Understand Rear Axle Forces in Car Suspensions w/ Instant Center Plot

[Tom Rauji]

I have no experience in tuning a suspension for drag race cars, but I'll give my opinion anyway.

How I explain this is as follow:

You rear end lifts up because it has more than 100% anti-squat. By tightening the rebound on your shocks, you slowed down the process. But the front end stayed the same and lift the same way, at the same pace. So, this must lead to a backward rake of the body (compared to the original setting), thus increasing the angle $\theta$. This leads to more anti-squat -> higher rear lift (the shocks slow down the process but they don't change the end effect) -> higher $cg$ -> higher weight transfer -> front wheel goes off the ground.

It's easy to get this confused.

The rebound is the collapse. The extension is the hit when in separation. I left the extension at my normal levels that are on the edge of distorting the sidewall. I only adjusted the rebound to control the upward tire bounce. This would keep the back higher longer, not lower. This is "normal" group opinion when running a real stiff sidewall tire like a radial tire. The shock manufacturer who made the radial valved shocks suggested half on extension and near full on rebound.

I would bet that if you tighten the front shock rebound as well, it would slow down the front lift too and once in synch with the rear, the body rake would stay as it was originally while the entire car lifts (the process would only be slower).

I didn't have dual adjustable on the front, but the fronts were set slow. This adds the front tire and suspension weight and whatever little bit the inertia helps to slow down rise. It really won't do much after one second or so because by then it has extended to the front travel limiters and all the weight is just hanging there solid.It hangs the weight there for about 200 feet (under 3 seconds) until the front settles and the tires start kissing the track..

I heard this reasoning of raising the rear end to «plant the tire». What people think it does is that the moment caused by the thrust force ($Th$) is «adding» a force to the ground. It does not. It cannot do that. The only thing it can do is create motion for the frame, i.e. raising it. The normal force ($N$) is only influenced by the weight and weight distribution of the car and the weight transfer. In any case, it will never exceed the total weight of the car (when the front wheels are off the ground, and only in that case).

I have not quantified this, I hate facts without numbers, but getting a number is on my bucket list. Certainly there is some amount of inertia involved in this that will help hit the tire. I'll post a slow mo video of an earlier launch while I was setting up bar positions.

The «added» force can only come from the fact that the $cg$ height is increased with a higher rear end, thus increasing the weight transfer.

There is a lot of initial slap there before the body can lift.

It's like using softer front springs to «plant the rear tires». Most people think it releases some extra energy that magically transfer to the rear end. It does not. The only thing it does is lifting your front end higher as the weight transfer begins and thus it raises the $cg$ height more than with stiff springs, leading to more weight transfer.

I hear that, too.

Of course it does not store more energy. The car weighs what it weighs. What it did in my old cars from the 1960s-1980's was increase the extension distance where the spring was contributing and allowing lift. Now I have the opposite problem. I want to keep the front down after a few hundred feet so I can still steer. Noty steering at 100 MPH can be bad, as can air getting under the car.

 

[jack action]

The rebound is the collapse. The extension is the hit when in separation.

I've always seen 'rebound' as what you call 'extension' (which I never heard). The opposite - what you also call 'collapse' - has many names though, such as 'bump', 'compression' or 'jounce':

But I still have a theory to explain the phenomena even with stiffening up the compression instead of the extension! Before, your rear end collapsed rapidly under the weight transfer. By stiffening up the shock, the process doesn't go as fast and the $cg$ remains high longer, therefore permitting more weight transfer.

There is a lot of initial slap there before the body can lift.

As soon as there is thrust, there is weight transfer. It is instantaneous, it is proportional. The fact that the body lifts, depends only on the suspension design. A car with no suspension still has weight transfer, even though the body - obviously - doesn't move in any way. In your video, it's probably the difference in air pressure between front and rear that throws you off. The softer rear tires squish a lot more under load than the stiffer front tire expand under the same load difference.

With the live axle, there is also the load transfer from side-to-side to consider. The following video demonstrate the phenomena:

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This car has no torsion resistance in the rear which leads to extreme torsion of the body. But even with a stiff torsional resistance, the effect is still there. Now, for the car in the video, when both front wheels are off the ground, there is no difference with a more stable vehicle (well, there may be an undesired positioning of the rear suspension links); it only looks crooked, that's all. But when at least one wheel touches the ground, it gives a reaction point to transfer the load from passenger-to-driver side on the rear axle and that can be bad.

This is what happen to the Holden in the next video, which always keep one front wheel on the ground. It always wants to initially steer right because the left rear tire has more traction than the right one:

​

 

[Tom Rauji]

I've always seen 'rebound' as what you call 'extension' (which I never heard). The opposite - what you also call 'collapse' - has many names though, such as 'bump', 'compression' or 'jounce':

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But I still have a theory to explain the phenomena even with stiffening up the compression instead of the extension! Before, your rear end collapsed rapidly under the weight transfer. By stiffening up the shock, the process doesn't go as fast and the $cg$ remains high longer, therefore permitting more weight transfer.

OK. I'll get on the correct terms.
I stiffened the bump or collapse. The rebound is half as it always was.

I have no issues with body roll. The body roll is caused by reaction to driveshaft torque. The engine torque is rotating the rear end up on the right side and down on the left. I have an anti-roll bar. It is a cross bar from frame rail to frame rail with roller bearings at the ends. It has links with heim joints from the rear end housing axle tubes to the bar. This allows the rear end to move freely up and down but forces the car and rear end to be level. It prevents drive shaft torque applied to the pinion gear from tilting the housing with respect to the body.

As soon as there is thrust, there is weight transfer. It is instantaneous, it is proportional. The fact that the body lifts, depends only on the suspension design. A car with no suspension still has weight transfer, even though the body - obviously - doesn't move in any way. In your video, it's probably the difference in air pressure between front and rear that throws you off. The softer rear tires squish a lot more under load than the stiffer front tire expand under the same load difference.

The rear tire has about 16 psi and is 12.5" cross section, 10.2" tread width, and 28 inches tall (with no weight). The rear tires initially flatten about twice (real rough guess) the amount they do with the whole car weight alone when the car is up on the wheels and rolling.

Something beyond weight goes on in the first 10 feet or so. They normally put a very sticky coating on the track as a traction aid. I can go on a non-prep track, using a loose rebound, and hit the tire hard enough (with enough anti-squat) to fully get on the back tires. About 20 feet out it starts to spin from lack of traction and the nose drops and tires go into uncontrolled spin. Something happens in the first few feet. As a matter of fact I can go on bare concrete without compound and if I loosen rebound it flattens the tire and plants, but as soon as the rear extension stops it spins. There is a little something going on with the initial "push" that digs the tires in, and that something goes away if I angle the arms or tighten rebound to not have that start extension. The better the track, the more I can slow the rebound without spinning and the longer the initial hit lasts. On a tight track with tight rebound settings I can get into the 1.1 second range for 60 feet. My issue is keeping the nose down. I'm not sure why it went up in the nose when I tightened the bump. That makes no sense to me. It is opposite what I expected.

 

[Ranger Mike]

Traditionally we used a 90 – 10 front shock set up. This shock takes 10% effort to extend so it is not hindering the front end lift. The 90% is to hold it up and keep it from compressing. This is one fine tune area to explore for several reasons. When you launch you are dealing with body roll in and X,Y and Z axis. You also deal with TIME. Hence , my 4-D comment. You can fine tune the “Weight Transfer” (really the x,y and z acceleration forces) by experimenting with an 80-10 left front shock and 90-10 rt ft shock. Same in the rear end. Usually a 50-50 shock was used on both sides but as the car lifts and twists , the left rear may need more higher setting on compression to counter the twist action. Again Time comes into play as to how long do you want to keep the front end at max lift. How quick do you want the front to settle. Hopefully way before the traps.

 

[Tom Rauji]

Traditionally we used a 90 – 10 front shock set up. This shock takes 10% effort to extend so it is not hindering the front end lift. The 90% is to hold it up and keep it from compressing. This is one fine tune area to explore for several reasons. When you launch you are dealing with body roll in and X,Y and Z axis. You also deal with TIME. Hence , my 4-D comment. You can fine tune the “Weight Transfer” (really the x,y and z acceleration forces) by experimenting with an 80-10 left front shock and 90-10 rt ft shock. Same in the rear end. Usually a 50-50 shock was used on both sides but as the car lifts and twists , the left rear may need more higher setting on compression to counter the twist action. Again Time comes into play as to how long do you want to keep the front end at max lift. How quick do you want the front to settle. Hopefully way before the traps.

Because of power levels and tires today, 50/50 rears and 90/10 fronts aren't useful on faster cars. Racers generally use two distinct rear shock settings, extension faster on radials and slow on bias sidewalls. They use two different rear shock "bump" or collapse settings, slow on radials and medium on bias. My car would go on its back at much less power if I used a loose rise front shock. The body front would have so much momentum it would be going up to the sky more than forward.

The fronts stay about the same regardless of rear tires in faster cars. Extension is slowed to prevent wheelies and collapse or "bump" is slowed to hold the front stable. Only extension (I guess I should call that rebound but the mode is actually extension from resting) is adjusted to reduce front end rise or increase rise on poor tracks. I could just copy what others do, but I want to understand exactly what happens physically. I don't think everything commonly accepted is factual, like energy stored in soft tall springs or instant center calculations that ignore effects of axle wrap forces. For example I know for a fact my upper control arms pull backwards and do not push forward at all. They do not react like a real ladder bar or four link (which I've had) when I change them, so I want to learn why the upper arm act differently.

My general interest in racing is the actual way things work, not how people say things work. I want to understand it in detail.

 

[jack action]

They normally put a very sticky coating on the track as a traction aid.

That increases the thrust you can put down before spinning, and weight transfer is proportional to thrust, and more weight transfer allows you to get more thrust! Of course you will be able to keep the front wheels off the ground the first few feet in such a case.

There is a little something going on with the initial "push" that digs the tires in, and that something goes away if I angle the arms or tighten rebound to not have that start extension.

That little something is your raised $cg$ that increases your weight transfer and allows for more thrust to be applied, which creates more weight transfer and so on. If you don't allow the rear end to lift (by removing anti-squat or by restraining it with damping), you won't raise the $cg$.

@Tom Rauji ,

I'm not going to go into an endless argument over this like I had with other racers before. My point is not to tell you what you experienced is not real, it is just to give you hints on what to look for.

I have never done an in-depth analysis of dragster launch, especially dynamically, but my knowledge of physics tells me that it is mostly a matter of $cg$ height that can explain all of these differences in hooking the rear tires. I'm telling you that to help you what to look for, not to tell you you are wrong.

Although, it is a dynamic phenomena (the time factor @Ranger Mike talks about), so when you accelerate the body in pitch, it will have to stop eventually and that inertia that needs to be stopped will momentarily overshoot its static resting position (how much the tire deform). But that has nothing to do with the geometry of the suspension design, per say (Although the stiffness of the suspension will influence that). If you have a suspension hitting its travel stops, that is not a smooth transition and it will also upset the weight transfer (again, that damn inertia).

The slick is also a weird beast. Under hard acceleration, a slick actually have a perceived increase in its friction coefficient. I'm not an expert on the matter but, from what I understood, it also have something to do with inertia, when the deformed tire «slaps» the ground.

I'm willing - and would be happy - to have people with better knowledge than me on the subject, telling me I'm wrong about all of that. But I need physics proof, with known theories, rather than people explaining me their feelings about it.

From my study on the subject, the modified typical street car with slicks is a special case where the $cg$ height to wheelbase ratio and weight distribution are just about perfect to be the tipping point where a full weight transfer can be completed. A $cg$ a little bit lower and the front wheel don't leave the ground, a little bit higher and you flip the car. I wouldn't be surprised that we are not even talking in 'inches' of difference. That is why the slightest modification in the body height makes such an impact.

Unless proven otherwise with science, I can't accept that there is any other thing than weight going on, especially when weight can explain everything.

Believe me, instead of looking into magical forces that come from who knows where, examine the $cg$ height, you might find some interesting answers.

 

[Tom Rauji]

I'm not going to go into an endless argument over this like I had with other racers before. My point is not to tell you what you experienced is not real, it is just to give you hints on what to look for.

I have never done an in-depth analysis of dragster launch, especially dynamically, but my knowledge of physics tells me that it is mostly a matter of $cg$ height that can explain all of these differences in hooking the rear tires. I'm telling you that to help you what to look for, not to tell you you are wrong.

Although, it is a dynamic phenomena (the time factor @Ranger Mike talks about), so when you accelerate the body in pitch, it will have to stop eventually and that inertia that needs to be stopped will momentarily overshoot its static resting position (how much the tire deform). But that has nothing to do with the geometry of the suspension design, per say (Although the stiffness of the suspension will influence that). If you have a suspension hitting its travel stops, that is not a smooth transition and it will also upset the weight transfer (again, that damn inertia).

The slick is also a weird beast. Under hard acceleration, a slick actually have a perceived increase in its friction coefficient. I'm not an expert on the matter but, from what I understood, it also have something to do with inertia, when the deformed tire «slaps» the ground.

I'm willing - and would be happy - to have people with better knowledge than me on the subject, telling me I'm wrong about all of that. But I need physics proof, with known theories, rather than people explaining me their feelings about it.

From my study on the subject, the modified typical street car with slicks is a special case where the $cg$ height to wheelbase ratio and weight distribution are just about perfect to be the tipping point where a full weight transfer can be completed. A $cg$ a little bit lower and the front wheel don't leave the ground, a little bit higher and you flip the car. I wouldn't be surprised that we are not even talking in 'inches' of difference. That is why the slightest modification in the body height makes such an impact.

Unless proven otherwise with science, I can't accept that there is any other thing than weight going on, especially when weight can explain everything.

Believe me, instead of looking into magical forces that come from who knows where, examine the $cg$ height, you might find some interesting answers.

OK, thanks for your time. I guess we have reached the limit.