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Old 09-21-2009, 03:25 AM
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Roll understeer

Do any of you guys know where on the web I might might be able to find some sort of calculator which will calcualte the amount of roll understeer that my car has based upon my 4 link mount positions? Also, what is deemed to be an acceptable level of roll understeer?

Thanks,

John

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Old 09-21-2009, 06:47 AM
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Forgot to mention this in my PM, John: The usual "rule of thumb" is to keep the lower links horizontal. This will force the instant center to be below the axle centerline and you'll always have roll understeer. You would then adjust the upper links for the amount of antisquat you desire.
http://www.racetec.cc/shope
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Old 09-22-2009, 08:08 PM
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http://www.pirate4x4.com/forum/showt...hreadid=204893
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Old 09-22-2009, 09:38 PM
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Triaged, I just looked at your 4link spreadsheet and I'm wondering if I'm understanding it correctly. It appears that the wheelbase is 108.5, the tire radius is 19.75, and the CG height is 34. When viewed from the side, the rear pivot for the lower link is 3 forward of the axle centerline and 19.75 up from the shop floor. The front pivot for the lower link is 47 forward of the axle centerline and 28 up from the shop floor. The rear pivot for the upper link is directly above the axle centerline and 28 up from the shop floor. The front pivot is 32 forward of the axle centerline and 32 up from the shop floor.

Now, if I am reading this correctly, it would appear that you are not using the SAE definition for antisquat. And, of course, there's no law against your doing that. But, since that is so very unusual, I would suggest that you warn your users that they should expect different results with most other spreadsheets available.

It appears that you have taken the ratio of 800 to 1500, multiplied it by the wheelbase, and used the result as the horizontal distance forward to a point which will lie on the 100 percent antisquat line. The vertical distance to the point would be the center of gravity height. The second point...to define the line...would be at the rear tire patch. The SAE definition uses the rear tire patch point and another point which is at the intersection of a horizontal line through the center of gravity and a vertical line through the front tire patch. Using your geometry...as I understand it...yields an SAE antisquat value of 103 percent.
http://www.racetec.cc/shope
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Old 09-23-2009, 04:44 AM
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Thanks for the replies guys but what are you trying to tell em Triaged? The link that you posted doesnt really go anywhere that I can understand?

EDIT - sorry, wasnt looking at the correct link! Doh!

Billy - I have used your IC location tool on your site many times now and have found it invaluable. Thank you. However, I can have many combinations of location points and was wondering how I can determine what each combination will give me in terms of roll understeer/ oversteer. From your post above (and your PM) I think I am correct in taking it that as long as the IC is below the axle centre line I will get roll understeer and the closer to the ground it gets the more there is?

Thanks

John
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Old 09-23-2009, 06:54 AM
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Quote:
Originally Posted by John Loudon
Billy - I have used your IC location tool on your site many times now and have found it invaluable. Thank you. However, I can have many combinations of location points and was wondering how I can determine what each combination will give me in terms of roll understeer/ oversteer. From your post above (and your PM) I think I am correct in taking it that as long as the IC is below the axle centre line I will get roll understeer and the closer to the ground it gets the more there is?

Thanks

John
When I was about 10 years old, my friends and I would build push carts out of 2x4s. Fortunately, there were no steep hills in the area, so there were no injuries. The steering mechanism consisted of a 2x4 "axle" that was pivotable centrally about the "chassis" 2x4 by a pop bottle cap that was sandwiched between the two with a nail driven through it. The driver steered with his feet and by a rope attached to both ends of the axle.

Well, beam axle roll steer involves that sort of steering, but at the rear of the car. So, to determine whether it's roll understeer or roll oversteer (or neither), all you have to do is figure out which wheel is moving forward and which wheel is moving rearward in a turn.

Suppose the instant center is at the same height as the axle centerline. Assume, also, that it remains at that height as the car turns left. The right rear would go into jounce as the left rear goes into rebound, but both would move forward...relative to the chassis...by the same amount.

Now, suppose the instant center is above the axle centerline. This time, as the car turns left, the right rear would move back as the left rear would move forward, resulting in roll oversteer.

(Note that tire loading is the same in both cases, meaning that this is not the same as the oversteer which causes dynamic instability. Only the required steering input has changed.)

Since the instant center is determined by the intersection of the link lines, a horizontal lower link will assure that the instant center will always be below the axle centerline and the car will always have roll understeer.

With an IRS, wheel movement forward or back might not cause roll steer. It would depend on the geometry.
http://www.racetec.cc/shope
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Old 09-23-2009, 07:38 AM
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Many thanks Billy
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Old 09-23-2009, 03:14 PM
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Quote:
Originally Posted by BillyShope
Triaged, I just looked at your 4link spreadsheet and I'm wondering if I'm understanding it correctly. It appears that the wheelbase is 108.5, the tire radius is 19.75, and the CG height is 34. When viewed from the side, the rear pivot for the lower link is 3 forward of the axle centerline and 19.75 up from the shop floor. The front pivot for the lower link is 47 forward of the axle centerline and 28 up from the shop floor. The rear pivot for the upper link is directly above the axle centerline and 28 up from the shop floor. The front pivot is 32 forward of the axle centerline and 32 up from the shop floor.

Now, if I am reading this correctly, it would appear that you are not using the SAE definition for antisquat. And, of course, there's no law against your doing that. But, since that is so very unusual, I would suggest that you warn your users that they should expect different results with most other spreadsheets available.

It appears that you have taken the ratio of 800 to 1500, multiplied it by the wheelbase, and used the result as the horizontal distance forward to a point which will lie on the 100 percent antisquat line. The vertical distance to the point would be the center of gravity height. The second point...to define the line...would be at the rear tire patch. The SAE definition uses the rear tire patch point and another point which is at the intersection of a horizontal line through the center of gravity and a vertical line through the front tire patch. Using your geometry...as I understand it...yields an SAE antisquat value of 103 percent.
http://www.racetec.cc/shope
The value put on the front page for CG is for the overall vehicle. Using the unsprung mass (assuming they are concentrated at the wheel center) I calculated the sprung mass CG and the CoG for the sprung mass plus the front unsprung (and called it the Anti-Squat CG). With small unsprung mass there is little difference. Where can I find the SAE definition? I it uses just the unsprung mass CG right? Which one is the most accurate? I would guess it would be somewhere in between depending on mass ratios and stiffness.

For understeer/oversteer I calculated the axle roll axis as the line between the intersection of the upper links and the intersection of the lower links. If the links are parallel they are assumed to intersect at infinity. It isn't too hard to do on graph paper.


If the axle roll axis slopes down towards the front that is roll understeer. If the axle roll axis slopes up towards the front that is roll oversteer. Quite obviously if your lower links are parallel and flat you have neither roll understeer or oversteer.
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Old 09-23-2009, 05:03 PM
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Quote:
Originally Posted by Triaged
Where can I find the SAE definition?
When I referred to an "SAE definition," I was referring to the common understanding among automotive engineers. I can talk to other automotive engineers from around the world and when I mention "percent antisquat," I don't have to define it. There are certain reference books common to suspension engineers, one of which is the Millikens' Race Car Vehicle Dynamics. A definition for beam axle antisquat is found in Fig. 17a on page 619. The important characteristic is that a car with 100% antisquat carries exactly the inertial loading (weight transfer) through the links.

If you don't have the book, my site repeats the Millikens' definition. Well, I might as well repeat it here. The 100% antisquat line intersects the rear tire patch and the intersection of two other lines, one a horizontal line through the center of gravity and the other a vertical line through the front tire patch. The slope of this line would be the CG height divided by the wheelbase. So, to get the percent antisquat of a given setup, you'd construct a line through the instant center and the rear tire patch and then multipy the ratio of the slope of this line to the 100% slope by 100.

(Actually, the line should pass through a point below the rear tire patch at a distance equal to the tire radius times the ratio of "m" over "M," where "M" is the total weight of the car less the rear unsprung weight and "m" is the rear unsprung weight.)

Quote:
Originally Posted by Triaged

If the axle roll axis slopes down towards the front that is roll understeer. If the axle roll axis slopes up towards the front that is roll oversteer.
This is exactly that which is presented by the Millikens at the bottom of page 648. And, when I was teaching an engineering course with the book as a text, this is what I presented to the students. I have some problems with this, however, and I had intended to ask Doug about it. Thank you for reminding me.

When I look at your example, for instance, and see the instant center above the axle centerline, I see...during a left hand turn...the right rear moving back and the left rear moving forward, causing roll oversteer. Seems to make sense, but my "common sense" has led me wrong before.
http://www.racetec.cc/shope
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Old 09-23-2009, 09:54 PM
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The question really comes down to which CG to use. I will have to draw out and look at your m/M modification. I have RCVD. There is no mention of which CG to use (vehicle, sprung mass, other). It has been a while since I did all that work. I will have to lay out some free body diagrams and sort it all out again. I calculated the anti-squat just as Milliken and Milliken (ICz/ICx)/(h/l)...now what h? I will get back to you on this.

As for the roll axis thing I think of it this way.

What would happen if the lower link chassis mount and the upper link axle mount were at the same height off the ground. Now take the lowers and triangulate them all the way so that there is a single point at the chassis mount (making it an A-arm or Y-link). Now do the same thing with the uppers at the axle. There will be quite a bit of upward slope on the lower link but the axle would not steer with body roll. It would however shift the axle housing to the outboard side in a turn. If the links are not fully triangulated then you just have another Instant Center but in the top view. So the roll axis only is applicable for small angles of roll.

Last edited by Triaged; 09-23-2009 at 10:01 PM.
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Old 09-24-2009, 07:51 AM
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Quote:
Originally Posted by Triaged
There is no mention of which CG to use...
This is because the weight of the rear axle assembly is commonly ignored. This puts the antisquat lines neatly through the rear tire patch, which means the CG of the entire car is used. This is probably adequate, since the CG height is rarely known with any degree of accuracy. I have, in most of my spreadsheets, taken the rear axle assembly weight into account, even though the change in the answer is small.



Quote:
Originally Posted by Triaged
I calculated the anti-squat just as Milliken and Milliken....
Probably sliderule error. Happens to everyone. I check my work many, many times before adding a spreadsheet (engineers are a lot like TV's Monk), but, when my answer was different from yours, I still began to worry and resorted to my CAD to verify it. Yup! 103 %. Keep GIGO in mind and double check my understanding of your data before you start looking for errors in your work.

Quote:
Originally Posted by Triaged
It would however shift the axle housing to the outboard side in a turn.
It would, however, take more than this to bring about roll steer. The axle has to be rotated in plan view. I'm going to email Doug as soon as I finish this post. Let you know.
http://www.racetec.cc/shope
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Old 09-24-2009, 02:12 PM
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Quote:
Originally Posted by BillyShope
...the CG of the entire car is used...
That is what I had suspected. It sure would be nice if they specified vehicle CG and not just CG.

Quote:
Originally Posted by BillyShope
Probably sliderule error. Happens to everyone...
I guess I should have been more specific. While I used the same equation I did not use the same h (CG height). I used what I called the Anti-Squat CG (see 2nd tab) which is the Vehicle CG - Rear Unsprung Mass CG. I suspect that in the end this is quite the same as your r(M/m) modification. I will dig the equations you used out of the Java and see how they compare to mine. My modification of h is:
(Vehicle_CG_Height*Vehicle_Mass-Rear_Unsprung_Mass*Tire_Rolling_Radius)/(Vehicle_Mass-Rear_Unsprung_Mass)

Quote:
Originally Posted by BillyShope
...I'm going to email Doug as soon as I finish this post. Let you know.
I am interested to hear what Doug says about that. I have never designed something with flat lower links and most have had triangulated lower links.
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Old 09-24-2009, 03:35 PM
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Quote:
Originally Posted by Triaged
My modification of h is:
(Vehicle_CG_Height*Vehicle_Mass-Rear_Unsprung_Mass*Tire_Rolling_Radius)/(Vehicle_Mass-Rear_Unsprung_Mass)
This must be a typo. You've got "Vehicle_Mass-Rear_Unsprung_Mass" in both the numerator and denominator, which would mean that you're simply multiplying the CG height by the tire radius.

A free body diagram indicates that either the CG height of the entire car should be used...if the rear axle assembly weight is ignored...or the CG height of everything but the rear axle assembly if it is not.
http://www.racetec.cc/shope
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Old 09-24-2009, 03:45 PM
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excel follows the order of operations so it works out as [(h*Mtot)-(m*r)]/(Mtot-m)
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Old 09-24-2009, 09:57 PM
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Quote:
Originally Posted by Triaged
excel follows the order of operations so it works out as [(h*Mtot)-(m*r)]/(Mtot-m)
Understood. And, it isn't far from that which the free body diagram will give you.
http://www.racetec.cc/shope
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