roll.

Agreed. But I think it’s a whole separate discussion about the actual point vs. the conventional definition of panhard bar intersecting the centerline. I’d like to set that aside for now, as it was part of the reason why I would ‘dare’ to challenge the difference in observed body roll. And that challenge is/was quite specific to only the panhard bar.

But as that part was beaten into irrelevance in the other thread, I’d like to move on to the real part that I wanted to discuss below in bold:

Relocating the PHB downward would result in more roll, and a need for more rear bar rather than less.

But I challenge the conventional thinking that lowering the roll center results in more body roll...and ‘need’ for more rear bar.

In a simple comparison with the only variable being a roll center change, I found, to my surprise that the lateral transfer was greater with the lower RC. In some of the examples, I think that would translate to one or two steps of bar adjustment for the same lateral cornering force. On the order of 50 to 100+ lb./in. increase of transfer for an assumed 1g. Which I am translating (perhaps incorrectly) as ‘need for less bar’ with the lower roll center.

I looked a various arrangements like OEM axle tubes and coilovers. And used assumptions like a horizontal static panhard orientation to help simplify the loaded vertical forces and reduce the number of iterations to solve the transfer at 1g steady state.

I also see how this should be a faster rate of transfer - assuming that it would take the same time to reach the steady state. Which I also think ‘agrees’ with needing less bar as Kenny Brown claims.

Thanks again, Norm and also for starting this thread.

Grant

 

[Norm Peterson]

In a simple comparison with the only variable being a roll center change, I found, to my surprise that the lateral transfer was greater with the lower RC. In some of the examples, I think that would translate to one or two steps of bar adjustment for the same lateral cornering force. On the order of 50 to 100+ lb./in. increase of transfer for an assumed 1g. Which I am translating (perhaps incorrectly) as ‘need for less bar’ with the lower roll center.

For starters, I'm a bit puzzled by the units in "50 to 100+ lb./in. increase of transfer for an assumed 1g". How are you getting those numbers?

I have my own spreadsheet that baselined pretty close to the K&C data published by Car and Driver a few years back for (IIRC) the Boss S197 Mustang. Even the roll in terms of degrees/g was within a few percent.

Lowering only the rear RC does increase the share of elastic total lateral load transfer. But while doing so, lowering the geo-RC also decreases the share of geometric lateral load transfer. Assuming no change to the height of the sprung mass CG there wouldn't be any change in total lateral load transfer (looking at the entire car, not just its rear suspension).

One thing that would increase (slightly) would be actual lateral movement of the CG due to roll - the CG to RC distance is increasing a little and the roll angle/g is also going up by a little. That would add a few lbs to the LLT, though this effect can safely be ignored as long as roll is held to small values.

I also see how this should be a faster rate of transfer - assuming that it would take the same time to reach the steady state.

I was going to get around to the element of time (maybe that should be 'tyme' on this forum ) a bit later. But the short story is that the geometric component of LLT happens almost immediately, while the elastic component of LLT takes longer to fully develop (springs and bars being much softer than linkages/bushings/brackets, and suspension frequencies being lower than structural frequencies, making quarter cycles of suspension movement take somewhere in the hundreds of milliseconds). You're going to get some progression in the LLT component of the vehicle's understeer-oversteer balance as the elastic component establishes itself, and a little more in the axle roll steer effect as the roll develops. That's going to feel different to the driver.


Norm

 

[Norm Peterson]

I should perhaps note that PHB-based roll center height migrations due to roll shouldn't vary very much as a function of the vertical distance between the static mid-PHB height and the sprung mass CG height.


Norm

 

[Grant 302]

For starters, I'm a bit puzzled by the units in "50 to 100+ lb./in. increase of transfer for an assumed 1g". How are you getting those numbers?

I’m using free body diagrams. Separate for the rear body and including the possible torque reaction from the front half. And separate axle assembly for the axle and tires.
Resolving the bar and spring reactions with iterations.

Analysis is only on left turns. My understanding through previous analysis is that leveling the bar alone reduces the geometric transfer on right turns. And that by default, right turns ‘suffer’ from too much bar anyway on stock panhard angled setup.

I have my own spreadsheet that baselined pretty close to the K&C data published by Car and Driver a few years back for (IIRC) the Boss S197 Mustang. Even the roll in terms of degrees/g was within a few percent.

Lowering only the rear RC does increase the share of elastic total lateral load transfer. But while doing so, lowering the geo-RC also decreases the share of geometric lateral load transfer. Assuming no change to the height of the sprung mass CG there wouldn't be any change in total lateral load transfer (looking at the entire car, not just its rear suspension).

I believe that’s all correct right up to the point where one or any of the examples loses grip on one axle.

I’ve looked at the rear only in two ways to simplify the models. First, with no torque reaction with the assumption that the front was coincidentally re-tuned to ‘match’ roll rates and second, include a torque reaction to simulate leaving the front suspension the same and unadjusted from baseline.

One thing that would increase (slightly) would be actual lateral movement of the CG due to roll - the CG to RC distance is increasing a little and the roll angle/g is also going up by a little. That would add a few lbs to the LLT, though this effect can safely be ignored as long as roll is held to small values.

Agreed. Ignored in all examples. But interesting that the lever arm does get longer with RC lowering when slightly angled coilover setup is considered.

 

[Grant 302]

I was going to get around to the element of time (maybe that should be 'tyme' on this forum ) a bit later. But the short story is that the geometric component of LLT happens almost immediately, while the elastic component of LLT takes longer to fully develop (springs and bars being much softer than linkages/bushings/brackets, and suspension frequencies being lower than structural frequencies, making quarter cycles of suspension movement take somewhere in the hundreds of milliseconds). You're going to get some progression in the LLT component of the vehicle's understeer-oversteer balance as the elastic component establishes itself, and a little more in the axle roll steer effect as the roll develops. That's going to feel different to the driver.

Agreed. And appreciate the correct usage of ‘tyme’ here.

 

[Grant 302]

I should perhaps note that PHB-based roll center height migrations due to roll shouldn't vary very much as a function of the vertical distance between the static mid-PHB height and the sprung mass CG height.


Norm

The movement isn’t ignored per se in my models. With the free bodies, only the movement of the pickup points is accounted for anyway.

It’s also somewhat proof against the conventional mid point of the bar definition for RC.

 

[302 Hi Pro]

Grant:

Thank you for your patience here as I have, perhaps a dumb question. Does it make a difference if the car has a live/solid rear axle like my S197 Boss 302, vs a S550 IRS Mustang?

Back in the day 2012, I ended up going with KB because his setup was winning championships. WhiteLine, Fay’s, & Griggs were not at that time. Cortex was not an option in 2012 that I knew about. But once they hit my radar screen in late 2013 early 2014 they seemed to return Mustangs to the podium.

I actually purchased a Cortex Watts Link set up, but never got around to installing it.

Thank you in advance.

 

[Grant 302]

Grant:

Thank you for your patience here as I have, perhaps a dumb question. Does it make a difference if the car has a live/solid rear axle like my S197 Boss 302, vs a S550 IRS Mustang?

Back in the day 2012, I ended up going with KB because his setup was winning championships. WhiteLine, Fay’s, & Griggs were not at that time. Cortex was not an option in 2012 that I knew about. But once they hit my radar screen in late 2013 early 2014 they seemed to return Mustangs to the podium.

I actually purchased a Cortex Watts Link set up, but never got around to installing it.

Thank you in advance.

No problem Dave. My opinion is yes. There are huge differences as well as many differences. Too many to discuss as they relate to this thread and its fairly specific scope.

If the root of your question is to discuss wether you should make the swap from KB to CorteX, I think we’d need to have a longer and separate discussion.

If I had to choose right now for my car, I think I’d try the KB relocation. Mostly because I believe in the benefits of a horizontal panhard and have limited my ride height specifically for that effect. Also for other reasons that might work with my current rear suspension parts and what I have available.

Not sure if you’ve seen the ‘Blacksheep hates watts links’ thread. Perhaps it would be a good read for you.

I don’t know if any of that helps at all, but I hope so!

 

[blacksheep-1]

My 2 cents, and I'm far from a suspension guy.
1. it's not a Watts...very good
2. I've found that when I'm trying to figure out suspension stuff that if I build a model out of balsa wood or even popsicle sticks, it helps me visualize what is actually going on
3. You don't need relocation brackets, if you decide to buy them I think Phoenix has a couple of million that they'd be happy to sell you.
4. rims are not wheels , just like clips are not magazines in a rifle
5, control arms run east and west, trailing (or leading arms) run north and south
6. I use Carroll Smith's books as references all the time, if you don't own the set, stop everything you are doing and buy them..right now.

Carroll Smith Books . The Official Carroll Smith Site

www.carrollsmith.com

 

[Grant 302]

4. rims are not wheels , just like clips are not magazines in a rifle

Weapons and guns. Lol.

I’m old enough to have qualified Expert on M-16 and M-60.

 

[Norm Peterson]

I’m using free body diagrams. Separate for the rear body and including the possible torque reaction from the front half. And separate axle assembly for the axle and tires.
Resolving the bar and spring reactions with iterations.

I think you're using the sort of analysis that separates 'front mass' from 'rear mass', perhaps with unequal CG heights.

The analysis I've worked up takes sprung mass as a single lumped mass, located along the chassis as a beam of finite torsional stiffness (around 15,000 ft*lbs/° for the S197 coupe). I'm also considering vertical tire stiffnesses as springs in series with the suspensions and the applicable 'half-lengths' of the chassis. No iteration necessary, and it does capture the amount of end-to-end chassis twist (around a quarter of a degree per g).

Analysis is only on left turns. My understanding through previous analysis is that leveling the bar alone reduces the geometric transfer on right turns. And that by default, right turns ‘suffer’ from too much bar anyway on stock panhard angled setup.

The S197's PHB right-side chassis pivot being higher than the axle-side pivot certainly would aggravate right turn geometric effects (and the ability to put power down).

I believe that’s all correct right up to the point where one or any of the examples loses grip on one axle.

True, but that's a limitation of any linear analysis. As a practical matter, all bets are off as far as LLT or roll is concerned once either end of the car comes 'unstuck'.

... interesting that the lever arm does get longer with RC lowering when slightly angled coilover setup is considered.

Isn't that a different way of looking at the effective vertical components of coilover spring rates than using trig functions?


Norm

 

[Norm Peterson]

It’s also somewhat proof against the conventional mid point of the bar definition for RC.

PHB midpoint as the geo-RC is at best an approximation. It's usually a pretty good approximation, but an approximation nonetheless. The full RC construction needs at minimum a second definition of lateral constraint in order to draw the axle's own notional roll axis, from which the geo-RC [defined as being at the axle line] can be determined. Even if that second lateral constraint is located "at infinity", the construction line can still be drawn.


Norm

 

[Grant 302]

I think you're using the sort of analysis that separates 'front mass' from 'rear mass', perhaps with unequal CG heights.

The analysis I've worked up takes sprung mass as a single lumped mass, located along the chassis as a beam of finite torsional stiffness (around 15,000 ft*lbs/° for the S197 coupe). I'm also considering vertical tire stiffnesses as springs in series with the suspensions and the applicable 'half-lengths' of the chassis. No iteration necessary, and it does capture the amount of end-to-end chassis twist (around a quarter of a degree per g).

That is what I’m doing. Iterations in this context are to resolve the ‘final’ reactions and bar angle. Plus the torque transmitted through the cut to the front half of the body.

The S197's PHB right-side chassis pivot being higher than the axle-side pivot certainly would aggravate right turn geometric effects (and the ability to put power down).

I hope people read and understand this. It’s a big reason to exclude watts link examples from this discussion.

True, but that's a limitation of any linear analysis. As a practical matter, all bets are off as far as LLT or roll is concerned once either end of the car comes 'unstuck'.

Yes, agreed, but it’s not difficult to estimate or ‘see’ what models will become ‘unstuck’ before others. It also seems clearer when damping reactions are added without turning the theoretical knobs.

Isn't that a different way of looking at the effective vertical components of coilover spring rates than using trig functions?

Yes. And I only brought it up as an example of things I’ve looked at before deciding to ignore. My interest is in correct order of magnitude comparisons over precise theoretical numbers.

——

So far, I see how the increased transfer per g with the lower roll center can ‘need’ less bar.

Perhaps the best way I can exemplify that is to clarify...that the lower rear roll center can reduce the need for rear and front bar(s) (or rate/stiffness - if one prefers).

It does reinforce my thinking that there are still many misconceptions about what needs to be adjusted when suspension geometry is changed. And ultimately where more grip comes from.

Thanks again for restarting and continuing this discussion. I appreciate the opportunity for ‘sanity checks’ that I can’t really get elsewhere.

 

[302 Hi Pro]

Grant, Norm:

All I can say is your conversation is above my pay grade as I’m just a regular guy. But thank you both for throwing this out there.

One of the comments I could relate to was the location of the OEM PH R/S chassis mount. It is very high indeed.

Norm: Did Ford use the same R/S PH chassis mount location on your Boss 302S?

 

[Norm Peterson]

Norm: Did Ford use the same R/S PH chassis mount location on your Boss 302S?

I'm afraid you're thinking of somebody else - my Mustang is an '08 GT with the 3-valve 4.6L engine.

It'd be interesting to find out if Ford relocated any of the rear suspension pivot points for any of their competition Mustangs, though.


Yes, the PHB location is relatively high. But I suspect that Ford did it that way in order to meet certain handling targets without having to call for heavier bars, stiffer rear springs, and more rear damping (I recall that the OE rear shocks made the car ride pretty harshly as it was, even with rear springs somewhere down around 140 lb/in).


Norm

 

[Norm Peterson]

That is what I’m doing. Iterations in this context are to resolve the ‘final’ reactions and bar angle. Plus the torque transmitted through the cut to the front half of the body.

I hope people read and understand this. It’s a big reason to exclude watts link examples from this discussion.
——
So far, I see how the increased transfer per g with the lower roll center can ‘need’ less bar.

Perhaps the best way I can exemplify that is to clarify...that the lower rear roll center can reduce the need for rear and front bar(s) (or rate/stiffness - if one prefers).

Still not seeing how this could work. If all you do is reduce the PHB height (keeping it horizontal), the car's total lateral load transfer for any given cornering g-level doesn't change. But the distribution of that LLT would move forward by virtue of the balance between front and rear geometric load transfer shifting toward being less rearward. While roll would increase, roll stiffness distribution is heavily front biased, so the rear isn't recovering any LLT that way.

I actually threw this at one of my latest sheets for a 2" lowering of the rear geo-RC, and to match the TLLTD present with a 185 lb/in bar would need a 300 lb/in rear bar. Roll stiffness distribution went from 73f/27r with the 185 bar to 69/31 with the 300 bar. There was no change in the amount of roll between those two cases, but (like you'd expect) there was about 0.1°/g more roll with the PHB lowered and the rear bar kept at 185, vs stock PHB height with the 185 (and a little more chassis twist with the PHB lowered).


Norm

 

[Grant 302]

Still not seeing how this could work. If all you do is reduce the PHB height (keeping it horizontal), the car's total lateral load transfer for any given cornering g-level doesn't change.

Are you sure about that?

I’ve looked at the sprung body with the bar initially level, and also level under load. The differences in elastic transfer per g seem clear to me when lowering the RC.

Differences in elastic transfer to the axle assembly appear to translate to the tire contact patches. Somewhat proportionately, and I don’t see any significant effects that I’m ignoring or excluding...at least not on purpose.

I’m thinking there’s something in there that you or your calculation are ignoring, perhaps in this context.

Perhaps you recall our discussion about the Phoenix car with two wheels in the air. I said something along the lines of “match the roll rates and watch both tires come up” When the torque transferred through the body is kept to zero under load, the rates are ‘matched’. That can be done in various ways, via spring, bar or RC. But my assumption is that is done (whatever need be) to allow the rear to have a lower RC and be allowed to roll to develop the same g load on the rear axle/half assembly.

 

[Norm Peterson]

Are you sure about that?

Absolutely. Total lateral load transfer depends only on sprung mass, sprung mass CG height, lateral acceleration, and track width(s). Geo-RCs do not affect the total, but they do affect how the LLT is carried down to the tires.

I’ve looked at the sprung body with the bar initially level, and also level under load. The differences in elastic transfer per g seem clear to me when lowering the RC.

Agreed so far. But this effect does not happen in isolation.

Differences in elastic transfer to the axle assembly appear to translate to the tire contact patches. Somewhat proportionately, and I don’t see any significant effects that I’m ignoring or excluding...at least not on purpose.

I think what you're neglecting is the reduction in rear geometric load transfer. As the CG to RC distance increases (and the elastic LLT along with it), the RC to grade distance decreases (it has to), and the geometric component of rear LLT decreases along with that. This is with the assumption that all four tires remain in contact with the pavement. The rear axle's geo effect drops off faster than its elastic effect increases.

I’m thinking there’s something in there that you or your calculation are ignoring, perhaps in this context.

Perhaps you recall our discussion about the Phoenix car with two wheels in the air. I said something along the lines of “match the roll rates and watch both tires come up”

I remember the picture, and FWIW I think there's more going on than just roll (roll + pitch due to forward acceleration).

In any event, the sprung mass CG has clearly moved upward, meaning that the usual assumptions as to how the CG to grade, CG to RC and RC to grade distances are inter-related are no longer valid. Once the first inside tire lifts off the ground, the elastic load transfer shifts from its nominal distribution (typically something like 70f/30r) to 100% going to the axle whose inside tire is still on the ground. Linear analysis (what both of us are using) cannot handle abrupt discontinuities like that.

And once both inside tires are off the ground, no further load can be transmitted from one side of the car to the other and the car is now rolling about points on the ground somewhere within the contact patches. Granted, there will be some range of relationship between front and rear roll stiffness (and other things) that will be more apt to result in both wheels coming up.

When the torque transferred through the body is kept to zero under load, the rates are ‘matched’. That can be done in various ways, via spring, bar or RC.

I have to disagree with that. The general consensus is for TLLTD (f:r distribution) to be somewhere around 5% more front-biased than the car's total weight (ends up being about half that - maybe 3% - in terms of the Mustang's sprung mass weight distribution). Which means that the front suspension by being stiffer in roll than the rear suspension is always stealing a bit of roll moment away from the rear suspension, and this "stealing" of roll moment from one end of the car to the other is what roll stiffness tuning does to cause the handling balance to shift. Stolen roll moment = chassis torsion, and I'm not at all convinced that zero here should be a design goal.

But my assumption is that is done (whatever need be) to allow the rear to have a lower RC and be allowed to roll to develop the same g load on the rear axle/half assembly.

I think it's here. Roll is not the independent variable that drives the loads and how they are carried to the tires. Roll is only the visible result of load transfer happening through a support system (the suspension and tires) that is not infinitely rigid against roll.


Norm

 

[Norm Peterson]

I hope nobody is thinking I have anything against lowering the PHB and also reducing the amount of rear bar. I don't, not where you might have a clear reason for doing them together, anyway.

Offhand, the only reason that comes to mind where you would do those together is where you're specifically looking to improve acceleration traction on corner exit. Not for tuning understeer-oversteer handling balance unless you're also planning on running significantly more rear spring to make up for what you gave away in bar.


Norm