Outer Limits 4x4 Board

I'm toying with going to coils on my 1.0 sierra. I'm mostly interested in accurate axle location and no axlewrap rather than crazy flex - it's for Victorian tracks not a travel ramp.

Here the short version - My basic question is this - my main variable will be roll centre, is there a rule of thumb or guide for what's the best setup? is it related to COG, or is lower/higher better?

Long version:

As a result, and based on a desire to have balanced roll stiffness front and rear, I'm planning Range rover front radius arms front and rear. These should provide all the travel I need and allow some rear roll stiffness due to the bushing bind inherent in these designs. I've seen too many coil cars with very unbalanced roll stiffness front to rear to want to build a loose 3/4 link rear and then try and add sway bars, stiff shocks etc to try and make it balance.

I also have experience with my Gwagen which is a radius arm design front and rear and I like its behaviour, except for the too high rear COG.

I'll be using OME N76 shocks all round. Springs are undecided, but may be Calmini Vitara rear or equivalent vitara lift spring.

My basic question is this - I understand my main variable will be roll centre, and I can control this with the relationship between the panhard mounts as the roll centre will be effectively 1/2 way along the panhard rod.

so, I don't have a lot of choice in the front due to space constraints and a desire to match the draglink angle, but in the rear I have alot more freedom - so is there a rule of thumb or guide for what's the best setup? is it related to COG, or is lower/higher better?

It seems that most manufacturers aim to have the panhard level with the axle centreline at ride height, (and going lower than this isn't really feasible) but then some buggies seem to have very high panhards with parallel 4 links and the rear a frame designs seem to have a fair bit higher roll centre.

I've heard SPOA cars cheat back some stability over SPUA due to a higher roll centre but I'm a little bit confused as to why this is the case, but I think it might be because the car stays "over" the obstacle more rather than the body rolling away from the axle assuming a levelish body and an articulated axle.

I don't want to have lots of compression travel so I'll also be running the arms pretty much horizontal at ride height.

Can anyone give me any pointers?

Steve.

Rear roll centre should be higher than front roll centre.

If the roll centre is considerably lower than COG of the unsprung mass, then on side slopes, the body will tend to flop over and the COG will move further to the down hill side further affecting stability.

With a high roll centre, the axle and wheel assembly moves to one side relative to the body during articulation. This may affect your tyre to guard clearance.

Related to the this side shifting with articulation, on high speed climbs, the inertia comes into play and this gives stiffer effective suspension. I.e. lower roll centre will allow the suspension to articulate better at speed, which can help on climbs that need speed.

i look forward to some of the more knowlegeable guys replies..
To my knowledge:
low roll centre=body roll, nearer vertical wheel path
high roll centre= less body roll but the wheel path is less than desirable.
the roll centre is the imaginary, instantaneous point that the body and axle pivot around in relation to each other. so when a wheel hits a bump, the wheel cannot simply move up, it must more in an arc about the roll centre. so when the roll centre is above the ground your car is driving on(always the case), the wheel will have to translate sideways in relation to the body of the car to move up. seeing as the tire is bound to the ground through friction it does not want to move sideways. instead the body is shunted sideways.

it is all a compromise and there is not a simple lower or heigher is better.
building your centre of gravity super low is very important because it allows you to run a lower roll centre without the body roll.

thats my understanding.

jim

Everybody is making far too much sense - is this still Outers?

I don't know much about roll centres, but have a minor comment about panhards. As many understand, the less "parallel" the panhard is to the axle the less "symmetrical" the suspension's behaviour - I think the roll centre effectively moves depending on which side is compressed.

I also had a conversation about panhards with the engineer who passed my Paj: he had previously performed some calculations on the stresses in panhard mounts (I think more related to race cars than 4wds) and was surprised at the forces involved - he wasn't keen on the idea of lengthening panhard mounts, which would effectively increase leverage on the mounts. He believed it was better to live with the inconsistencies of a non-horizontal panhard.

Steve, have a look at disco 2 front arms, they are 100mm longer than RR/Def/Disco 1 and have 69mm od bushes as aposed to 50mm but both share a 5/8 bolt .... the bush seperation is greater to allow for the bigger bush but the increase in rubber is greater...

the only other difference is the chassis end, RR/Def/Disco 1 have a pin end and Disco 2 has an eye....

Serg

-Scott- wrote:Everybody is making far too much sense - is this still Outers?

I don't know much about roll centres, but have a minor comment about panhards. As many understand, the less "parallel" the panhard is to the axle the less "symmetrical" the suspension's behaviour - I think the roll centre effectively moves depending on which side is compressed.

I also had a conversation about panhards with the engineer who passed my Paj: he had previously performed some calculations on the stresses in panhard mounts (I think more related to race cars than 4wds) and was surprised at the forces involved - he wasn't keen on the idea of lengthening panhard mounts, which would effectively increase leverage on the mounts. He believed it was better to live with the inconsistencies of a non-horizontal panhard.

I think you're pretty much right on there and the engineer is as well.

My patrol definately handles bumps in the road alot worse with lift than it did at a more stockish suspension height. You can definately feel the body shifting around and also reflects in the steering. Lets not even consider the live axle bump steer which is apparent with ANY live axle vehicle not just patrols.

uninformed wrote:Steve, have a look at disco 2 front arms, they are 100mm longer than RR/Def/Disco 1 and have 69mm od bushes as aposed to 50mm but both share a 5/8 bolt .... the bush seperation is greater to allow for the bigger bush but the increase in rubber is greater...

the only other difference is the chassis end, RR/Def/Disco 1 have a pin end and Disco 2 has an eye....

Serg

I've seen the thread on the various arm configurations and whilst the extra length and larger bushes would be nice, I like the idea of the pin at the chassis.

The sierra is very light and I wouldn't be surprised if I have to remove a bolt on one side, almost regardless of bush size, particularly on the front, to lower roll stiffness enough. I'm used to setting up sierras with rear springs in the front and they have very low roll stiffness in the front, however, I may not have enough weight to flex the chassis end with the D2 bolt configuration so I'd prefer the pin.

I'm also a being a bit of a cheapskate- my guess is the range rover/early disco arms are a fair bit cheaper.

I'll be aiming for a horizontal panhard rod at ride height in the rear. I can't quite achieve that in the front due to steering geometry, but I have low lift so the drag link is at a pretty shallow angle- bumpsteer won't be a major problem

Thanks to everyone for the responses!

Steve.

Yom wrote:... Lets not even consider the live axle bump steer which is apparent with ANY live axle vehicle not just patrols.

Not correct, unless you change ANY to any stock in that statement.

Triangulating the link geometry can totally eliminate bump steer. Bump steer is related to the slope of the roll axis. A horizontal roll axis = no bump steer. But won't eliminate bump steer due to flogged bushes.

Bush65 wrote:

Yom wrote:... Lets not even consider the live axle bump steer which is apparent with ANY live axle vehicle not just patrols.

Not correct, unless you change ANY to any stock in that statement.

Triangulating the link geometry can totally eliminate bump steer. Bump steer is related to the slope of the roll axis. A horizontal roll axis = no bump steer. But won't eliminate bump steer due to flogged bushes.

John are you referring to axle roll axis or vehicle roll axis...im guessing axle.

if so, are you saying that if you have 0 degrees axle roll understeer/oversteer that there will be little or no bump steer.

0 degrees can be achived if the radius arms are level(from center of axle casing to center of chassis bush of arm....

Serg

uninformed wrote:

Bush65 wrote:

Yom wrote:... Lets not even consider the live axle bump steer which is apparent with ANY live axle vehicle not just patrols.

Not correct, unless you change ANY to any stock in that statement.

Triangulating the link geometry can totally eliminate bump steer. Bump steer is related to the slope of the roll axis. A horizontal roll axis = no bump steer. But won't eliminate bump steer due to flogged bushes.

John are you referring to axle roll axis or vehicle roll axis...im guessing axle.

if so, are you saying that if you have 0 degrees axle roll understeer/oversteer that there will be little or no bump steer.

0 degrees can be achived if the radius arms are level(from center of axle casing to center of chassis bush of arm....

Serg

axle roll axis.

Yes

Level radius arms will have negligible bump steer while they are near level. When one wheel goes up and the opposite down, the arc move the axle forward the same amount on both sides.

Triangulated 4 link with lowers close together at chassis end and uppers close together above axle, and roll axis near zero, sloping down a little toward the front is the ideal set-up for best bump/roll steer characteristics. This arrangement experiences little change of the roll axis as the suspension flexes.

When the axle roll axis is horizontal neither side wheel will move forward of the other as the axle articulates.

Edited to deleted incorrect comment about radius arms and anti-squat/dive.

John, my understanding of antidive doesnt have anything to do with the angle of the radius arm.....

example:

draw front and rear wheels at side view, with said wheelbase.

draw chassis end points of front radius arms and rear trailing arms.

draw a horizontal line at center of gravity

draw a vertical line which represents front/rear brake bias.... if its 65% front then the vertical line is placed 65% back, of the wheelbase, from the front axle center line towards the rear axle center line.

draw a line that conects the front contact patch, through the front chassis mount point of radius arm to the vertical brake bais line

draw a line that conects the rear contact patch, through the rear chassis mount point of trailing arm to the vertical brake bais line.....

now the height that the front angled line and rear angled line pass through the vertical brake bais line represents the amount of antidive(front) and antisquat(rear) the vehicle will have, this is in relation to the center of gravity line.

so if the front and rear lines pass through the brake bais line at the height of center of gravity there will be 100% anitdive and antisquat.... heigher will be more % lower less %...

clear as mud?????

im basing this on a rover type suspension.. radius arm + panhard rod front, trailing arm + A frame rear.... both radius arm and trailing arm are parrallel when viewed from above...

please let me know if im missing something, everything or on the right track.

Serg

also forgot to add, the spring rate and shocks used will play a big part... in any design

Serg

Serge,

Sorry, my bad. I went back and put that line in my previous post as an afterthought before posting. My mind was on link suspensions, not radius arms.

The lower link needs to be angled up toward the chassis for anti-dive/squat.

Radius arms are not links, and they can develop anti-squat/dive even when level. The tractive/braking force at the tyre patch can give lift at the chassis end of the radius arm through bending forces transferred through the pair of bushes at the axle end.

Bush65 wrote:Serge,

Sorry, my bad. I went back and put that line in my previous post as an afterthought before posting. My mind was on link suspensions, not radius arms.

The lower link needs to be angled up toward the chassis for anti-dive/squat.

Radius arms are not links, and they can develop anti-squat/dive even when level. The tractive/braking force at the tyre patch can give lift at the chassis end of the radius arm through bending forces transferred through the pair of bushes at the axle end.

no worries John, im here to learn.

from the book that i have been looking at, it doesnt give antidive/squat examples for each type of suspension... so im wondering how it chnages going from radius arm to link?

i understand what you are saying with regards to the rotation of the axle casing effecting the radius arm... like a geared lever. and that makes me think that a single bushed link would behave differently... but from the book it looks like the line drawn from contact patch, through chassis mount of front/rear link to vertical brake bias line is important...even the drawing shows the front link running uphill to the front of the car(showing understeer)

it talks about the fact that rarely is 100% antidive used, that it seldom exceeds 50%

Serg

thinking more about this (antidive/antisquat under braking), i understand what John is saying about the 2 bushes acting on a radius arm, but im also thinking there would be some sort of leverage on the bottom links of a 3 link or 4 link... as the axle casing rotates underbraking, isnt the top link going to be put into tension and the bottom link being forced back into the chassis... so my question remains, is antidive mostly related to the angle from contact patch through chassis bush, and just like antisquat under acceleration, antidive will be effected by wheelbase and height of COG.

so lenght of front lower link, whether it be radius arm or 3/4link, will determine antisquat, as will link angle(from side view) but you will still have anitsquat even if the lower link/radius arm is angled down hill to the chassis, ie front axle roll axis understeer, depending on wheelbase, brake bias and COG

now back to what steve was talking about, roll centers:

looking at a stock vehicle, lets say a landrover defender(what i know) you have a front roll center height lower than rear. now raise the vehicle on springs only, the front roll center height changes, rasies, but the rear stays where it is, this is because the front is determind by the panhard rod, its height where it intersects the center line of chassis width. the rear is the center of the rear ball joint that is mounted to the axle casing so it doesnt move.

for a vehicle that sees speed, ie motor way and road use are we wanting a lower roll center or higher? i know that low roll centers will produce a more unstable rig on sideslopes due to the fact that body will roll about the axles more... but how does it effect on road handling

regards to above, still keeping the vehicle roll axis lower front to rear...

im guessing when people talk hi and low axle roll centers it is in relation to height of COG?

cheers, Serg

uninformed wrote:im guessing when people talk hi and low axle roll centers it is in relation to height of COG?

I think it's got to be a relative thing - COG below roll centre, the body would want to stay level during articulation, and would lean IN to a corner. Wouldn't it?

-Scott- wrote:

uninformed wrote:im guessing when people talk hi and low axle roll centers it is in relation to height of COG?

I think it's got to be a relative thing - COG below roll centre, the body would want to stay level during articulation, and would lean IN to a corner. Wouldn't it? [/quote

if the COG was BELOW roll center im calling that high roll center, which would cause the body to tilt duing articlulation.....think of it as the righthand wheel articulating up, the point at which the whole thing pivots is not so much the roll center but the laft hand wheel, so the higher the roll center the more the body will move/tilt during articulation.... draw a tall triangle and a short triangel, same base width, tip them both one way, pivoting on the left corner and see how far the top point moves left to right compared to each other..... so the roll center is the point on which the BODY rolls or moves about on the axle, remember we are talking about live/solid axle rigs here not independent.... so its not so much the pivot point of the axle but the pivot point of the body...


please bush 65/strange rover/anyone let me know if im on the right track...

Serg

One other thing that hasn't been mentioned.
You don't want your roll centre(s) to migrate from below to above the suspension as it cycles.

uninformed wrote:thinking more about this (antidive/antisquat under braking), i understand what John is saying about the 2 bushes acting on a radius arm, but im also thinking there would be some sort of leverage on the bottom links of a 3 link or 4 link... as the axle casing rotates underbraking, isnt the top link going to be put into tension and the bottom link being forced back into the chassis... so my question remains, is antidive mostly related to the angle from contact patch through chassis bush, and just like antisquat under acceleration, antidive will be effected by wheelbase and height of COG.

so lenght of front lower link, whether it be radius arm or 3/4link, will determine antisquat, as will link angle(from side view) but you will still have anitsquat even if the lower link/radius arm is angled down hill to the chassis, ie front axle roll axis understeer, depending on wheelbase, brake bias and COG

For anti-squat or anti-dive, the lower link will be in compression and the upper link in tension (assuming rear during acceleration).

There is a horizontal force at the tyre contact with road. This force goes to the chassis through the lower link. The horizontal force at the chassis mount (Edit:) is proportional to (equal deleted - end edit) the horizontal force at the tyre contact.

Now, because the link is angled up toward the chassis, it is also produces a vertical up force at the chassis mount - it applies lift to the chassis as well as horizontal push. The compression in the link is equal to the horizontal force (Edit: delete between the tyre and road end edit) divided by the cosine of the angle between the road and the link. The vertical force is the horizontal force times the tangent of the link angle.

The upper link has to prevent the axle housing from rotating, and this is where the lever principle comes into determining the force in the upper link. When looking from one side, imagine there is a lever with a fulcrum (pivot) at the point where the lower link attaches to the axle housing, one end where the tyre contacts the road and the other end where the upper link attaches to the axle housing.

From this lever, the tension in the upper link can be determined. Now if the upper link is angled up toward the chassis it will apply a vertical down force as well as a horizontal force at the chassis mount.

Subtract the vertical down force from the upper link from the vertical up force from the lower link will give the anti-dive force.

Now the graphical methods given in text books for percentage of anti-squat (or anti-dive) take into account the position (height and horizontal) of the centre of gravity. They use the position of the instant centre of the lower and upper links because it is easier for the graphical method because it simplifies resolving the combined forces in the upper and lower links.

But forces can not be transferred through air along an imaginary line angled from the tyre contact patch. They can only be transferred in the links. These other lines are simply a graphical method of solving the trigonometry of the link forces and the transfer of inertia through the centre of gravity.[/i]

Because the reaction force during cornering is resolved at the centre of gravity, if the roll axis passed through the centre of gravity, there would be no body roll.

If the centre of gravity is below the roll axis the body will pivot so the centre of gravity is below the roll axis on a side slope. This is like a plumb bob hanging from a string - where the sting is anchored is the roll centre, the centre of gravity is at the plumb bob.

Edit: To make a vehicle go around a corner it is necessary to have a force that acts toward the centre of the curve radius. This force is created by the angle of the tyres to the straight ahead position and acts at the contact patch between the tyres and road. This is called centripital (not centrifugal) force.

Now one of Newtons laws tells us that every force has an equal and opposite reaction. Thus there is a reaction radially outward through the centre of gravity. This reaction is what causes body roll.

Another consideration for roll centre height is the jacking of the outside wheel.

If you have a high roll centre, as the vehicle leans into a corner the outside suspension won't compress, but the inside still extends. The result is your COG gets higher as the vehicle leans. Eventually ending up shiney side down.

For this reason high performance vehicles have quite low roll centres, using spring and swaybars to control body roll. The result is a vehicle which pulls it's COG lower as the body rolls in corners. But as you can imagine, that type of suspension tune doesn't give much wheel articulation so it ain't much use for a dedicated 4wd.

Bush65 wrote:

uninformed wrote:thinking more about this (antidive/antisquat under braking), i understand what John is saying about the 2 bushes acting on a radius arm, but im also thinking there would be some sort of leverage on the bottom links of a 3 link or 4 link... as the axle casing rotates underbraking, isnt the top link going to be put into tension and the bottom link being forced back into the chassis... so my question remains, is antidive mostly related to the angle from contact patch through chassis bush, and just like antisquat under acceleration, antidive will be effected by wheelbase and height of COG.

so lenght of front lower link, whether it be radius arm or 3/4link, will determine antisquat, as will link angle(from side view) but you will still have anitsquat even if the lower link/radius arm is angled down hill to the chassis, ie front axle roll axis understeer, depending on wheelbase, brake bias and COG

For anti-squat or anti-dive, the lower link will be in compression and the upper link in tension (assuming rear during acceleration).

There is a horizontal force at the tyre contact with road. This force goes to the chassis through the lower link. The horizontal force at the chassis mount must equal the horizontal force at the tyre contact.

Now, because the link is angled up toward the chassis, it is also produces a vertical up force at the chassis mount - it applies lift to the chassis as well as horizontal push. The compression in the link is equal to the horizontal force between the tyre and road divided by the cosine of the angle between the road and the link. The vertical force is the horizontal force times the tangent of the link angle.

The upper link has to prevent the axle housing from rotating, and this is where the lever principle comes into determining the force in the upper link. When looking from one side, imagine there is a lever with a fulcrum (pivot) at the point where the lower link attaches to the axle housing, one end where the tyre contacts the road and the other end where the upper link attaches to the axle housing.

From this lever, the tension in the upper link can be determined. Now if the upper link is angled up toward the chassis it will apply a vertical down force as well as a horizontal force at the chassis mount.

Subtract the vertical down force from the upper link from the vertical up force from the lower link will give the anti-dive force.

Now the graphical methods given in text books for percentage of anti-squat (or anti-dive) take into account the position (height and horizontal) of the centre of gravity. They use the position of the instant centre of the lower and upper links because it is easier for the graphical method because it simplifies resolving the combined forces in the upper and lower links.

But forces can not be transferred through air along an imaginary line angled from the tyre contact patch. They can only be transferred in the links. These other lines are simply a graphical method of solving the trigonometry of the link forces and the transfer of inertia through the centre of gravity.

great info John, first of all let me confirm some basics: the axle casing wants to rotate in the opposite direction to the wheel in acceleration, therefore underbraking the axle casing will want to rotate back the same direction as wheel rotation? yes or no?

i understand (some what ) what you are refering to with regards to the forces applied to the links, and that air isnt a great link.... but when we refer to antisquat or anti dive, are we not refering to the behaviour of the vehicle, in percentage, rather than the force applied to a single link..

the book im reading is "fundamentals of vehicle dynamics" by Thhomas D. Gillespie.

quote" therefore, to obtain 100% anti-dive on the front and 100% anti-lift on the rear, the PIVOT for the effective trailing arm must fall on the locus of points defined by these ratios" end quote

the equation uses spring rates, COG, wheelbase...

you refer to text books using the instant center of the upper and lower links, but i cant see how this would work with the method Gillespie is using because IC's can be way out in front (for rear axle) way out behind (for front axle) or even a virtual IC of infinity if the lower links are parrallel when viewed from above...

here is another way to look at it: take 2 identical rigs lets say 37 inch tyres, 115 inch wheel base etc etc, now rig 1 has a front lower link length of 1000mm and its front axle roll axis is 0 degrees, the link is level at road height. Rig 2 has a lower link lenght of 1500mm and its front axle roll axis is 0 degrees, the link is level at road height. Everything except for the lower link lenghts are exactly the same on each vehicle, wont rig 2 handle bumps better/transfer less energy up the link into the chassis and more vertical wheel movement absorbing the impacts better????


but it will have less anti-dive under braking than rig 1....

so what im asking is can a rig can still achive a percentage of anti-dive for the front axle underbraking even if the lower link runs downhill from axle to chassis???

Serg

I'll take a stab, can you post up the ISBN number for that book, I really should get one.
I spent years working on mountainbike suspension geometry, some of it applies directly to other vehicles, some of it doesn't (i.e. drive chain).

uninformed wrote: so lenght of front lower link, whether it be radius arm or 3/4link, will determine antisquat, as will link angle(from side view) but you will still have anitsquat even if the lower link/radius arm is angled down hill to the chassis, ie front axle roll axis understeer, depending on wheelbase, brake bias and COG

I believe so, a downward angle on the links (talking radius arm front end here) reduces antisquat under braking, but unless the pivots are below the road level there will still be antisquat behaviour.
Braking couples the wheels to the links, the result is similar to a line drawn straight from contact patch to radius arm pivot. To get this line horizontal (i.e. remove all vertical forces) you need to get the pivot to the road.

The logical extension of this is lifted trucks have more antisquat under braking, lowered trucks have less. Hence the fitting of lowered suspension brackets to some lifted vehicles.

uninformed wrote: great info John, first of all let me confirm some basics: the axle casing wants to rotate in the opposite direction to the wheel in acceleration, therefore underbraking the axle casing will want to rotate back the same direction as wheel rotation? yes or no?

Yes

uninformed wrote: i understand (some what ) what you are refering to with regards to the forces applied to the links, and that air isnt a great link.... but when we refer to antisquat or anti dive, are we not refering to the behaviour of the vehicle, in percentage, rather than the force applied to a single link..

We're talking about the overall result of the linkage. The upward component of the pushing links minus the downward component of the pulling links.

uninformed wrote: you refer to text books using the instant center of the upper and lower links, but i cant see how this would work with the method Gillespie is using because IC's can be way out in front (for rear axle) way out behind (for front axle) or even a virtual IC of infinity if the lower links are parrallel when viewed from above...

An IC at infinity (either in front or behind, it makes no difference) means the links are parrallel. With this the angle the links are working at has prime importance.
If they're both parrallel and horizontal then there should be 0% antisquat/antidive.
But it's an artificial situation unless you've got rockhard springs.

uninformed wrote: here is another way to look at it: take 2 identical rigs lets say 37 inch tyres, 115 inch wheel base etc etc, now rig 1 has a front lower link length of 1000mm and its front axle roll axis is 0 degrees, the link is level at road height. Rig 2 has a lower link lenght of 1500mm and its front axle roll axis is 0 degrees, the link is level at road height. Everything except for the lower link lenghts are exactly the same on each vehicle, wont rig 2 handle bumps better/transfer less energy up the link into the chassis and more vertical wheel movement absorbing the impacts better????


but it will have less anti-dive under braking than rig 1....

Yes

uninformed wrote: so what im asking is can a rig can still achive a percentage of anti-dive for the front axle underbraking even if the lower link runs downhill from axle to chassis???

Serg

Yes, until the radius arm pivot or IC (simplification) ends up below ground level.

cheers Kiwibacon,

fitting lowered suspension brackets on a rasied vehilce will also reduce the front axle roll axis oversteer, and also have the same effect as longer lower links with regards to transferring forces up the link to the chassis.

wheel base will also change the anti-dive anti-squat... ie take landrover defender 90,110 and 130 all have exactly the same suspension set up... maybe only difference is rear axle roll center height as the 90 has a rover diff and the 110,130 has a p38 rover diff so ball MAYBE be a little different in height,.... but anyway all 3 run 235-85r16, the 90 will have the least amount of anit-suat and the 130 the most.....

once again its the ratio of wheelbase/COG height for anti-squat under acceleration and wheelbase/COG height/front to rear brake bais for anti-dive, anti-lift under braking....THIS IS VERY SIMPLIFIED.

Serg

ISBN 1-56091-199-9

got it form amazon.com they have loads and loads of books like this, most WAY over my head....

Serg

uninformed wrote:cheers Kiwibacon,

fitting lowered suspension brackets on a rasied vehilce will also reduce the front axle roll axis oversteer, and also have the same effect as longer lower links with regards to transferring forces up the link to the chassis.

wheel base will also change the anti-dive anti-squat... ie take landrover defender 90,110 and 130 all have exactly the same suspension set up... maybe only difference is rear axle roll center height as the 90 has a rover diff and the 110,130 has a p38 rover diff so ball MAYBE be a little different in height,.... but anyway all 3 run 235-85r16, the 90 will have the least amount of anit-suat and the 130 the most.....

once again its the ratio of wheelbase/COG height for anti-squat under acceleration and wheelbase/COG height/front to rear brake bais for anti-dive, anti-lift under braking....THIS IS VERY SIMPLIFIED.

Serg

Another little quirk from the way I was describing things. I was just talking about the vertical forces from the suspension, not the forces resulting from the COG rocking around above.
I.e. pivots at ground level give no squat/dive from the suspension geometry, but the front end will still compress freely (and rear extend) from the weight shift. The magnitude being a result of the COG height above ground, the wheelbase and the spring/damper rates.
It's really easy to generalise, from there it gets really complicated really quickly.

Thanks for the number, I'll chase it up later. Milliken is another revered one but I haven't read it.

uninformed wrote:... the axle casing wants to rotate in the opposite direction to the wheel in acceleration, therefore underbraking the axle casing will want to rotate back the same direction as wheel rotation? yes or no? ...

Yes

uninformed wrote:.... but when we refer to antisquat or anti dive, are we not refering to the behaviour of the vehicle, in percentage, rather than the force applied to a single link...

Expressing anti-squat and anti-dive as a percentage is a usual.

When a vehicle is stationary or traveling at constant speed the springs are at their static ride height.

During acceleration (or deceleration) there force resulting in the acceleration acts at the tyre contact with the road and is coupled with an equal and opposite reaction (inertia) at the centre of gravity.

Now to achieve equilibrium, extra vertical forces are added/subtracted to the static weight acting on the springs. This extra vertical force is called squat during forward acceleration (when the load on the rear springs increase and the load on the front springs reduces). During braking the load on the front springs increases and reduces at the rear springs.

The values of the extra forces at front and rear depends upon the wheelbase and height of the centre of gravity.

With some types of suspension it is possible and desirable to have the geometry of the suspension arranged so that the forces induced in the links during the acceleration (or deceleration) counteract the squat (or dive) force that would otherwise compress/extend the springs.

In the case of 100% anti-squat (or anti-dive), the vertical component of the forces in the links will exactly cancel the squat (or dive forces) and the spring height will be unchanged.

The anti- forces may be of any value and do not have to be 100%. They may be greater than 100%.

Note: these anti- forces are a result of the vertical component of forces in the links at the chassis mounts. There is nothing else that connects to the chassis which can exert the anti- forces.

During acceleration we are usually concerned with the rear suspension for anti-squat and disregard what happens at the front. During braking we look at the front and disregard the rear. This is because the links at those places transmit the greater forces - also if the front suspension has good anti-dive characteristics, it won't harm anti-squat and vice versa.

uninformed wrote:... the book im reading is "fundamentals of vehicle dynamics" by Thhomas D. Gillespie.

quote" therefore, to obtain 100% anti-dive on the front and 100% anti-lift on the rear, the PIVOT for the effective trailing arm must fall on the locus of points defined by these ratios" end quote

the equation uses spring rates, COG, wheelbase...

you refer to text books using the instant center of the upper and lower links, but i cant see how this would work with the method Gillespie is using because IC's can be way out in front (for rear axle) way out behind (for front axle) or even a virtual IC of infinity if the lower links are parrallel when viewed from above...

The instant centre is just another name for what Gillespie calls the pivot for the effective trailing arm.

What Gillespie has stated is correct.

uninformed wrote:...here is another way to look at it: take 2 identical rigs lets say 37 inch tyres, 115 inch wheel base etc etc, now rig 1 has a front lower link length of 1000mm and its front axle roll axis is 0 degrees, the link is level at road height. Rig 2 has a lower link lenght of 1500mm and its front axle roll axis is 0 degrees, the link is level at road height. Everything except for the lower link lenghts are exactly the same on each vehicle, wont rig 2 handle bumps better/transfer less energy up the link into the chassis and more vertical wheel movement absorbing the impacts better????...

Instant centre is called that because it's location is only fixed for a particular instance. It can change as the suspension geometry changes on bumps etc. (the exception is when the chassis mount for the upper and lower links is at the same position).

The change in the location of the instant centre will normally be greater with shorter links.

uninformed wrote:... but it will have less anti-dive under braking than rig 1....

so what im asking is can a rig can still achive a percentage of anti-dive for the front axle underbraking even if the lower link runs downhill from axle to chassis???

Serg

We are discussing link suspension not radius arms. A radius arm is not a link - by definition a link can only resist forces applied along the axis of the link.

Take a pole vaulter as a similar example. When the vaulter digs the far end of the pole into the ground the vertical component of the compression force in the pole lifts the vaulter into the air. If the pole vaulter caught the far end of the pole on something overhead while running with the pole in front, the pole would drive the vaulter to the ground (it could not possibly lift the vaulter over a high bar).

Back to the front link suspension. Under braking the lower link is in compression and the upper link is in tension. Also the force in the lower links is much higher than the force in the upper links.

So it is possible that the lower link could be angled slightly down, so that it exerts only a small vertical down force on the chassis. And angle the upper link steeply down so that it exerts a higher vertical up force on the chassis. But this geometry will be impractical because of other affects (like rotating the pinion of the diff down and causing binding of the u-joints).

Bush65 wrote:For anti-squat or anti-dive, the lower link will be in compression and the upper link in tension (assuming rear during acceleration).

There is a horizontal force at the tyre contact with road. This force goes to the chassis through the lower link. The horizontal force at the chassis mount must equal the horizontal force at the tyre contact.

Now, because the link is angled up toward the chassis, it is also produces a vertical up force at the chassis mount - it applies lift to the chassis as well as horizontal push. The compression in the link is equal to the horizontal force between the tyre and road divided by the cosine of the angle between the road and the link. The vertical force is the horizontal force times the tangent of the link angle.

The upper link has to prevent the axle housing from rotating, and this is where the lever principle comes into determining the force in the upper link. When looking from one side, imagine there is a lever with a fulcrum (pivot) at the point where the lower link attaches to the axle housing, one end where the tyre contacts the road and the other end where the upper link attaches to the axle housing.

From this lever, the tension in the upper link can be determined. Now if the upper link is angled up toward the chassis it will apply a vertical down force as well as a horizontal force at the chassis mount.

Subtract the vertical down force from the upper link from the vertical up force from the lower link will give the anti-dive force.

Now the graphical methods given in text books for percentage of anti-squat (or anti-dive) take into account the position (height and horizontal) of the centre of gravity. They use the position of the instant centre of the lower and upper links because it is easier for the graphical method because it simplifies resolving the combined forces in the upper and lower links.

But forces can not be transferred through air along an imaginary line angled from the tyre contact patch. They can only be transferred in the links. These other lines are simply a graphical method of solving the trigonometry of the link forces and the transfer of inertia through the centre of gravity.

The way you have worked out the link forces here isnt correct. To work out the compression in the lower link you have to do the " lever with a fulcrum " thing... a big vertical seperation of the links at the diff produces less lower link compression than a small vertical seperation of the links at the diff ...so you have to consider the link seperation to determine the lower link force. Is not just a case of "The compression in the link is equal to the horizontal force between the tyre and road divided by the cosine of the angle between the road and the link". Of course you have to take into account of the angles as well so there will still be a few cosines in there.

Sam

Bush65 wrote:
So it is possible that the lower link could be angled slightly down, so that it exerts only a small vertical down force on the chassis. And angle the upper link steeply down so that it exerts a higher vertical up force on the chassis. But this geometry will be impractical because of other affects (like rotating the pinion of the diff down and causing binding of the u-joints).

Isnt this how radius arms work??? A single radius arm is essenciantly two conventional links with verticle seperation at the diff and zero seperation at the chassis. A radius arm works quiet well even when it angles down to the chassis...it actually doesent matter how or where it angles...its only the chassis mount that counts in terms of suspension dynamics.

Sam