motion ratio help

[stanglou]

I was wondering if anyone could explain to me in more depth what a motion ratio is. Herb Adams just isn't cutting it. thanks
lou

[astroracer]

The motion ratio for any given shock is the distance from the inner pivot points of the LCA to the lower shock attachment divided by the distance from the ball stud centerline to the inner LCA pivots X 2. This gives you the ratio that the lower shock travels in respect to the lower ball joint travel.
You can also look at this as a lever arm. The further inboard the lower shock attachment is from the ball stud the more leverage the weight of the car has on the spring/shock and the stiffer the spring needs to be to do the same amount of work to hold up the car. Putting the lower shock mount the farthest outboard as is possible makes for a better ratio thus reducing the amount of spring rate required.
I hope this helps...
Mark

[stanglou]

am i hearing this right, the motion ratio is

distance from LCA inner pivot to lower shock pivot/length of lower armX2

I know that you should try to get the shock as parallel to the arm as you can, and as far out as you can, but i was also confused about the spring motion ratio(66 mustang spring rides on upper arm) is that also a design factor? what isa good motion ratio for the shock and spring?

[wally8]

I believe you have to go out to the centerline of the tread for the last value, not just to the outer ball joint to get the total leverage.


Wally

[jyeager]

Don't know if you can ask what a good motion ratio is. The ratio just determines how you spring and dampen the car.
One design goal is to have the spring/shock mount as far out toward the lower ball joint as possible and another design goal is to keep them as near vertical as possible.

There is a formula for angle correction factor that is based on the spring angle from vertical and the spring rate: ACF = (cos(springAngle) * Spring Rate)

The motion ratio in a nutshell quantifies the ratio between movement of the wheel and movement of the spring, and it's calculated as the guys above said (assuming an A-arm suspension of course).

You then use the motion ratio and the angle correction factor, among other things, to figure out the wheel rate.

Is this to figure out the appropriate spring rate for your application? That's not easy. There is a formula for this: C= WR/(MR)*(ACF), where C = spring rate. But the problem is that the calculation for WR (wheel rate) is based on the spring rate! So there's a circular dependency! Oh well, The best advice I got from Herb Adams' book was that the car should be able to sustain a 1G bump before the suspension bottoms on the stops. So if you use your corner weights you want to figure out what spring rate it would take to for that amount of weight to compress the spring half the total travel. If you have a total of 4" travel in your coilovers, then you want the weight of the car to compress it half way and a 1G bump will compress it the rest of the way. This isn't as easy as figuring out your sprung weight and dividing by 2. You need to take the angle correction factor in to account as well as the motion ratio. But that probably gives you enough to go on. Clear as mud?

[astroracer]

The leverage force is applied at the ball stud.
The tire/wheel is unsprung mass and is not used for this calculation.
Here is one of the calculators I use...
http://www.proshocks.com/calcs/imotion.htm
This will get you pretty close without running the suspension through a design program like Performance Trends...
I was wrong in my first post... The quotient should be Squared, not multiplied by 2... Sorry.
Mark

[astroracer]

am i hearing this right, the motion ratio is

distance from LCA inner pivot to lower shock pivot/length of lower armX2

I know that you should try to get the shock as parallel to the arm as you can, and as far out as you can, but i was also confused about the spring motion ratio(66 mustang spring rides on upper arm) is that also a design factor? what isa good motion ratio for the shock and spring?

I should have clarified. The "shock" in my equation is a coil-over shock so the motion ratio will apply equally to both pieces. A separate shock/spring will need the equation ran on both components and the numbers will differ accordingly although most separate shock spring applications are colinear so the single calc will still apply.
Mark

[wally8]

Thanks Mark. That makes sense now that I think about it more. I better go change my spreadsheet. That will teach me to blindly copy formulas without thinking through them first.


Wally

[Norm Peterson]

It will probably help if you look at each component of motion ratio as a motion ratio in itself so that you remember to square each one. Then you multiply all the [MR]^2 pieces together for the overall answer. This works regardless of where the spring or shock is relative to the wheel. And it works correctly for figuring the effect on rate as a function of the angle correction (no matter what has been presented on one other site in particular). Has to, to satisfy consistency in the basic formulas.

With most common independent suspensions, you have the spring/shock/sta-bar attachment position on the arm relative to the arm length between pivots, spring/shock angle (and probably something analogous with the sta-bar), and a third little MR that addresses the situation where the center of the tire contact patch is not at the same distance from the FVIC as the load-carrying ball joint.

Stick axles with spring seats on the axle tubes have the angle thing and the ratio of the distance between spring seats on the axle and the wheel track for roll only (for 2-wheel bump motion, this "track MR" is taken as 1.00). If the springs are on the control arms, the math becomes much like that for an independent suspension that's been flipped into side view plus a MR that accounts for the distance between the loaded arm pickups on the axle and the rear track (4 little pieces of MR all together). Like the other "track MR", this is 1.00 for 2-wheel bump purposes.

Wally - you'll really appreciate the spreadsheet method of running these numbers if you set it up in terms of the basic length and angle dimensions and let the computer do ALL the math. If you'd like a review done on it at any point, just let me know. I've already got this stuff incorporated into a lateral load transfer distribution spreadsheet, so I'm not trolling for free tech off somebody else's time & effort.

Norm

[Norm Peterson]

Is this to figure out the appropriate spring rate for your application? That's not easy. There is a formula for this: C= WR/(MR)*(ACF), where C = spring rate. But the problem is that the calculation for WR (wheel rate) is based on the spring rate! So there's a circular dependency! Oh well, The best advice I got from Herb Adams' book was that the car should be able to sustain a 1G bump before the suspension bottoms on the stops. So if you use your corner weights you want to figure out what spring rate it would take to for that amount of weight to compress the spring half the total travel. If you have a total of 4" travel in your coilovers, then you want the weight of the car to compress it half way and a 1G bump will compress it the rest of the way. This isn't as easy as figuring out your sprung weight and dividing by 2. You need to take the angle correction factor in to account as well as the motion ratio. But that probably gives you enough to go on. Clear as mud?

That's where either experience or a little more investigation through the literature comes in. You can start with a wheel rate that you know from experience is at least in the ball park. Or you can start from an analytical position with some ride frequency and corner weight to establish a starting point for wheel rate. Either way, there will be a certain amount of iterating to follow.

With ride frequencies considered for both front and rear, you'll likely end up with a better match between front and rear springs for ride considerations (something that becomes more noticeable as your shocks start losing their damping, BTW). So even if you start straight away from direct initial estimates of wheel rates, it's worth running a couple of quick calculations (or throwing them at another spreadsheet ) to see what your ride quality can be expected to be like at least in terms of pitch motion.

Norm

[jyeager]

Yes, that's a great point. It seems that mathematical equations can't get you the perfect spring rate without trial and error (or in this case, perhaps simulations or iterating through the formulas).
I completely forgot to mention the design goal of having the same suspension frequency at the front and rear.
Thanks.

[Norm Peterson]

Actually, you want the rear frequency to be slightly higher than the front frequency so that it completes its first full cycle at the same time that the front does (compensating for the time delay that it takes the car to travel one wheelbase).

Although this "flat ride" goal is seen primarily as a ride comfort consideration, there's even some performance benefit to be had for at least starting with this in mind - if the shocks don't have to damp pitch motions in addition to heave and individual wheel bump motions, they will either be more effective or perhaps last longer.

Just a little food for thought - since the spring/shock/etc. angle rarely remains constant, wheel rates are nearly always slightly rising or falling. That makes the above an approximation, so it's not worth getting too fussy with exact frequencies or "flat-ride" speeds.

Norm

[element180]

FOund this at the Atlas F1 board

a, I must love to argue or somethin. Now the subject is on motion ratio's, always been taught, disregarding angles at the moment

a = dist from lower arm axis to ball joint
b = dist from lower arm axis to spring mount

MR = b/a

While reading over Milliken on the subject it becomes pivot point to wheel, not ball joint, which makes sense as the torque is reacted at the wheel and we are tryin to find wheel rate, not ball joint rate, that thing is just along for the ride. But then I figure that the wheel doesn't actuallt rotate around the lower arm axis, but the IC.

Then I come across Herb Adams in Chassis Engineering with his equation of

a = dist from lower arm axis to spring mount
b = dist from lower arm axis to ball joint
c = dist from IC to ball joint
d = dist from IC to wheel center

MR = (a/b)^2 * (c/d)^2

Sounds about right, but something still doesn't seem to be clickin on all cylinders, anyone have any insight? I've got some MR numbers from Bill Mitchell's program for our car, but Mr. Mitchell is tight lipped at the moment over the subject. But I have seen many a program use the first equation to figure out motion ratio's, and that seems scary.

[Norm Peterson]

Usually, the c/d ratio (using your nomenclature) is within a couple percent of 1.00 with the chassis at its static ride height. After squaring for wheel rate purposes, it's still only 'off' by 5% or so. That's for a car with reasonably stock-ish geometry and wheel offset.

Note also that the FVIC component of motion ratio is slightly variable in both ride and roll modes as the FVSA lengths vary. A rather complicated formula could be written to cover this variability in "c" and "d", but nobody would ever use it outside of developing a spreadsheet or other computerized analysis.

I suspect that most people figure that keeping the theoretical numbers within 5% is close enough most of the time. Then again, I've seen the spring angle correction factor not being squared (it should be), so I hope I'm not assuming too much.

Just for comparison, the 5658, 5660, 5662, and 5664 Moog springs are in approximately 10% rate steps.

Norm