MaXJohnson said:
No, what I'm saying is that the usual diagrams that you see on here, PBB, etc is correct for calculating anti-squat for a 2WD vehicle, but not for 4WD. This is not a difference is how you determine the placement of your instance centers, but rather how you compare IC reaction with the CG.
Look at it this way. You can draw a diagram of your rear suspension links in the side view to determine where your IC is. Compare the IC location with the anti-squat neutral line (rear contact patch to CG height above front axle) to determine AS%. Now do the same for the front suspension links to determine front anti-lift. Here's the problem. The values you get assumes that each axle get 100% of the engine torque available.
This is wrong. In a part-time transfercase (no center differential) each axle only recieves 50% of the torque. This means thatpyour calculated AS% and AL% are double their actual value. Some fulltime transfercases split torque on an uneven basis, front to rear, say 60%-40%. This would have to be f`ctobmd in as well.
If, for example, you calculated 80% anti-squat for the rear axle and 60% `nti hift for the front; the total anti-pitch force available through a 50-50 transfercase would be 1/2 the sum of these two values. My previous post indicated that the total anti-pitch force available would be the average of the front and rear percentages
(80%+60%)/2 = 70%.
This application of calculating the TOTAL 4WD anti-squat/lift values is derrived from an example in one of Forbe's Aird's books for determining total anti-dive/lift under braking. The method of determining the individual values is correct, but I am having trouble with his interpretation of the total force acting on the chassis being an average of the two individual values.
What all this means is that if you have a significant difference in the link design between the front and rear suspensions (most do) then the common method being tosses about will produce a significant error.
Max (Willis),
The 70% answer (something less than 100%) is not to be discounted because the forces at the two IC's that define AL and AS superimpose and appear to cancel out the vertical force component on the GC. I imagine you are uncomfortable with the missing resistance to the total mass acting through the CG and gravity? (I am)
Drawing the FBD for the two suspensions allows us to identify the CG contribution acting on each system, and when the respective portion of the mass applied to each IC is calculated the total mass acting on both axles does work out (rather than 70% it totals 100%). The forward IC (the rear axle) is resisting (working against) it's portion of the weight, and the rearward IC (the front axle) is complementing (working in the same direction as) the weight (and interestingly enough, against anti-squat).
If we look at the vertical forces, the rear axle system torque force pushes up against 80% of the vehicle weight, and the front axle system torque force is pulling the vehicle weight down 10% (80-10=70%), but the actual vehicle weight applied at each IC is not an 80/20 or 80/-10 split (it's not a function of the available torque, we have 100% of the vehicle weight). The actual weight applied at each IC is the percentage of total vehicle weight defined by the distance away from the CG, and the portion of weight resistance applied to each suspension system is the limit on how much each contributes to the chassis pitch. The imbalance between the available torque and the appied resistance (weight on the IC lever arm) provides the motivation for the dynamic movement between the suspension and the chassis. 80% front IC lift, acting on 60% of the mass about the CG, will get the front lifting more than the rear when it has -10% lift (anti-lift) on the 40% of the mass that is acting on the IC that is rear of the CG. Move the IC closer or farther away from the CG and the imbalance between the two suspension systems contribution to the chassis pitch can be equalized or made more diverse.
In your example the front of the vehicle would pitch up faster than the rear (somewhat like what is observed on radius arm XJ's). The difference in feel the driver experiences (chassis rotation about a location near the drivers seat or the rear bumper) has a lot to do with the confidance to be had when challenging a climb like the dump bump. If the front pitch is significantly faster than the rear, moving the instant chassis rotation center back, the movement of the CG is accelerated and the throttle induced pitch control becomes sensitive (and much more sensitive when the seat is also being lifted more with each throttle touch). What the radius arms guys feel is the accelerated front chassis pitch moving the CG back in addition to placing the AS% in an unstable position (well past 100% and growing with more throttle application). Fix a limit strap and you place a limit on the throttle induced pitch acceleration (the contribution of the front suspension IC about the CG is removed from the two force moment that pitches the chassis).
The short arm guys have the same AS% for the approach angle, but the front of the chassis is not pitching as fast. It feels more stable because the front suspension is contributing to chassis rotation on the rear of the chassis, moving the instant center of the chassis rotation forward. The front axle torque reaction on the short arm chassis (anti-lift) resists the growth of rear AS% (it slows the rapid acceleration of the AS%). The total chassis lifts, not just the front end of the chassis. The tires on both axles lose traction rather than accelerate the tip-over feeling (or the XJ climbs).
The two IC's are acting on the chassis as a two force moment about the CG. The instant chassis pitch moment (in a perfect traction world) is a factor of the IC distance away from the CG and imbalance with the torque split between the axles. The AS & AL of each system provides a factor to compare the percentage of force working on the springs and links, but all the vehicle weight and resistance is still applied through the IC of each suspension system.
The IC location defines the leverage of the suspension system acting on the chassis in a horizontal plain (how leverage about the axle is used to lift the chassis weight). Raising or lowering the IC on a vertical line without changing it's horizontal distance away from the CG changes the AS%/AL%, or the efficiency of the system to convert the applied vertical force to horizontal motion (how much is stored in the suspension springs compared to directly transferred to the links for the rest angle of the vehicle), but is will not change the share of force rotating the chassis (other than that being applied at the spring tower mount rather than the IC, something that complicates analysis).
This independence between the IC and AS% is one reason why one vehicle will climb without jacking and wheelhop, and another will become very unstable, even when both have the same relative IC leverage. We have PBB folks calculating AS% recommendations without regard to the IC length or height, and IC location (forward or rear of the front axle) without reference to the IC height (the factor changing the AS%). There is no reliable rule of thumb for IC distance from the axle and CG, or AS%, and to quote one parameter without the other is ignoring the independence of the two. Quoting answers for the front and rear, is just as much of a swag (but I know you understand this well).
Bob,
I am pleased to have the input of someone who has reverse engineered the dynamics of the XJ (I assume) to advise DC on what was required to build a better evolution of the four link (the RAM truck). I can see the improvement in axle steer, pinion angle gain, and bumpsteer, but all improve with longer arms and the wider track that a full size chassis allows. We are confined by the XJ track and wheelbase.
"There is a distinct difference between the two in perfromance of the suspension. As it relates to the anti-dive discussion, the XJ has 18% and the Dodge has 36%. The Dodge has far less non-symetrical axle steer due to linkage compound ratios when co,mpared to the XJ/MJ."
The later design has more equal length arms reducing the non-symmetrical action, and longer arms working a longer wheelbase that allows acceptable suspension compliance with the steeper anti-dive. The vehicles are different in wheelbase, CG & weight distribution, and we have to accept the suspension performance will be different. What I want to know is what (in your opinion) improved the performance of the later design the most, and if it can be applied to a modified XJ system?
Were more equal length controls arms a significant benefit (reducing the non-symmetrical axle steer)?
Was raising the front system IC or shortening the IC distance from the CG (the two factors that can raise the AD%) a benefit (and what, IYO, was the more beneficial change)?
Anything else (I am always willing to share opinion and learn something new)?
I have photos of many of the late 80's and early 90's XJ/MJ that were in SCORE competition (and still know a few of the people who wrenched and rode in them as well) as I was involved in Class 11 and 1/2-1600 at the time and used my XJ for chase and prerunning (with me always looking and asking for applicable improvements). I find the comparison of what worked for the long arm systems for off-road racing, systems that did not worry as much about ground clearance, to be helpful but not the answer for a dual purpose rockcrawler and street runner. Was there any system improvement (or design) that you saw as a benefit that did not rob ground clearance or require the chassis and fender tubs to be highly modified (a design change that can be easily applied to the XJ chassis)?
Willis,
Take Max's advice to heart, as the stability and pinion angle gain improvements will provide a good initial platform if the design is to be cut and rehashed on the XJ or on paper (welded or web-welded). There is a point where the XJ frame and axle (and all the stuff in the way) will limit the design (lets call it the BezzWall), and it will likely dictate the final design compromise.
If you read (and agree with) the above description of the front suspension and the impact of the front IC on the chassis pitch rotation, then it makes sense to locate the front system IC well behind the transfercase crossmember and CG. You would certainly not want it find it ahead of the CG on an incline (IMO) as it would make the chassis pitch very throttle sensitive. I have not played with a modified XJ on rocks as much as others on this board, and do not have feedback other than that expressed in the long and short arm debates, so I am as eager to listen to advice on what works as much as you.
FWIW, I see no reason to delete the panhard rod and draglink steering as long as it is designed to be relatively level at rest. The fixed three link (the wishbone, rather than the assymetrical upper link Goatman runs) deletes the need for the panhard bar, but invites complicated steering (hydro, electric fixed rack, or some other axle mounted steering actuation). I am not that comfortable with full hydro steering on the street, at speed, and I have not seen a good axle mounted electric rack & pinion system.
I have a family birthday, a funeral, and a wedding anniversary to tie up my week so I leave you folks to hash all this out.
Too bad about the Jackman guys-there was an excellent product and they were victil to0dxactly what I was referring to-someone that thought they knew more than the engineer that originally designed the wheels. A lot of people got hurt (both literally and figuratively speaking) on that mess.....
