Vehicle Dynamics

[Brian Smith]

This is my second year designing the suspension for our car. I attended the Claude Rouelle seminar. That was great! But wow did I leave there with more questions than I thought possible.

Some seemingly simple questions that I just cant answer...

Assuming that I can have a car with 50/50 f/r weight distribution,

Why should the front rollcenter be lower than the rear?

Why should the front track be wider than the rear?

Why should we have more front roll resistance?

It seems that if I am using the same tires front and rear then the front and rear suspensions should be the same or similar. I realize that there is an argument that you need more roll resistance front to leave grip for acelleration on corner exit at the rear. But say we were designing for cornering only. Latera accel is much more important than longitudinal.

Why are longer controll arms better? I can achieve the same rollcenters,Instant centers, rollcenter envelope, Instant center movement ect with short or long arms. Although having a very long bottom and a short top does make the front view sal shortenn quickly.


Weight transfer

Elastic weight transfer depends on damping, springs and Moments of inertia. Does this mean that lateral elastic weight transfer starts at 0 (at the start of the turn) and reaches its maximum value when the car is at max roll angle about 1/3 into the turn?

What is the difference in a car with a high moment on inertia (say in roll) and a car that is heavily damped. Could the elastic weight transfer speed be the same.

At the seminar Claude showed a car with high pitch moment of inertia going over bumps that caused excessive pitch. The cars wheels left the ground. A bad thing. But if the track was not bumpy a high moment of nertia would be a good thing. It delays longitudinal elastic weight transfer. Right?

How many teams try to get 50/50 f/r? I see that it would hurt braking and accel, but would help in the turns (i think?) and could be benificial.

[ben]

<BLOCKQUOTE class="ip-ubbcode-quote"><font size="-1">quote:</font><HR>Originally posted by Brian Smith:
Why should the front rollcenter be lower than the rear?

Why should the front track be wider than the rear?

Why should we have more front roll resistance?

Why are longer controll arms better?

Elastic weight transfer depends on damping, springs and Moments of inertia. Does this mean that lateral elastic weight transfer starts at 0 (at the start of the turn) and reaches its maximum value when the car is at max roll angle about 1/3 into the turn?

What is the difference in a car with a high moment on inertia (say in roll) and a car that is heavily damped. Could the elastic weight transfer speed be the same.

At the seminar Claude showed a car with high pitch moment of inertia going over bumps that caused excessive pitch. The cars wheels left the ground. A bad thing. But if the track was not bumpy a high moment of nertia would be a good thing. It delays longitudinal elastic weight transfer. Right?

How many teams try to get 50/50 f/r? I see that it would hurt braking and accel, but would help in the turns (i think?) and could be benificial. <HR></BLOCKQUOTE>

My 2 cents:

There is a longitudianl component of lateral accleration due to body side slip angle. A higher rear roll centre can create a larger jacking force to prevent the car squating as a result of this.

The front track should be wider than the rear to avoid hitting cones with the inside rear wheel :-) Carrol Smith presents an argument about diagonal weight transfer for this one but I can't remember it off the top of my head, anyone?

I'm not sure you would need more front roll stiffness. We were nice and neutral with a 45% front mass distribution and 53% front roll stiffness. Design a few options between 45 and 60% front and test.

Long control arms aren't as important as a narrow track width and a low CG. Suspension geometry effects are linear around such a small travel so as long as the SAL is correct statically it will stay as such.

Can't think of a detailed answer on the weight transfer Q's at this point, only to say that the track is bumpy so don't assume otherwise.

Ben

[IsheeM]

Excuss my stupid question, but how do you calculate roll stiffness and how does it factor into the grand scheme of things?
Thanks,

[fade]

milliken shows how to calculate roll stiffness. its units are sitffness / degree roll so it determines the roll angle caused by the rolling moment loaded through the springs etc.

[Charlie]

<BLOCKQUOTE class="ip-ubbcode-quote"><font size="-1">quote:</font><HR>Originally posted by Brian Smith:
At the seminar Claude showed a car with high pitch moment of inertia going over bumps that caused excessive pitch. The cars wheels left the ground. A bad thing. <HR></BLOCKQUOTE>

I believe you have it backwards? Inertia makes a car react slower. It is more stable. Less intertia makes the car more nimble, and more twitchy, and less stable. A car with low longitudinal intertia would be more likely to pitch its way off the road than a car with high intertia.

[Brian Smith]

So you are saying that with low inertia, the force from the bump would pitch the car more. And with high inertia the frame will pitch less and let the suspension work. That makes sense because with low inertia there is a bump pushing the car up but nothing pulling it back down.

So why don't I see gas tanks on noses and radiators in the rear.... wait, you guys did one of those didn't you Charlie. Was inertia your reasoning for that?

[Storbeck]

I'll take a stab at these questions and if I'm wrong somebody will probably correct me, then we'll all learn.

I think the reason why people usually say the front roll center should be lower than the rear is because usually the cg of the front of the car is lower than the rear, or more accurately if you drew a line down the neutral axis of the car it would slope down as you go forward, the idea is to keep the distance from the neutral axis to rc roughly equal on both ends. This is not necesarily true with our cars.

You want both tracks as wide as possible without the physical size of the car causing it to be slower because it doesn't fit through the course as well. The rear will clip cones more than the front so the compromise usually ends up with the rear smaller.

More front roll resistance so you have reserve traction in the rear for pushing forward, as you said. Also if your front track is wider you can have more front roll stiffness with the same weight transfer, that's why you wanted the wide track.

If you can achieve your goals with shorter arms go for it because they'll probably package easier. Don't forget about scrub though. Not saying you don't want any, just pointing out that it's a factor you didn't mention. Are you sure you can achieve all those things with the shorter arms, or speculating?

Elastic weight transfer depends on the things you said, reaches maximum at steady state cornering. Actually depending on your roll damping coefficient, it could overshoot then come back to steady state, depends on if you're overdamped in roll or underdamped. Most of our cars are overdamped in roll.

Static weight transfer speed could be the same, but you might be compromising your damping coeficient in ride on the heavily damped car, that's why people don't want to use that option.

Don't remember the high pitch moment of inertia thing at the seminar, but I might have been a little sleepy at that particular moment. I agree with what Charlie said.

Don't know about the number of teams at 50/50, we're at about 48/52, but I don't know if that's what was intended or just what it is.

If nothing else, you don't see high pitch moments of ineria because you can't have a high pitch moment of inertia without having either a high yaw moment of inertia or high center of gravity, both of which are bad.

What are any of us talking about?

[Frank]

Why should the front roll center be lower than the rear?

IMO, there is no good reason, perhaps it stems from the amount of pitch that a car can generate in either direction, ie, a roll centre stability issue.

It seems that on some solid axle designs it becomes difficult to get a low rear roll centre, so perhaps it has become habit.

Perhaps you can control transient behavior slightly by influencing the load through the shock/damper units.

Roll centre adjustment is somewhat analogous to anti-roll bar adjustment on some cars. It is often used as a "gross change"�, and the finer adjustment left to the ARB's.

Why should the front track be wider than the rear?

Can achieve differing roll resistance for given spring rates.
Don't hit cones.
(Too complicated for me answer) stability issues...
I like front 50-75mm wider than rear for FSAE (we had 100, but didn't like it)

Why should we have more front roll resistance?

After playing with a few cars that differ greatly in static weight distribution, I suggest that (front roll resistance ratio) FRRR is NOT necessarily an arbitrary number for a given tire. I suggest it is probably more like a few percentage points more front than your static weight split.

I also suggest that, used in design, it is worthwhile to always know the FRRR. Use the FRRR as a design metric to be used comparatively, not absolutely.

You must remember that it is ONLY a useful comparative measure when you accurately know the motion ratio, when (with reasonable accuracy) know the tire spring stiffness, and when you have a vehicle static weight distribution that is not being constantly changed, (and in fact a fully laden vehicle). (( the 10kg put onto the front of the car the week before competition is not helpful)).

For example, we calculate with certainty our motion ratios, and then after the car is produced, experimentally measure the motion ratio (not easy to do) to verify it. After the vehicle is fully laden and ready to drive, we pick our springs. The springs are tested using our own Instron machine, and the dampers are set on a damper dyno.

Finally, you must remember that the require roll stiffness ratio depends on the static (usually rear only for us) toe settings. Basically again stating the obvious that everything in a suspension system is interactive.

Why are longer control arms better?

Do you mean long wishbones?
Less camber gain in bump, for all other things being equal.

What is the difference in a car with a high moment on inertia (say in roll) and a car that is heavily damped. Could the elastic weight transfer speed be the same.

Neglect moment of inertia in roll on these cars.
Transient dynamics studies should definitely include the MMOI in pitch

How many teams try to get 50/50 f/r? I see that it would hurt braking and accel, but would help in the turns (i think?) and could be beneficial.

If you are using a 4 cylinder, it becomes difficult to make the car rear heavy without resorting to a long wheelbase.

[Charlie]

<BLOCKQUOTE class="ip-ubbcode-quote"><font size="-1">quote:</font><HR>Originally posted by Brian Smith:
So you are saying that with low inertia, the force from the bump would pitch the car more. And with high inertia the frame will pitch less and let the suspension work. That makes sense because with low inertia there is a bump pushing the car up but nothing pulling it back down.

So why don't I see gas tanks on noses and radiators in the rear.... wait, you guys did one of those didn't you Charlie. Was inertia your reasoning for that? <HR></BLOCKQUOTE>

Our radiator was driven primarily by weight split and packaging.

I can spew theory all day. http://fsae.com/groupee_common/emoticons/icon_wink.gif Some of it might actually be right. But to say what you want in a design, thats a bit harder. I wouldn't say you want as much intertia as you can get, but how much, I'm not sure.

I don't think you want the car to take so long to pitch it never stabilizes. That might make the driver uncomfortable. However, if it was instantaneous, it would shock the tires and they might even leave the ground like in Claude's example.

[Brian Smith]

"Originally posted by Storbeck

Are you sure you can achieve all those things with the shorter arms, or speculating?...
... If nothing else, you don't see high pitch moments of inertia because you can't have a high pitch moment of inertia without having either a high yaw moment of inertia or high center of gravity, both of which are bad."

Well I know that I can achieve the same Rollcenter, Instant center, rollcenter movement, and IC instantaneous tangent trajectory (not sure about exact instant center movement) with short arms.

Is a high yaw moment of inertia bad? It seems like it would give the driver plenty of warning before a spin. Yeah it would also slow turn in responce. So how much is too much?.. grrr

"Originally posted by Frank
Neglect moment of inertia in roll on these cars.
Transient dynamics studies should definitely include the MMOI in pitch"

Neglect moment of inertia in roll, what do you mean? Is that Mass Moment of Inertia?

....and why do all the sportscar guys say that front and rear overhang is the devil. I guess its just good to not scrape the ground in pitch. Its also good to have all the wheels as far appart as possible on any track more open that an FSAE track.

[Kevin Hayward]

Brian,

Front and Rear overhang affect both yaw and pitch moments of inertia ... not roll. I would tend to agree with Frank about ignoring roll moment of inertia. Pitch and yaw moments are the ones to worry about.

The thing is figuring out the relative affects of the pitch moment is not too difficult. However I would say the transients in yaw are probably more important ... mainly because you have no spring and damper package in the yaw plane to tune with. That pretty much just leaves lateral tyre compliance and damping and vehicle geometry (ie track and wheelbase) to determine behaviour ... no elements to really tune.

That is pretty much why nobody in FSAE can give you a definitive answer as to the ideal wheelbase / track combination ... even if they did it would be dependant on the tyres, rims and yaw moment of inertia they run. Instead you are left with a partially subjective judgement based on the limited information available.

...

As for vehicle track dimensions I think you needto look a bit further than just the load sensitivity of the tyres ... which is the reason for wider tracks ... i.e. wider tracks = less load transfer for the same lateral accelleration.

Namely a tyre generates grip by having a slip angle. The peak force is generated at a particular slip value. This peak slip value is dependant on tyre loads. It may be a higher slip angle for higher loads, or a lower slip angle for higher loads. In fact most empirical tyre fits assumes that the peak slip angle movement is a non-linear movement and not 1 to 1. Basically in different load regions a higher load can produce either a higher or lower peak slip angle.

This is incredibly dependant on the tyre used. At the front end of the car you can take care of most of that by different Ackermann settings and hence can run a wider track to reduce lateral load transfer overall.

However at the rear you have no such option ... unless you rear-steer (which can be done passively if you wish). So dependent on the tyre you may want a narrower or wider rear track as it will affect the difference in slip angles of the rear tyre. The inner tyre will always run at a higher slip angle. Decrease the track and this difference is reduced. Increase it and it is increased. Ultimately some car / tyre packages will have ultimate grip with different rear tracks as a result. This is usually not much of an issue for wider radius corners as the differnces between slip angles at the rear become miniscule. However the problem is magnified on a FSAE style track and probably goes some way to describing why a smaller rear track may be beneficial.

Another issue is drivetrain characteristics. The more locked a differential a smaller track will aid in cornering as the understeer tendencies will be reduced. This means the wider the track the more open the differential needs to be (assuming an optimum is somewhere between locked and open). Given that a FSAE car generally sports a Torsen differential with an installed TBR (Torque Bias Ratio) betwwen 2.5:1 and 3:1 this would indicate that a relatively narrow rear track may be desired ... again this is dependant on other vehicle attributes such as weight balance.

...

If it is looking complicated then it is starting to apporach some idea of how complex the task actually is ... It only gets more complicated from here and I am sure a lot of people have stopped reading by now.

The practical way out is to find out what is accepted practice ... it is usually accepted because it works ... try to understand the reasoning behind it ... because it can be flawed ... make some starting decisions ... because if you try to fence sit on this stuff you will go nowhere ... and finally accept that you cannot do it perfectly because we as mere human beings are not designed to understand the intricacies of those black rubber donuts ...

but it is pretty fun trying to figure it out.

Kev

[Storbeck]

Ignore moment of inertia in roll?

This statement baffles me. How can you know anything about the transient behavior of your car going around a corner if you don't account for moment of inertia in roll? Isn't the rate at which the car rolls, and elastic weight transfer happens, determined mostly by moment of inertia in roll and shocks?

This is F esential information, you see I mean?

Do you mean to not worry about the moment of inertia in roll of the car about the neutral axis, and only account for the portion from the parallel axis theorum I=mr^2 where r is the distance fromt the neutral axis to the roll axis? I could see how that may be reasonable though I'd have to do some calculations before I really beleive it.

[Kevin Hayward]

Storbeck,

I suppose I probably need to clarify my stance a little when I mentioned ignoring moment of inertia in roll.

I did not mean ignore it in terms of analysis ... rather my stance is not to worry about it while designing. There is little you can do to drastically alter it from a design standpoint ... short of drastic measures. I would say of all the cars in FSAE with similar weights would show simialr roll moments of inertia. This is not the case with the moments in pitch and yaw which can be affected more dramatically by design decisions.

I do not advocate not considering it from an analysis and damper tuning view point.

However with all due respect even analysing the roll moment of inertia in roll makes little difference to overall tuning ... more of a fine tuning sort of deal. This sort of fine tuning is much better suited to track work where the real thing is occuring rather than a simulation.

In the end you have four dampers connected to each corner (generally). The properties of which will be initially set to deal with pitch and warp (single wheel motions). There is no chance to set them up for roll motions alone. Given that the roll moment of inertia is generally quite small compared to the pitch the requirements of that mode sort of dominate the angular vehicle control issues.

So while I admit you should look at the roll moment of inertia I ask:

1. How can you alter it significantly in the design of a vehicle? (without adding dumbells on flagpoles)

2. Given a particular value how is it drastically affecting your damper settings that are generally setup for other issues?

...

As for the roll situation you have two main moments to counteract with the spring/dampers and tyres ... one is the action of a lateral force acting through the centre of gravity and one is the effect of the inertia of the body. How much bigger is the first compared to the second. Is the roll moment of inertia small enough that the response can be assumed as instantaneous? What do you consider close enough to consider instantaneous?

So as absurd as it sounds I stick with my initial comment that it is not something to get too wound up about ... and certainly not something that should dominate peoples thinking while just staring out ... as Brian the initial poster indicated he was. There are much more important issues.

Kev

[Storbeck]

Kev, hey I'm just starting out too. I'm here to observe and learn more than debate. I figured that might be what you meant, as I clumsily tried to explain in the second part of my post. You're saying don't agonize about mounting something four inches from the centerline of the car rather than eight because it won't effect roll MOI enough to matter.

[Storbeck]

Somewhat relevent to this thread, is there any truth to this theory. Your overall moment of inertia in roll comes from two components, the moment of inertia of the car about the cg, or more accurately the neutral axis, and the distance from the cg to the roll center, or more accurately the neutral axis to the roll axis. You can control the latter component with roll center height.

If the time required for elastic weight transfer is controled by moment of inertia in roll and shocks, and you want to have the shocks tuned for optimum road compliance, so ideally you don't want to use the shocks to control the rate of elastic weight transfer by compromising road compliance, you could use roll center height to tune elastic weight transfer. Higher roll center, faster elastic weight transfer, lower roll center, slower. This can be controlled independantly from the front to the rear of the car.

So as you enter a turn you want more grip on the front of the car, because that's where the breaking and turn-in come from, so you want slower elastic weight transfer in the front than the rear. As you are mid way through the corner you want more even weight transfer, and coming out of the turn you want the weight transfer to be primarily at the front of the car, because the back is pushing forward. This would mean you want the front to "unload" the elastic weight transfer more slowly.

This philosophy would give you a higher roll center in the rear than in the front. Actually it would give you a smaller distance from the roll center to the neutral axis at the rear than the front. So roll center height would depend on the angle of your neutral axis and the distance from it on that end of the car.

Is there any truth to this theory? It would explain the common notion that the front should have a lower roll center. Are there any teams out there that tune transients with roll center height, not shock settings?

[Brian Smith]

Brilliant!
Thanks Storbeck. That explanation on rollcenter heights makes perfect sense.

<BLOCKQUOTE class="ip-ubbcode-quote"><font size="-1">quote:</font><HR>Originally posted by Storbeck:
Somewhat relevent to this thread, is there any truth to this theory. Your overall moment of inertia in roll comes from two components, the moment of inertia of the car about the cg, or more accurately the neutral axis, and the distance from the cg to the roll center, or more accurately the neutral axis to the roll axis. <HR></BLOCKQUOTE>

Parallel axis theorem Ja=Jb+(m*d^2)

Ja=Inertia around roll axis
Jb=Inertia around Cg
m=unsprung mass
d=distance from roll axis to Cg
correct me if im wrong

Say we do what Mr. Hayward said and adjust dampers for pitch and warp. If our roll MOI is too small our roll damping will be too low. If our MOI is too large our roll damping will be too great. This is if we are looking only at elastic weight transfer.

So now another question. If we could design in any amount of inertia about the roll axis we wanted, what would it be?

I guess I am asking,

How do we determine the best roll acceleration value?

[clausen]

This is a good thread.

Don't forget that this "front cog and rear cog" stuff is a load of cobblers. A rigid body has one cog and all "inertia forces" act through it and nowhere else. This idea of of having the roll axis parallel to the "mass centroid axis" is pretty commonly talked about, but if you think about it, it becomes obvious that it's an idea that doesnt make sense.
On the face of it I think that the sensible thing to do would be to use a horizontal roll axis if you had a 50/50 weight distribution, higher at the rear if the weight distribution was rearward biased, and vica verca. I guess that's assuming you want transitional weight transfer to happen at the same rate. I don't konw if you do.
Actually, now that I think about this some more, I think I'm more confused.
I understand how the roll centre height effects moment of inertial in roll (parallel axis theorm). This depends soley on the distance from the cog to the roll axis, and the roll ineria about the cog (always fixed in this discussion). So if you started with a car with 50:50 weight and equal RC heights, lifting the RC 10mm at the front, or at the rear, should have the same effect on the way the car reacts transitionally? The car is an (almost) rigid body, so you cant have the front half starting to roll before the rear half or vica versa? Clearly the steady state balance will be different becuase the non-elastic weight transfer F/R distribution will be effected.

Anyone care to comment on this (possible drivel)?

[clausen]

<BLOCKQUOTE class="ip-ubbcode-quote"><font size="-1">quote:</font><HR> So if you started with a car with 50:50 weight and equal RC heights, lifting the RC 10mm at the front, or at the rear, should have the same effect on the way the car reacts transitionally? <HR></BLOCKQUOTE>

No, thats not right, but the effect that the moment of inertia in roll has on the transition should be the same?

[IsheeM]

I would disagree that the front and rear center of gravity is unimportant or non-existent. However, how would you calculate this...any ideas?

Thanks,

[BryanH]

quote
------------------------------------------------

No, thats not right, but the effect that the moment of inertia in roll has on the transition should be the same?

------------------------------------------------

Paul, the chassis may be one entity but is connected to terra at 4 separate flexible points, a higher cog at one end with your 50/50 + equal roll centres would result in diagonal pitch on turn-in ?

[Brian Smith]

I see a lot of question marks http://fsae.com/groupee_common/emoticons/icon_smile.gif

So considering that the chassis is rigid, can we have faster elastic weight transfer on one end? We decided earlier that elastic weight transfer% was equal to body roll%. So is it possible for the front to roll faster than the rear? I know some people use strain gauges on their pushrods. Anyone care to share?

Seems like Claude showed us how to fix the "problem" of the front rolling more (or less) than the rear. Look at damper speeds through the corner. Fix it by changing the damping to get same body roll at each end. This fixes chassis flex.

Are we sure that elastic weight transfer% is equal to body roll%?
Does anyone know of any books dealing with elastic weight transfer?
Is there anything in RCVD?

[clausen]

Michael, I think that if you try hard enough to work out how to calculate the front and rear cog you'll come to the conclusion that its a nonsense. You can't physically find them using tilt tables or anything like that simply becuase everything happens through the actual cog. If they dont mean anything on a tilt table, then surely they wont mean anything in a corner either?
If the car is sitting on a tilt table, and you move the engine up and down 200mm, all you'll see is that the cog goes up and down. You wont see the inside rear eventually lift off the ground while the front stays put (unless your chassis is made of rubber.
I think it was Ortiz that has pointed all of this out ina couple of different places recently, including RCE.

Bryan, I'm sure thats not right, but you've helped me think about all this in a different way,

If you picture the car on some sort of rig where the cog was fixed in space, and you had sliding pads at each contact patch to similate cornering forces as they occur on turn in, I think it might give some clue ot why we need higher r/c at the rear. Maybe it's because the contact patch forces at the rear lag behind those at the front, on turnin, that you need a higher r/c at the rear to get nonelastic weight transfer happening quicker at the rear, so that it can sort of "catch up" to the front?
Does this make sense?

But then Mini's have the front r/c at well up above the ground, and the rear on the ground, and they're super responsive.

Brian, I think you can defintely have faster elastic weight transfer at one end than the other - thats what happens when one end is stiffer than the other. This doesnt mean that roll happens quicker at one end than the other. I would say that total elasitc weight transfer % = total body roll %, but you cant split up one end from the other (unless the chassis is made of rubber)
I think here its helpful to picture the chassis fixed in space at its cog and have different forces acting at the contact patch similating what happens in transitions.

[Storbeck]

As far as the whole front cg and rear cg thing. I like to think of it not as two points but as a neutral axis. If you had a rectngle parallell to the ground it would have a neutral axis parallel to the ground, if you lifted up the rear, the neutral axis would slope up toward the rear. Most people refer to the front and rear cg are really talking about the height of the neutral axis as it passes between the wheels. I have no idea how you'd go about measuring it. This is the same with the roll centers, it's acutually a roll axis that connects the front and rear roll centers.

The more I contemplate my little theory about the moi's and rc heights the more I think it's wrong. For that to work you would have to have the front and rear of the car rolling at different rates, which is imposible. However you still can have the lag from elastic weight transfer effect one end of the car more than the other, the rear with it's higher roll center would have more geometric weight transfer, the front would have more elastic weight transfer. The elastic weight transfer would happen at the same rate front to rear, there would just be less of it in the rear. More of the geometric weight transfer which happens instantly. Kind of the same end result I guess.

That would have nothing at all to do with moment of inertia in roll though.

Clausen wouldn't the mini be a different game because of the front wheel drive. Also I bet there is way more weight on the front.

[Brian Smith]

Well the roll acceleration is a function of the moment of inertia in roll. So it does affect the speed of the transfer, but not the distribution of elastic and geometric.

Im not sure if I would even look at the neutral axis thing. Lets say we could move all of the components infinately close to the Cg. would anything change? Just forget about moments for a moment... http://fsae.com/groupee_common/emoticons/icon_wink.gif

OK, why do we want a rollcenter that is anywhere above ground? If it were well below the ground, it would delay elastic transfer nearly forever. Underground rollcenters even lower maximum weight transfer. Do we just want cars that are easy to drive at their maximum performance. Meaning that we want a car that reaches steady state quickly and the driver knows whats going on. Then he knows where the limit is and can be nearer to it more of the time.

Even though, to delay transfer would create a supirior car, mabey just hard to drive on the edge.


RCVD says that Chevy Chaparal thought the quickest way around the track was to go from one steady state to another as quick as possible. They did change there thoughts on this though.

[Kevin Hayward]

Storbeck & Brian,

I think I finally get the misunderstanding. The moment of inertia in roll is a physical property of the vehicle. It appears in your workings that you are including the moment due to lateral forces in your definition of moment of inertia in roll. As far as I understand this is not correct terminology.

The moment due to the lateral forces (acting through the COG) are of course dominant in roll and can be tuned in the system.

Kev

[Frank]

http://www.uq.edu.au/fsae/statics.xls

I'd appreciate if anyone could find errors in this spreadsheet

Notes:

Blue cells drive everything.

The "equivalent natural frequency" is just something I thought up, a design metric to compare different cars. It is sprung mass undamped natural frequency using the "equivalent spring" 1/Keq=1/Ksping+1/Ktyre

The tire deformation stuff was used to predict roll centre movement in "suspension analyzer 3D". The calculations are not iterative.

The roll calculations are only good for small geometric weight transfer (ie. roll centre near ground plane).

Regards

Frank

http://www.uq.edu.au/fsae/

[Brian Smith]

I am not too great at checking others work, but I didnt find anything wrong. The numbers make sence. Do you think there is something wrong with it?

[Denny Trimble]

Frank,
Your "equivalent spring" is what Milliken calls "ride rate". "Wheel Rate" = Kspring * IR^2 = Kw.

1/Kr = 1/Kt + 1/Kw

So yes, it is an important design metric http://fsae.com/groupee_common/emoticons/icon_smile.gif

The spreadsheet looks good, I haven't checked it, but we made something similar.

[Frank]

I don't know what I'm asking.

There seems a number of ways to write such a spreadsheet.

Essentially, you are approximating a multi DOF system. The trick is in which way you do it.

That sheet works well except when you have either of:

A large geometric weight transfer
B soft and differing individual tire stiffness

Essentially, they're always going to be just a "predictor", because track ratios, Ackerman, static toe, and the Cf you can generate will dictate what you need.

And I guess the whole thing is limited by how well you know the dimensions (numbers) of your car.

Even "roll stiffness ratio" is only a predictor in itself, and there's probably a few different ways you can calculate this "metric".

In the end its probably more valid looking at individual wheel weights and track ratios, than the "roll stiffness ratio".

Any which way, it seems to follow Claude's spreadsheet (somewhat).

http://www.uq.edu.au/fsae/transfer_metric.xls

can anyone else share a spreadsheet to compare methods

[Omer]

hi all
we are a first year team and i design the suspension.some help needed.
I'm confused with the milliken way to calculate roll rare ride rate spring rate etc.
I unerstood total load transfer depend on 3 factors only,mass,track width and cg height but using milliken equation(page 587) to find load transfer with different roll rates i change the total load transfer (i mean front+rear)without changing anything else what is the reason for that?how roll rates control total load transfer?

did anyone used his iterative method?or do you use a simpler equations?

I don't want to use ARB on our car and with having stiffer springs to compinsate is it a ballpark idea?

I understood 2-3 hertz are good frequency but for what speed and what radii?

wow, sorry for all my nagging,I like to understand things all the way but it seems like there are too many variables interactive with eachother.

the longer the reply will be the happier it will make me.

[Z]

This is the first time I've read this thread. Now, how to put this tactfully....

A lot of what you read in Racecar Vehicle Dynamics textbooks is a load of BS!!! http://fsae.com/groupee_common/emoticons/icon_smile.gif

And while I am sure that Carroll Smith/Claude Roulle/etc., had/have a tremendous amount of experience in motorsport, some of what they say is also BS.

Way back when racecar chassis' were deliberately made to be very flexible, it might have made sense to talk about separate front and rear CG's. Likewise, with some types of beam-axle location it makes sense to talk about a "roll-centre" (although even here the definition can vary). With typical modern independently-sprung, (reasonably) rigid chassis racecars, concepts like "front and rear CG's", "mass centroid axes", "roll and pitch centres", "instant axes for suspension movement", etc.,... are somewhere between misleading simplifications, and utter rubbish.

The "mechanics" (ie. the subjects of kinematics, statics, and dynamics) necessary to understand vehicle dynamics was worked out more than 150 years ago, ie. before the first horseless carriages were built. For some reason many modern car designers don't bother referring to this body of work, and instead continue to propagate the "in trade" fairly tales above.

If you want a good understanding of racecar dynamics get a good (which probably means old) book on mechanics, and learn it.

The (reasonably) rigid chassis/body of a car has one CG, and 3 MoI's about its 3 principal axes. Likewise the four wheel assemblies. There are force vectors (and small couple vectors) at each of the four tyreprints, that together act on the car. Also some aero force vectors. The mass of the five bodies (ie. in a simplified model consisting of the main body + four wheel assy's) resist these tyreprint and aero forces with "inertial reaction forces" that can be treated just like any other forces - d'Alembert's principle. The suspension has different compliances in different directions, and also some velocity sensitive components of force (from the dampers), that determine how it distorts when squashed between these tyre and inertial forces.

The fact that you are dealing with a "racecar" is totally irrelevant - it could be any other sort of mechanical system.

End of rant...

(Well, it annoys me that all this stuff was worked out so long ago, yet it is ignored by so many modern "experts" - many of whom charge big $$ for their books/seminars http://fsae.com/groupee_common/emoticons/icon_smile.gif)

Z

[BryanH]

Dear Z,
150 years ago, Casey Jones comes back from a test run and tells the designer "it's on rails" he wasn't kidding.....
pretty sure racing slicks weren't around when those Tomes were writ.
If you want to follow this line of thought re dynamics you need to explain why even sprint karts are very sensitive to changes in front or rear ride height (a major chassis tuning tool)
Come to think of it every car I've played with was sensitive to "rake"

[Z]

Originally posted by Bryan Hester:
... you need to explain why even sprint karts are very sensitive to changes in front or rear ride height
Karts have flexible chassis.

All "low flying" vehicles have aero forces that are sensitive to rake - the closer to the ground, the more sensitive.



Come to think of it every car I've played with was sensitive to "rake"
Many suspensions have properties that vary with ride height, and hence also with rake.
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One of the things that really annoys me is that many of the "experts" like to repeat the saying "The laws of physics are immutable", or some such. So why don't they find out what those laws are!

Example: Suspension Expert "When the suspension makes a small movement the upright rotates about an 'Instant Axis', which is defined as the line through the front-view and side-view 'Instant Centres'."

Crap! (I would be interested if anyone could post the correct "description" for 3-D instantaneous movements. It was well known 150 years ago. http://fsae.com/groupee_common/emoticons/icon_smile.gif)

Z

[BryanH]

Good Grief. Z you seem to be expert in reading whatever you want to see into a situation. eg the Gordon Murray Brabham Rollerskate. Murray was never talking about foward traction, the thing had no mechanical grip due to insufficient weight tranfer to outside tyres in cornering = COG too low!
btw there is virtually zero aero effect on a sprint kart, many pple have been there & tried that.
The real crap is believing that tyre load sensitivity is the Holy Grail, If you believe that you will never understand race car behaviour and all your theories will be based on crap!
The fact is that the cog of the front (or rear) effects the load on the outside tyre of tha particular end, and you have to load up the outside tyre enough to actually get some grip! Bottom line is best lap times at a particular track with a particular level of grip is about having not too much or too little grip at each end, COG of front/rear does have to be accounted for.

[ben]

I'm with Z on this. This thing about front and rear CGs is rubbish.

Bryan, yes you have to consider the loads on all the wheels, but this can be done without resorting to a false concept of front and rear CGs. Please enlighten me if I'm wrong though.

I think roll centres are a good means of statically estimating the ratio of front:rear anti-roll, but the fundamental assumption behind roll centres make tracking them as obsessively as some do strange. To clarify - the kinematic roll centre is not a centre of rotation of the sprung mass.

Ben

[CMURacing - Prometheus]

Originally posted by Z:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Bryan Hester:
... you need to explain why even sprint karts are very sensitive to changes in front or rear ride height
Karts have flexible chassis.

All "low flying" vehicles have aero forces that are sensitive to rake - the closer to the ground, the more sensitive.



Come to think of it every car I've played with was sensitive to "rake"
Many suspensions have properties that vary with ride height, and hence also with rake.
Z </div></BLOCKQUOTE>

it seems as though there's an even easier way to describe this...by changing front and rear ride height, aren't you also effectively changing your cg location and f:r weight distribution? i.e., if we raise the rear ride height and keep the front the same, we're effectively rotating the chassis about the front axle, with the cg moving in an arc (forward and up)?

or am i now oversimplifying?

[Z]

Originally posted by Bryan Hester:
Good Grief. Z you seem to be expert in reading whatever you want to see into a situation. eg the Gordon Murray Brabham Rollerskate. Murray was never talking about foward traction, the thing had no mechanical grip due to insufficient weight tranfer to outside tyres in cornering = COG too low!
So from that same article - Murray, re: the BT55 "Lowering the centre of gravity so much was wonderful for going around corners...". And Murray re: designing the all conquering McLaren MP4/4 "The Honda engine was too high so I spoke to Honda immediately and they lowered it. I think the crankshaft height was reduced by about an inch and a half...".

Raising CG height would be one of the easiest things you can do on a car. Lowering it is much harder and costs a lot more. Murray lowered the CG as much as he could on both those cars. The MP4/4 won 15 out of 16 races. What have I misread??

----------------------------------------------------------------------------------

Mike,

Even if you keep the CG height the same, and just make a change to rake (pitch angle), some or all of the following can happen:

Change in F:R weight distribution ('cos wheels don't move vertically rel. chassis in side view).
Change in track dimensions (as above in front view).
Change in toe angles (shouldn't happen, but can be slight).
Change in camber, and rate of camber change.
Change in front and side-view "anti's" (ie. notional "roll and pitch" centres).
Change in remaining wheel travel (wheels become droop or bump limited at different roll angles).
Change in spring rate (if using rising or falling rate springs).
Change in damper stiffness (as above from geometry of damper).
Change in aero lift/downforce and its F:R distribution (negligible effect at low speed, huge effect at high speed).
And I'm sure there are more that I can't think of right now...

Edit (31/08/2005): Thought of another one;
Change in front castor angle (so change in front camber, and overall wedge (if non-zero offset/trail), during steering movements).

Edit (24/09/2005): And another one:
Change in slope of longitudinal principal axis of body, which changes longitudinal load transfer due to yaw velocity (ie. dynamic imbalance of rotating body).

Changing rake moves the F and R suspensions in different directions, so it is not surprising that it effects F:R handling balance (again, think about a car with the same rising rate springs F and R). It is not necessary to invent "a theory of front and rear CG's". http://fsae.com/groupee_common/emoticons/icon_smile.gif

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Anyone care to suggest the "correct" or "natural" description for 3-D motions, one body relative to another? (It is not a "rotation about an Instant Axis"). I am curious about this because I learnt it at an early age and it seems quite simple and obvious. I've never seen it correctly explained in any book on vehicle dynamics, suspension design, etc...

Z

[Z]

Further to the issue of "front and rear CG's".

IF the chassis is flexible, then, yes, you have to consider the locations of the many masses that make up the whole car. BUT, you also have to consider how these masses are structurally connected, and how they feed their inertial forces to the front or rear wheels.

For example, it is possible to completely change handling balance while having exactly the same mass distribution, but a different structural arrangement. Specifically, pre-1930's racecars had very flexible chassis - deliberately, for a soft "twist mode". Because they mounted the big, heavy engines on three points - 2 at the rear bellhousing and 1 under the nose - the engine leant on the centre of the chassis rails and they had fairly neutral handling. If they mounted the engine with 2 points at the front and 1 at the rear, the engine leant more heavily on the front wheels and they had understeer, even with no other changes of CG height, F:R distribution, rake, springs, etc. This is easy to test! A naked Ford F100 chassis/drivetrain is a good starting point.

Racing textbooks that talk about "front and rear CG's" usually also recommend a chassis that is as rigid as possible. I have never seen any sort of mention of the effects in the above paragraph (ie. the chassis-compliance/mass-distribution being included in the roll-moment-distribution equations). Sounds like a half-baked theory to me. http://fsae.com/groupee_common/emoticons/icon_smile.gif

Z

[CMURacing - Prometheus]

z, have you bought the maurice olley notes that milliken/milliken just edited and published through SAE? i've been reading through my recently purchased copy and it seems more up your alley (ie "old school mechanics")...there's lots of places where milliken mentions olley's method of "calculating" things involving concepts like drafting scale models and then measuring the answer.

but to answer your challenge of 3-d kinematics, my dyanmics text (recently dug up from the box in my basement, last fall was soo long ago) hits on three major ways of describing motion: relative velocities (lots of variables to keep track of and a lot of vector algebra), instant centers (easily visualized, and with a good to-scale drawing, analyzed on paper), and moving reference frames, which are all sorts of crazy. instant centers may not have been the first way we all learned, but its probably got the most bang for your buck.

[BryanH]

Dear Z, re the MP4, the engine was only 1 part of a well balanced package. Gordon learn't much about mechanical grip with the BT55. With the MP4 he wanted the engine lower to equalize the F/R COG to minimize change in balance in low speed and high speed cnrs! IMHO the B194 Bennetton & variants were actually the best chassis of the era.

[ben]

Originally posted by Bryan Hester:
Dear Z, re the MP4, the engine was only 1 part of a well balanced package. Gordon learn't much about mechanical grip with the BT55. With the MP4 he wanted the engine lower to equalize the F/R COG to minimize change in balance in low speed and high speed cnrs! IMHO the B194 Bennetton & variants were actually the best chassis of the era.

I'm assuming you mean MP4/4 (the '88 McLaren)? What's the Benetton B194 got to do with anything either?

Bryan, when you say equalize the front and rear CGs do you mean w.r.t the road surface, roll centre heights, what? Also how do you descretise the sprung mass into two discrete masses?

Furthermore if you assume a rigid chassis, what is the difference between two masses rigidly linked and an equivilant single mass at an equivilant single CG position?

Ben

[Z]

Originally posted by CMURacing - Prometheus:
z, have you bought the maurice olley notes that milliken/milliken just edited and published through SAE?
Mike, Yes, and I would recommend "Chassis Design, Principles and Analysis" to any FSAE'ers who want a broader view of chassis/suspension design. In fact, I would recommend it above Milliken's other book "RCVD". The Olley notes cover most of the important stuff in RCVD, and also give a lot of other insights that don't appear in more modern books. It also has some stuff that is irrelevant these days but is good background, and it misses most of what was happening in Europe (usually 10+ years earlier than in the US) but that is to be expected http://fsae.com/groupee_common/emoticons/icon_wink.gif.

Olley was somewhat out of step with (and in a sense, ahead of) his times because he prefered an algebraic approach to suspension analysis - see Chapter 7, Suspension Linkages, where he uses simple first and second order algebraic approximations to the suspension arcs. Personally, I prefer the geometric methods that were common back then (briefly covered in book), but that's because I like to think spatially rather than sequentially (temporally). Trying to explain stuff in ascii is a real pain! http://fsae.com/groupee_common/emoticons/icon_smile.gif



...but to answer your challenge of 3-d kinematics...
The idea on one 3-D body's movement relative to another body, being a "rotation about an Instant Axis" is close, but only half way there. There is something missing! I'll wait a bit longer before giving clues...

Z

[Z]

Bump.

Dynamics - n. 1. the branch of mechanics concerned with forces that change the MOTIONS of bodies,... (Collins English Dictionary).

So if you want to understand Vehicle Dynamics you really have to understand 3-D motion first.

So you should have a simple but universally applicable way of describing the motion of one body relative to another. Eg the motion of a car body relative to ground, or of a suspension upright relative to the car body.

Now an "Instant Axis" is a good way of describing, say, the motion of a door as it swings relative to the wall (the IA is down the middle of the hinges). What about the bed of a lathe as it slides along the lathe's runways? Well, just say the runways are not perfectly straight, but slightly bowed so that they are 1 micron higher in the middle than at the ends. For a 2 metre long bed this would put the Instant Axis 500 kilometres below the lathe and running at right angles to it (not that far away, really). For a mathematically "perfectly flat" lathe the IA would be at "infinity", and again at right angles to the motion. So the Instant Axis is looking pretty good...

BUT! Are there any 3-D motions of one body relative to another that can NOT be described as "a rotation about an Instant Axis"? Of course! And they should be bleeding obvious to any self-respecting engineer!!!

So what is the simple and universal description for 3-D motions??? http://fsae.com/groupee_common/emoticons/icon_confused.gif

Don't let me down guys. Someone must know this... http://fsae.com/groupee_common/emoticons/icon_smile.gif

(Note: The 2-D version of the Instant Axis, namely the "Instant Centre", IS correct. But we don't live in a 2-D world.)

Z

(Edit: Added some emphasis..)

[Denny Trimble]

XYZ positions, roll pitch yaw (or any other scheme) rotations.

[Z]

Originally posted by Denny Trimble:
XYZ positions, roll pitch yaw (or any other scheme) rotations.

Correct, but there is a simpler description (if you could see it that way...).

Ie. For a "general" motion, the deltaX, Y and Z's of different points on the moving body are generally different. So which point, or points, do you pick for a natural/elegant/simple description?

The "Instant Axis" would suggest that some points - those along the IA - have no movement (dX=dY=dZ=0). Is it always possible to find such points???

Z

[murpia]

Are we talking about Transformations?
Ian

[CMURacing - Prometheus]

Z--

I agree with you on Olley's notes (and, funnily enough, so does milliken, and they're upset SAE isn't pushing it like they did RCVD).

the obvious points to pick are the centers of mass of the two objects. these will only move translationally, so now you have relative translational velocities and accelerations, and you only need to express the angular quantities for the individual bodies.

[Denny Trimble]

Any point you pick will only move translationally, it's just a point. I think Z is hinting at picking "center points of rotation" or something like that.

[Z]

Originally posted by Denny Trimble:
I think Z is hinting at picking "center points of rotation" or something like that.
If the "Instant Axis" concept was correct, then there would always be some points (those along the IA) that had no relative translation (dx=dy=dz=0). Enough hinting - for most motions this is not true! So the Instant Axis is a flawed concept ... although it is close. http://fsae.com/groupee_common/emoticons/icon_wink.gif

Here is the problem as it relates to suspension design. Millikens' RCVD says that "the Instant Axis [defines the] motion of the knuckle relative to the body" (p612, chapter 17, "Suspension Geometry", written by Terry Satchell). Using the points where this IA pierces the "front-view" and "side-view" planes gives the notional "roll" and "pitch" centres. These centres are then used for all sorts of dynamic analysis (eg. kinematic and elastic load transfers, etc.). So it is important to know their location accurately. Later on (p632) "the design is now complete except for fine-tuning the tie rod" (to get the right sort of bump-steer curve).

BUT! If the IA "defines" the motion of the knuckle, then how can the bump-steer behaviour be independent of the IA. Ie how can you have many different bump-steer curves with the same IA? Answer: the IA only "defines" the motion of the kingpin (or steer-axis), which is a line and not a 3-D body.

So you get computer programs for suspension design that give roll and pitch centres according to the IA concept, and from these most of the dynamics is worked out (to 6+ decimal places!). Then, in another obscure part of the program, roll and pitch "anti's" (essentially the same thing) are calculated according to the slope of the tyreprint centre's movement during bump (ie. its slope away from vertical). These two methods often give quite different results (up to 10% sometimes) when they should be the same! The flaw is in the IA concept.

So, say you have the car body as fixed reference frame, and the knuckle as moving body. You draw up a grid in the knuckle's XYZ frame, give the knuckle a small movement, and join up all the knuckle's original grid points with arrows pointing to their final positions. If the movement was a "rotation about an IA", then the arrows of grid points along the IA will be of zero length, and all the other arrows will form a swirling pattern about the IA, with longer arrows the further away from the IA.

This only happens in exceptional cases. For general motions the pattern of the arrows (ie. the instantaneous displacements, or inst. velocities) is a little bit different. What is it???

(Hint: think about general motions that aren't "rotations about a simple hinge". http://fsae.com/groupee_common/emoticons/icon_wink.gif)

Z