Getting the spring rate right

[YellowDuck]

The following is the procedure I used to figure out the correct rear spring rate for my bike (2006 Sport 1000). The same thing should work for the biposto, but of course you would have to divide the loads between two shocks.

First, I needed some measurements.

1. Ratio of shock compression to vertical sag. Simply measure the vertical sag of the bike and the length of the shock for two different loads. I used bike sag and rider sag. It doesn’t matter if you measure the whole shock length or the spring length (since it is the difference we are interested in), but I found spring length convenient. For sag, measure from a repeatable point at the axle (I used the tick mark on the adjuster plate), to some repeatable point directly above (I used a bit of dirt on the rear cowling).

ratio = (shock length 1 – shock length 2) / (sag 1 – sag 2)

On my model, the ratio is exactly 0.7.


2. Sprung rear weight. I got this for both bike alone and bike + rider, with the rider in normal position. Measured it just by putting the rear wheel on a bathroom scale, with the front wheel at a similar height. You don’t need the front weight measurements, but I did them anyway for fun. The bike weight was distributed close to 50/50 (202 front / 224 rear), but the rider weight fraction was 62% on the rear. My numbers were:

Bike weight (rear) = 224 lbs
Bike + rider weight (rear) = 346 lbs

Next, you need to know how much of what you just measured is actually unsprung weight (rear wheel, brake, swingarm) at the axle. You could do this by supporting the bike with a bar through the swingarm pivot resting on jackstands, disconnecting the rear shock, and weighing the wheel assembly again with the tire on a bathroom scale. I was too lazy so I just guessed 40 lbs.

So, the sprung weights are as follows:

Sprung bike weight (rear) = 224 – 40 = 184 lbs
Sprung bike + rider weight (rear) = 346 – 40 = 306 lbs


3. The last thing I needed was a measure of the force exerted by the shock alone, without the spring. I just compressed my Penske 8983 by 30 mm against a bathroom scale, and read 55 lb (strictly, I should remove the weight of the shock from that, but mine was too light to measure with my scale). Shocks have very little stiction, so it was hard to get a steady number, but I eventually convinced myself that I had it close enough.


With these measurements, you can calculate the required spring rate (or so my theory goes!). Let’s work in inches and pounds, since those are the units they use for the springs (at least for the Hyperco springs that Penske uses). 1 inch = 25.4 mm.

I decided that I wanted 10 mm of spring preload (that’s spring compression, not sag). 10 mm / 25.4 mm per inch = 0.394 inches.

I also wanted 30 mm of rider sag with that preload. 30 mm / 25.4 mm per inch = 1.181 inches. However, that is vertical sag. To convert it to spring compression, we have to multiply it by our ratio from step 1. So, 1.181 x 0.7 = 0.827 inches.

So, my total spring compression (preload + sag) = 0.394 inches + 0.827 inches = 1.221 inches.

Next, how much weight will that have to support?

From above, sprung bike + rider weight = 306 lbs. However, that is vertical – we need to convert to force along the spring axis, by dividing by the ratio from Step 1.

306 lbs / 0.7 = 437 lbs

Now, subtract from that the force provided by the shock without a spring:

437 lbs – 55 lbs = 382 lbs.

The ideal spring weight is then that force divided by the desired total compression

= 382 lbs / 1.221 inches = 313 lbs / inch.

So, in this case I will install a 300-lb spring, and add a few mm of preload extra.

***********
Why did I measure sprung bike weight (no rider)? To calculate how much bike sag I would get.

bike sag = ((sprung bike weight) / ratio – (shock force) – (preload force)) / (spring rate) / ratio

where the “preload force” is the preload spring compression x the spring rate, in this case

preload force = 0.393 x 300 = 118 lbs

So, bike sag will be
(184 / 0.7 – 55 – 118) / 300 / 0.7
= 0.428 inches
x 25.4 = 10.9 mm

Rider sag is calculated the same way, but replacing bike sprung weight (184) with bike + rider sprung weight (306). The result in this case is 31.9 mm.

*************

In case someone is looking at springs specified with different units, the following might be useful.

To convert a lbs / inch rate to a kg / mm rate, divide by 56.1

To convert a lbs / inch rate to a N / mm rate, divide by 5.72

e.g., my 300 lb / inch spring could also be called a 52.4 N / mm spring.

[YMRacing]

I thought most of you Canadians spoke English!

Good info, thanks.

[simonknight]

The spring rate of the standard Ohlins shock is (I quote a response form Ohlins):

"32 N/mm (3.26 Kg/mm or 183 lb/inch) which is very close to being our softest rate! This is very unusual compared to the Ducati shock springs. But this all has to do with the design of the bike. The linkage ratio, swing-arm length etc."

Note that it is not 90 N/mm implied by the usual method of reading the Ohlins spring part #.

This designed for a rider up to 175lb in gear. I weigh 190 in gear and find this spring plenty stiff.

[YellowDuck]

Thanks for the info. Made me nervous when I read that, but in the end I still trust my math. Also, I have the data from the Penske with the 500-lb spring to compare to, so it is not just theoretical.

The only way such a light spring would work would be if the Ohlins shock had a LOT of internal force independent of the spring. Which is entirey possible.

[simonknight]

Ohlins logic for the low spring rate seems to be related to the leverage / position of the shock. How does your calculation take that into account?

[YellowDuck]

By using the ratio of spring compression to vertical movement of the bike (sag). That is a much higher number (0.7) on our bikes than on most sportiblkes with linkage-type setups, which is the major reason that the spring rate has to be so low.

If the shock was connected to the swingarm directly above the axle, and was oriented perfectly vertically, the ratio would be 1.0, and the calculation would be a lot easier!

My calculations don't account for the "progressiveness" of the geometry though. As the swingarm rises, the shock becomes a little more perpendicular to the swingarm, which increases the effective rate. Not by much though. That is a much bigger effect in linkage-type designs, and is one reason why the basic architecture of the rear suspension on our bikes is a bit inferior.

[Gizmo]

a non linkage leverage ratio can be progressive as well, linkages aren't needed all they do is control the progression becauses on most designs you can't fit the shock in where you need to design in that progression. they usually want to put it between rear of engine and rear whell where it sits vertically when to ger progression they need the top mount to move forward and down ( i think its that way for more?)

the leverage ratio will be low, it looks like its a much longer stroke shock so the spring weight reduces as well.

its unlikely they'll run high compression damping on a low leverage shock but one has to wonder how much suspension performance was taken into account compared to look.

[YellowDuck]

That's my current concern with the Penske. If they had no idea about the correct spring rate, who's to say that they put the right shim stacks in it?

The shock I received came with a nice manual listing all the possible internal damping configurations, but no specs on what was actually installed! I have asked the supplier to provide those as well.

If it turns out to perform well as it is valved now, I would like to be able to tell the rest of you guys exactly what the specs are.

[luther_r]

Thanks for keeping us updated YD. I'll do the same as I get my YSS rear tuned.

[MajorSoftie]

Originally Posted by Gizmo

a non linkage leverage ratio can be progressive as well

That was the thinking behind "lay-down" rear shocks in the period shortly before manufacturers began going to mono-shocks. "Lay-down" shocks provided a rising leverage ratio between suspension travel and shock travel, although not nearly as much as is possible with linkage arrangements.