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.
