The Mark Ortiz Automotive
Presented free of charge as a service
to the Motorsports Community
Reproduction for sale subject to restrictions. Please inquire for details.
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: firstname.lastname@example.org. Readers are invited to subscribe to this newsletter by e-mail. Just e-mail me and request to be added to the list.
WHY NOT GO FOR 100% CAMBER RECOVERY?
I enjoyed this newsletter on a car dear to my heart [referring to the issue about Corvair rear suspension, April 2008]. I had a question though. I am about to begin installation of a C5 Corvette rear end into my V8 car, using an adapter I designed to couple to a big car Saginaw 4 speed. I will need to center the engine in the car, and then design/build all new rear suspension. The question is how much camber gain to design in. You mentioned 50% as a typical gain. Why would you not design for more, even 100%?
I am planning to use two trailing links, and SLA with the lower arm horizontal, and the upper arm angling down to the transaxle. The Corvette uses a beefy CV joint axle, which I will adapt to the corvair drive spindle.
Interestingly, if you remove the tailhousing from the Saginaw, the output shaft slides into and engages the pinion gear in the Corvette axle, with about 1" gap for the adapter plate. The splines match. Thank you GM! The ring gear is about 8.75" in diameter, and comes in ratios of 2.73, 3.15. 3,45. 3,73 and more. To line up the rear wheels with the axle will require the wheels to be moved back about 1.5", slightly less if the drive axles can angle forward a little.
Camber gain usually refers to the change of camber in degrees, per inch of wheel travel. Its units then are degrees per inch. It is commonly measured with the car stationary in the shop, the springs removed and the anti-roll bars disconnected. When you see a single number for this, it’s most commonly the camber change in the first inch of compression from static. It increases as the suspension compresses and decreases as the suspension extends, if the upper arm is shorter than the lower. Conventionally, change toward negative in compression and toward positive in extension is taken as positive camber gain.
Camber recovery is the percentage of the roll angle that is recovered at the wheel when the car rolls. If the wheel leans the same amount as the body, that’s zero camber recovery. If the wheel leans half as much as the body, that’s 50% camber recovery. If it doesn’t lean at all, that’s 100% recovery.
For a car with a 57.3” track width (57.3 being approximately 180/π, the number of degrees in a radian), 1 deg/in of camber gain gives 50% camber recovery. To get 100% camber recovery, we have to have 2 deg/in of camber gain. The problem with that much camber gain is that the camber changes too much in situations other than roll: in longitudinal acceleration, over humps and dips, over bumps, and with fuel burn-off and other load variations.
With a passive independent suspension, it is impossible to have zero camber change in both ride and roll. The best we can do is to strike a compromise between the two, so that we don’t have any big camber changes in any situation. With a 57.3” track, one degree of roll is one inch of displacement difference at the wheels, or ˝” per wheel. Two degrees of roll is twice that: 2” per wheel pair or 1” per wheel. So if the camber gain is 1 deg/in and camber recovery is 50%, we have one degree of camber change per inch of wheel movement in both ride and roll. The only way to get more camber recovery without more camber change in ride is to increase the track. This also reduces lateral load transfer and thereby increases cornering power, but unfortunately it makes the car bulkier.
The formula for instantaneous rate of camber gain is:
dφ/dz = tan-1(1/Lvsa)
φ = camber angle, degrees
z = suspension displacement at the contact patch center, inches
dφ/dz = first derivative of camber with respect to suspension displacement (instantaneous camber gain), deg/in
Lvsa = length of virtual swing arm
This formula also works with units of length other than inches, provided you use the same units for z and Lvsa. Note, however, that 1deg/mm of camber gain is nowhere near the same as 1deg/in.
A simplified version is:
dφ/dz = 57.3/Lvsa
One question that sometimes arises is whether to measure Lvsa horizontally, or along the force line. Unless the instant center is at ground level, the true or vector length will be greater than the horizontal distance to the instant center. The radius on which the contact patch moves is actually the true or vector length, right?
Well, yes. But also, if the instant center is anywhere other than ground level, an inch of contact patch movement about the instant center is not a vertical inch; it's some lesser amount. And it turns out that the ratio of vector to vertical motion at the contact patch is the same as the ratio of horizontal to vector swing arm length. This ratio is also the cosine of the force line's angle of elevation.
So if you use vector distance for the swing arm length, and apply the formulas, you get the rate of camber change per vector inch of wheel movement, and if you use the horizontal distance, you get the rate of camber change per vertical inch. Convert a vertical inch to vector inches, and use the
vector swing arm length to find the camber change rate per that unit of distance, and you get the same number as if you hadn't converted, and used the horizontal distance.
Formula for instantaneous rate of camber recovery is:
Rφ = (1 – dφ/dθ) * 100% = (t/(2Lvsa)) * 100%
Rφ = camber recovery, in percent
φ = camber angle, degrees (measured with respect to the road, not the car)
θ = roll angle of sprung mass, degrees
dφ/dθ = first derivative of camber with respect to roll, i.e. the instantaneous rate at which the tire leans per degree of body roll
t = track width
Lvsa = virtual swing arm length, taken horizontally
GYROS FOR ROLL STABILITY
Has anyone ever used a vertical axis flywheel to damp pitch and roll through gyroscopic effects?
Ignoring practical considerations and assuming a low drag (vacuum), high RPM, low weight, probably counterrotating disc layout, how beneficial would this be to the ride quality of an off road (desert racing) vehicle?
Would it be worth adding a system to slow either disc independently, via brakes and one way clutches, in order to gain active yaw control? Could such a system ever completely replace the normal steering system (ignoring reliability concerns)?
In your opinion, how would the gyro damping compare to interconnected suspension systems?
Has anyone tried fully active suspension systems in a desert racing environment (thinking of the bose demonstration videos here)?
I will confess to some lack of expertise in desert racing, as I have had absolutely no clients or even acquaintances doing it, but to my knowledge nobody has used fully active suspension off-road. I would think it would eat a huge amount of power. Active roll control, and maybe also pitch control, employed to allow soft passive suspension to absorb bumps, might be more efficient. Power consumption was a big part of what killed Lotus's fully active system in the '70's. It ate about as much power as it took to drive the car in cruise mode on the highway, so it had nasty effects on fuel consumption. Fuel thirst might be more tolerable in a racing environment, but in off-road applications the energy consumption would be higher than in road use, due to the much greater movement of the suspension.
For road racing, active suspension looks more appealing, but it's illegal in all existing classes, for reasons of cost containment and car parity. Probably if it started to become a threat in off-road racing, the same thing would happen there, for the same reasons.
The gyro idea is interesting. I had to scratch my head awhile, and even play with a bicycle wheel, but I concluded that if you had two flywheels lying one on top of the other, spinning at equal and opposite velocities, you really would still have stabilization, and the precession effects in both perpendicular axes would cancel out.
I decided you could call this a gyro sandwich. (Sorry. I couldn't resist.)
This would make the sprung mass resist roll and pitch accelerations, and it might therefore allow use of softer suspension. If the suspension could be softened, it might be possible to have some benefits similar to interconnected suspension. The idea could also be used with interconnected suspension.
Have you ever seen a Segway? It has two wheels, one on each side. It uses an electric gyro to keep it from falling over in pitch. There was also a vehicle called the GyroCar about forty or fifty years ago that used a vertical flywheel. It was basically a full-bodied motorcycle, with a door to get in and out, and no holes to put your feet down. It had two small, retractable wheels like training wheels on a bicycle, which deployed for parking. With the flywheel running, it would hold itself upright while sitting still, without the parking wheels.
As for speeding up and slowing down the flywheels differently to create yaw moments and steer the vehicle, yes you could create yaw moments that way, but as soon as you did that the flywheel speeds would no longer be equal, and you'd start getting unintended precession effects. I think you'd probably want conventional steering.