Motion Ratios

In the adjusting coilover ride height section of the wheel alignment course, Andre makes the comment that the motion ratio of a Macpherson strut is 1:1. In the context of adjusting the ride height, this comment is pretty inocuous. Many internet sources will "confirm" that the motion ratio of a Macpherson strut is close to 1:1, such that it is generally considered received wisdom.

Actually, it is probably closer to 0.9, which does go against intuition and arguments based on measuring lever arms. The motion ratio may not be that significant to ride height adjustment, as that is an iterative process, but it is critical to calculating suspension frequencies.

While Dixon's "Suspension Geometry and Computation" (p. 287) will confirm my assertion, it isn't book learning that prompts this thread. After installing damper pots, calibrating them to damper movement, and attempting to correlate the damper travel and wheel travel I simply could no get my measurements to confirm the 0.96 motion ratio I have assumed for years. It is actually closer to 0.86. That is enough to shake one's faith in the internet!

I have concluded that the only sure way to obtain motion ratios, or to confirm the ratios you have calculated/assumed is to measure them.

I offer this as food for thought, and maybe fodder for a future course dealing with wheel rates, unsprung weight and suspension frequencies.

There may be a little confusion as there are several different things in play here - and it's [**** THAT late!] 4am here, so a mite sleepy and can't recall exact terminology. It isn't helped by some schools having the wheel to spring, and some having the spring to wheel as the ratio.

The motion ratio of the wheel to the strut is indeed 1:1 as the wheel and stub axle move together when the spring is compressed.

However, it is also less than that if you consider the strut is inclined, so 1" of vertical motion of the wheel is going to be a little more than 1" - and just to make it more fun, because the track control arm moves in an arc, the bottom of the strut is also moving in an arc and so the strut inclination angle is changing through it's range of travel.

You may have other factors - but it isn't that difficult to figure out the formulae for what you want to know.

Hi James, some good stuff in there! On this topic, it really depends on the assumptions you make along the way and what references you use. My thinking on this is that as the lower part of the strut body is fixed to the upright, the difference in MR you are measuring is coming from the inclination angle of the strut (relative to vertical), which I think is what Gord is also referring to. Often we are defining the MR as vertical wheel travel vs strut displacement (which is not vertical travel).

As Gord says, everything is moving in arcs as well. So if you really want to be pedantic about it, using a constant MR in the first place isn't going to cut it, as you can imagine the MR is constantly changing. In saying that though, for a MacPherson strut in a road race car (where the travel is going to be limited anyway) the MR will be so close to constant, it will be fine! This tends to become more of an issue in highly non-linear suspensions like you find with inboard-type setups.

It's a good point you bring up though, and it will definitely become more of an issue when strut inclination angles and suspension travel increase for calculating spring, and damping parameters! 😃 This will be a good discussion for our upcoming suspension course.

It was, ta. :-)

(Speaking stricly Macpherson strut here) The standard way to estimate MR is to constuct a 2-D model based on the front view. A few deficiencies in this approach:

1) the inclination of the strut tube in side view (essentially the caster angle) is ignored

2) assuming the suspension has anti-dive built into it, the outer ball joint moves forward (i.e. out of the page) with compression, which is also ignored.

3) in my case (BMW) the suspension has two outer ball joints, and motion occurs about a virtual outer ball joint that moves with the suspension and can only be solved accurately with 3-D suspension kinematic software. It can be approximated as fixed for discussion.

4) the instant centre defining the camber gain (i.e. the one we usually talk about) defines the instant swing arm, which is relevant only with respect to the camber gain curve. It has no relation to the MR.

5) the outer ball joint moves in an arc defined by the wishbone projected into the vertical plane we are examining.

6) in that same plane the wheel centre lies further outboard than the outer ball joint, and it moves in an arc not centred on the outer ball joint arc. Because it lies further outboard, it moves vertically more than the outer ball joint.

7) assuming a motorsport application and a decent amount of negative camber, the intersection of the wheel centreline and the road lies further outboard than the wheel centre. This point moves vertically more than the wheel centre or the outer ball joint.

8) it is unknown where he centre of pressure is within the contact patch, but it is likely not on the centreline of the wheel, for a cambered wheel. Since MR (or strictly MR^2) is mostly relevant with respect to the relationship between tire vertical forces and spring forces, this introduces some uncertainty. A simplifying assumption would be that the centre of pressure is vertically below the wheel centre, and that would get rid of the problem of point 6).

So, Tim, I certainly agree that definitions are important. Likely we want to know MR to tune a specific suspension frequency. Assuming MR=1 will definitely overestimate our suspension frequency. When testing confirms that, it would be easy to assume that the difference is due to the tire, but the MR error will be a large part of it. In order of decreasing confidence, I trust: measured suspension frequency, measured MR (appropriately defined), MR from a 3D kinematic model, MR from a 2D front view model. This said, even a simple 2D model, as attached, using representative geometry, will show that the MR (defined by wheel strut tube compression/wheel centre vertical height change) will show an MR appreciably less than 1. I have assumed a virtual outer ball joint location to provide zero scrub radius just for argument's sake.

Thanks for that detail James. I think if you're wanting high precision on the MR, then using a 3D model is a good approach, followed by validation by measuring the MRs on the car, this has always been the process I have taken. There are a number of pieces of full kinematic modelling software out there to do this for you, alternatively, you can also make use of a generic CAD system to get the same results (it will just be a clunkier process).

In the end, it really depends on what you are using the MR for. It sounds like by measuring it yourself you have a good understanding of what you have on your car. I'm not sure I would be getting too carried away with calculating the exact theoretical suspension frequencies, it sounds like the information you have already is perfectly sufficient for this. These theoretical numbers are great for getting in the ballpark for rolling out off the trailer in the window, but real-world testing will quickly take over.

What I mean is, the real installation stiffness and dynamic response of your chassis, suspension and tyres will quickly swamp differences in theoretical calculations of frequency response. Let alone the actual track surface you are running on. Testing, on a post-rig in conjunction with being on track is the final word on tuning the suspension.

Based on what you understand about your kinematics already (it sounds like you have a good grasp), I would be moving to modelling it in a 3D kinematics package (or CAD) then validating with measurements on the car. Past that, you've simply got to run the car on track and find what ill work best in the real world!