rear axle motion ratio

in order to calculate rear axle wheel rate starting from coil spring rate, I'm in need of Motion Ratio value. I've been looking for A and B dimensions and spring angle as from image. Since I've found nothing here around, can anybody tell some measure or design values ?

 

I'm doing my homework to calculate chassis front and rear NF (Natural Frequency) starting from OEM front and rear coil springs rates and unsprung mass. Last week I received one brand new BC racing coilover set for my 2007 II Gen Prius and as BC Racing coil springs are much stiffer than OEM, I would like to make a comparison with new NF.

Some measures I've made under the car have given me some more information. Rear axle Motion Ratio (A/B) should be around 0,8 but I'm not satisfied with my measures. It's hard to get some precise measure. I have to find a new measuring method to increase precision.

 

this thread is GREAT ! I was ready to pay for weigh my car somewhere on 4 scales, but with your thread Agent J, I don't even have to waste my time and money !! There are weight values I was in need of. And what more ? now I can confirm values with or without driver: I was starting from 1375 kg without driver and now adding your 75 Kg driver we reach 1450 Kg which is very close to your total 1467 Kg. GREAT JOB !!

 

GREAT idea ! I never thought this could be a way. I don't know if I'll try this way but many thanks for the idea !!

 

I'm back from two days working on BC Racing coilovers to set coil spring preload and static ride height. As these BC Racing coilovers settings come new from factory, they won't work at best in my opinion. Both spring preload and static ride height seem to be something more suitable for the worker who has to assemble all parts together before putting it in the box and ship it around the world. In a nutshell spring preload is too much less than needed and static ride height too hight. I'll post news as my work will progress...

 

I'm back with new measures of rear axle Motion Ratio. As suggested by hlunde I moved to measure displacement values directly on the car in order to validate previous results based on geometrical method. Using two digital calibers placed one at the wheel and the other at the rear axle lower strut mount, I've made seven measures with different motions each time. After having set rear suspension at OEM static ride height, using a jack to move rear axle up and down, here are the seven results:



This average value matches geometrical rear axle Motion Ratio computation in mm previously made as Dimension A/Dimension B = 325/405 = 0,802. Now I can rely on this fact and go on with NF and WR computation.

Here some pictures of measuring sessions:

 

I’m back from few drive sessions and what can I say about BC Racing Coilovers ?

1. U N B E L I E V A B L E ! Unbelievable the way this car goes faster on the road with these BCs !! As fast as you want or can imagine. I would summarize this way: these BC Racing Coilover increase your heart rate !! Unbelieveble !! The way this II Gen Prius has been considered slow and boring for years is just wrong and you can overcome this opinion replacing your springs and shocks. You’ll find you have something that can go fast, very fast !! When I say fast I mean you are faster than other cars on everyday road almost all the time. Engine goes up and keeps pushing more and more as you attack, go in and out a turn. This car is not the same anymore ! It’s definately a SPORT car.

2. How this aggressive coilover set is not harsh at all !! You have something quite near to a race car and can afford on an unbelievable ride comfort !! I belive this is due to shocks monotube design that makes response quicker, eliminating dead working zones where you have dry friction and no suspension travel at all (suspension has to work to WORK)

 

Hi Agent J, nice to hear from you.. well, I sat front lowering at -25 mm and rear at -20 mm from OEM static ride height. If you are replacing your shocks consider BC coilover is an aggressive setup: it's firmer thought not harsh so you will bounce a bit on the road (not with flat asphalt) and this setup will bring more noise into the car even if we don't have spherical ball upper mount (both front and rear) but rubber (harder than OEM). Consider I'm running with the softest (1/30) damping settings both front and rear: it's more than enought !! Springs have no rubber in their upper and lower seats. The whole car changes and it's not anymore a zen vehicle, it calls you to push it fast, very fast. You can kill everything on the road: unbelivable !!

No wheel alignment at the moment and fuel consumption has raised as we know it happens when you are more than a bit out of alignment. No H&R camber bolts anymore with BC as you have buttonhole to make the camber adjustable. I sat it at maximum possible negative camber and at a guess shoul be -1,5 degrees. Will let you know the value next days when I'll go for alignment.

 

Here are some measures made on BC Racing coilover kit for II gen Prius:

FRONT
- Shaft diameter: 20 mm
- Spring: 5 kg/mm rate, internal diameter 62 mm, free height 220 mm, wire diameter 10.5mm, weight 1.21 KG
- Single coilover assembly weight: 5.63 KG
- Stroke 130 mm
- Strut thread pitch: 1.5 mm
- Free bump stop height: 41 mm

REAR
- Shaft diameter: 12.5 mm
- Spring: 4 Kg/mm rate, internal diameter 62 mm, free height 190 mm, wire diameter 11.5 mm, weight 1.41 KG
- Single coilover assembly weight: 3.87 KG
- Stroke 114.5 mm
- Strut thread pitch: 1.5 mm
- Free bump stop height: 36 mm

 

Soft setting is fine. Softest (0/30) damping setting (both front and rear) gives something located in Under Damped level area and that's what I like when I drive the car, whatever drive style comes me up: zen or aggressive.




Rear axle is for sure more Under Damped than front axle. Anyway it seems there is no need to increase damping level as I have both comfort and control in turns.

Assuming 1406 Kg as car mass (2/3 tank), 90 Kg as (left in Italy) driver, 59,8 % front axle and 40,2 % rear axle distribution, 9 % as unsprung mass (both front and rear) the theoretical Chassis Natural Frequency (NF) I've obtained with 5/4 spring rates is:

NF Front: 1,76 Hz (versus OEM 1,21 Hz)
NF Rear: 1,50 Hz (versus OEM 1,26 Hz)

 

In order to refine my math method to calculate chassis NF (Natural Frequency) I'm moving to obtain precise unsprung masses values. Front and rear at least. But each one of the four corner would be the best. Before starting to weight the unsprung masses directly on the car, I would be grateful to anyone already know these values... many thanks