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Discussion Starter #1
This will be the thread about leaf spring tech....

I will be trying to copy some discussion and posts from another thread into this to get it started.
 

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There is very little info on Hotchkiss leaf spring geometry. Even in 'Race Car Vehicle Dynamics' by Milliken there is very little info.

Basically only this picture....



There is a little text, but it doesn't help much.
 

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From Jalbrecht42....

Yeah I'd be curious to see if you can dig anything up. I may be wrong, probably am, but I think the diagram up above may be backwards. (That is, I believe a flatter or "less vertical" shackle corresponds to a lower effective spring rate.)

For example with a perfectly vertical shackle it should result in an 1:1 ratio; if your spring rate is 300 lb/in for instance, the instantaneous effective rate with that shackle would be 300lb/in I believe.

Now the other far extreme, if your shackle was parallel to the ground, any amount of force would cause the system to compress; effectively the spring rate would be 0 (ignoring the lengthwise forces applied to the spring, which you can't really do..).

Anyway thinking of those two extremes suggests to me that at angles in between, the more leaned over (less vertical) the shackle, it seems the lower the effective rate will be.

I played with some examples in CAD, and it seems to be consistent with this. For example comparing a 30 degree angle at ride height (30 degree from vertical) to a 60 degree (from vertical) it appears as though the 30 degree reduces the effective spring rate by around 10%, and the 60 by about 20%.

Anyway I don't want to derail this thread and I do want to recheck my numbers, but I'm curious to know the truth and/or see where I screwed up....

Since I'm sketching things anyway, could you tell me more about your springs, shackle and mounts: distances, spring length, free arch, thickness, number of leaves, claimed spring rate, etc?


From Mieser....

Spring rate. There has to be a vertical component to the spring rate in regards to the shackle. If the spring is rated for say 100lbs/in, we know that for every 100lbs added, the spring moved 1". If the shackle is also swinging in a way that adds or subtracts vertical movement, that is going to have an effect on spring rate. If you compress the spring 1", but if the shackle movement also lets the axle displace vertically, then you have just lowered spring rate. The reverse should also be true. You could also get yourself into a position where the shackle has nowhere to swing, or cannot accommodate the change in spring length, which could lock the system ( or approach an infinite spring rate? ). To calculate this we would need to make an accurate model of the length/arch of the main spring leaf. We wouldn't really need to know spring rate, you could just graph the vertical displacement of the entire system vs the vertical displacement of the spring.

From Tgomes1987

I think this leaf spring discussion should get it's own thread so CJ3BL's thread isn't too plugged up with this. It would be nice to get this explained and discussed. I can't seem to find anything on calculating how the shackle angle effects the spring rate yet. Maybe since most people just go to coils or coilovers when they get into this not much is out there.

I've quoted the section on shackle mechanics below where I got the picture. After reading your post I went and read through the whole section a few times. It sounds like you are on to something because the second part talks about the jacking effect with the spring eye moving up and down also effecting spring rate in the opposite manner.

More information to ponder I guess...

Jeep Parts, Jeep Accessories & Jeep Soft Tops From The Jeep Parts Experts - Quadratec

Shackle Mechanics

The angle of the shackle can stiffen or soften a spring's normal rate. You can determine the effective angle of a shackle by drawing a line through the middle of both spring eyes and a line through the shackle pivots. Then measure the angle formed by the two lines (measure ahead of the shackle - see illus. 3). You can increase the effective rate of a leaf spring by decreasing the shackle angle. An increase in shackle angle will produce a decrease in the effective leaf spring rate of a leaf spring.
A good starting point for shackle angle is 90 degrees. In this position the shackle has no effect on spring rate. Keep in mind that the shackle angle changes (and consequently the spring's effective rate changes) whenever the suspension moves. Also, the shackle's angle will change whenever you change the chassis' ride height, the arch of the leaf, the load on the leaf, or the length of the shackle. Since the shackle direction changes when the leaf is deflected past a flat condition, you should avoid deflecting the right rear leaf to an extremely negative arch condition. This could cause a very large shackle angle at high loads and consequently a very soft spring rate. Excessive body roll and poor handling could result. You can correct this problem by decreasing the shackle angle, increasing the arch, of the spring by increasing the rate of the right rear leaf spring.

Shackle length is another factor affecting the rate of a leaf spring. A short shackle will change its angle (and the effective rate of the leaf spring) quicker than a long shackle upon deflection of the leaf. There is a second shackle effect on the stiffness of the rear suspension that counteracts and sometimes exceeds the shackle?s effect on spring rate. This second effect occurs whenever the shackle swings in its arc and moves the rear spring eye vertically.

The vertical movement of the rear spring eye causes a jacking effect. If the shackle movement forces the rear spring eye downward, the leaf will deflect and exert an upward force on the chassis that will add stiffness to the rear suspension. Conversely, the shackle will reduce suspension stiffness if t causes the rear spring eye to move upward during suspension travel.

The stiffening effect occurs during suspension deflection whenever the rear spring eye is ahead of the upper shackle pivot and the shackle is moving rearward (see illus. 4, example B). In this position, however, the shackle also produces a softening effect by reducing the effective rate of the leaf spring (due to the large shackle angle). The overall effect to the stiffness of the rear suspension is determined by the greater of the two shackle effects. Under opposite conditions, you can expect a reversal to the above effects. If the rear spring eye is located behind the shackle pivot (illus. 4 example A) the shackle effect will tend to reduce suspension stiffness whenever the shackle moves rearward. However, the small shackle angle will tend to stiffen the spring's rate. The overall effect to the suspension's stiffness is determined by the more dominant of the two shackle effects. Keep in mind that the movement of the rear spring eye (from its static position) is mostly forward under racing conditions.

If a leaf goes into negative arch the travel direction of the shackle changes and the shackle effects change. Handling is not consistent under these conditions.

The second effect of the shackle can be enhanced by increasing the length of the shackle. Generally, the second shackle effect (jacking)is dominant.
 

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Picking up from this thread it got me thinking about a question/curiosity I've had for awhile about leaf spring rates and how they are effected by shackle angle.

My basic assumption about the way this works goes something like this:

(from above)

For example with a perfectly vertical shackle it should result in an 1:1 ratio; if your spring rate is 300 lb/in for instance, the instantaneous effective rate with that shackle would be 300lb/in I believe.

Now the other far extreme, if your shackle was parallel to the ground, any amount of force would cause the system to compress; effectively the spring rate would be 0 (ignoring the lengthwise forces applied to the spring, which you can't really do..).

Anyway thinking of those two extremes suggests to me that at angles in between, the more leaned over (less vertical) the shackle, it seems the lower the effective rate will be.

Well this is what I always assumed to be true until one day I bothered to try to look it up on the internet and all I could find is this image, repeated all over the place:



So my thought is, "Okay, either that's backwards, or I'm just confused". Well I've re-read the text and various websites and I'm still confused.

I'm a visual person, so I decided to draw out a few cases and see what I see. Tell me what you think, if this is right or if I'm missing something completely.

(continued next post)
 

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I decided to start with the parts and geometry CJ3BL is using on his build since that's what peaked my curiosity.

To start with here's some numbers, mostly just an educated guess on my part, but this is really just for example anyway. (After doing this spreadsheet, CJ3BL told me the springs are actually .24" thick, but close enough for now).



I just used a generic spring rate formula that I found plastered all over the web:

10000000 x Number Leaves x width x thickness^3 / free eye-eye length of spring = spring rate [in/lb].

His initial geometry is as follows (YJ included for reference)



With that I then drew up a case with a 90 degree shackle angle (where the angle is the measurement between a line drawn through the spring eyes and a line drawn through the shackle holes). I had to iteratively play with my model and spread sheet to find a spring hole-shackle hole distance that resulted in a 90 degree angle at the expected 700lb load (based on the above table). I know it's hard to read, but I put the numbers in the sheets below. Also note, this example is just for the rear of his Willys.



If someone was a little better at trig than me, they could surely do all of this in a spreadsheet... anyway, here's my simple spreadsheet (It's just based on numbers from my CAD sketch)



To define some terms here:

A) Spring condition. Compressed flat, ride height and at free arch/no load.

B) Relative shackle angle is the angle between a line drawn through the spring eyes and a line drawing through the shackle holes.

C) Angle from vertical is the measured angle between the shackle and a vertical line

D) Axle vertical travel is the vertical distance the axle has traveled for each condition.

E) Spring arch height is the distance from a line drawn through the spring eyes and the furthest point of the arch centerline of the main leaf of the spring.

F) Distance spring compressed is the relative distance the arch has traveled relative to a line drawn through the spring eyes. (spring arch height minus free arch height).

G) Force in spring is simply the spring rate x F (dist the spring has compressed).

H) Force at axle is factoring in the motion ratio of the spring to actual motion and force felt at the axle. =F/D*G

This last one is the one I'm mostly likely to have messed up, but the way I'm thinking of this is similar to a cantilever shock for example. If you have a 2:1 ratio for instance, you would have double the travel a the wheel or 1/2 the spring rate at the wheel as felt at the shock. In this case the ratio changes throughout the spring travel, so these numbers only apply at this particular point.

I) Is the average spring rate in this position = H/D (force at axle/ total travel to get to that point)

J) Is the horizontal distance from the FWD spring eye to the shackle mount. In all cases the vertical distance is fixed at 6.438"

I then repeated this same thing, adjusting the sketch and solving for "ride height" at shackle angles of 80, 70 and 60 degrees. The only adjustment made is to the ride height shackle angle and the "J" distance.





 

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There's a few things I've oversimplified here:

For one, I'm ignoring the compressive force this load puts on the shackle. I believe this force will act to try to straighten the spring pack, further reducing the effective spring rate. I believe the more flat the shackle, the more pronounced this effect but conversely the more compressed (flatter) the spring is, the less this effect will act to straighten the spring. So it may cancel out kinda sorta. Don't know.

I also assumed a constant spring rate in all of these conditions which probably isn't the case. I believe the more arched the spring, the higher the rate. The spring rate formula above does seem to account for this, but I did not solve for the spring's rate at each arch position.

I'm now starting to wonder if this is not a good assumption.. but I do notice that there is more arch in the "stiffer" (90 degree for example) ride height conditions vs the 'softer' conditions. So the effect on spring rate may be even more pronounced than indicated.
 

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Discussion Starter #8
A lot to think about for sure....

Some other ideas to ponder.

-There will be some kind of twist-rate component to the leaf spring when the axle is articulating.

-Interleaf friction.

-What happens when the spring is pushed into negative arch.

-What happens when the axle pulls the spring beyond static arch on droop?
 

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Brennan,

I also have some leaf spring info from a chassis dynamics section of an old Chevy Power Catalogue I can contribute if you would like it.
Talks about forces that induce S bend in springs and how moving the front of the springs inward induces anti roll (in the rear) etc. other good info as well.
I'll dig it out and send it to you in a e-mail so you can post it up.
 

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My head hurts:flipoff2:all I know is that my springs work very well:D
Good! My goal was to take something simple and overcomplicate it. :homer:

I like leafs because they are simple and can work great. But I've also been in a number of leaf spring rigs that are all over the road, ride rough, or have otherwise terrible manners. A lot of it has do with things like friction (why a new YJ might drive fine but a clapped out 200k mile one rides like a shopping cart on a cobblestone road) but geometry surely plays a big role too.

I've seen some that work great, some that don't. I think they can be very tunable, and think it's worth understanding what is happening when we move the hangars around to make the shackle angle "look" right.

-What happens when the spring is pushed into negative arch.

-What happens when the axle pulls the spring beyond static arch on droop?
I don't think there is anything magical about springs going into negative arch. The length, thickness and material really dictates just how far the spring can flex without yielding (permanently sagging). For the same material of the same size, I don't see how a spring with 6" of arch flexed flat would be really any different than a spring with 3" arch flexed 3" past flat.

Assuming you aren't yielding the spring, it appears that the rate will increase slightly because the shackle angle will be headed in a more vertical direction. (The spring end will be moving down while the axle is moving up). Easy enough to add to my sketch and see..

When it droops below static arch the axle is pulling the spring down (stretching it). I think it would have a similar spring rate, but now the force is acting in the opposite direction. I think things like the gaps between the spring clamps and main and the way the lower leafs fit against the main will have a big impact on what that spring rate is.


Anyway the takeaway I have from what I looked at is:

-A flatter (less vertical) shackle angle results in a softer spring rate.
-This also results in a little more travel (just like changing the lever ratio on a cantilever shock, or leaning a coil over on a solid axle).

I still don't understand why this seems to contradict the standard shackle angle diagram.

I don't understand why this particular Rubicon Express spring seems to be too short for a stock YJ. From what I see you'd want the shackle hangar moved a bit closer to the spring hangar to prevent shackle inversion at max droop, regardless of what spring rate you might want. This makes me think I did something wrong, but I don't know what.
 

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I am using Rubicon Express reverse eye Yj springs on my 3B. I figured that since they were meant for a Yj, I went with the same shackle hanger to spring hanger centers on a stock Yj, which is 44 inches. My shackles are 4 inches center to center and it seems to be a pretty good fit.
 

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Good! My goal was to take something simple and overcomplicate it. :homer:

I like leafs because they are simple and can work great. But I've also been in a number of leaf spring rigs that are all over the road, ride rough, or have otherwise terrible manners. A lot of it has do with things like friction (why a new YJ might drive fine but a clapped out 200k mile one rides like a shopping cart on a cobblestone road) but geometry surely plays a big role too.

I've seen some that work great, some that don't. I think they can be very tunable, and think it's worth understanding what is happening when we move the hangars around to make the shackle angle "look" right.



I don't think there is anything magical about springs going into negative arch. The length, thickness and material really dictates just how far the spring can flex without yielding (permanently sagging). For the same material of the same size, I don't see how a spring with 6" of arch flexed flat would be really any different than a spring with 3" arch flexed 3" past flat.

Assuming you aren't yielding the spring, it appears that the rate will increase slightly because the shackle angle will be headed in a more vertical direction. (The spring end will be moving down while the axle is moving up). Easy enough to add to my sketch and see..

When it droops below static arch the axle is pulling the spring down (stretching it). I think it would have a similar spring rate, but now the force is acting in the opposite direction. I think things like the gaps between the spring clamps and main and the way the lower leafs fit against the main will have a big impact on what that spring rate is.


Anyway the takeaway I have from what I looked at is:

-A flatter (less vertical) shackle angle results in a softer spring rate.
-This also results in a little more travel (just like changing the lever ratio on a cantilever shock, or leaning a coil over on a solid axle).

I still don't understand why this seems to contradict the standard shackle angle diagram.

I don't understand why this particular Rubicon Express spring seems to be too short for a stock YJ. From what I see you'd want the shackle hangar moved a bit closer to the spring hangar to prevent shackle inversion at max droop, regardless of what spring rate you might want. This makes me think I did something wrong, but I don't know what.
Your analysis is pretty interesting alright! Thanks for working it up using my project parameters as an example. What a bonus, as I can benefit very directly from the discussion!

The drawing with the "90degree" positioning that your earlier post references comes from Quadratec. Here's a link for everyone: Jeep Parts, Jeep Accessories & Jeep Soft Tops From The Jeep Parts Experts - Quadratec

I also pondered why the RE springs I have seem too short to prevent inversion on YJ hanger geometry (as best I could find for YJ reference dimensions). On the rear spring, there's a travel limit rearward from the shackle hitting the bumper on a YJ since the shackle pivot is up in the rail. For simple retrofit use on a YJ without boomerang shackles, maybe that's a practical constraint that would keep RE from making the spring longer.

In my case, as you show, I shortened up the hanger eye to eye distance slightly to avoid inversion. I checked this by cycling the single main leaf and it may be cutting it close at the current spacing. On the other hand, the full pack may not droop as much, so i may actually have more margin on the risk of inversion once I put the full spring pack back together. It is something I'm going to check when the full vehicle is together... so i have lots of time to see where this spring thread leads!

On your analysis of rate effects:
The referenced Quadratec article discusses both an effective spring rate change from shackle angle but also an effective rate change from a "jacking" effect. It sounds like the shackle angle effect on rate and the jacking effect on rate can offset each other, with one dominating over the other depending on the geometry and operating condition.

Your analysis drawing and data are like the the "case A" jacking effect figure and discussion. Your analysis is showing a softening effective spring rate with greater shackle angle (from vertical) and this is consistent with the "jacking effect" they describe.

You had mentioned previously that your analysis seemed to be running counter to the posted 90 degree / angle effect drawing from the Quadratec article. Looking at your methodology, I'm wondering if what you are modeling is actually this jacking effect, not the angle effect. Your model shows the effective rate change due to the upward rotation of the shackle creating more vertical compliance to soften the effective rate. This seems to be the case A jacking example. The article also indicates that in this geometry, the shackle angle effect is stiffening the rate - countering the the jacking effect to some extent. It is not too clear when one or the other starts to dominate.

I ordered the SAE design & application book for leaf springs and will see if it can shed some light on the two different shackle effects.
 

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I have my shackle at a neutral angle and the spring itself angled to give me a short high instant center
 

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Your analysis is pretty interesting alright! Thanks for working it up using my project parameters as an example. What a bonus, as I can benefit very directly from the discussion!

The drawing with the "90degree" positioning that your earlier post references comes from Quadratec. Here's a link for everyone: Jeep Parts, Jeep Accessories & Jeep Soft Tops From The Jeep Parts Experts - Quadratec

On your analysis of rate effects:
The referenced Quadratec article discusses both an effective spring rate change from shackle angle but also an effective rate change from a "jacking" effect. It sounds like the shackle angle effect on rate and the jacking effect on rate can offset each other, with one dominating over the other depending on the geometry and operating condition.

Your analysis drawing and data are like the the "case A" jacking effect figure and discussion. Your analysis is showing a softening effective spring rate with greater shackle angle (from vertical) and this is consistent with the "jacking effect" they describe.

You had mentioned previously that your analysis seemed to be running counter to the posted 90 degree / angle effect drawing from the Quadratec article. Looking at your methodology, I'm wondering if what you are modeling is actually this jacking effect, not the angle effect. Your model shows the effective rate change due to the upward rotation of the shackle creating more vertical compliance to soften the effective rate. This seems to be the case A jacking example. The article also indicates that in this geometry, the shackle angle effect is stiffening the rate - countering the the jacking effect to some extent. It is not too clear when one or the other starts to dominate.

I ordered the SAE design & application book for leaf springs and will see if it can shed some light on the two different shackle effects.
I had the link on the original post but it must have gotten lost in the copy and paste so thanks for re-posting that.

It sounded like from that article that the jacking effect tends to be dominant but I am hoping the SAE design book can shed more light on how to determine when each effect dominates.
 

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I had the link on the original post but it must have gotten lost in the copy and paste so thanks for re-posting that.

It sounded like from that article that the jacking effect tends to be dominant but I am hoping the SAE design book can shed more light on how to determine when each effect dominates.
It's a great article TGomes1987! . Thanks for your original post link. I couldn't find it in the new thread, and didn't want to lose it. Sorry I didn't give you credit for your original posting of it.

From reading the article again, to me it seems like the angle and jacking effects are described separately but are really are continuous aspects of the geometry.

At a resting position of 90 degrees (as defined in the article drawing) the shackle is at the position that allows the greatest change in spring length to support compression and decompression of the spring with the least amount of shackle rotation. If the spring was mounted so that the fixed and shackle eye were level, then at this 90 degree position there would also be the least weight jacking- since in a range of rotation near 90 there is little change in the weight bearing role of the shackle- it's basically in direct compression along it's length. (Note - I'm not advocating to mount the spring level as there are other reasons not to- this is just for discussion of shackle effects). So basically at the 90 degree position the shackle is at the position that provides the most responsiveness to spring length change from spring compression and decompression, with the least weight jacking.


As the rest position moves away from 90 in either direction, then the shackle has to rotate through a greater angle to achieve the same spring lengthening amount, since it's rotation now has a greater vertical component and a reduced horizontal component. In addition, the amount of vertical movement of the shackle now plays a bigger role in balancing the weight load with the lengthening / shortening of the spring. Depending on which direction away from 90 the rest position is set, the direction of rotation either acts to lift the weight of the vehicle or let is drop further than the spring would on it's own - which is where the "weight jacking" effect description comes in to play.

I think the model Jalbrecht42 put together may be primarily modeling the weight jacking effect on static spring rate as the shackle position moves father away from 90. At the same time you can also see on his graphics how the amount of shackle rotation is increasing as the rest position moves away from 90, in order to achieve the same lateral accommodation of the spring length change. So while the effective static spring rate is changing with different rest angles, the dynamics of the shackle and spring movement are also changing. With the resting angle at 90 the shackle can respond to spring length change the fastest since it takes a smaller rotational angle, and it has no appreciable jacking effect in handling response. As the rest angle moves farther away from 90, the shackle response will be slower due to the longer angular displacement needed, and weight jacking effects on handling will start to be more evident. Whether that's good or bad I don't know! I think that's how the geometry works, but I sure have a ways to go to fully understand the trade-offs. Fun stuff!
 

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Discussion Starter #18
From what I am reading about the 'jacking' effect, they are just talking about if the shackle is changing vertical displacement of the spring eye.

If the shackle eye is moving DOWN vertically, it makes spring rate rise.
If the shackle eye is moving UP vertically, it makes the spring rate drop.

Many vehicles ( full size trucks ) also have shackles that are the other direction. The fixed eye for the shackle is below the spring eye. I have heard those refereed to as 'tension' style shackles.

I don't think they are talking about anything to do with actual chassis dynamics, just effective spring rate.

Once the spring goes flat the shackle is going to reverse it's direction of travel. That would cause the spring rate to start rising past a certain point.

Also, I think we have basically proved that the standard drawing about shackle angle vs spring rate, we commonly see, is wrong. Even in the ideal situation where the shackle is at the perfect angle, the spring rate is still not linear or even consistent as the shackle moves through it's arc.
 

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Agreed on your description of jacking effect.

While the article does address the shackle position effect on spring rate, I do think the resting shackle angle effects the dynamics of the suspension response. The more I think about it, the 90 degree recommendation of the notorious drawing may have merit primarily for dynamics reasons.

While the shackle effect on effective spring rate is of interest, to me it doesn't make a lot of sense to set shackle angle primarily for it's effect on spring rate. It seems like the position should be set to allow the spring to cycle most effectively, and with an additional constraint of avoiding inversion at full droop.

If a different spring rate is desired, it seems to me to make more sense to choose different springs rather than move the shackle resting angle at the expense of how it responds dynamically to spring cycling.

I'm thinking the 90 degree position may have it's merit in having the most responsive shackle movement accommodation of changing spring length in suspension cycling, and greater handling stability due to minimum jacking.

The "Slider" idea is accomplishing a similar idea, taken a step further - i.e. the spring rate isn't effected by a rotational shackle constraint at all, and there's no jacking effect. However, sliders introduce different friction and clearance sloppiness considerations.

Fun stuff to think about.
 

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SAE HS-788 Leaf Spring Design & Application Manual

I bought the SAE HS-788 design manual. It's got a lot of great info in a compact volume. Highly recommended if you like to geek out about leaf springs. It has a very good chapter on "Installation Effects", as we've been discussing. It's pretty detailed in it's approach so it takes some careful reading and study (at least for my slow poke brain). Here's some qualitative excerpts on points we have been discussing:

"When one eye is fixed and the other eye is shackled, two effects will result. As the spring deflects, the length of the chord changes, and the shackle will swing and change it's angle. In swinging, the shackle may lift or lower the eye of the spring and with it the point of load application. This is the first shackle effect. When the shackle is not perpendicular to the datum line of the spring, the shackle load will have a longitudinal component, either compressing or stretching the spring between the eyes. Compressing will decrease the rate of the spring, while stretching will increase the rate. This is the second shackle effect."

This is basically the same info as described in the Quadratec article cited previously. The first effect is the same as the "jacking" effect described in that article, and the second effect is the same shackle angle effect shown in the well known drawing in the Quadratec article. The drawing "A" position (with stiffer rate) corresponds to the SAE description of stretching causing increased rate. The "B" position of the drawing (with softer rate) corresponds with the SAE description of compression decreasing the rate. So , I believe the SAE handbook supports the Quadratec shackle angle drawing (for solely the angle effect).

An interesting point in the SAE manual relative to the second (angle) shackle effect is:

"In the second shackle effect, the compressing or stretching of the spring changes when the shackle passes through the vertical position. The amount of shackle effect depends on the load which the spring carries rather than on the rate of the spring."

I thought this was an interesting point -in other words the magnitude of the shackle angle effect varies with the amount of load.

Beyond these qualitative statements, there's some quantitative charts that get to the specifics of how these factors interact to change effective rate. These show non-linear effective rate curves based upon nominal spring rate, shackle position, shackle length, camber, and load variables. However the charts use some terminology and conventions that are not too obvious.

I'm going to try to work through my build set-up (as described by JAlbrecht's earlier posts), putting it into the terminology that the book defines so that I can better understand the use and meaning of the charts. I don't have complete data for my springs, but I think I can do some estimations for missing specific spring data for the sake of example. If I get it to work out, I'll post it along with applicable charts.
 
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