Not a mathematician, not an insider, I just drive the four-wheeled things and ride and race the two-wheeled things. With that in mind ... this is not simple.

Here's a youtube channel worthy of study: https://www.youtube.com/watch?v=faw9NeBM3n0

SO. What would you like to quantify, or even describe?

Roll steer and bump steer are quantifiable things. It is possible to quantify the amount that both the front and rear wheels steer in response to suspension movement. This is a function of the mechanical design of the suspension (easy) and the amount the suspension moves (not so easy - and variable, depending upon circumstances).

Compliance steer is harder, but possible, to quantify. The suspension-arm bushings deflect. The wheels deflect. The steering-rack mountings deflect. The subframe mountings deflect. The unibody deflects. Where do you stop?

Then there's tire behaviour ...

The experts in the field speak of the "understeer budget" in which they add up quite a few of the effects in order to make an assessment of the stability of the vehicle.

But ... It isn't simple. In the video above, the Tiguan behaves safely but uncomfortably most of the time, but when pushed, it does something that isn't supposed to happen. There have been many other examples over the years. Jeep Grand Cherokee a couple generations ago was one of them. The Mercedes A-class a couple decades ago was another. The Toyota Hilux was another. There have been many others that misbehave but remain safe.

What happens under one particular set of circumstances doesn't necessarily mean that's what happens in other conditions. The Tiguan linked to above, behaves nicely in the slalom test.

So I hop in my supposedly understeery front wheel drive car, and go out on a rain-soaked motorway on tires that are perhaps not the best, and I have to lift the throttle while doing an emergency lane change. Lift-throttle oversteer?

The suspension that works in dry smooth pavement (moose test) isn't necessarily going to work properly on bumpy broken pavement or on gravel or dirt. In fact, it almost certainly won't.

So ... Under what circumstances do you want to quantify how a vehicle behaves? Is your assessment going to be relevant in other circumstances?

There are a few cars that have done well in that moose test. A few Tesla models are among them. Ever had a ride in the back seat of a (pre-refresh) Model 3 or Model Y on rough roads?

Very simple. An Understeer/Oversteer/Neutral Steer function is the first partial derivative of the average steered road wheels minus the Ackermann gradient with respect to steady state lateral acceleration (by definition). Expressed as units of degrees per g. Degrees of the Reference steer angle, gs are Ay/9.806. It is NOT a scalar constant. It can be positive in one Ay zone, zero, and negative throughout the vehicles operating range in the same car during any one test. Many methods to quantify including step, frequency response, constant radius, constant speed, and constant steer tests, all of which may give you slightly different answers because of the methodology, test procedure, and data post-processing techniques.

Another valid viewpoint is the change in turn radius per unit lateral acceleration. Curvature (as the inverse of turn radius) changes by changing Ay also is a good measure. We use the inverse because the radius is infinite when going just about straight ahead, sp plots tend to be large. So, the change in curvature per Ayg is a function which has a derivative and indicates under, over or neutral behavior. when the slope is negative (curvature decreasing) the vehicle is understeering, positive it's oversteering. Zero slope indicates neutral steering. This allows you to measure the system properties without a steering maneuver. For example, I have measured the understeer of my boat with 3 different propellers. The Mercury High-Five 5 bladed prop gives me a neutral steer bass boat. The 3 blade stock prop is horribly understeering. A 4 bladed aftermarket prop was also understeering but less than the 3 blade.

BTW: I just recently measured the understeer of my golf cart using my Samsung phone. It has all the signals you need: speed & yaw velocity. I used the Physics Toolbox app to record the data (at 400 Hz no less), tossed the data into a Matlab program and Bingo !

The humorous side of the answers you get are from papers, magazines, and forums is the connection between vehicle dynamics and religion: No facts, observations or measurements, just faith, feelings, and wishful thinking. The connection/relationship between understeer as a steady-state description and transient response is very direct.

The most ridiculous statements I hear, see, and read are how their 'Neutral Steer' car has yaw velocity overshoot. Sorta like "My dead cat has a pulse".

https://imgur.com/a/WnaoSIi
https://imgur.com/WtB0h7b

One of the more entertaining things to do with a bicycle model is to try a step steer with an understeer, oversteer and neutral setup. The results are not what armchair drivers expect.

Here's one way to approach an understeer budget https://en.wikipedia.org/wiki/Bundorf_analysis but there are others

The neatest practical definition of understeer is Mark Donohue's original experiment, driving around a constant radius skidpan at gently increasing speed. If you have to add more steering wheel angle you've got understeer at that speed and latacc, and if you don't you have neutral steering, at that speed and latacc. If you have to wind steering wheel angle off then you have oversteer. This works in the non linear range as well.

Olley's original definition used the crown of the road as a steering disturbance, I don't like that one as much.

One confusion with Donohue's experiment is if you kick the tail out and drift around the skidpad with a RWD. This is an entirely different game, yet one that is intuitive to many drivers, if occasionally expensive.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

They are all bad for pretty much the same reason: Transient response in the kill-zone.

" we never hear about it being quantified, at least in consumer automobile publications."

The values change due to every single factor one can identify. Where the passengers are, how much they weigh, how much the tires have worn, what the tires are, the tire inflation pressure, what the temperature is, is the road wet, and so on. The best one can manage is the tendency and even that doesn't seem particularly useful. The typical consumer should not be operating the car where small changes are significant.

I had an old car with bias belted narrow tires; moved to slightly wider radials and the car went from plowing into a significant turn to following the steering wheel. No idea where that would fit in consumer automobile publications.

It is, to say the least, surprising that we develop a car around a target tire, and then the consumer is free to fit any old cheap black round thing when the first set wear out (and I've never tracked understeer vs tire wear if it comes down to it). And then they sometimes only change tires on one axle (guilty as charged m'lud). We just have to assume there is enough leeway built into our target ranges that it won't suddenly turn into an oversteering monster. The whole field of aftermarket tire technical data is rather shocking considering those 96 square inches of contact patch are the only thing keeping the car under control.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

Actually the values don't change that much from say, 1000 miles to 30,000 miles on the car. This is by design not luck or accident. Same with weight distribution from Driver only to GVW. Based on ride height changes, tire durability, and steering stiffness performance specs. But the first set of crap replacement tires has to be taken into account, to, depending on how many vehicles you sell. This is because NHTSA doesn't work with percentages of failures, only counts. So many car makers (especially European), limit their production to avoid the magic count number. It gives them higher sale prices, which then is used to address other refinements & benefits.
Your old car on bias tires was from a different market era whose drivers probably could easily manage the sloppy (by today's standards) steering, lateral, and roll characteristics, concentrating on good 'ride'.
The cars had ginormouse amounts of camber and aligning moment compliance in the steering system amplified by bias tire properties. All that went away with radial tires. Radials because of rolling resistance decreases for mandated fuel economy requirements. Huge reduction in aligning moment stiffness, loss of camber stiffness (and even an occasional sign change deal (more camber hurts sideforce generation instead of increasing it). This lead to linear range understeer levels from 66 -8 deg/g at 0.15 gs, down to 2.5 to 4.0 deg/g on radials. FWD added a bit, but better tire load sensitivity fixed most of that with bigger sizes and sidewall characteristics.