Weight Distribution vs. Polar Moment (Yaw Intertia)

[crazy280]

Some newer cars come with computerized yaw control, for example the non-american-market Mitsubishi Evolutions. It works by controlling the power to each of the four wheels, individually, during cornering. Pretty amazing stuff!

[johnc]

This was to allow space for twin exhausts and to provide a clear exit from under the car to aid with aerodynamics (having an under belly pan and maybe some venturi a la ferrari 430.

 

A custom fuel cell with a 7 degree rise bottom in basically the stock location will work wonderfully as the top of your rear diffuser. That's what the Rusty Old Datsun had.

[katman]

A custom fuel cell with a 7 degree rise bottom in basically the stock location will work wonderfully as the top of your rear diffuser. That's what the Rusty Old Datsun had.

 

'Tis also what 2 time ARRC ITS winning 240Z of Chet Wittel had. You sir, are a freakin' genius!

[johnc]

I thought about this diffuser idea as applicable to an ITS 240Z and I figured a wide muffler placed vertically close to the fuel cell on the driver's side would work well as one side of the diffuser. But I could never figure out how to legally (and safely and without attracting too much attention) do the same on the passenger side of the diffuser. I thought about making a fuel pump/filter bracket similar to the one in the pictures of the ROD out of some thick sheet metal, but the pump and filter would have to be awfully low to keep folks from throwing paper.

 

I'm glad to hear that you guys had also figured it out. I like being associated with a better class of people...

[pparaska]

Thanks for the education, John.

 

Kim's point of view on this has interested me, that is that having more forward weight was an advantage in hillclimbs. I guess that MAY be true, but I always wonder if the car was set up with less front weight and the suspension setup tuned properly if it could have been faster.

 

I did like Mike is talking about and decided that the battery should be behind the passenger seat, not behind the tower. I have problems putting a lot of mass outboard of the axles, but that's gut feel, not engineering.

 

I don't like the fuel cells I see hanging down so much below the back edge of the valance - it doesn't look right to me for several reasons. Unfortunately, to do otherwise means a custom job. Probably why I just run the stock tank...

[tube80z]

Kim's point of view on this has interested me, that is that having more forward weight was an advantage in hillclimbs. I guess that MAY be true, but I always wonder if the car was set up with less front weight and the suspension setup tuned properly if it could have been faster.

 

Okay, I came to the game late. Is the 55/45 discussed above front to rear or rear to front? I was a little lost on that one.

 

For what it's worth I ran at the Bogus Basin hillclimb with my car, which is L6 powered and 2 percent heavy with me in it to the rear. My first run up the hill was faster than any I've seen from previous results from Kim. While this doesn't mean anything it seems to be the argument that he uses for why rear weight isn't needed.

 

Forward weight bias for hillclimbs is generall seen in Pikes Peak cars. If you look at the 4WD monsters this is how most of them are setup. I think it has to do with trying to get equall traction from the tires at a dynamic state. Not really something we'd see translate over to paved hillclimbing.

 

Most of the fast EMOD cars autoxing are heavy to the rear. They do this to help with traction out of corners. They generally try and hit a 45 front to 55 rear target and work well. My tube frame car is built to try and hit this number and the back of the engine is 1.5 inches of the car centerline (completely behind the firewall with a 5.0 Ford).

 

Good discussion though. It seems to validate my weird little view of the world. FP Z car using GT engine setback and little 13 inch wheels and tires. The only thing I saw missing here that relates to PMOI is gyroscopic forces from the rotating components. Which is why I think 16 inch wheels are wrong for an autox car.

 

Cary

[johnc]

Mark Ortiz's latest newletter expands on this topic.

 

REAR PERCENTAGE OR POLAR MOMENT?

 

I am wondering about the relative merits of Front / Rear Weight Distribution versus Polar Moment of Inertia. I road-race a Mustang in a class that allows extensive engine and suspension modifications to late-model muscle cars, but the rules are strict enough to prevent extensive body, floorpan, and frame modifications. As a result of the rules, and the large V8s, the cars are inherently heavy in the front end – usually to the tune of 51-55%, depending on platform, fuel load, etc. So when deciding on the placement of heavy components (such as batteries, fuel cells, ballast, etc.) I’m wondering what the ideal position is. Obviously lower is always better, but how far back is ideal? You could place the masses as far back as possible to improve F/R balance, but at the expense of Polar Moment. You could put the mass in the center of the car, minimizing polar moment but failing to take advantage of an opportunity to improve the car’s balance. Or you could put it somewhere in between.

 

Instinctively, my engineering training tells me that the two things have different functions. F/R distribution should make the car generally behave in a more balanced fashion, and certainly more weight on the back tires will help corner exit traction – which is a key in this type of car. Keeping polar moment low should help keep the car rotationally responsive, and more willing to respond to corrections if the tail steps out.

 

Several years ago I ran a simple analysis, and found that the average cornering speed of the car seemed to be a determining factor between these two trade-offs. This was not an in-depth analysis. Basically I broke cornering down into the energy it took to rotate the car (start it rotating and stop it rotating) and the energy it took to redirect the velocity vector, and compared the two. It seemed to me that the faster the mid-corner speed, the more the velocity vector change became the dominant force requirement, and therefore we might assume the F/R balance would be more important. My analysis said that, in the kind of racing I do, F/R distribution would be far more important, but I’m surprised at the number of competitors, in amateur and pro competition, who seem to disagree. Of course, my analysis was simplified to a great extent, with numerous assumptions being made that are not necessarily always valid.

 

So I ask – how far back should I place that ballast, or those movable components? On an average road course, where mid-corner speeds probably average from 40mph to about 100mph or so, which would you deem more important? Would you place that ballast in the back bumper, or under the floorpan or inside the inside frame rail?

 

And as a secondary question – what would you consider the ideal weight distribution for a car of this type. Obviously, if I can achieve whatever I decide is “ideal”, then I want to work to reduce polar moment, but what is that “ideal” number – in your estimation of this type of race car? I’ve heard arguments for 50/50 and arguments for as much as about 58% rear weight. I tend to think the answer is closer to 55%, but I’m very curious as to your input on this matter as well.

Taking the last part first, the ideal rear percentage, or the desirable range, depends on your tire rules and the nature of the course. To a lesser extent, it is also influenced by the level of available grip, and by aerodynamics.

 

Suppose we have no tire rules, ample power, lots of freedom with our wings and other aero devices, and a track with serious straights and tight turns. Suppose also that the rules require rear wheel drive. In such a case, we might want as much as 65% rear, or even a bit more, and rear tires about twice the size of the fronts. We would want more than 2/3 of the downforce at the rear. We would want ample area in rear wing sideplates and/or tail fins, for yaw stability.

 

The reasoning here is that the car will spend a lot of its time accelerating longitudinally: accelerating forward out of the turns and down the straights, and accelerating rearward (braking) at the end of the straights. Propulsion comes only from the rear wheels, so we want as much of our weight on the rear as possible to maximize forward acceleration. Braking is shared by all four wheels, and if the car has ample braking capability, the fronts will do more than half of the braking even if they only carry a third of the car's weight at rest. This is due to the large amount of dynamic load transfer forward during hard braking. So for both forward and rearward acceleration, we want as much rear percentage as possible, at least within practical limits for a road racing car.

 

This would be so even if we are constrained to equal size tires front and rear. If our event is, say, a zero to 100 to zero competition (accelerate from a standstill to 100mph, then brake to a standstill, all in a straight line), we'd want to build the car so it just barely picks the front wheels off the ground at launch, or almost does so. Note that the rear percentage needed for this varies dramatically depending on the wheelbase, the c.g. height, and the amount of grip available. With a production-based car – relatively short wheelbase and high c.g. – and good drag slicks, the ideal rear percentage may be less than 50%. The grip of modern drag tires is so good that a 50/50 car can actually be limited by wheelstand rather than wheelspin. With a high c.g. and a short wheelbase, the ideal rear percentage varies dramatically with the grip level.

 

If we have more chassis design freedom, we'd rather have a dragster than a pro stock: long wheelbase, low c.g., lots of static rear percentage. With such a layout, rearward load transfer is less, and consequently dynamic rear percentage varies less with grip level. A single layout and setup will therefore be more nearly optimal over a wider range of conditions. With street tires or road racing tires, the ideal rear percentage will be considerably over 50%. As long as the car doesn't have to turn, we'd want to build it like a dragster, even if the front and rear tires have to be the same size.

 

Of course, the questioner here doesn't have such design freedom, nor is he running on a track with no turns. I'm just examining extreme cases, to illustrate some points.

 

The opposite extreme case would be a skidpad competition: the car just has to corner at the highest possible constant speed. Accelerations now are almost purely lateral. We might suppose that the ideal design here would have equal-size front and rear tires, and 50% static rear weight. That is

 

 

indeed close to correct, although if we can use unequal tire sizes, we can get as good cornering from a tail-heavy car as from a 50/50 one. If there are no limits on tire size, two practical considerations will limit us: camber control and steering geometry. We can control camber about equally well at both ends of the car, but there is a case for using smaller tires on the front from the standpoint of steering dynamics. If we do that, we want the car tail-heavy, roughly in proportion to tire size.

 

Oddly enough, the radius of the skidpad affects the optimum rear percentage. This is a bit counter-intuitive, but it's true. Really small skidpads (or really tight turns) call for a more tail-heavy car than the tire sizes would suggest, and really big skidpads (or really big turns) call for a more nose-heavy car. The reasons for this are of different natures for the two cases.

 

On a really small skidpad, such as the 50-foot diameter one used in Formula SAE competition, the front wheels track noticeably outside the rears, even when the tires are sliding. Consequently, the drag forces of the front tires, especially the heavily loaded outside front, act at a larger radius than the radius the c.g. is following, and the propulsion forces from the rear tires act at a smaller radius than the c.g. is following. This creates a yaw moment out of the turn, and tightens the car (adds understeer). Additionally, in some cases there may be effects from a limited-slip differential or a locked rear that create understeer in small-radius turns.

 

When the turn radius is really large, the car will need to transmit substantial amounts of power through the rear tires just to maintain constant speed. On really fast turns, the car may actually be near full power, and not gaining any speed at all. The rear tires are transmitting hundreds of horsepower, just to overcome aerodynamic drag and the induced drag from the front tires as they run at a slip angle.

 

This means that the rear tires are using a substantial portion of their performance envelope, or traction circle, to propel the car, so they have less of their capability available to generate lateral force. The car is consequently subject to power oversteer. The best way to counter this is to have a disproportionate amount of aerodynamic downforce at the rear of the car. However, in many classes, including stock cars running on high-speed ovals, the rules may not allow the aerodynamic devices needed to achieve this. It then becomes desirable to make the car a bit nose-heavy to add understeer and counter the power oversteer.

 

I am not trying to confuse the issue. I am merely pointing out that, as the questioner has already come to appreciate, we cannot state categorically that a particular rear percentage is ideal. It depends on other factors.

 

That said, the questioner appears to be correct that in his class, more rear percentage is better, within the limits imposed by the rules, without going above minimum legal weight. And there is indeed a tradeoff in such a situation between getting good rear percentage and reducing yaw inertia (polar moment of inertia in yaw, commonly "polar moment" for short). I agree with the questioner's tentative conclusion that it is better to go after rear percentage and forget yaw inertia, for road course applications.

 

It is interesting to consider what it might take to make us go the other way, and put the ballast closer to the middle. I think we might do that if we were autocrossing, particularly if a large part of the course was made up of a long, constant-speed slalom, and if the course had no significant straights, so that the car was continually cornering and continually changing direction, and never had to spend a lot of time accelerating longitudinally – in other words, if there was a lot of yaw acceleration and relatively little longitudinal acceleration.

 

But no road course is like that. Almost all of them have serious straightaways, and few really abrupt transitions. A car with large yaw inertia will tend to understeer into the slower turns and oversteer coming out, but to some extent the driver can overcome the entry understeer with trailbraking, and the exit oversteer by using an "out fast" line and judicious throttle management.

[mom'sZ]

John:

This was a great thread and I'm glad you revived it. So if I'm getting this right, for a road racing car, weight distribution is more important then polar moment of inertia. Indeed, hanging weight at the extreme ends of the car to help improve weight distribution is better then keeping it more centrally located to gain less 'polar moment' at the cost of poor weight distribution... right? for a road racing car, not autoX. In fact adding polar moment of inertia (by say hanging heavier pieces out near the ends of the car) will help make the car more stable, easier to drive at the limit and easier to catch once you've past the limit? I'm sorry for such ignorant questions. Could you (or anyone) explain the term 'polar moment of inertia' or 'polar moment' as it pertains to vehicle dynamics a little for me?

[johnc]

A better term is Yaw Inertia. Yaw is the spin of the car around an imaginary pivot - like a top. In an airplane yaw is when the plane is moving at an angle to the actual direction of flight. Yaw is easily seen as a plane is landing in a crosswind, the plane is pointing into the wind a little bit and appears to be flying sideways.

 

Yaw Inertia is the resistance to yaw. Yaw Inertia is affected by tires, track, wheelbase, alignment, aerodynamics, weight, and weight distribution. For this discussion we are just focusing on the relationship between weight distribution and yaw inertia.

 

Weight distribution affects the amount of forced needed to induce yaw and the force needed to contorl or stop yaw. A car with a 50/50 weight balance where all of the weight is inside the wheelbase has very little yaw inertia. Like a top where most of the weight is centralized, it spins easily and quickly. A car with a 50/50 weight balance where most of the weight is hanging outside the wheelbase has a lot of yaw inertia. Like a gyroscope, it takes some effort to get it spinning and spins slower then the top given the same amount of initial force.

[mom'sZ]

thanks for an excellent explaination John. So... my assumption that more polar moment of inertia will make the car more driveable at the limit is correct? As in Jon Mortensen's example of the mid engine 510 being undriveable. So, the terms 'polar moment of inertia in yaw', 'polar moment' and 'yaw inertia' are basically interchangable as they pertain to this discussion? If I'm understanding this correctly, the added weight out toward the ends of the car make the control inputs required to initialize a direction change greater, but this results in a more stable ride, and greater driveability at the limit. The s30 is a 'heavy' handling car anyhow, not really suited to autoX or parking lots. Seems almost like more 'yaw inertia' kind of gives you more 'leverage' to catch the car once it begins to spin and makes the car spin 'slower' so you have more time to catch it. This sounds like a better setup for racing. When I road raced motorcycles, I didn't mind the bike sliding, just so long as it did so in a predictable manner instead of just spitting you off. In the begining I learned to go faster by using junkier tires that slid sooner then the high dollar stuff, but did so in a more predictable manner.

[JMortensen]

I'd like to think that you can autox an S30...

 

Here's another problem not really addressed yet. Having a whole bunch of weight up front tends to make a car understeer and tends to make it worse under braking. Anyone who has seen a 911 at the track knows that they tend to oversteer and can outbrake just about anything. The problem comes when an unexperienced driver in a 911 gets onto the track. Suddenly that rear weight doesn't become an AID to stability, it becomes a DETRIMENT. Well, that's not strictly true. 911's aren't unstable per se, they're just more stable traveling backwards. If you built your ITS Z and were a couple hundred pounds light, I'd be careful about bolting on a 200 lb bumper.

[johnc]

Extreme examples of high and low yaw inertia cars are good as examples only. In the real world of racing too much or too little of anything is not good.

 

In the world of autox 240Zs have done very well and still do well here in Southern California. I'm building a Solo2 SM2 240Z for a customer right now.

[260DET]

Talking of Porsches, had an interesting conversation with a former Porsche race driver who described how driving a Porsche was quite different to most other cars. He incidentially was not a Porsche fan, loves Datsuns.

 

On slower corners Porsches are good he said because their usually superior braking can be used to good advantage, braking deep into the corners. It was then a matter of getting the car pointing in the right direction as soon as possible and using the usually superior traction to drive early out of the corner. There was not much finesse in it, hard braking, quick turn, blast away out.

[mom'sZ]

I'd like to think that you can autox an S30...

I've never autoX'ed before. I went up to Ft. Pierce where the central Florida region holds autoX's every month for the first time in March just to check it out. This past month I was to sick to go but I'm hoping to give it a try here in May. Any tips for a newb?

If you built your ITS Z and were a couple hundred pounds light, I'd be careful about bolting on a 200 lb bumper.

With the new weight break I don't think that is going to be an issue. I had just heard opinions both ways and was trying to understand better.

[tube80z]

my assumption that more polar moment of inertia will make the car more driveable at the limit is correct? As in Jon Mortensen's example of the mid engine 510 being undriveable. So, the terms 'polar moment of inertia in yaw', 'polar moment' and 'yaw inertia' are basically interchangable as they pertain to this discussion?

 

I think in terms of this dicussion the terms are used interchangedly but that's not necessarily correct. As Ortiz points out more yaw intertia will make the car understeer on entrance and oversteer on exit because of the resistance to changing direction. While this may seem like it is more stable you do have the issue of once it it's starts to go it is that much harder to get back. So it's not always better.

 

In the case of an autox car it is more important to be able to change direction more quickly than generate ultimate cornering numbers. In the case of the mid-engine 510 that's really more about a poor chassis making it undriveable than anything else. 510s have poor camber control in the back, a lot of squat, and when you couple this with wide sticky tires and power you get the antics the Jon describes of Dennis' car. What I don't think gets mentioned is that this car still has more yaw intertia than something like a formula ford, which are very good autox cars.

 

If you happen to be fortunate enough to take the motec seminar by Claude Roulle he'll share a lot of info about ballast placement and yaw intertia and how much of a tuning tool it is. I have to run ballast on my autox car. One trick I use with it is changing the ballast. When it is cold and I need to get more heat into the tires I will put teh weight at the outer ends of the car, increasing the yaw inertia. This creates a measureable increase in tire temps.

 

Cary

[JMortensen]

I've never autoX'ed before. I went up to Ft. Pierce where the central Florida region holds autoX's every month for the first time in March just to check it out. This past month I was to sick to go but I'm hoping to give it a try here in May. Any tips for a newb?

As much caster and neg camber as you can get in the front up to about 7ish and -3.5 degrees, and about 1/4" toe out. Rear about 1/2 degree less camber, 0 toe or slight toe in if you can adjust. That's for radials. Bias ply requires a lot less camber. Try to steer smoothly, and late apex as early as possible (that's an old autox mantra). The less you steer the faster you go. That ought to keep you busy!

With the new weight break I don't think that is going to be an issue. I had just heard opinions both ways and was trying to understand better.

It's kind of a moot point on a Z, since we aren't trying to fix a drastically nose or tail heavy car. I'd like to see 47/53 or so for weight distribution. The one time I put mine on scales it was 49.4/50.6 and the cross weights were within 10 lbs just the way I had been driving it. So I was hoping to make all these adjustments, got done weighing it and pretty much said "Huh, wasn't expecting that" then put the scales away and gave them back to the guy who loaned them to me.

[mom'sZ]

As much caster and neg camber as you can get in the front up to about 7ish and -3.5 degrees, and about 1/4" toe out. Rear about 1/2 degree less camber, 0 toe or slight toe in if you can adjust. That's for radials. Bias ply requires a lot less camber.

The tires are Toyo Ra1s or whatever they're called. And the suspension geometry I've got something I think is going to work OK as well. I was thinking more technique. Could you explain the old autox mantra of late apex as early as possible? I'm familiar with the term late apex from my bike days. I also noticed the track changes every time. How do you learn the new layout quickly, do you draw it out on paper? just in your head. How do you relate what it looks like walking it with how it will be at speed in a car? Maybe I'm over thinking this and once I try it it will come more natural. Also, it seemed everybody had there windows rolled down, is this to be able to hear the tires?

[JMortensen]

"Late apex as early as possible" means that you want a late apex, but you want to get on the power as quickly as you can. Late apexing you already know. It's important to late apex in autox because there are basically no straightaways. If you did a perfect apex like you would on a 90 degree turn at the track you won't be able to transition for the next corner fast enough. If you early apex you're off the course. The sooner you apex the corner successfully the sooner you can get on the power. So late apex as early as possible means get around the corner well, and at the same time get the power down as quickly as you can.

 

Walking the track is the trick to autox. It does change every time, which is part of the fun/frustration. You have to be able to look at a turn and figure out where your line is going to be, what gear you're going to be in, etc. I used to autox with 2 clubs. One had one course walk at the beginning of the day. Sometimes you didn't run until 5:00 in the afternoon. That's when it's really difficult. The other club was a little easier. Morning and afternoon were broken up and there was a course walk at 9:00 and a course walk at 1:00. If your group isn't running first or working first, you're lucky. There's usually at least one spot on most courses that catches people out. If you can determine what that spot is, you can spectate there. Then when you're assigned to work the course, try to work there as well. Hopefully with all the watching you'll have figured out the best way around when it comes to driving the course. Find the most experienced person you can, and walk the track with them and ask questions. At the NASA events I used to attend Dennis Hale and his wife Peggy used to announce that they would take first timers on the course walk and they'd always have a whole gaggle of newbies around when they walked the course. Walk it several times if you can. Sometimes there is time, sometimes not.

 

Couple other tips: look where you want to go! Just like motorcycles, if you're focused on NOT hitting that oil slick that you're staring at, you're GOING to hit the oil slick. If you focus on your apex, you are going to hit the apex. Look ahead too. Don't focus 20 feet in front of the car. Look ahead, this will enable you to get the entrance to the next corner right. It's kind of like hitting a baseball. You have to see the corner way out there, then watch it all the way in until you hit the apex, then get lined up for the next corner (hopefully keeping the next corner in mind the whole time). Sometimes on a slalom or something like that I won't look at the apex, I'm looking at the next cone. This is because the turn you're in is already done, if that makes any sense. Also, I think most autoxes post a course map. If you run last, look at the course map before you drive. When you get in the car try to drive the whole course in your head. And if you've totally forgotten the course, take it easy on the first run and figure out where you're going, and try to remember that on your subsequent runs.

[tube80z]

Could you explain the old autox mantra of late apex as early as possible? I'm familiar with the term late apex from my bike days. I also noticed the track changes every time. How do you learn the new layout quickly, do you draw it out on paper? just in your head. How do you relate what it looks like walking it with how it will be at speed in a car? Maybe I'm over thinking this and once I try it it will come more natural. Also, it seemed everybody had there windows rolled down, is this to be able to hear the tires?

 

For a beginning autoxer the best thing to do is to walk the course with someone experienced and in a similar car/class if possible. Most of the time you'll be welcomed and the person will share information. Watch and ask questions about what line they would drive and ask why. Generally in a slow area you need to minimize the distance driven even if that means you do some weird unintuitive things as it waill almost always be faster.

 

When you start driving you want to work on car placement first. Getting very close the the cones and being consistent for your runs. It's much better to come into the corners going too slow and then getting on the power early. Most beginners have a tendency to try and carry in too much speed and overslow the car at the apex and blow the exit. Another thing I see all the time is someone holding steering lock for too long, which slows the car down and often upsets it for the next transition.

 

Generally, when I walk the course I'm looking at the spacing of objects (turns, gates, etc.) to see if they increase, decrease, or stay the same. I also pay a lot of attention to the pavement, just dragging your foot every now and then can tell you if there's more or less traction in a certain area (parking lots are notorious for getting polished areas). Does the pavement stay level, rise up, or fall away? Very important. That's usually what I'm looking for.

 

Most clubs will have someone with a lot of experience or maybe a national level competitor. They will usually be willing to ride with you and give you pointers. Take every advantage of this you can. And if they are willing ride with them. And remember, this is supposed to be fun. If it's not you're trying to hard

 

Hope that helps,

 

Cary

[JMortensen]

Does the pavement stay level, rise up, or fall away? Very important.

That brings back memories! We used to autox at this airport in Santa Maria, CA. There was a bump in the pavement that my friends and I called the "stadium truck jump". In reality it was probably 6 inches high and gradual enough that if you drove your car over it normally I doubt that you'd even notice it. But when you were hanging it out on the edge of traction, it felt like a big jump. You could actually get about 1" of air off the thing if the course and the car was set up right. It was the best part of that whole space IMO. Every time it was like a "what are they going to do with the stadium jump this time?"