A new free vehicle dynamics resource - Dan's Vehicle Dynamics Corner

[Tim.Wright]

Originally posted by Z:
Under/oversteer can be thought of in terms of "static margin". Roughly speaking, this is the plan-view-longitudinal-distance between the car's CG and the (roughly lateral) Line-of-Action of the resultant force vector from all four wheels. If the CG is in front of wheel-force-LoA, then understeer. If CG behind LoA, then oversteer. If CG right on LoA, then neutral.

Not sure that's right. In a steady corner, the tyre resultant force is going to go through the CG isn't it?

My understanding of the static margin is that its the distance from the CG to the neutral steer point. The neutral steer point is the longitudinal location which will give a neutral response if you apply a lateral force there. I.e. the slip angle response will be the same front and rear.

I have just done a quick calc on a bicycle model with 50% mass dist and an understeer (measured as delta of front to rear slip angles) of 3deg/g which I think is probably closer to a road car but anyway... I've calculated the neutral steer point and found that the static margin is in the order of 400mm. Obviously, the more neutral the car is, the smaller the static margin is and then a higher percentage of the balance is coming from the tyre Mz. However, at this point you are really trying to pick very small changes in balance so it doesn't really make sense to be speaking in terms of percent.

So, my feeling then is that the Mz would be interesting if you are really trying to accurately represent your slip angles to within a few percent. But for sure I wouldn't go as far as saying its a first order effect. At least not in steady state.

I think it would be important when assessing the response of road cars because people are interested in small changes of balance which are giving tactile feedback to the driver. But in this case, you are talking very small values.

[ChassisSim]

Hey Guys,

Tim - your on the right track on that one - 400mm for a static margin is a tad high but in terms of some rough rules of thumb it's not that far out. That being said you've got the heart of this nailed.

Z - Here's some food for though my friend. The self aligning torque is intrinsically linked to the force being generated by the tyre. If we are going to do some rough rules of thumb of calculation the static margin we have,

SM = (mom_arm_f*C_f - mom_arm_r*C_r)/(C_f + C_r)

Here we have,

SM = static margin
mom_arm_f = Front moment arm to the c.g
mom_arm_r = Rear moment arm to the c.g
C_f = Change in front tyre force/change in slip angle
C_r = Change in rear tyre force/change in slip angle

Giving the self aligning torque the considerable benefit of the doubt we can write for the moment arms front and rear

mom_arm_f = a + self_aligning_torque_arm_f
mom_arm_r = b + self_aligning_torque_arm_r

Remember the numbers we discussed before, on a FSAE car, 800mm plays 50mm, and that's being pretty generous. Also remember as we get close to the peak grip of the tyre the self aligning torque moment arm falls away. Consequently as I stated before the moment arm effect of the axle blows away the self aligning torque.

To put this in perspective let's revisit some moment arms from our previous example.

Axle moment from lateral force to c.g = 125*9.8*0.8 = 980 Nm
Moment arm self aligning torque = 125*9.8*50e-3 =61.25 Nm

The difference in the moments speaks for themselves. Also that self aligning torque will drop away as we hit the maximum force of the tyre.

Where the self aligning torque will make its presence felt as the car gets close to a static margin of zero. A static margin close to 0 should not be confused with neutral steer. When we hit a static margin of 0, you’re right on the borderline of being able to control the car. The concept of static margin was originally developed by the aerospace industry to quantify pitch stability. I can tell you from experience that long before you hit a static margin of 0 the driver will be totally spooked, and the effects of self aligning torque is the equivalent of shuffling the deck chairs on the Titanic. I learnt this one the hard way.

Anyway Guys I hope this clears a few things up.

All the Best

Danny Nowlan
Director
ChassisSim Technologies

[Tim.Wright]

Danny, I agree regarding the drop off in controlability, though I would have thought that a static margin of zero is theoretically neutral steer.

It might not be what a driver would feel or describe as neutral, but from a vehicle dynamics point of view, at a static margin of zero, the front and rear slip angles are the same. to me thats a neutral car.

[Z]

Originally posted by Tim.Wright:
Not sure that's right. In a steady corner, the tyre resultant force is going to go through the CG isn't it?

My understanding of the static margin is that its the distance from the CG to the neutral steer point. The neutral steer point is the longitudinal location which will give a neutral response if you apply a lateral force there. I.e. the slip angle response will be the same front and rear.

Tim,

Oops! Yes, I worded that poorly (should have checked my definitions!). I have editted my above posts to make more sense.

Also, I prefer to think in terms of unsteady conditions. So if a car is cornering neutrally around a skid-pad (say), then it has the inwardly directed resultant tyre force LoA (from all four tyres) passing through the NSP, and this is in balance with the outwardly directed centrifugal force from the CG, which is also at the NSP. Now if the driver gradually increases speed (with same steer angle), then both the centrifugal and tyre forces also increase. But if, as the tyres approach "saturation", the pneumatic trail decreases, then the resultant of the tyre forces moves forward, and this together with the centrifugal force forms an over-steering yaw couple. So the tail starts sliding outward.
~~~~~o0o~~~~~

Danny,

You have;
"mom_arm_f = a + self_aligning_torque_arm_f
mom_arm_r = b + self_aligning_torque_arm_r"

I would say; mom_arm_f = a minus self_aligning_torque_arm_f.

Putting this into your equation for Static Margin has the a and b subtracting, while the two self-aligning-torque-arms add together.

Also, there is nothing impossible about a CG behind the NSP. In fact, can be common on holidays when the boot is fully loaded! Thankfully, yaw-damping and low speeds can make it controllable.

Z

[ChassisSim]

Z,

My friend a couple of things,

*The moment arm definition I've just put in as a general plus. It's up to the end user to put in the sign they want. If I was going to be fussy about it I would have it in as a minus but I was using it as a point of illustration. Anyway the numbers due to self aligning torque are still very small.

If anything to give it a proper treatment I'd have to include the self aligning torque as its own derivative in the Static Margin equation. This is where things get real interesting. Looking at say some F3 tyre results for various cambers you are looking at peak tyre forces of 5000 N with the corresponding self aligning torque peaks being at about 100 Nm. Where things take a particular twist is after the slip angles have passed the peak self aligning torque. The lateral forces still have a bit of gradient left in them, but the self aligning torque curves have flattened out. This in concert with the small numbers of the self aligning torque pretty much renders the self aligning torque as a passenger for the Static Margin particularly as we get close to the peak grip of the tyre.

*The yaw damping is actually part of the Static Margin. Both Milliken and I gave very detailed treatments of this in our respective books. This also has its background in aviation stability and control which is our respective backgrounds.

When you’re close to the static margin being 0 you’re at the cusp of unstable behaviour. I've flown aircraft with low and positive values of static margin and as a race/data engineer I've seen cars with low values of static margin and it is ugly. For the automotive case when you at this point as I stated in my last post the self aligning torque will have some impact but it's like shuffling deck chairs on the titanic.

All the Best

Danny Nowlan
Director
ChassisSim Technologies

[ChassisSim]

Hey Guys,

In light of what has been discussed here recently I think you should get an awful lot out of this,

http://www.chassissim.com/blog...c-race-car-stability

It's about transient racecar stability and the static margin in particular.

Enjoy

Danny Nowlan
Director
ChassisSim Technologies

[Tim.Wright]

Originally posted by Z:
Also, I prefer to think in terms of unsteady conditions. So if a car is cornering neutrally around a skid-pad (say), then it has the inwardly directed resultant tyre force LoA (from all four tyres) passing through the NSP, and this is in balance with the outwardly directed centrifugal force from the CG, which is also at the NSP. Now if the driver gradually increases speed (with same steer angle), then both the centrifugal and tyre forces also increase. But if, as the tyres approach "saturation", the pneumatic trail decreases, then the resultant of the tyre forces moves forward, and this together with the centrifugal force forms an over-steering yaw couple. So the tail starts sliding outward.

I follow you, and I do agree that the Mz would make up a large percentage of the understeer for a neutral or near neutral car, but my argument (and I think also Danny's) is that a large percentage of (practically) nothing is still nothing. Or at least safe to neglect.

Granted that neglecting or including Mz for a neutral tending car might change the sign of the calculated understeer, but if you think what this means in terms of alfa_front - alfa_rear, you are talking decimals of a degree and probably not detectable by the driver.

To come back to Danny's point too, you are already up shit creek if you are operating in this region anyway so to me its not important to know if your balance is +0.2deg/g (calculated with Mz) or -0.2deg/g (calculated without Mz). Either calculation (and probably your driver too) is going to tell you that you are too close to neutral steer.

This is also true in your example of the road car with a lot of rear mass. There is not going to be a lot of difference in the vehicle response if the neutral steer point is 20mm in front of the CG or 20mm behind it. Only that one is mathematically understeering, the other is mathematically oversteering. If you were to drive or simulate both cases I wouldn't expect you to see much of a difference.

[ChassisSim]

Hey Guys,

A couple of things for this week.

First things first I'd like to acknowledge the life of Allan Simonsen who was killed at the LeMans 24 Hour race on Saturday. I knew Allan, but more importantly other members of the ChassisSim community knew him better than I. Not only did they rate him as a driver, but he was well respected as a man. This is something that should be remembered and celebrated.

Also I think it is a timely reminder, that even though what killed him was a bad combination of circumstances it really re-iterates the point of safety when designing your cars. Ladies and Gentleman the price your pay for driving at the edge of a vehicle's performance envelope is that occasionally you'll fall off and someone may get hurt or even killed. If you can't make you peace with this you are in the wrong business. That being said as engineers we must take every precaution to ensure we have done everything we can to protect the drivers. There are no shortcuts in this business.

The other thing I wanted to touch is I've just put a post on my blog that consolidates the ChassisSim circuit modelling process,

http://www.chassissim.com/blog...s-the-complete-guide

What this post does is it puts under one roof all the video tutorials and documents you'll need to create a high fidelity circuit model for lap time simulation. It's all based on what has been done in the field so it should be a great resource for all of you.

All the Best

Danny Nowlan
Director
ChassisSim Technologies

[ChassisSim]

Hey Guys,

I've been seeing a lot of traffic recently about dampers and how to crunch the numbers. The following is good food for thought,

http://www.chassissim.com/blog...using-damping-ratios

It was a series of articles that was originally published in Racecar Engineering. It was about what to look for in damping rates and how to calculate them.

Next week I'll post some state space analysis stuff.

Enjoy

Danny Nowlan
Director
ChassisSim Technologies

[ChassisSim]

Hey Guys,

I realise I'm preaching to the choir on this one, but check this out,

http://www.chassissim.com/blog...-you-need-simulation

It outlines why you need to use simulation.

Enjoy

Danny Nowlan
Director
ChassisSim Technologies