Linked Suspensions Bible

[AgitatedPancake]

Haha you're not obligated to do anything at all, so everything you share is appreciated! Just the fact that we seem to be on the same page helps affirm that I'm not interpreting things incorrectly. I kinda want to design something with this configuration now

 

[Treefrog]

I am finding that the ability to tune this type of setup means that just because it may not change much in one setup, does not mean it does in another almost identical setup. And that's without using and abusing axle movement and rotation.

Regarding the lines not looking perpendicular, it is visual. I checked arm length throughout travel and plotted a circle over it to double check.

I may not be obligated, but curiosity is a strong motivator.

I get the feeling I may be adding this into a 4-link calculator at some point. And maybe to a test version of it much sooner.

This concept has put two thoughts in my head. First is ditching the slider stop and increasing wheel rate purely through geometric means. And second, a possible workaround for hard to package leading arm front suspensions.

Image time.

 

[Treefrog]

I can't help but wonder what sort of fun can be had with angling the line of pivot. And having a different mounting widths on the axle for the links and the shocks.

 

[Treefrog]

Working on generating some other plots and graphics and generated this while I was at it. It shows the volume used by the suspension components through travel. The rear is trailing arm, front is 3-link with axle mounted shocks. Showing driveshaft space as well. Rear is low pinion, centered. Front is high pinion, offset. Track bar is see through to not block stuff. Trailing arm shocks are below the link and it solves them to be as extended as possible for a given travel. General shape matters more than exacts.

 

[Treefrog]

For a while now something has been bothering me. When we run numbers through the standard 4-link calc, all that matters from a numbers standpoint is 4 lines (2 upper, 2 lower) going side to side and two points where we want the links to intersect. As long as the links start and end on the lines and go through the points, they will report the same output curves. So the difference between them must be in 3d. Obviously, the convergence angle changes. The recommended minimum of 40 degrees is ignored for this discussion.

First up is the 4 suspension setups. Full width, half width uppers, half width lowers, and all at half width. To get the half width locations, the Y values at both ends of the links are multiplied by 0.5. The values used is the front suspension that is the default entry in the 4 link calc.

Hope no one is colorblind.

First up is a gif showing the 4 suspensions. The image is the values that would be returned by the normal 4-link calc. Notice they are identical.

The two values we can look at with ease are the anti's and axle steering during articulation. Next two images show these. As usual, trends matter over values. These plots were created using wheel travel as the solving condition.

It may be a bit hard to see, but not only is the high and low points of the anti are changing, but so is the % anti. It should be noted that all anti's are done with 100% bias to the axle and no splitting of traction to the wheels is occurring.

It is inversly mirrored along the equal travel line. Though it is not visible, the max and min values are changing slightly, a few hundredths of a degree. I had thought there was more difference between them when I had started generating these plots. The simulated suspension has pretty long links. While typing this up, I ran it again with about 10 inch shorter links, the plots showed higher amounts of steering, but did not appear to show any change in behavior. From having played around with the 3d solver while working on it, I think that having less flat links will change where flex steer concentrates.


While looking at articulation, we can narrow down to just the full width suspension and take a closer look at what is going on with some things. These were solved based on shock length. First thing to look at is what wheel travel is doing as the shocks are cycled.

Color bar is probably useless here, but oh well. It should be noted that the sides are not straight, there is some curve to them.


The other thing we can look at is the driveshaft lengths and U-joint angles. Front and rear are looked at. Rear is low pinion, centered. Front is high pinion, offset. The bottom row is the rear. I missed changing the names when copy pasting and I am not rerunning it to regenerate the high resolution data. I don't feel like waiting another 4+ hours.

Interesting but not surprising that the centered rear pinion has the most extreme lengths at equal travel. Similar for the offset front, it has heavy influence from travel of the closer wheel. U-joint angles were slightly more surprising, but make sense in retrospect. Closer the pinion is to the wheel, the less it moves with the opposite wheel.

If any one wants me to investigate what happens to a certain aspect between these 4 suspensions that I didn't cover, just ask. I do have some more plots I want to generate. I want to look at what happens when you mess up fabricating and a mount ends up in the wrong spot. I know from running some tests while developing the 3d solver that it predictable changes the antis, flex steer, etc. some.

 

[Treefrog]

Two more plots. In these, the lower axle negative y mount is moved .5 inches closer to the center than the positive y lower axle mount. The two plots show the difference in antis and wheel travel. These plots were generated solving for the shocks. The base suspension is the full width from the previous post. If the difference is greater than 0, it means that the positive side value is greater. Usual disclaimer about looking at trends and not hard values.

 

[Treefrog]

Generated another plot this morning. Wanted to look at lateral forces on the links vs convergence angle split. Equation used is:

2*sin(upper angle / 2) + 2*sin(lower angle / 2)​

The math works out that equal upper and lower angles is the maximum forces for a given total convergence angle.

 

[Treefrog]

Guess the easiest way to understand why you want certain AS numbers is to fully understand What AS is/does.

2wd explanation here. When you hit the gas, there is a torque moment that acts on the axle housing at the same time there is a longitudinal load transfer of weight to the rear. ( I would love to discuss which happens first) If your geometry is setup for 100%AS, 100% of that longitudinal weight transfer will be held through the links. The shocks will not have compressed at all. The suspension still work, it's not locked up solid, it is still free to move and absorb bumps. The links are just holding the amount of weight that transferred to the rear wanted to squat the ass end.

Now if you go above 100%AS, say to 125%. When you hit the gas in the same rig with the same amount of longitudinal weight transfer, the links will be trying to hold 25% more weight than is being transferred to the rear and the rear end will lift.

At 50%AS, your links are holding 50% of the Longitudinal load transfer. So if you had zero% AS and the rear squats 5", at 50% the squat would only be 2.5".


Where it gets fuzzy for me is while the suspension can still move while the links are holding X amount of load, there's still a fuck ton of force loaded in the links.

This seems like a fun discussion. Hope you don't mind me moving it to this thread. I don't want to derail a build thread.

I think that the load transfer is instantaneous with the engine torque. The suspension moving and the engine not going to max torque instantly, means it takes a moment for the vehicle to feel like it transferred load.

As a complete side note, I wonder how much perceived transfer load there would be for something with 100% AS or greater.

The relationship between link loading and how easy it is for the suspension to move has been unclear. I wonder if it has something to to with the line from the tire contact to the IC that the force is said to be applied along. Or maybe something about the torque the links create about the chassis.

 

[gt1guy]

I don't mind at all. It's very interesting to me. There was a long thread on it back in the days of Corner-Carvers.

The jest of the question came down to this....What happens first? The longitudinal transfer of load or the loading of the links through a torque input? Does the AS% increase as the torque input increases? With 100%AS, does the rear lift until the full lateral load transfer has taken place?

It come down to a reaction to a reaction ..... but what is the instigator? If you take off from a dead stop really slow.....nothing happens.

 

[Treefrog]

I don't mind at all. It's very interesting to me. There was a long thread on it back in the days of Corner-Carvers.

The jest of the question came down to this....What happens first? The longitudinal transfer of load or the loading of the links through a torque input?

I think both happen at the same time and are caused by the vehicle accelerating.

Does the AS% increase as the torque input increases?

I don't think so. There is a curve of AS vs travel. I think AS changes with. Assuming rwd for simplicity.

With 100%AS, does the rear lift until the full lateral load transfer has taken place?

By definition, 100% AS means no lift or squat.

It come down to a reaction to a reaction ..... but what is the instigator?

Driveshaft torque-> wheel torque -> acceleration -> load transfer and link loading

If you take off from a dead stop really slow.....nothing happens.

But it does. It just isn't noticable.

 

[gt1guy]

Now set up the geometry for 150%AS and take of from a dead stop really slow. What happens?

 

[Treefrog]

Now set up the geometry for 150%AS and take of from a dead stop really slow. What happens?

Imaging that there is no shock seal friction, it should lift up, very slightly.

 

[93blackxj]

Also have to realize there are 2 components to the AS and load in the links. The axle moment from engine torque as well as the lateral forces created in the links from the axle accelerating/pushing the body forward.

Driveshaft torque-> wheel torque -> acceleration -> load transfer and link loading

To me, there is no weight transfer without acceleration and no acceleration of the center of mass without link loading. So I see it more as Driveshaft torque > wheel torque > link loading > acceleration > load transfer. But I think your "acceleration" is more referring to the axle from the wheel torque which I understand.

But I think this all happens so fast that its all virtually simultaneous and cant really say that one or the other happens first.

I think both happen at the same time and are caused by the vehicle accelerating

This one I might can agree with but will take some convincing. Yes the weight transfer is caused by acceleration, but link loading from torque input caused by vehicle acceleration seems debatable. On one side, I say acceleration of the vehicle cant happen without link loading. If we are talking about axle acceleration I could agree. But if you want to get technical, link loading comes from the torque reaction due to friction. No friction, no reaction, no link loading, and no acceleration. So I guess I could see where you come from with that statement.

But then that also opens another can of worms and I think about a steep ledge or climb. You can be spinning tires with no forward acceleration and there would still be forces in the links from torque input. But you could also say there is still a component of acceleration now due to gravity since you are on an incline. Statement invalid haha.

 

[Treefrog]

Also have to realize there are 2 components to the AS and load in the links. The axle moment from engine torque as well as the lateral forces created in the links from the axle accelerating/pushing the body forward.

Combining the torque reaction and the pushing link forces is what makes suspensions hard to fully analyze. I'm trying to convince myself that I don't need to write a force based analyser.

To me, there is no weight transfer without acceleration and no acceleration of the center of mass without link loading. So I see it more as Driveshaft torque > wheel torque > link loading > acceleration > load transfer. But I think your "acceleration" is more referring to the axle from the wheel torque which I understand.

You've got me thinking about it and reconsidering. Though I think driveshaft torque and wheel torque are simultaneous. And link loading and acceleration are simultaneous.

But I think this all happens so fast that its all virtually simultaneous and cant really say that one or the other happens first.


This one I might can agree with but will take some convincing. Yes the weight transfer is caused by acceleration, but link loading from torque input caused by vehicle acceleration seems debatable. On one side, I say acceleration of the vehicle cant happen without link loading. If we are talking about axle acceleration I could agree. But if you want to get technical, link loading comes from the torque reaction due to friction. No friction, no reaction, no link loading, and no acceleration. So I guess I could see where you come from with that statement.

Imagine pushing a two blocks with a spring between them. You push the first block. Once you've overcome friction, it starts to move, loading the spring(links). Once the force on the spring overcomes the second blocks friction it starts to move. Now add a second spring weaker than the first so they are side by side from above. When you push, the second block will rotate some as it moves.

But then that also opens another can of worms and I think about a steep ledge or climb. You can be spinning tires with no forward acceleration and there would still be forces in the links from torque input. But you could also say there is still a component of acceleration now due to gravity since you are on an incline. Statement invalid haha.

Climbs are another can of worms. Just because you are not accelerating or moving doesn't mean no force. It just means there's an equal and opposite force. Same as going down the road.

 

[gt1guy]

Now set up the geometry for 150%AS and take off from a dead stop really slow. What happens?

Imaging that there is no shock seal friction, it should lift up, very slightly.

Ok. Now we have two vehicles that are exactly the same. Both have the 150%AS geometry. Both start moving from a dead stop slowly. Both do this at 1000RPM. One vehicle puts out 7.5 lb/ft of torque @1000rpm, while the other puts out 500lb/ft of torque at that same 1000rpm.

Now we have a large delta in torque input loading, but no difference in the speed (or timing) of it happening. And by beginning to move slowly there's an almost immeasurable amount of longitudinal load transfer

How do the two vehicles react?

Personally, I think they would react exactly the same. I don't think either one would do anything until a rearward longitudinal load transfer began to take place. In other words, without a load transfer there is no AS.

 

[Treefrog]

Ok. Now we have two vehicles that are exactly the same. Both have the 150%AS geometry. Both start moving from a dead stop slowly. Both do this at 1000RPM. One vehicle puts out 7.5 lb/ft of torque @1000rpm, while the other puts out 500lb/ft of torque at that same 1000rpm.

Now we have a large delta in torque input loading, but no difference in the speed (or timing) of it happening. And by beginning to move slowly there's an almost immeasurable amount of longitudinal load transfer

How do the two vehicles react?

Personally, I think they would react exactly the same. I don't think either one would do anything until a rearward longitudinal load transfer began to take place.

So If I am reading this right, two vehicles steady state rolling at 1000 rpm at the engine. One keeps going unchanged or applies a little throttle and the other guns it.

Or is one vehicle putting out more torque to go the same speed?

If it is the first one, the 500 truck would lift more.

If the second one, it should be lifting more as well.

In other words, without a load transfer there is no AS.

I am beginning to wonder if squatting is not acceleration based but force based.

 

[gt1guy]

So If I am reading this right, two vehicles steady state rolling at 1000 rpm at the engine. One keeps going unchanged or applies a little throttle and the other guns it.

Or is one vehicle putting out more torque to go the same speed?

If it is the first one, the 500 truck would lift more.

If the second one, it should be lifting more as well.

I am beginning to wonder if squatting is not acceleration based but force based.

I guess I did word that a bit goofy.

Both vehicles begin from zero mph, then they both slowly begin to move forward up to 2 mph in 10 minutes (just made up numbers). So they are both side by side at all times. They both have to run at 1000rpm to achieve the 2 mph in 10 minutes. Only difference is the amount of torque each engine puts out at the 1000rpm.

The 2mph in 10 minutes is just to all but eliminate lateral load transfer. But we know math can still give us a number..........so we'll make the road slop slightly down hill to zero out the math.

So again, I think they would react exactly the same. I don't think either one would do anything until a rearward longitudinal load transfer began to take place. In other words, without a load transfer there is no AS.

Since a lot of 4 linked drag cars run really high AS %'s...................Do we see the rear end lift way up when they start a burnout? I understand that the tires themselves will grow as they spin faster, but we can ignore that part of it.
It's doing everything a drag car does during a run.............except moving, which means no load is being transferred to the rear. And yet the rear of the car just sits there with a 4 link that very well could be setup with 100+%AS.

 

[Treefrog]

I guess I did word that a bit goofy.

Both vehicles begin from zero mph, then they both slowly begin to move forward up to 2 mph in 10 minutes (just made up numbers). So they are both side by side at all times. They both have to run at 1000rpm to achieve the 2 mph in 10 minutes. Only difference is the amount of torque each engine puts out at the 1000rpm.

The 2mph in 10 minutes is just to all but eliminate lateral load transfer. But we know math can still give us a number..........so we'll make the road slop slightly down hill to zero out the math.

So again, I think they would react exactly the same. I don't think either one would do anything until a rearward longitudinal load transfer began to take place. In other words, without a load transfer there is no AS.

Would you mind clarifying what you mean by react? As long as they have reached steady state at 2 mph, the time to accelerate shouldn't matter.

Since a lot of 4 linked drag cars run really high AS %'s...................Do we see the rear end lift way up when they start a burnout? I understand that the tires themselves will grow as they spin faster, but we can ignore that part of it.
It's doing everything a drag car does during a run.............except moving, which means no load is being transferred to the rear. And yet the rear of the car just sits there with a 4 link that very well could be setup with 100+%AS.

I think they do lift. See cars at 15s and 1:39. The amount of squat or lift is related to the torque that is being put down. Once the tires break free, there isn't as much torque.

I am beginning to think that anti squat is just an easy geometric way to do quick predictions of what to expect and that load transfer is part of that and in effect is imaginary. Kind of like roll centers. Whether the vehicle lifts or squats is based on the forces in the links and not load transfer.

 

[arse_sidewards]

I guess I did word that a bit goofy.

Both vehicles begin from zero mph, then they both slowly begin to move forward up to 2 mph in 10 minutes (just made up numbers). So they are both side by side at all times. They both have to run at 1000rpm to achieve the 2 mph in 10 minutes. Only difference is the amount of torque each engine puts out at the 1000rpm.

The 2mph in 10 minutes is just to all but eliminate lateral load transfer. But we know math can still give us a number..........so we'll make the road slop slightly down hill to zero out the math.

I think you've over-constrained the comparison.

Think of it in terms of input torque at the pinion. If the vehicles are identical other than engine torque and suspension geometry and they are accelerating identically then the forces at the pinion input must be the same.

The wet fart engine and the bajillion horse torks engine are both applying the same load to the drive train because the vehicles and conditions are otherwise equivalent.

If the bajillion horse torks engine was actually wide open and supplying full torque and still only accelerating as fast as the vehicle with the wet fart engine then the resistance to increased acceleration would be coming from somewhere other than the vehicle and drive-train (in practice this usually is rotating assembly inertia).

 

[93blackxj]

So again, I think they would react exactly the same. I don't think either one would do anything until a rearward longitudinal load transfer began to take place. In other words, without a load transfer there is no AS.

I would have to disagree. Watch a high horse power car on a dyno. Depending on AS value and location of IC the rear end will squat or separate. Watch a high horse power rock bouncer on the dyno in 2wd and a lot of times the front will even raise up from the moment being applied to the chassis from the links. There is no lateral acceleration and no weight transfer but the suspension still moves.

I do see where you are coming from but I dont think you can go as far as saying there is no AS without load transfer. I think it could be something a long the lines of how I mentioned there are 2 components of anti squat. Torque based anti squat and force based anti squat. And maybe without acceleration there is no force based anti squat and only torque based anti squat.

 

[93blackxj]

I think they do lift. See cars at 15s and 1:39. The amount of squat or lift is related to the torque that is being put down. Once the tires break free, there isn't as much torque.

Agreed, they do not lift like they would going down the track because they are not transferring the amount of torque/power to the ground in a burn out as they are in a pass. The amount of force in the links depends on torque applied. More torque applied means higher acceleration and higher loads in the links.

I am beginning to think that anti squat is just an easy geometric way to do quick predictions of what to expect and that load transfer is part of that and in effect is imaginary. Kind of like roll centers. Whether the vehicle lifts or squats is based on the forces in the links and not load transfer.

Im with you, anti squat is just a method that has been established to some what predict what the suspension is going to do in a flat ground perfect situation.

 

[gt1guy]

Agreed, they do not lift like they would going down the track because they are not transferring the amount of torque/power to the ground in a burn out as they are in a pass. The amount of force in the links depends on torque applied. More torque applied means higher acceleration and higher loads in the links.




Im with you, anti squat is just a method that has been established to some what predict what the suspension is going to do in a flat ground perfect situation.

That's engine torque twisting the chassis. Notice how one side raises more than the other. The rear never raised.

Would you mind clarifying what you mean by react? As long as they have reached steady state at 2 mph, the time to accelerate shouldn't matter.

I think they do lift. See cars at 15s and 1:39. The amount of squat or lift is related to the torque that is being put down. Once the tires break free, there isn't as much torque.

I am beginning to think that anti squat is just an easy geometric way to do quick predictions of what to expect and that load transfer is part of that and in effect is imaginary. Kind of like roll centers. Whether the vehicle lifts or squats is based on the forces in the links and not load transfer.

React = The action through the axle and links to whatever the AS geometry is setup to. As in if the drag racer dumps the clutch on a run in anger, the AS reacts to the rearward longitudinal load transfer.

2:14 in the vid you posted, the car actually shifts during the burnout. All you see is a little bump where the tires speed up. I think the best example of what I'm getting at is at 3:23. Perfect camera angle. Shifts during the burnout and them makes his run. So you can see both ways the same suspension reacts with and without load transfer.

Load transfer is very real, there's no way to get away from it. It's real when accelerating, braking and cornering.

Anti Squat geometry is also very real........we can see the effects of it's existence.

My opinion is that there has to be a load transfer before there can be an AS reaction. The load transfer is the primer and AS is the powder so to speak.

I think you've over-constrained the comparison.

Think of it in terms of input torque at the pinion. If the vehicles are identical other than engine torque and suspension geometry and they are accelerating identically then the forces at the pinion input must be the same.

The wet fart engine and the bajillion horse torks engine are both applying the same load to the drive train because the vehicles and conditions are otherwise equivalent.

If the bajillion horse torks engine was actually wide open and supplying full torque and still only accelerating as fast as the vehicle with the wet fart engine then the resistance to increased acceleration would be coming from somewhere other than the vehicle and drive-train (in practice this usually is rotating assembly inertia).

I think you're right my example has a flaw. The high torque vehicle would have to leave a lot of "potential" energy on the table to remain even with low torque vehicle.

Good catch

 

[gt1guy]

I do see where you are coming from but I dont think you can go as far as saying there is no AS without load transfer. I think it could be something a long the lines of how I mentioned there are 2 components of anti squat. Torque based anti squat and force based anti squat. And maybe without acceleration there is no force based anti squat and only torque based anti squat.

Some how I missed this earlier. Definitely an interesting concept.

Would you not need to know the max (engine/driveshaft/whatever) torque available as the input?

 

[gt1guy]

Just thought I'd add this to the thread. Don't know how many of you have heard of Mark Ortiz, But he used to write a column in Racecar Engineering every month called "The Consultant".


This is from 2015


I wrote Mark Ortiz a while back with some questions about designing a link front suspension on my Jeep. For those who have never heard of him, he runs a chassis consulting service, has a monthly column in Racecar Engineering and puts out the monthly Chassis Newsletter. This months news letter is on the questions I had, so I thought I'd share. The bolded part in quotes is my questions to Mark.

July 2015

From me

I was wondering if you could shed some light on designing a 4-link suspension for the front of a 4 wheel drive vehicle? Vehicle in question is a new style 4 door Jeep JK. I'm designing a custom long arm 4-link front and rear.

The stock geometry is four longitudinal links and a Panhard bar. What I'm doing is a double triangulated with no Panhard bar. Uppers converging at the axle and the lowers converging at the crossmember for the trans. Steering will be full hydro w/double ended ram. No mechanical steering box or drag link (so no bump steer). Coilover shocks mounted outboard on the axles.

I will be running this set up front and rear (rear, minus the steering of course). It's actually a pretty standard design in the 4x4/rock crawling world.

As I said, I'm kind of at a loss as to how the front reacts to the forces.

I've attached the Excel 4link calculator with my design on it.

Main question has to do with anti-squat. On acceleration there is weight transfer off the front end, so would designed in A/S actually end up being pro-lift? I'm thinking it would only act as A/S during braking. I'm kind of at a loss as to how to look at things with regards to the front end.

There is a large offroad community that would be very interested in your thoughts on this.

This was Marks response

I am a relative newcomer to offroad chassis. I haven’t had clients in offroad motorsports. However, I have new neighbors here at the shop who do quite a bit of fabrication for offroad vehicles and also run offroad vehicles of their own. I find the whole field very interesting, but I should emphasize that I’m still in the steep part of my own learning curve and my thinking is still rapidly evolving.

I have at least gotten wise to this: there is a huge diversity of “offroad” vehicles and activities. If anything, there is considerably more variety than there is “on road”. And there isn’t any single set of desired properties for an offroad suspension system, any more than there is a single set of desired properties for all vehicles operating on pavement.

Returning to the original question, how do we understand longitudinal “anti” effects in a vehicle where all four wheels are driven, especially at the front, and what properties do we want in this regard? Taking the last part of this first, there is not a single answer for all applications. It depends on what we’re doing with the vehicle.

Usually, we do not speak of anti-squat when referring to the front wheels. Anti-squat means a tendency of the rear suspension to jack up under power, countering the tendency for the rear suspension to compress due to rearward load transfer. The corresponding property at the front is anti-lift: a tendency to jack down under power, countering the tendency for the suspension to extend. Under braking, we can have anti-lift at the rear. The corresponding upward jacking tendency in braking at the front is called anti-dive. All of these can be considered forms of anti-pitch.

Negative anti-lift is pro-lift; negative anti-dive is pro-dive – and so on.

100% anti-squat is the amount of anti-squat that will make the rear suspension neither extend nor compress in forward acceleration. That doesn’t mean the car won’t pitch. It just means it will pitch entirely by rising at the front; the rear won’t go down.

For front wheel drive, 100% anti-lift is the amount that will cause the front suspension to neither extend nor compress in forward acceleration. Again, the car will still pitch, but it will pitch entirely by squatting at the rear; the front won’t come up.

Likewise, in braking 100% anti-dive or anti-lift is the amount that will result in zero displacement at the end in question when braking.

Although linguistic evolution has given us four different terms for these effects, they are all fundamentally the same thing: jacking effects resulting from longitudinal ground plane forces.

In all cases, including also jacking resulting from lateral ground plane forces, jacking force equals ground plane force times jacking coefficient. Referring to the graphic in the main page of the attached spreadsheet from the questioner, the jacking coefficient corresponds to the slope of the force line, the green line lowermost in the frame. The slope of this line equates to the ratio between jacking force induced by the suspension linkage and the ground plane force applied to the system.

The slope of this line is also the inverse of the instantaneous slope of the path that the contact patch center follows as the suspension moves, when the wheel is locked in a manner appropriate to the situation being considered (i.e. braking or propulsion). In the case shown in the spreadsheet, the force line has about a 1 in 4 slope. This means that for every pound of longitudinal ground plane force, the suspension induces a jacking force of about a quarter of a pound. In this case, when the force is forward (propulsion), the jacking force is downward (anti-lift).

The spreadsheet is evidently designed with rear wheel drive in mind. The 100% anti-squat line shown is correct, assuming that the other wheel pair doesn’t contribute to propulsion. In that situation, 100% anti (in this case anti-lift) happens when the force line intercepts the opposite axle plane at sprung mass c.g. height (light blue horizontal line). In that situation, it is also impossible to get any jacking effect at the opposite axle at all, because there is no ground plane force there.

That of course is not the case with four wheel drive, except maybe if drive to the rear is disabled. When both front and rear wheels contribute longitudinal force, as in braking with most vehicles and with all wheels driven, we need a steeper force line slope to get 100% anti at a given axle. However, we can get jacking forces at both axles.

The procedure when solving graphically is to lay in what I call a resolution line at a location corresponding to the ground plane force distribution between the two axles, and compare the heights of the intercepts of the front and rear force lines and that resolution line to the height of the sprung mass c.g. If, for example, the front wheels make 60% of the ground plane force, the resolution line is 60% of the wheelbase from the front axle. If the front wheels make all the ground plane force, as in the spreadsheet, the resolution line is 100% of the wheelbase from the front axle, as shown.

If the vehicle has a center differential, we have a known ground plane force distribution, at least until some locking is imposed on the center differential. However, when we have a locked transfer case, we do not have a known torque distribution. We have a 1:1 driveshaft speed distribution, and a highly variable torque distribution and ground plane force distribution.

If the vehicle is running straight and there is similar traction at both ends, we will have close to 50/50 ground plane force distribution. However, if one end has more traction than the other, there will be more torque to that axle and more ground plane force from that wheel pair. When traction is good at both ends and the vehicle is turning, often the torques and ground plane forces are not only unequal but opposite in direction. The front wheels will follow a longer path and consequently need to turn faster than the rears, but be unable to. The rear wheels will then drive and the front wheels will drag. There will be reverse torque on the front drive shaft and extra torque on the rear drive shaft to counter that. The ground will exert rearward force on the front contact patches and forward force on the rear contact patches. In the questioner’s vehicle, the front will try to lift under these conditions. When it’s propelling the vehicle, its jacking forces will try to hold it down instead.

So there’s considerable uncertainty about what the induced jacking forces are going to be, because of the extreme variability of the ground plane force distribution. Do we at least know what we want the jacking forces to be?

Sort of, but that varies with what we’re doing with the vehicle. For an application such as offroad racing or Global Rallycross, we want the jacking forces to fight pitch, but not too much. If we get too greedy with our antis, we will get wheel hop on pavement or other high-traction surfaces.

For mud, things are different. There, we want both ends to jack up under power, vigorously. Why? Because when we’re stuck, sometimes the momentary tire load increase when we goose the throttle and the suspension pushes up against the frame will get us moving. It doesn’t always work, but in a useful percentage of cases it will.

And for crawling? I’m not sure it matters a whole lot, since the speeds and accelerations are so modest. I think probably the most important thing for a crawling suspension is to have huge travel, and a combination of stiffness in roll and softness in warp.

 

[Treefrog]

Some how I missed this earlier. Definitely an interesting concept.

Would you not need to know the max (engine/driveshaft/whatever) torque available as the input?

I don't think so. For roll, yes. But for antis, the torque on the wheel is equal and opposite to the torque on the axle housing. So if we assume 1g acceleration, and know tire size, we get the forces and torques on the axle housing. We can use that to get forces on the links. Which gives us an acceleration and pitching torque on the chassis.

 

[gt1guy]

I don't think so. For roll, yes. But for antis, the torque on the wheel is equal and opposite to the torque on the axle housing. So if we assume 1g acceleration, and know tire size, we get the forces and torques on the axle housing. We can use that to get forces on the links. Which gives us an acceleration and pitching torque on the chassis.

I forgot we can change the acceleration (G's). Which along with the weight, you CAN math out the torque output.

So wouldn't that kind of be a "yes" even though you don't have to have that number in front of you?

 

[Treefrog]

I forgot we can change the acceleration (G's). Which along with the weight, you CAN math out the torque output.

So wouldn't that kind of be a "yes" even though you don't have to have that number in front of you?

Maybe yes? Using G's bypasses needing the gear ratio to get driveshaft torque.

 

[gt1guy]

Maybe yes? Using G's bypasses needing the gear ratio to get driveshaft torque.

Agreed G's bypasses needing a lot of other information. I guess my point was that IF you wanted to, you could work backwards to get the actual torque output of the engine/drive shaft/R&P.

Kind of like if you punched in 3G's acceleration, you better not be running a 4cyl engine missing one plug wire. If you did that all your results will be wrong.

So because G's bypass a lot of important info, it now becomes very important to be accurate.


Side note:
At 1G (or a little above it, don't remember) of lateral load transfer going around a corner, the oil will be up on the sides of the oil pan and you better be running a dry sump system.

 

[Treefrog]

I was trying to argue with myself that I didn't need to make a force based suspension calculator. I did not win. For simplicity, steady state acceleration, no body roll, rwd and shock is vertical through the axle centerline. The results were not what I expected.

I believe that 0 torque about the sprung CG would be no squating. Force increase to the ground during steady acceleration is the same as the link vertical force at the chassis and the increase in spring force to counter the chassis torque.

I'm still not entirely sure how this all relates to suspension stiffness from loading.

 

[Treefrog]

Agreed G's bypasses needing a lot of other information. I guess my point was that IF you wanted to, you could work backwards to get the actual torque output of the engine/drive shaft/R&P.

Kind of like if you punched in 3G's acceleration, you better not be running a 4cyl engine missing one plug wire. If you did that all your results will be wrong.

So because G's bypass a lot of important info, it now becomes very important to be accurate.

The reason I like G's is it ignores stuff like motor capabilities and gear strength and allows for more arbitrary discussion.

Side note:
At 1G (or a little above it, don't remember) of lateral load transfer going around a corner, the oil will be up on the sides of the oil pan and you better be running a dry sump system.

1G lateral load is the same as a 45 degree side slope at 1.4g.