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From digest.v6.n277 Fri Mar 7 11:56:47 1997
From: Pete Read <>
Date: Tue, 25 Feb 1997 11:54:49 -0800
Subject: Re: <All> Progressive Spring Mechanics

Thomas Murphy and Jennifer Stork weren't convinced by my earlier description of how progressive springs work. Of course, my first reaction was that they are crazy <grin> -- actually more like panic because I hate to put out misleading information. Fortunately they both were gracious enough to give their reasoning rather than just calling _me_ crazy.

After a moment of self-doubt, I quickly removed the spring from a ball-point pen in my desk to double-check myself (more below). I'm still quite sure my statements are accurate. Let me draw a better picture and give more details. Maybe after this you'll either agree or be too worn down to care any more.

Thomas Murphy writes:
>In Pete Reads last post on this subject he postulated that progressive
>springs compress in steps. My mind would like to disagree. As the
>coils compress, I think they make contact with each other in the same
>way that your foot hits the ground: ie, the heel first, rolling towards
>the toe. If this is true, then the change in spring frequency would
>be more or less continuously variable, not variable in "steps".

Jennifer Stork writes:
>While a spring does look like a series of active coils when it's
>viewed from the side, it actually is all a single, continuous coil,
>and any "bottoming" that takes place (compaction of the spring) is
>going to proceed millimeter by millimeter up through the spring--much
>more gradual than the sort of coil-by-coil progression you describe.
>While there would be some sort of "step" effect if the progressive
>rate springs were made of wire that increased in thickness in big
>jumps, I believe that the tapers (or thickening) of the wire in a
>spring is much more gradual than this.

Both aren't convinced that spring coils compress in a parallel fashion. Thomas talks about the coils hitting "heel first" and rolling forward. Jennifer says any bottoming proceeds millimeter by millimeter up through the spring....tapers (or thicking) of the wire in a spring is much more gradual.

Well first of all, my point was in regard to progressive springs using constant diameter spring wire. I briefly mentioned tapered wire as another method for creating progressive springs, but it's much more expensive to manufacture. Most suspension coil springs are made from fixed diameter wire with constant pitch or distance between coils (there is usually a slight change in pitch at the ends so they can be more square with the spring seats). The normal aftermarket progressive springs are usually constant diameter wire with varying pitch to dynamically change the number of active coils (one or more coils touch).

Suspensions don't bottom on the coil springs. That would damage both the springs and the suspension mounts. Instead some type of rubber bump stop is always used to limit travel. Normal constant pitch springs don't touch coils at all (except a little at the ends because of the slight change in pitch as mentioned above). Progressive springs do intentionally touch one or more coils to reduce the number of active coils and increase the rate.

As Jennifer says, springs are all one continuous coil or wire. The BMW springs I've seen have all been right-hand wound, meaning that the spring coils move farther away as you travel clockwise along the wire (right hand rule). If the pitch is constant, you can place a vernier caliper anywhere between the coils and the distance will be the same.

Think about unwinding the spring so that it's just a straight metal bar. Twist in opposite directions from both sides. The bar (spring wire) will be put in torsion. Because the wire is constant diameter, the deflection (twist) will be even all along the bar.

Now wind the bar back into a spring coil. When the spring is compressed, the spring wire twists the same way -- evenly along its length. The coils start out equidistant (parallel) and remain that way because the deflection is even all along the wire as the spring is compressed. If coils bottom on each other, the parallel motion of the coils ensures that the whole coil touches virtually at the same time -- not step-by-step or millimeter-by-millimeter.

Progressive versus Straight Rate Spring

Here's an example. I'm looking at a catalog picture of some Eibach Pro-Kit springs. The front springs are constant rate while the rears are progressive. The rear springs have 10 total coils, with the top and bottom coils wound much closer together (less pitch). I'm going to assume the end coils are inactive because they rest on the spring seats. This leaves eight active coils.

Below, I've tried to draw cross-sections of progressive and straight rate springs, both at normal ride height and compressed. This still doesn't look quite right because the coils are actually at an angle because of the winding. To use some numbers, let's say that the starting rate is 175 lb/in for both.

Spring rate is inversely related to the number of active coils (see Calculating Spring Rate below). The straight rate spring remains at 175 lb/in because no coils touch as the spring is compressed.

On the progressive rate spring, notice that coils 1&2 and 7&8 are wound more closely together (less pitch than the other coils). As the spring compresses, those coils bottom on each other, reducing the number of active coils and increasing the spring rate.

  Progressive Rate Spring                    Straight Rate Spring  
Normal             Compressed               Normal          Compressed
- ----------         --------------           ----------      ----------
                                            O  (1)   O

O (1) O 1&2 7&8

           \ smaller                        O  (2)   O   all
O  (2)   O / pitch                                     \ same   
                                                       / pitch
                                            O  (3)   O
O  (3)   O                                                   O  (1)   O
                   O  (1)   O \ 1&2         O  (4)   O       O  (2)   O
O  (4)   O         O  (2)   O / touch
                                                             O  (3)   O
                   O  (3)   O               O  (5)   O
O  (5)   O                                                   O  (4)   O
                   O  (4)   O
                                            O  (6)   O       O  (5)   O
O  (6)   O         O  (5)   O
                                                             O  (6)   O
                   O  (6)   O               O  (7)   O
O  (7)   O                                                   O  (7)   O
                   O  (7)   O \ 7&8
O  (8)   O         O  (8)   O / touch       O  (8)   O       O  (8)   O
- -------------  ----------------------       ------------  -------------
Eight Active   Six Active Coils                   Eight Active Coils
Coils          (two less 1&2, 7&8 touch)          (coils do not touch)

Initial rate:

175 lb/in, 8 active coils

Rate when coils 1&2 touch

200 lb/in 7 active coils (175 x 8/7)

Rate when coils 1&2 and 7&8 touch

233 lb/in 6 active coils (175 x 8/6)

In this example, the progressive spring rate changes in 25-33 lb/in steps (1&2 and 7&8 don't initially touch at the same time).

Calculating Spring Rate

W^4 x G
Spring Rate K (lbs/in) = -------------

8 x N x D^3

W - Wire diameter of spring

G - 12,000,000 for steel springs

D - Spring coil center diameter (inches). Measure to middle of

spring coil, not outer diameter.

N - Number of active coils, free to move, not touching other


This is the general equation for calculating spring rate. It shows that spring rate is directly related to the number of active coils, N (e.g. reduce the number of coils by half and double the rate).

It also illustrates the importance of wire diameter, W (increases to the forth power). Many times, wire diameter is the only change between different springs for a series of cars.

For example, the E28 528e and 535i have similar front springs with the same seven coils, but slightly different diameter spring wire (535i = 0.527 inch, 528e = 0.514 inch). Because the springs are the same except for wire diameter, the percent difference in spring rate is easily found.

(535i) 0.527^4

  • = 1.105 = 10.5 percent higher rate for 535i (528e) 0.514^4

Ball-Point Pen Test

And finally, a real world look at springs. Disassemble a click-type ball-point pen. Notice that the spring wire is constant diameter and the pitch (except for the very ends) is also constant -- a straight rate spring.

Compress the spring completely and see that the coils all touch at the same time. Now grab the coils at the center point (halving the number of active coils) and notice that the spring rate doubles.

Is everyone convinced yet or just worn down?

Pete Read
'88 M5
Arlington, VA

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