F8x Motion Ratio and Wheel Rates

[tke743]

I hd a hard time finding this. Thought it might be helpful for people here. (Note, my understanding is that Wheel Rate = (Spring Rate*(Motion Ratio^2)), please correct me if wrong.)

Front
Motion Ratio - 0.96
Wheel Rate - Spring rate * (0.96^2)= Spring Rate *0.92

Rear
Motion Ratio - 0.47
Wheel Rate - Spring rate * (0.47^2)= Spring Rate *0.22

With this Wheel Rates are
F8x CP/CS - F182#/in, R151#/in
Base F8x - F163#/in, R131#/in
Ohlins - F475#/in, R291#/in

This might explain the Ohlins "Truck Springs" in the rear. FYI, they now have a bumpy track setup of F342#/in and R1086#/in springs. This gives a Wheel rate of F315#/in and R240#/in.

[EricSMG]

I think your formula is accurate but I'm questioning the rear motion ratio - that seems pretty low. I would be surprised if the rear wheel rates are actually lower than the front... this has not been the case with any previous chassis to my knowledge. Rear rate is always higher to achieve flat-ride (where the front and rear of the car settle at approximately the same time when a bump is hit - the only way for this to happen is with a higher rear wheel rate). It certainly doesn't feel that way on the road - rear feels quite a bit more 'sprung'.

You sure about that rear motion ratio? I would expect something more like .6 - .7. Is the rear spring really closer to the inner CA bolt than it is to the outer?

Going out to the garage now to eyeball this...

Edit - no sir. The lower CA is ~16" in length. The spring's center-line sits at roughly 6" inbound from the outer bolt (it's much closer the wheel). This would give us a motion ratio of roughly .625 (10/16).

From this, your rear CP wheel rate would be in the 275lb range. Much more plausible.

[M3SQRD]

Originally Posted by EricSMG

...

Going out to the garage now to eyeball this...

Edit - no sir. The lower CA is ~16" in length. The spring's center-line sits at roughly 6" inbound from the outer bolt (it's much closer the wheel). This would give us a motion ratio of roughly .625 (10/16).

From this, your rear CP wheel rate would be in the 275lb range. Much more plausible.

Motion ratio is calculated using the distance to the centerline of wheel, not the distance to the outer end of the control arm.

[guess2098]

I don't understand this but when psi build me a ttx, they told me the best spring rate they use so far is front 517 and rear ~450 (not on top of my head). Noted rear 450 is true coilover.

Could you calculate it and give me some clue...

[EricSMG]

Originally Posted by M3SQRD

Motion ratio is calculated using the distance to the centerline of wheel, not the distance to the outer end of the control arm.

Correct. The outer end of the CA is roughly at the center of the wheel. As I said, I eyeballed it but either way, the rear spring sits considerably outboard of the center point and thus results in a rear wheel rate that is notably higher than the front. How much I do not know but I am certain this is the case.

Simply look at the rear suspension and no other conclusion can be made - it's obvious.

That said, I will more closely measure/calculate and report back.

[M3SQRD]

Originally Posted by EricSMG

Correct. The outer end of the CA is roughly at the center of the wheel. As I said, I eyeballed it but either way, the rear spring sits considerably outboard of the center point and thus results in a rear wheel rate that is notably higher than the front. How much I do not know but I am certain this is the case.

Simply look at the rear suspension and no other conclusion can be made - it's obvious.

That said, I will more closely measure/calculate and report back.

Check out this thread:

https://f80.bimmerpost.com/forums/sh....php?t=1351805

[EricSMG]

Originally Posted by M3SQRD

Check out this thread:

https://f80.bimmerpost.com/forums/sh....php?t=1351805

No way. That would mean the spring sits closer to inner bolt - not even close.

But again, I'll precisely measure and report back. I could be wrong but highly doubt it based on my measurement today.

[F3IGHTY]

Originally Posted by EricSMG

No way. That would mean the spring sits closer to inner bolt - not even close.

But again, I'll precisely measure and report back. I could be wrong but highly doubt it based on my measurement today.

I agree .47 makes no sense. I think it's actually around .685 and the number provided in the other thread was already squared.

[EricSMG]

Originally Posted by F3IGHTY

I agree .47 makes no sense. I think it's actually around .685 and the number provided in the other thread was already squared.

Exactly, makes no sense.

I'd bet a large sum of money that it's in the 6-7 range as previously suggested. And you're probably spot on since .685 squared = .47.

And THAT's why blindly quoting other threads (without diving in to really understand the content) gets us in trouble.

I'll try to get an accurate measurement tonight after work. Stand by.

[bbnks2]

Originally Posted by F3IGHTY

I agree .47 makes no sense. I think it's actually around .685 and the number provided in the other thread was already squared.

Originally Posted by EricSMG

Exactly, makes no sense.

I'd bet a large sum of money that it's in the 6-7 range as previously suggested. And you're probably spot on since .685 squared = .47.

And THAT's why blindly quoting other threads (without diving in to really understand the content) gets us in trouble.

I'll try to get an accurate measurement tonight after work. Stand by.

Just looking at a picture of the M4 lower control arm I measure motion ratio to be .59^2 and wheel rate = .35

Not sure how Ohlins came up with .47^2 = .22. I think they presented .47 as the wheel rate meaning it was already squared. In that case they would be putting the motion ratio at .68. That is too high to me. I do get a MR of .65*.65 = .42 IF I measure to the beginning of the spring. However, I think you should be measuring to the CENTER of the spring which puts it at the .59 I came up with.

This makes me question if I've been measuring correctly by measuring from the center of the spring. It kind of does make sense that the outer edge of the spring is still providing the same roll resistance as it get displaced. Either way, .22 is way too low. I would put it at .35 (measure to center of spring) or .65*.65 = .42 (measuring to outer edge of spring).

There are other factors to the calculation that I am not taking into account. Like, where are they measuring from in regard to the control arm length? I have always read you measure from the bolts NOT the wheel. This is where all the lever action is being generated. Things pivot at their joints not at the outside edge of the wheel... Static camber also kind of dictates that you're carrying more load on the inside edge of the tire when driving in a straight line so measuring lever arm length as the outside edge of the wheel makes less sense. Go-Karts, electric cars, and SAE cars get really technical with their suspension tuning and every 3d modeling I've seen is measuring suspension kinematics from pickup points, not outside edge of tires. I would think the wheel moves up and down the same distance as the knuckle pick up point does. The wheel sits flat (generally) and does not travel in the same exact plane of motion as the arc of the lower control arm. Hence, why you gain/lose camber as the wheel goes up and down... the wheel is pivoting at the pickup points.

Then you also have to factor in the spring angle and the other controls arms affect on the relationship. This seems to be pretty insignificant factor though. Using the E9x M3/1M/135i as an example, people have measured spring travel relative to wheel travel by hand and came out to very similar results to how I measured above using a picture. For the 1M, I come up with a motion ratio of .53 and it has been manually measured to be .567*.567 = .32 wheel rate! The "official" number has been posted as: 0.563:1. Close enough to be used to check the .47 number presented above... this leaves me asking questions of how Ohlins measured to come up with their number...



One of the easiest to understand articles presenting motion ratio calculations:
https://ismasupers.com/downloads/tec...20ratios-4.pdf

As shown above in the 1M example, measuring in this way falls pretty close to ACTUAL measurements done by hand. Here is how I am applying the formula (MR = Length B-C / Length A-C):


If you wanted to account for any spring inclination (<10* in our case) then this would be a more accurate calculation of the motion ratio:


As you can see, they are measuring from the pickup points to the springs centerline!

[tke743]

Originally Posted by EricSMG

Exactly, makes no sense.

I'd bet a large sum of money that it's in the 6-7 range as previously suggested. And you're probably spot on since .685 squared = .47.

And THAT's why blindly quoting other threads (without diving in to really understand the content) gets us in trouble.

I'll try to get an accurate measurement tonight after work. Stand by.

I appreciate the effort to verify, I'm very interested in what you come up with. Just an FYI, I was not blindly quoting other threads. I received these numbers directly from Ohlins.

[EricSMG]

Originally Posted by tke743

I appreciate the effort to verify, I'm very interested in what you come up with. Just an FYI, I was not blindly quoting other threads. I received these numbers directly from Ohlins.

Hey - no worries. I actually meant other guy who *seemed* to blindly quote the other thread without really understand the content.

In hindsight I may have been a little aggressive with that statement... my main point was that just because a number is presented in a forum doesn't even remotely mean it's accurate.

In this case, Ohlins is incorrectly calling the number they gave you the "motion ratio" as there is no possible way the motion ratio is <.50. What they gave you was the factor used to calculate wheel rate, most likely.

Originally Posted by bbnks2

However, I think you should be measuring to the CENTER of the spring which puts it at the .59 I came up with.

Great post! And I agree with the above, which is what I did yesterday to come up with 6/10 = .60... so our numbers align. But as I said, I'll be very careful and measure center of spring and center of wheel and report back. I'm betting it's still right around .60... give or take an inconsequential amount.

[bbnks2]

Edited*** because it was a bad example. I've since found out that the m235ir uses a true rear coil over so the spring rates actually are fairly neutral with only a slight understeer bias.

[stevehifi]

Guys any progress on this thread? Did you end up with the appropriate motion ratio?