Designing the Satchell Link

[boodlefoof]

Hey guys. Sorry for another long post (I've gotta break that habit) but I could use some help.

I've been pouring over old threads for awhile both here and on CC.com. I think the Satchell link design for my Datsun 240-Z project is coming along well, but I would like any input you might have.


The car: 92'' wheelbase, 62'' track width both front and rear, and I am guessing it will come out to about 2000 - 2200 pounds when done. Front suspension has an RCH of 3''.


The Satchell link (current design):

RCH is 10.9'' in its present iteration
Upper link axle housing mount = 16.5'' high (3.5'' over axle CL)
Upper link frame mount = 15.5 high''
Upper link down angle from rear to front is 1.7*
Upper links are parallel in plan view and 34'' long
Lower link axle housing mount = 8'' (5'' below axle CL)
Lower link frame mount = 9.75''
Lower link up angle from rear to front is 3.5*
Lower links are at a 45* inward angle and are 28.3'' long
Side view swing arm length is 72.5''
Anti-squat is 101%

There appears to be mild understeer, but I am unsure of how to calculate a percentage. For example, in a 3* roll, the axle housing has moved about .17'' (forward on the outside axle relative to the roll, rearward on the inner axle relative to the roll). By 5* of roll the axle has moved .3'' at either end.


The questions...:

1. I'm unsure whether this is or isn't too much roll understeer... based on what I've read, I'm shooting for around 2-3% roll understeer. I can easily increase or decrease the understeer by adjusting the angle of the upper arms in side view.

2. How high of a RRCH would be acceptable? It seems that I've read posts describing anything from 8''-15''. There is lots of info talking about FRCH, but RRCH seems more of an enigma.

At present, the lower arm axle mount point only gives me about 2'' - 2.5'' of clearance from the flat belly pan design, thus limiting my suspension droop to 2'' (as would be regulated by axle bump stops). I would like to raise the lower arms an inch to give myself some extra clearance, but doing so raises RRCH to about 11.6''.

On a side note... man this Suspension Analyzer program gets buggy when dealing with the rear suspension!

Thanks for any help all.

[Norm Peterson]

I'll have to toss this at a 3D-ish 4-link spreadsheet when I get home (in lieu of better information at that time, I'll make an educated guess as to the lateral separation of the chassis/axle pivots of the lowers being 13" & 53" respectively).

I should think that the inclination of those plan-view-parallel uppers would set the rollsteer value at the tangent of whatever side view angle they were at, in this case tan(1.7°) = 0.0297, or about 3% rollsteer. That your axle end motions suggest about 11% rollsteer leads me to suspect that some plan view convergence between the uppers is unintentionally present in the model.

FWIW, the 3.5° inclination of the lowers appears to be as viewing the lowers in their true length. In side view projection, that 1.75" difference in pivot heights and the 20" projected link length make for an apparent angle of 5°, which is the more useful angle for working up the SVIC coordinates (3.5° up-angle used directly in SVSA calculations will give you a 93.5" SVIC X-coordinate rather than 72.5").


Norm

[boodlefoof]

Thanks Norm. I appreciate it. If you (or anybody else) is interested in the exact coordinates I'm working with... they are as follows...

X,Y,Z => X = outboard from center, Y = height, Z = forward (positive) or backward (negative) from axle centerline. Both sides are symmetrical.

Upper link frame = 23, 15.5, 33
Upper link axle = 23, 16.5, -1
Lower link frame = 5, 9.75, 20
Lower link axle = 25, 8, 0
Tire is 26'' tall.

According to the program, this makes my IC height 14.34, at 72.45'' forward. It is also what calculated my side view link angles (1.7* upper and 3.5* lower).

Unless the program is doing something wrong, there is no convergence in plan view on the upper arms. I had considered putting some convergence in to help lower the RCH (just 2 inches inboard at the frame reduces RCH about 1/3''), but cockpit space is already going to be at a premium. I'd prefer to keep theim parallel.

[Norm Peterson]

Different coordinate system
X = longitudinal, positive forward, zero at rear axle rest position
Y = lateral
Z = vertical

Note the tiny plan view skew in the uppers - that's only to sidestep a divide-by-zero problem.

I settled on an 18" CG height after an initial guess plus one fully defined configuration.


4Link11
Filename/Descr. boodlefoof 240Z Satchell

INPUTS
LCAchassisX 20.00 in
LCAchassisY 5.00 in
LCAchassisZ 9.75 in
LCAaxleX 0.00 in
LCAaxleY 25.00 in
LCAaxleZ 8.00 in
CGHeight 18.00 in
Wheelbase 92.00 in
RideHeightChange 0.00 in
LCAchassisZChange 0.00 in
LCAaxleZChange 0.00 in
RearTireRollingRadius 13.00 in
UCAchassisX 33.00 in
UCAchassisY 23.00 in
UCAchassisZ 15.50 in
UCAaxleX -1.00 in
UCAaxleY 23.01 in
UCAaxleZ 16.50 in

CALCULATED PARAMETERS
LCAlength 28.34 in
LCAplanviewlength 28.28 in
LCAsideviewlength 20.08 in
LCAslope 0.0875 in / in
LCAconvX 25.00 in
LCAconvY 0.00 in
LCAconvZ 10.19 in
UCA/LCA overall 1.200
UCAlength 34.01 in
UCAplanviewlength 34.00 in
UCAsideviewlength 34.01 in
UCAslope -0.0294 in / in
UCAconvX 78233.00 in
UCAconvY 0.00 in
UCAconvZ -2284.50 in
UCA/LCA planview 1.202
UCA/LCAsideview 1.694

OUTPUT (at static ride height)
AntiSquatX 72.45 in
ROLLCTRHEIGHT 10.921 in
AXLESTEER 2.93 %
ANTISQUAT 101.16 %
AntiSquatZ 14.34 in
RateOfRCHChange 0.51 in / in
RateOfAxleSteerChange 2.95 %/in
RateOfAntiSquatChange -29.99 %/in


Anti-squat and roll steer are not fixed parameters, BTW. In your geometry, anti-squat percentage drops and roll steer increases as rear ride height decreases. I see about 10% roll steer (vehicle understeer direction) showing up at a decrease of about 2.5" in rear ride height. Vehicle pitch is not considered. I have plots of both.


If rollsteer really is closer to 11% at static ride height, I'd like to see the explanation.


Norm

[boodlefoof]

Thanks Norm! You're the man! I am still learning, and this is exactly why I wanted some opinions on the design before I went out and put it together. I'm not entirely sure what is or isn't considered to be ideal yet.

The outputs I calculated are the same, I just can't (or haven't figured out how to) plot the graphs as you have, or roll steer as a percentage. The roll figures I mentioned before are in a roll with no dive. I just told it to calculate axle location change at X* roll and it spit out those numbers.

The questions that pop out at me now are these:

First, some observations about roll steer. I'm still a little confused about the roll steer curve and its effects on driving. Based on the graph, yes there is about 3% at ride height and it gets up to about 10% at 2.5'' bump. I believe the calculations are correct. So, questions...

1. Is such a roll steer curve acceptable?

I'm sure that slowing the roll steer gain in bump is a good idea, but I'm having trouble imagining a scenario where I'm in that great a rear bump while cornering... at least not with the anti-squat I am trying to build in. On the other hand, I'd hate to have enough anti-squat to lift the car enough to put me in positive roll steer coming out of a turn! Of course, the lift in the car will be limited via bump-stops as I mentioned (to probably 2-3'').

2. Will roll steer in bump have any impact on driving in a straight line? It seems that going to 2.5'' bump could only happen on major accelleration (or if I'm on a bumpy road). It seems that if roll steer is changing that much in straight bump, effecting both wheels evenly, it won't affect performance. Please, correct me if I am wrong.

3. Any tips for changing things to slow the bump steer curve? I'll toy with it some more tonight and see what I can come up with.

Second, does that anti-squat curve look good? Again, I'm not sure what is or isn't good, so is 30% per inch is ok? Again, I'll toy around with it tonight and see if I can reduce the loss while maintaining my other variables.

Third, back to the RCH. Should I aim to lower it from 10.9'' or would raising it slightly (say, up to 12'') cause problems?

Thanks again.

[boodlefoof]

Well, here is some more info to add into the mix. Last night I indeed spent some time tinkering with the suspension and I think it has improved. Let me know if you all agree.

I made the upper arms level in side view rather than angling down slightly towards the front. I have read on CC.com that this will give more neutral roll steer. Additionally, I raised the lower arms slightly and increased their angularity slightly. This slowed down roll steer change. I figured out the graph function and compared this to the previous design above. Whereas the previous design had axle lead moving .17'' at 3* roll and .30'' at 5* roll, the figures are down to .11'' at 3* roll and .18'' at 5* roll.

The anti-squat curve looks to be right about the same slope, but I've increased the AS at ride height to 119%.

In playing with the design I've found that shortening the upper arms will flatten the AS curve (slower AS loss in bump), but at the same time this speeds up the roll steer curve. Also, I've always heard that as a rule of thumb the links should be as long as possible, so I feel kind of strange trying to shorten them.

However, if I shorten the upper arms to 21'', I see a significantly better AS curve with only a very small roll steer change... which puzzles me.

This new test also raises RRCH to 11.31''

Here are the figures (with original long upper arms).

Upper link frame = 23, 16.5, 33
Upper link axle = 23, 16.5, -1
Lower link frame = 5, 10.75, 20
Lower link axle = 25, 8.5, 0

[Norm Peterson]

. . . but I'm having trouble imagining a scenario where I'm in that great a rear bump while cornering... at least not with the anti-squat I am trying to build in. On the other hand, I'd hate to have enough anti-squat to lift the car enough to put me in positive roll steer coming out of a turn!

I'd be careful about building in too much A/S unless drag racing is in this car's future. Anti-squat's evil twin is anti-lift, which can result in brake hop or force some sacrifice in rear braking capability as a band-aid. 50% or so seems to be more where cars set up with handling as the #1 priority seem to fall.

There's a separate line of thought regarding A/S, at least as it applies to auto-x - specifically A-Mod (the home of some wild one-off specials). That's to intentionally use relatively little of it. The reasoning is that if you simply let the rear squat a bit, the rear roll center will drop, as will rear lateral load transfer. Translation: more grip becomes available for accelerating off the corners as the rear squats because the front is being forced to do more of the work resulting from the lateral forces.

2. Will roll steer in bump have any impact on driving in a straight line? It seems that going to 2.5'' bump could only happen on major accelleration (or if I'm on a bumpy road). It seems that if roll steer is changing that much in straight bump, effecting both wheels evenly, it won't affect performance.

No. But if you encounter bumps while cornering - even perfectly timed two-wheel bumps - the rear axle will steer back and forth slightly. That probably does more to provide a vague or uneasy feeling back to the driver than it does to actually reduce measurable performance. Then again, lack of confidence in the car will tend to make you drive it slower. You can estimate rearward load transfer and compute the amount of spring compression/squat that would occur, and then reduce that using the A/S% to see just what you need.

Simple Example: If you have 2.5" of bump travel available, 2000 lbs of sprung weight, 1g acceleration, and a 18.4" sprung CG height, that's 400 lbs of extra rear force (200 per side) under acceleration. Given a medium-ish 100#/in rear wheel rate, that would be 2" squat with zero A/S. 50% A/S means only 1" of squat, leaving 1.5" of bump travel remaining.

3. Any tips for changing things to slow the bump steer curve? I'll toy with it some more tonight and see what I can come up with.

Roll steer gain in a Satchell link is dictated by the side view length of the uppers. The value with the car at rest is then defined by their inclination.

Second, does that anti-squat curve look good? Again, I'm not sure what is or isn't good, so is 30% per inch is ok? Again, I'll toy around with it tonight and see if I can reduce the loss while maintaining my other variables.

My thoughts are that it falls off a bit quickly, and that you might have traction right off that goes away on you. Stiffer springs than you might otherwise fit could be a workable band-aid.

Third, back to the RCH. Should I aim to lower it from 10.9'' or would raising it slightly (say, up to 12'') cause problems?

I would definitely not raise it. Elsewhere in the world of modifying stick axle suspensions is a growing trend toward bringing that RC down. Jon A (of corner-carvers and FRRAX) has posted some fairly detailed evaluations of his own experiences. And that's in a 101" wheelbase car. I suspect that there's a range of vehicle roll axis inclination over which the car works best, and that for pavement and turning both ways it's small, maybe within something like 3° or so. The car that I own that has a nearly horizontal vehicle roll axis feels far more nimble than either of the cars that have markedly steeper ones - and that car has, relatively speaking, the smallest tires and narrowest wheels of the bunch.


[Edit] - Anti-squat curves are generally "Lazy S" shaped, which depends on the relative side view inclinations of the uppers and lowers. The plot looks really weird when the curve reverses itself twice within the range of suspension motion, but at least the absolute values don't change all that much under those circumstances.


Norm

[boodlefoof]

Thanks again for your insights Norm.

I've been playing with my design more and have found something interesting that seems to go against conventional wisdom... In fact, I think I might have to add these observations to the "Really Long Trailing Arms" thread over at CC.com.

Typically, you hear that the longer the links, the better. Many people seem to think this will help to keep RRCH from moving, thus making the car more predictable. So, I had been designing to get the longest links possible. On the bottom side, this comes out to the roughly 28'' links. On the upper side, the spaceframe design really will acommodate anything up to 60'' at the extreme. Currently, I had been playing with a roughly 30-35'' upper link (as this is a convenient mount point on the frame and a link this length won't need to be as beefy as a longer one).

The thought occurred to me though that perhaps there is an optimum upper link length relative to the lower length, much like in a double A-arm front suspension. I thought "Perhaps going with too long an upper would actually be detrimental to the design?"

So, as I tried to flatten the AS curve I found that I could do so by shortening the upper link as I mentioned earlier in this thread. I had been looking primarily at the AS curve and the understeer curve, trying to reduce AS loss while not increasing roll steer too much.

Then, I happened to look at what was happening to RCH depending on upper arm length. I found that there does appear to be an ideal upper length relative to the lowers for the purpose of stabilizing RCH migration in bump. It appears to be around 21.5'' on my setup.

Here are the numbers, which I think are pretty interesting... RCH change does the following in bump all else being equal:

Ride height / 30'' upper arm RCH / 21.5'' upper arm RCH

0'' bump / 11.30 / 11.31
1'' bump / 10.90 / 11.30
2'' bump / 10.50 / 11.30
3'' bump / 10.10 / 11.31
4'' bump / 9.71 / 11.35

The same thing happens in lift - the long arms gain roughly .4'' RCH per inch lift while the shorter arms don't change RCH by more than .04'' over the entire range of motion!

Additionally, with the shorter arms AS loses about 20% per inch of bump as opposed to 30% per inch with the longer arms.

Meanwhile, roll steer with the short arms moves from 0% at ride height to 7.9% at 4'' of bump, while figures for the long arms are a range of 0% to 5.2%.

It seems odd that the shorter arm actually appears to be a better setup on paper??? What do you think?

[g-roadster]

Norm: Interesting discussion on the Satchell Link. Thanks for your input. A couple of points about the Satchell Link: The roll center is determined by the intersection of the two lower links, If you want to minimize roll center migration relative to the frame bring these inner pivots as close together as possible. Making a large A frame with a ball joint would be a solution for minimum roll center migration but would increase stress on the single ball joint rather than two and reduce your alignment adjustment possibilities. Roll steer is controlled by the upper links, adjusting the length and inclination affects roll steer. You hinted at this in your discussion.

I am designing the g-roadster with a Satchell link rear suspension. So far I have only laid this out graphically. I feel comfortable doing this as I have designed everything from large space craft to small optical systems from the drafting board. But I do realize the limitations of graphical only design. What program are you using for your suspension analysis? I will need to get a program, or access to one, to refine my front and rear suspension designs. Recommendations appreciated.

Norm, if it wouldn't be too much trouble could you do computer run for my Satchell link design?

Not sure what: RideHeightChange, LCAchassisZchange, LCAaxleZChange are in your inputs.

[boodlefoof]

g-roadster,

Thanks for the point about the lower arm attachment points. I tinkered with bringing the lower link frame attachment points closer together. I think I've got them about as close as I can to clearance the driveshaft with some comfort room. I did find though that bringing them closer together also increases the slope of the roll steer curve.

I'm using "Suspension Analyzer" from Performance Trends. If you google it, you'll find their website. They allow a free 10 day demo download that allows you to use all functions of the program. Otherwise, purchase price is something like $350! It will give you the outputs for your design based basically just upon the XYZ mount points for your trailing arms.

[Norm Peterson]

RideHeightChange allows you to input a ride height change due to a change in vehicle loading or a spring height change for a quick ,if slightly dirty, set of results.

LCAchassisZchange is simply a lowering (or raising) of the chassis side LCA pivots relative to some baseline value, and perhaps useful if you have multi-hole or otherwise adjustable chassis side pivot pickups. It's just another way of modifying the LCAchassisZ data that could provide a hint about what you were thinking when you look at the sheet in a year or whenever. Also slightly approximate.

Ditto for LCAaxleZChange, which is where one would enter changes in LCA attachment elevation at the axle brackets. AKA relocation or anti-squat brackets.

P.S. One can perform moderately sophisticated geometry and engineering analyses using Excel or similar spreadsheet software once the necessary equations have been worked out.

P.P.S It's not much trouble at all to run a few of these every so often. After all, there are less than 20 separate inputs (symmetry has been assumed). But I'd rather handle this sort of consulting via e-mail, as the amount of allotted attachment space is limited.


Norm

[boodlefoof]

For those interested, I have built the Satchell link! I slotted the mount bracket holes to allow for adjustability of the height of each mount point. That way, I can test-drive the car with the suspension set up for different roll-steer, anti-squat and RCH and see what works best for me.

Pics are up at: http://www.geocities.com/boodlefoof/...spension6.html

[jaybee]

Interesting but I have to confess I really don't understand. To me it looks like an upside down triangulated four link, how does that make it behave differently?

[Norm Peterson]

(1) The geometric roll center is generally several inches lower, meaning that the rear spring/sta-bar/shock package will differ. It also migrates a bit more in the vertical direction (not necessarily a bad thing, BTW). This is probably the largest difference.

(2) Wheel torque reactions are not carried through the axle tubes and into/through the pumpkin. Axle ends are better-supported longitudinally.

(3) The roll steer vs ride height curve is different.


Norm

[FoxGranadaChuck]

I am bumping this thread wondering what it would take to adapt a Satchell link rear suspension to an AMC Pacer.

I was just musing this the other day after I had just watched an episode of Sports Car Revolution. One of the hosts on that show had driven a highly modified AMC Pacer. My imagination got to thinking about a Pro-Touring Pacer. My thinking is that a forward-thinking car (in the Seventies) should have a forward-thinking rear suspension design (such as the Satchell link).

[boodlefoof]

FoxGranadaChuck,

Well, the Satchell packages pretty nicely, so I don't see why you couldn't adapt it to the Pacer. Pardon my ignorance, but the Pacer is RWD correct? It would just be a matter of building the frame structure to support the links.

[pav8427]

Norm,
Not to hijack, but you mentioned Excel spreadsheets, and I was wondering if there might be some out there to download so a person could play with different set ups to narrow down a design?
I have a few; one for IFS, 3-link and 4-link, but would like to evaluate from different angles prior to getting a Performance Trends package.

Doug

[FoxGranadaChuck]

FoxGranadaChuck,

Well, the Satchell packages pretty nicely, so I don't see why you couldn't adapt it to the Pacer. Pardon my ignorance, but the Pacer is RWD correct? It would just be a matter of building the frame structure to support the links.

Yes, the Pacer is indeed RWD. I was thinking of fitting a Mopar 8 3/4 rearend housing with the Satchell Link fittings on a conceptual level.

[FoxGranadaChuck]

By the way, exactly HOW do you set up a Satchell Link suspension?! I know what it looks like. I was just wondering how you set it up for a particular car.

[Norm Peterson]

Norm,
Not to hijack, but you mentioned Excel spreadsheets, and I was wondering if there might be some out there to download so a person could play with different set ups to narrow down a design?
I have a few; one for IFS, 3-link and 4-link, but would like to evaluate from different angles prior to getting a Performance Trends package.

Doug

The only other sheet that I know of that's available for download is Greg Locock's "SLARCK". I have several sheets in some state of off and on development (functional but mostly not in very presentable/user-friendly format and lacking the 'HELP' page that I've started to include).


Norm