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## How To Calculate Spring Rates

Published: July 16, 2012
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With the purchase of some super cheap shocks for the front, I need to calculate the lbs/in of the springs I had.

I don't have a lot of room up front and you can buy these American made 295mm dirt bike shocks for £25 brand new, with free delivery on a certain popular auction site.

They looked too tempting, but when they arrived they did look a Little smaller than I expected or hoped for.

The shocks come with springs but the lbs/in aren't stated.

## How do I calculate coil spring rate?

Ideally you'd do this with a spring rate checker; a heavy hydraulic press that takes up quite a bit of valuable workshop space, not to mention a ££££.

1. I don't have one and haven't got the room
2. I can't carry one around the auto-jumbles

Luckily, if the springs are uniform, with evenly spaced coils, you can measure them and use the following equation:

Spring Rate = Gd4

8ND3

OK, so that's not a totally easy sum to do in your head but a mobile phone with calculator app allows you to do it standing in a field.

G = Torsional modules for steel = 11.25 x 106 or 11,250,000  (A constant)

d = diameter of wire in inches

N = Number of active coils

D = mean coil Diameter in inches

8 = a constant for all coil springs

Putting it all together:

Spring Rate = 11,250,000 x 0.4724   = 943lbs/in

8 x 6.5 x 2.253

That's an awful lot for a car.

There is about an inch of adjustment space to increase the number of coils (N=6.5) and I could also reduce the diameter of steel used (d=0.477).

Spring Rate = 11,250,000 x 0.36754 = 300lbs/in

8 x 7.5 x 2.253

I'm no expert, but the wire diameter is getting a little thin. Plus with coils this size a small variation in wire diameter or mean coil diameter has huge effects on spring rates.

What if I made up some bigger spring seats to take 3" coil springs and 11mm (0.433") wire?

Spring Rate = 11,250,000 x 0.4334 = 300lbs/in

8 x 6.1 x 33

If I make up some new spring seats, these shocks would have the right spring rate, but even then I'm still not sure about their damping capability. Shame, because they are engineering bling!!

### What spring rate are my giant DRZ400 coil-overs?

Spring Rate = 11,250,000 x 0.454 = 316lbs/in

8 x 6.75 x 33

Ok, so they are giant, but they have about 4" of travel.

That leaves me three options:

• buy some brand new coil-overs designed for kit cars like this
• have a shuffle and fit in those huge DR400 items
• look at some other bike shocks like the Yamaha R1 and R6

Watch this space...

UPDATE

I've bought a set of nearly new single adjustable steel AVO coilovers for a bargain £25 each. They have an open length of 13" and a closed lenght of 9". They came with 4 springs but they are all different spring rates and lengths.

I therefore had to calculate some spring rates. I did some quick research on the exact wire diameters and came up with:

• 0.343 inches
• 0.362 inches
• 0.375 inches
• 0.393 inches
• 0.406 inches
• 0.437 inches
• 0.468 inches
• 0.5 inches
• 0.531inches

I found this chack which was quite handy : http://www.centuryspring.com/pdfs/12-228compression.pdf

The coilovers take a spring with a mean diameter (D) of 2.75 inches. Armed with these figures I was then left to work out which wire gauge (d) and number of coils combo (N) gave me roughly 300 - 325lbs.

I came up with :

• 0.437" (d) and 9 coils (N) = 274lbs
• 0.468" (d) and 10.5 coils (N) = 281.1lbs
• 0.406" (d) and 6.5 coils (N) = 282.7lbs
• 0.437" (d) and 8.5 coils (N) = 290.1lbs
• 0.468" (d) and 10.5 coils (N) = 294.9lbs
• 0.437" (d) and 8 coils (N) = 308.2lbs
• 0.468" (d) and 10.5 coils (N) = 308.9lbs
• 0.468" (d) and 10 coils (N) = 324.7lbs
• 0.437" (d) and 7.5 coils (N) = 328.8lbs
• 0.468" (d) and 9.5 coils (N) = 341.4lbs
• 0.468" (d) and 10.5 coils (N) = 352.2lbs
• 0.437" (d) and 7 coils (N) = 352.3lbs
• 0.468" (d) and 9 coils (N) = 360.4lbs
• 0.437" (d) and 6.5 coils (N) = 379.4lbs

The ideal coil length for these coilovers looks to be 8 inches maximum. From the above attached chart, the nearest spring would be stock number 73276 (304lbs):

 O.D. Stock No. Free Length I.D. Rate Sugg. Max. Defl. Sugg. Max. Load Solid Length Wire Dia. Total Coils In mm Inches mm In mm Lbs/in N/mm In mm Lbs N In mm In mm 3.156 80.16 73276 8.00 203.2 2.282 58.0 304 53 2.3 59 703 3126 4.63 117.6 0.437 11.1 10.6

This stock part basically confirms that my maths is O.K. but a custom spring would need to be made if I wanted closer to 325lbs; which is likely but not a problem these days.

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