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Mark Ortiz Automotive is a chassis consulting service primarily serving oval track and road racers. This newsletter is a free service intended to benefit racers and enthusiasts by offering useful insights into chassis engineering and answers to questions. Readers may mail questions to: 155 Wankel Dr., Kannapolis, NC 28083-8200; submit questions by phone at 704-933-8876; or submit questions by e-mail to: email@example.com. Readers are invited to subscribe to this newsletter by e-mail. Just e-mail me and request to be added to the list.
EQUAL WHEEL RATES RIGHT AND LEFT, OR EQUAL FREQUENCIES?
I race a front wheel drive
car. In stock form the corner weights are really skewed with both the engine
and driver located in the front left of the car. There are 2 schools of
thought as far as the best way to address when building a race car.
A) Run equal spring rates on each axle pair. Then corner balance the car as best as possible and live with unequal static ride heights.
B) Set the ride heights equal left and right. Then run different spring rates on each corner based on the achieving equal suspension frequencies per axle pair.
Whatís your opinion?
If the suspension is adjustable for ride height, by any means at all, it should be possible to get any desired ride heights regardless of spring rates or static wheel loads. Or, more precisely, it should be possible to get any right/left tilt, and any fore/aft rake, and any average height, with any diagonal percentage.
But in any case, when the car is significantly left-heavy, and it turns both ways, is it better to have similar wheel rates left and right, or similar frequencies right and left?
We might mention first of all that there are sprung mass frequencies and unsprung mass frequencies. If the unsprung masses are similar on both sides of the car, but the sprung masses are different, then there is no way to get both the sprung and unsprung frequencies identical on both sides. But the questioner is referring to the sprung mass frequencies.
In terms of ride dynamics, it is desirable to have the right and left sprung mass natural frequencies similar to each other. In extreme cases, a lightly damped car may ďgimbalĒ, or experience some roll and yaw with pitch, when subjected to sequential bumps at the front and rear, or when subjected to lateral, longitudinal, or yaw jerk (abrupt acceleration change). With the relatively heavy damping
used in race cars, tuning sprung mass frequencies is less important, but itís still desirable to spring for flat ride when possible, and that means having similar frequencies right and left.
There is another reason for going stiffer on the heavy side, and it has nothing to do with getting the frequencies right for flat ride. When the car is left-heavy, it tends to turn right under braking and left under power. That means that when trail braking into a left turn, the car tends to be tight (understeer), and when powering out, it tends to be loose (oversteer). In a right turn, itís the opposite: loose in, tight out, compared to a left turn.
When the car is stiffer on the left, that means the left side sees more load transfer than the right in longitudinal acceleration. Under braking, the car de-wedges (loses inside rear + outside front percentage) for a left turn and gains wedge for a right turn. Under power on exit, the car gains wedge in a left turn and loses wedge in a right turn. There is no guarantee that this effect will accurately compensate for all effects of left-heaviness when the wheel rates give equal sprung mass frequencies right and left, but at least the compensation is in the needed direction.
In the real world, we will usually be constrained by available spring rates, so even achieving truly equal sprung mass frequencies right and left will not be possible Ė we will just try to come fairly close, using springs we can buy. If we want to be really fastidious, we will test individual springs to determine their actual rate, rather than relying on the advertised rate. In any case, I would not be afraid to go a bit stiffer on the heavy side of the car.
TWO-WHEELER THAT DOESNíT LEAN, BUT SHIFTS WEIGHT LATERALLY?
An idea that one of my friends came up with, and has been investigating for a while, is a "bike" with race-car slicks. For his machine he was thinking of utilising a pair of very wide low-profile tyres. They would not camber like regular motorcycle tyres do. They would stay perpendicular to the road, always upright. His idea is that the main body of the "bike" would not lean but would laterally translate relative to the wheels. For example, in a left turn the body of the "bike" (engine and "rider" and all) would be displaced to the left far enough to exactly counter the rightwards overturning tendency. He's "designed" (I should say sketched) his suspension system. It relies on power hydraulics and electronics to operate.
My feeling is there may be a better, more "natural" way to achieve the desired result. Instead of shifting the body laterally in response to the front wheels steering (after they have steered), thus allowing cornering forces to already be generated, it would be better if the body could be moved laterally just before the front wheels steer.
This idea is similar in a sense to what Phillip James' FTC three wheeler is doing. See the site http://www.tiltingvehicle.net/technical.html and also patents WO2005075278 and US2008238005- both cover the same material wherein the steering of the front tyre/s is the result of the vehicle
leaning (shifting mass). Note: the steering does not initiate the lean, it is the leaning which causes the wheels to steer.
This is much like the bicycle servo-steer mechanism outlined in the excellent Pierre Ethier SAE paper and also on website http://www.clevislauzon.qc.ca/Professeurs/Mecanique/ethierp/2-wheels/index.htm ... Again, the mass is moved (leaned or tilted), THEN the steering of the front wheel develops as the result.
I am thinking that something similar could be achieved by sliding the body sideways and having the front wheel steer occurring as the result of that action. I suspect that it may be possible that the correlation between lateral translation of the vehicle body and front wheel steering could be arranged to occur by utilising a mechanical linkage system. If this is possible it would negate the need for much of the electronic sophistication my friend wants to rely on. He'd likely still need the power hydraulics if the vehicle weight was high though.
Any comments or ideas on this?
The second paper cited alludes to nine different theories of how the rider of a two-wheeler initiates a turn. I have not studied this rather complex question to the degree that others have, and I certainly have not taken videos of motorcyclists, and slowed them down and analyzed the motions, but I will attempt some reasonably intelligent commentary nonetheless.
The case of a narrow three-wheeler or four-wheeler that is leaned simply to avoid rollover is different from the case of a two-wheeler. Also, it matters a lot whether the wheels lean, especially with a two-wheeler. And in all of these cases, the needed lean angle or lateral c.g. shift of the vehicle is not a simple function of front wheel steer angle.
In the case of a two-wheeler, the vehicle is unstable in roll. That is, it will not stand up on its own when not in motion. Colin Chapman reputedly said, ďSilly things, motorcycles. If you let go of them, they fall right over.Ē In the case of a narrow three-wheeler or four-wheeler, even with suspension thatís very soft in roll, the vehicle does not fall over unless the line of action of the vector sum of all x, y, and z forces acting on the c.g. intersects the ground plane outside the polygon described by the contact patches. When the vehicle is not single-track, the suspension can roll the vehicle within certain limits, because it has a base of support of some width to push against. When the vehicle is single-track, everything depends on a complex inertial balance. We canít just shift the c.g. laterally, without something else happening.
Letís first consider what keeps a bike upright when itís moving. The bike is always trying to tip one way or the other, because its center of mass is above the line of support described by the two contact patches. But as soon as the bike develops a roll velocity, gyroscopic precession induces a yaw acceleration that tends to bring the contact patches back under the c.g. This doesnít make the vehicle hold itself upright for any distance without rider intervention, but it does make it rideable by most humans. If we push a trike and just let it roll, it will go sort of straight for a while, probably
turn to one side eventually, and stop without falling over. If we push a bike and just let it roll, it will go a short distance, then tip to one side, turn to that side but not enough to catch itself, and fall over. The bike will have an increasing roll velocity, and an increasing yaw velocity, but the yaw wonít keep up with the roll to the point where the vehicle will right itself.
The fact that the bike is unstable in roll makes it easy to initiate roll acceleration. This can be done in more than one way. If the roll acceleration needed is fairly small, just letting the bike tilt the desired way is sufficient. The riderís job is not so much to make the bike lean or turn as to arrest the lean and turn as needed to keep the vehicle upright and on course.
In all cases, however, the dynamics of the vehicle are highly dependent on precession. When the wheels are leaned, they try to yaw in the direction they are leaned. When the wheels are yawed without being leaned, they try to lean opposite to the direction of yaw. This means that if we lean the wheels into the turn, the bike will yaw in the desired direction. But if we try to steer the front wheel and keep the wheels upright, precession will roll the bike out of the turn.
The two main ways that a person initiates a turn on a bike are to roll the bike into the turn with the hips, and to use front wheel precession to roll the bike into the turn by momentarily steering the handlebars out of the turn. The former method is used most of the time. The latter method is used when an abrupt turn is required, usually to dodge an obstacle.
A bike can steer like a two-track vehicle at very low speed. The front wheel is steered a lot, the bike leans very little, and the rider balances the bike as best he can. The maneuver is only slightly less difficult than a track stand (balancing the bike essentially motionless). If we try to steer a bike like that at speed, gyroscopic precession will make the bike lean out of the turn and steer the opposite way than we intended. Indeed, the main element of learning to ride a two-wheeler is to learn not to try to steer it that way.
It may be that some genius can devise a way to make a two-wheeler turn at speed without leaning the wheels into the turn, but I would not bid on a contract to develop the algorithm, and I certainly would not try to do it with any mechanism that mechanically shifts ballast or sprung mass simply in relation to front wheel steer angle.