A Arm Load Calculations

[maxhouck]

Hello all,

I am from the University of Missouri's FSAE team and am working on the suspension for this year. I'm at a roadblock on trying to size the a arms.

I have already calculated the expected tire forces, and used our suspension geometry to do a 'truss analysis' of the system. From here we can see the expected tensile and compressive loads for all of our different cases (accel, cornering, braking, bump, and combined cases). From here I did some basic buckling calculations using the Euler formula to find the critical load. The consensus here was that we can run 1/2" 0.035 tubes for pretty much everything and we would have plenty of room for safety. However, the euler formula assumes perfectly concentric loading, which is never going to be true. We can estimate some error for manufacturing tolerances and calculate the eccentric loading case, and this still gives us a plenty of room for safety under realistic manufacturing tolerances.

I know from past experience that realistically if all of our a-arms were this small (1/2 inch 0.035) they would likely deflect a lot and possibly break. It seems that the error comes from the fact that our suspension links are not all 2 force members like we assume when we did our load calculations. The fact that the ends are welded together at the outboard spherical means they can exert a moment, and introduce bending into the situation. This is where I am stuck - I don't think it is possible to look at it like a basic statics problem if you make them "welded" joints. Short of running extensive FEA using our load cases on each corner, are there any calculations that can be done in order to estimate the amount of eccentric loading/bending that will be put into the arms? It seems that this will be of greater magnitude than any perfect tension/compression forces that we can calculate using basic static analysis.

Hate to be that guy that just posts to ask everyone to do the work for him - but I'm just curious if there is anything that can be done here short of "just overbuild them and test the car" or doing all the FEA, which it seems we are going to have to do. If you'd like to see specifics on what I have done so far I'd be happy to share.

[BillCobb]

1) Do the FEA. Why is this such a hard task.

2) Make up a plastic model and do some fringe pattern analysis (old school).

3) Build a real to print arm and fixture it. Apply loads, strain gauge the pockets.

4) Build a real arm into a Kart or a lawn mower even. Curb impact (head on) and curb push-away ( side load while parking).

See if it lives. Then acid etch the arm(s) and retest a few times. They will talk to you.

[DougMilliken]

Special loading cases for autocross cars -- cone strike and cone drag.

[Mikey Antonakakis]

In addition to what Bill and Doug mentioned, rather than taking a "will it break" approach, figure out how much deflection you can live with. I'm definitely no expert here, but think in terms of camber and toe (and??) compliance. If you get that down to an "acceptable" level, strength probably won't be a problem. As they suggested, use FEA, you already have figured out the loads so it's only marginally more work to run the simulation.

[jd74914]

Structures experts I know suggest always keeping buckling factor of safety > 8-10 to account for unknowns.

Like suggested above, do the FEA and see what it says. I'm surprised your hand calcs show 1/2-0.035" is OK. Perhaps they work as pure two force members (no push/pull rod loading). We built a past car with that size lowers, and sure enough yielded them (someone did the hand calc with the wrong loads-done again it showed they were very close to yield at pushrod attachment point).

[Claude Rouelle]

Buckling factor of safety > 8 ????????

[Claude Rouelle]

To accounts for "unknowns"?????????

[onemaniac]

Buckling factor of safety > 8 ????????

No need for such big surprise. I witnessed a similar number for "rule-of-thumb FOS" from my experience working at an engineering consulting firm. It's one of those "We don't have time for this, just size it up" decisions that are often made by the project managers or senior engineers.
For racecar design it might sound absurd but the assembly weight is often at the bottom of the priority list in big machineries.

[maxhouck]

Yes, the issue with the current calculations is that they assume everything is going to be a two force member. This is why the calculations say we can get away with such a small tube, while in reality because they are welded together and the pushrod puts a significant bending load into the lowers, they are unrealistic. The reason I was hesitant to do FEA was because I and our team are pretty inexperienced with it, but I guess its time to dig in and learn how to run it and analyze results properly. Just wanted to get some discussion going to see if there were any other methods, because we have heard from design judges before "dont waste your time doing FEA on every single part, because you're probably doing it wrong".

And yes, at the end of the day, I know many will say "just make it X OD and Y wall thickness and move on", but I feel that we are at the point where we can be taking these things one step further in order to make a lighter car. The weight difference between the 5/8" .065 a-arms (~9.3 lbs total) we had on our 2017 car and the 1/2" .049 a-arms (~5.7 lbs total) we had on the 2016 car is a pretty signficant amount of weight to save (or not to save).

[Claude Rouelle]

Not all the judges are right. Some of them would need an OptimumG seminar. In any case it is up to you to defend your opinion with the most objective and well quantified analysis
. Only fools will reject any good rational analysis.

[Claude Rouelle]

And I have been wrong myself at least a few times! In fact many times! :)
But less and less.

[Adam Farabaugh]

Even if the pushrod attachment is welded, you can point the line of action through some point (at some percentage of peak load given your expected geometry) to minimize moments.
The hand calculations will be accurate if you just figure out the geometry and include moments. I would be more suspicious of your loads than a well-reasoned hand calc.

As to the general problem of member sizing, you develop two requirements, strength (area) and stability (inertia). From this you can directly solve for the two degrees of freedom of the member (diameter and wall thickness).

[jd74914]

To accounts for "unknowns"?????????
Perhaps unknown is not quite an accurate term. Doing basic statics and assuming a 2 force member has the potential to be very non-conservative in buckling. I'm not advocating such a ridiculous FS with FEA, just for really basic hand calcs. And certainly not that high for hand calcs for bending, etc.

[Z]

Maxhouck,


... calculated the expected tire forces, and ... can see the expected tensile and compressive loads for all of our different cases (accel, cornering, braking, bump, and combined cases).
...
Short of running extensive FEA using our load cases on each corner, are there any calculations that can be done ...

All the FEA in the world will not help you, when your assumed worst case loads are WRONG.

Or put another way, ask the wrong question, and you are guaranteed to get the wrong answer, whether you use hand-calc or FEA.

Doug gave you a big clue to the right answer, in the third post this thread.


Special loading cases for autocross cars -- cone strike and cone drag.

"Cone drag" is when the cone, especially its stiff base, gets wedged under a lower wishbone and lifts that corner of the car OFF THE GROUND. So do a simple hand-calc of the wishbone-tube being loaded in its middle, in BENDING, by the corner-weight of the car.
~o0o~

Here are three more potential "worst case loadings" that would be considered by diligent engineers.

1. Car is finally finished and is about to be loaded onto the trailer for its first test session. So Super-Student-1 picks up his corner of the car by the middle of one of the upper-wishbone tubes. Same bending load as above "cone drag", but on an upper tube.

2. After some repairs the car is finally on the trailer. Super-Student-2 decides to secure the car, so it doesn't get damaged in transit, by tying it down with heavy-duty ratchet-straps. He attaches these to the centres of the wishbone-tubes. Similar or greater loading to above, but down not up.

3. More repairs, and the trailer+car finally make it to the test-track. SS-3 has just finished his double-cheeseburger-with-extra-creamy-sauce, so his hands are a bit slippery. So while unloading the car from trailer, this time using the correct grip on the wheel and NOT on the centre of wishbone-tube, the wheel slips out of his grip. Oops! His corner of the car falls about a foot onto the hard ground. Or maybe it falls 2 feet, or 3 feet? You do the "bump" calcs.
~o0o~

Key questions you should be asking yourself are these.

Do we build a super-fragile, F1-style, car, that has every component optimally "optimised", with Safety-Factors <1.1, and that conveniently gives us a great excuse for failing to complete endurance yet again (ie. "...because the car was optimally optimised")?

Or do we build a robust car, suitable for the "amateur weekend autocrosser", that can survive the bumps and bruises that amateurs, and students, will subject it too, and that is thus able to score many points by "completing all dynamic events"?

Do we want to win Design Event, or all the Dynamic Events?

Z

[Z]

Max,

While I am here...


...I feel that we are at the point where we can be taking these things one step further in order to make a lighter car. The weight difference between the 5/8" .065 a-arms (~9.3 lbs total) we had on our 2017 car and the 1/2" .049 a-arms (~5.7 lbs total) we had on the 2016 car is a pretty signficant amount of weight to save...

So how much do your pushrods-&-rockers weigh?

And the extra chassis structure needed for the rocker-mounts?

Do you really need all that stuff?

Z

[DougMilliken]

"Cone drag" ... wishbone-tube being loaded in its middle, in BENDING, by the corner-weight of the car.

Could be even worse, depending on overall ride rates and the amount of lift. If the suspension is stiff, it's nearly like picking up one leg (one corner) of a 4-legged table, which gets you ~half the weight of the table.

There is also "SS-4" who decides to use a suspension link as a step stool to get something off a nearby high shelf.

[Z]

Doug,


Could be even worse ... which gets you ~half the weight [of car, bending the tube]...

Yep! :)

Z

[Mikey Antonakakis]

Thank you to Z and Doug for reminding me and everyone else of some of the other load cases, which for most teams will be more frequently encountered than anything found on-track... Although I don't think a-arm strength will be an issue for our team ;)

[Claude Rouelle]

In design judging I often ask this question: you have 6 linkages per corner of the car. 2 for the bottom wishbone, 2 for the top one, 1 for the push or pull rod (or direct actuation) and one for the toe link. You have 4 corners that makes it 24 linkages.
I could add other thinks like ARB droop link or ARB bearing cap attachment on the chassis or rockers axis attachment on the chassis. But let's keep this example simple.

Let say you car goes on a skid pad at 1,5 G lateral, constant. That is steady state. The question is" what linkage gets the highest force and is it a compression or a tension?" in 90 % of the cases the students do not have an answer and they have to think for a while to give me one.

Then I have to wonder how the rod ends and the suspension tube sizes have been determined.
And without the force at the inboard suspension pickup points what inputs were chosen for the chassis FEA study.
And without the force at the outboard suspension pickup points what inputs were chosen for the uprights FEA study.
How were the compliance calculated?

Worse: They tell me after thinking that the highest load in a left turn is the rear leg of the RR bottom wishbone. OK.... seems logical if not quantitatively at least qualitatively.....
Then I ask what is the size of the bottom RR wishbone rod ends: they tell me 8 mm (which sees way to big for a decent, light FS car)
OK... then what is the size of the top RR wishbone rod ends? "Also 8 mm" Wait a minute: you just told me that the lowest wishbone has highest load that the top one. Is there one which is over engineered or the other under engineered. Or both?
The usual BS is: "Well we did this to decrease the number of different parts we have to manage"
Yeah.....

I expect students to do load suspension and chassis load cases BEFORE that do any parts FEA.
- Basic lateral. If you have a tire model that is good but you do not need to be perfect to be useful.
If your car is 200 KG (driver included that is 140 Kg car and 60 Kg car totally achievable), the weight distribution is 45 % front and take 3 G, make the LF + RF lateral grip = 200 * 3 * 9.81 * 0.45 and distribute the grip let's say 85 % on the outside and 15 % on the inside.
- Basic braking: 200 * 3 * 9.81 = 6000 N. 35 % Fx on each front wheel and 15 % on each rear wheel
- Basic acceleration (RWD): 200 * 1.5 * 9.81 = 3000 N and put 50 % on each rear wheel
- Make a combination of the first and second case of first and third case. Remember that tires have a traction ellipse not a traction rectangle . You can NOT have 3.5 G of lateral AND longitudinal
- Take each of the previous test add 1.5 G vertical under each of the wheels
- Do not forget to include the vertical reaction at the tires to the aero downforce at each wheel
- Make sure you simulate things unusual but possible, like braking and going backward. A few years a go in GP2 a driver spun the car and while going backward he jumped on the brake pedal.... and broke the two lower rear wishbones.
I heard about the same issue from hill climb drivers.

I would expect any decent good FS team to already have at the design judging event these load cases printed and filed in a binder and the laptop open with the software they use. All good team (5 %) do!


No FEA studies before these load cases.

[mech5496]

Fully agree with you Claude, in all but one; manufacturability and reduction of spare parts inventory for the sake of cost reduction totally makes sense as an argument, as long as the team understands the compromise.

[Claude Rouelle]

Harry (and all),

Worth to ask....

What is the cheapest?

- 20 rod ends of 6 mm or 10 rod ends of 6 mm and 10 rod end of 5 mm?

- 1 rod end of 6 x 1.0 left and one of 6 x 1.0 right OR one 6 x 1. 25 right and 6 x 1.0 right. In the second case you increase the adjustment resolution of, for example, a toe link by 8 as in the first case 1 turn would make 2 mm of length change and in the second case 0.25 mm length change (1.25 mm IN and 1.0 mm OUT or the other way around)? Considering that a small toe adjustment has a huge influence on the car behavior (especially rear)....

- Instead of 2 rod ends of 6 mm, 2 spherical joints of 6 mm and make the adjustments (push or pull rod, toe link) with shims?

[maxhouck]

Thanks everyone for the helpful discussion! After some more work, its clear the cone strikes (or people standing on or lifting the car) from A-arms is the worst case load.

In the 3 FSAE cars I have been around in my time here, we have only had one “super student” issue, and that was a rack of tubing falling over in the trailer and landing directly onto an upper wishbone. Took us one night to remake it, and we were back out testing the next day. We have always been very good about teaching new people how to properly lift the car, and which parts of it they can stand/sit on safely. Not that it will never happen, but it happens so rarely that I would rather just remake the links or have spares ready to go than need to make them stronger and heavier.

The cone strike/cone drag case is important though, and is guaranteed to happen several times a year. After doing simple worst case bending situations, lifting up ¼ or ½ the weight of the car, this is what determined the sizes of our lower wishbones, front and rear. These loads were more significant than any induced by accelerating or hitting bumps.

Our front uppers are pretty heavily loaded by our pullrods, and our rear uppers (we are running pushrods in rear) are the lightest loaded of them all. These numbers come from our analysis from different load cases and suspension geometry as Claude has described. Its good to know that if we have him for design we will do well at least on this topic – I agree with and have already done everything he described.

One question I still am not sure of an answer to is how much deflection/compliance is significant. It seems the wishbones will likely never yield, but they will definitely have some potential to deflect and introduce some compliance. Part of me says “well I know we can’t measure toe much more accurately than 1/16 of an inch, so maybe half that much compliance would be no big deal”. But another part of me thinks “well if we have some compliance in the a-arms, and some compliance in the spindle, and some in the inboard sphericals, and some in the outboard sphericals…” then we get this tolerance stack-up affect that could make things much worse. I am aware of software that exists to analyze compliance in all these joints and tell me what it will do to my alignment, but how much is acceptable?



Max,

While I am here...



So how much do your pushrods-&-rockers weigh?

And the extra chassis structure needed for the rocker-mounts?

Do you really need all that stuff?

Z

Z: It is hard to just give weights for these two different cases, as the front half of our chassis and our rear structure are designed around having rockers, and would look a lot different if we were going to run direct acting. A lot of other changes would have to be made in order to package and get the desired motion ratios out of the Penske dampers that we are running this year. I know there are other longer dampers or different ways to package them, but we selected these dampers because we already have them and they've been reliable for us in the past (unlike our Ohlins), among other reasons. We actually did run direct acting front dampers last year, but have moved back to pullrods in the front for this year. I can give you two numbers that I have calculated: the tradeoff between CG height and weight. Based on the load sensitivity of the tires from TTC data (and validated by our own data), I’ve found that if you want to go 0.1 seconds faster around the skidpad you can either cut 40 lbs from the car or lower the CG by 1.59 inches (or get a better driver, or spend more time tuning, etc…). Our pullrods allow us to put the rocker and damper ~3-4 inches off the ground, which improved our CG significantly over a pushrod setup in the front, and still a little better than a direct acting setup. The argument that direct acting would be simpler and maybe lighter is valid, but I hope I have adequately defended our case. Either way, there are plenty of good teams with rockers, and plenty of good teams with direct acting shocks.

[Claude Rouelle]

"....I know we can’t measure toe much more accurately than 1/16 of an inch..."

That is why I do NOT believe in the fishing string method to measure toe.

I have seen some amateur racing guys using a laser beam attached to a fixture itself attached, for example, to the front rim and projecting a red point on a "flag" attached to the rear of the chassis or to the rear rim. And vice versa; rear beam projecting to the front.
See attached pictures.

Another idea; if you really want to use the fishing string to measure the toe, I would not only advise you to look at the difference of (fishing string to front of the rim) - (fishing string to front of the rear of the rim) which gives you the toe in mm....
....but also [(fishing string to front of the rim) +(fishing string to front of the rear of the rim)]/2 which would be in fact a measurement of the distance from the fishing string to the rim is the rim was flat.
Then compare that measurement of the LF with the RF (and LR with RR); if the 2 measurements are not the same that means the car is not symmetrical and the two 1/2 tracks are not equal. Up to you to find out why: chassis, upright, wishbone, rim....

In a perfect world the 2 fishing strings should be parallel and the middle of the distance between the 2 fishing strings should correspond to the inline axis of the car.
It would be good the tubes that hold the fishing string (tubes that should be perpendicular to the inline axis of the chassis) are attached to brackets that fall (with pins for example) in holes that are in the chassis and that theses holes were part of the chassis design and manufacturing.

These are the kind of tons of tip and tricks that are shared in the OptimumG Data Driven Seminars

[Mikey Antonakakis]

I am aware of software that exists to analyze compliance in all these joints and tell me what it will do to my alignment, but how much is acceptable?
This is the part with the real engineering! I don't think anyone can conclusively tell you how much is acceptable, you have to take what you (and your team) knows about your tires, your drivers, your kinematics, etc., and figure out the relationship between compliance and performance, the "cost" relationship between performance factors (e.g. mass and yaw inertia vs. camber loss), and where you think the balance point should be. There are countless tools you can use to help, like decision matrices, lap time simulations, etc., but the hard part is wrapping your head around all the primary and secondary impacts of the different options, without forgetting about them (similar to the cone strike/drag discussion).

[Claude Rouelle]

Well, Mikey and Maxhouck, how much will one degree or one 1/10 of one degree on let's say the LR tire toe or camber will change your lateral and longitudinal acceleration, your yaw moment, your balance, your control and stability on entry and your control and stability at the limit?
Make at least that steady state analysis.....

[Mikey Antonakakis]

Well, Mikey and Maxhouck, how much will one degree or one 1/10 of one degree on let's say the LR tire toe or camber will change your lateral and longitudinal acceleration, your yaw moment, your balance, your control and stability on entry and your control and stability at the limit?
Make at least that steady state analysis.....
Sounds like a very good place to start :)

[Claude Rouelle]

By experience the 2 priorities I would focus on are 1) Rear toe compliance Vs Fx and 2) Steering compliance. Always good to measure and/or simulate it with steering rack locked AND steering wheel locked. That way you know what additional compliance there is the steering column

C is the enemy of C&C. Compliance is the enemy of the driver Control and Confidence

[DougMilliken]

No need to reinvent anything, there is an excellent small book, "A Chassis Alignment Procedure" -- recommended:
https://www.barnesandnoble.com/w/a-chassis-alignment-procedure-michael-w-velten/1115530973

[Claude Rouelle]

Indispensable but not sufficient

[sidkash14]

By experience the 2 priorities I would focus on are 1) Rear toe compliance Vs Fx and 2) Steering compliance. Always good to measure and/or simulate it with steering rack locked AND steering wheel locked. That way you know what additional compliance there is the steering column

C is the enemy of C&C. Compliance is the enemy of the driver Control and Confidence

Every real object known used in engineering has compliance. Tires, springs, bridges and buildings have compliance. Hell, even the international space station has compliance in its structure.
I think it's incorrect to make a blanket statement saying 'compliance is the enemy'. I would argue that lack of understanding of compliance and how it affects handling is the real enemy. Too many formula teams (even when I was on the team) would see compliance as an evil being that we need to conquer without understanding what it actually is.

Here's some good resources on how compliance affects vehicle dynamics - http://papers.sae.org/2002-01-1218/, http://papers.sae.org/760713/, http://papers.sae.org/760711/ along with Fundamentals of Vehicle Dynamics by Thomas Gillespie and RCVD by Milliken have plenty of information on how to integrate compliance into your model.

You don't need a multi-body vehicle dynamic simulation to incorporate compliance into your simulation. If you are modeling tires, springs etc. then you're modeling compliance.

Back to the question of 'how much compliance is acceptable'? I would rephrase that question to 'what is compliance doing to my vehicle handling'?
Then you approach it in a more practical way of integrating it into vehicle design rather than chasing shadows in an attempt to 'eliminate it'.

[Claude Rouelle]

Sid,

You are already "polluted" by the passenger car industry where compliance is a necessity for ride, comfort, noise decrease and simply reliability: car manufacturers could not warranty a car with no bushing and just rod ends for 100,000 miles. Uprights and chassis would simply fall apart after just a few hundreds miles.
On a race car if you notice a bit of play in a pushrod rod end you just change. Or if yo have a good car race car like a Dallara there will be a user manual telling you after how many km what rod end / bearing etc... has to be replaced.

You need to put my comments in the context of race cars and/or this forum and FSAE / FS where I have been judging for many years and where I see every year real s**t boxes where compliance is awful, make the car undriveable and wasn't clearly a part of the design process.

Before even deciding if they have too much or not enough compliance (if there is such a thing as "too much compliance" for a race car), students should at least give themselves (and later on design judges) basic numbers in simulation and in workshop measurements like the ones in the attached spreadsheet.
The reality is that 95 % of them don't even know what I am speaking about!
And I am not even speaking about combined efforts (like Fy and Fx and Fz and Mz and Mx all together) or non linear numbers; just basic numbers.

I have been in racing for 40 years and I never heard any race car designer or race car engineer complaining about too much compliance! In fact every year, n very new car, they try to reduce it and most of the time they succeed.
Of course there are compromise to make with cost, weight etc... but there isn't such a thing as too much compliance!

[sidkash14]

Claude,

I never said 'increase' or 'decrease' compliance. All I said was compliance must first be understood before labeling it as good or bad (increase or decrease?).
Which is why in my post I offered literature material that'll help students understand the why and how of compliance before they implement the 'what' of compliance (Simon Sinek anyone?)

I think I did put my comment in the context of this forum and Formula Student in general, which is a student engineering competition. :)

[Mikey Antonakakis]

Claude, I think the table you showed is a great way to visualize and communicate these factors efficiently. I know you just made it very quickly as an example, but I am wondering if it is more useful to present them in a more non-dimensional (or normalized) manner.
For instance, some hypothetical amount of toe compliance presented in deg./kN could be a very good number for a sedan, but very poor for a Formula SAE car. Would be better to show it as, for instance, deg./G, or deg./percent of maximum capability?

Sid, I think your comments came across very clearly, or at least I understood them as a way to encourage thinking about "why" before "what," as you (and Simon) say.

[Claude Rouelle]

Mikey,

Of course it would be good to show the influence of compliance on (as I wrote earlier) on grip, balance, stability and control (on entry and at the limit), all other things (tires, springs weight distribution, etc...) being the same.
Only that kind of analysis, validated by good on-track test drivers opinions will tell you what is a "low enough compliance" . That is what, as a design judge, I expect the students to do.

Sid, we are on the same wave length.

Worth to direct people to Simon Sinek again: whether it is engineering or non-engineering issues start with WHY. https://www.youtube.com/watch?v=u4ZoJKF_VuA

[Z]

Maxhouck,


One question I still am not sure of an answer to is how much deflection/compliance is significant...
Part of me says “well I know we can’t measure toe much more accurately than 1/16 of an inch, so maybe half that much compliance would be no big deal”. But ... we get this tolerance stack-up affect that could make things much worse...
...how much is acceptable?

Here is one of my posts from 2005 giving a rough guide to "...how much is acceptable".

http://www.fsae.com/forums/showthread.php?5332-Caster-Camber-Steering-shims&p=92714&viewfull=1#post92714

Half way down this next post I give a rough guide on how to determine "the significance of things". (You can skip over the Gyro stuff.)

http://www.fsae.com/forums/showthread.php?4063-Jacking-force&p=127273&viewfull=1#post127273

The reason I give "10%" as the starting point for "significant" is simply that ... we have ten fingers!

Imagine you are helping tune the engine on the dyno, and you are in a rush, and there are spinning metal bits, and you accidentally get ALL your fingers chopped off. Bummer! This will have a major effect on your future lifestyle. You won't be able to brush your teeth, or wipe your backside, or do a whole lot of other everyday things. So this 100% loss of fingers is an OVERWHELMINGLY BAD influence on your performance.

At the other extreme, imagine you just lose a bit of skin on the tip of one finger. A quick application of some antiseptic alcohol, taken internally of course, and a bandaid, and you are good to go. In a few weeks you will have forgotten what finger it was, and will have to look closely for the teeny little scar in order to tell the newbies about your heroic engine tuning efforts.

The middle ground is when you lose one finger. Not a major hindrance to your performance, but annoying when, say, you want to count past nine.
~o0o~

In VD-performance terms you might choose as "SIGNIFICANT", a change in toe-angle that generates 10% of the tyre's peak Fy force. This delta-toe-angle is different for different tyres, and varies according to where you are on the tyre-curve. But as round numbers I would suggest that 0.1 degrees is "starting to become significant", and 0.5 degrees is already "quite significant".

Compare these numbers with, say, a sudden change in toe-angle of 5 to 10 degrees, which would reasonably be described as "overwhelming", because the sudden increase of Fy to its maximum would very likely spit the car off the track. At the other extreme a toe change of 0.01 degrees would probably have an immeasurable effect on Fy, given all the variables of grip coming from the track itself, such as dust, coarser or smoother gravel, and so on.

So your suggested figure of a bit less than 1/16 inch, say 1 mm measured at rim (= ~0.2 degree), of total toe-compliance is a reasonable limit to aim for. A little bit more won't cripple you, in the same way that you can still function reasonably well with two fingers missing. But a lot more is generally BAD.

And at the other extreme there is no point spending vast resources chasing 0.1 mm total toe-compliance (= ~0.02 degree), because that will NOT make your car "significantly" faster.
~~~o0o~~~

Claude,


I never heard any race car designer or race car engineer complaining about too much compliance!
... there isn't such a thing as too much compliance!

For the sake of the students' understanding of this issue, did you not mean to say "...there isn't such a thing as too much stiffness"???

Z

[Claude Rouelle]

Z, Thank you for correcting me: of course I meant "I never heard any race or race car car design engineer complaining of too much stiffness (or too little compliance". Must have been jet lag! Claude

[Z]

Claude,

I get them mixed up too.

Z