The Mark Ortiz Automotive
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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: 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.
SPINDLE INCLINATION SPLIT
Can you explain the effects of king pin angle and king pin angle split from one side to the other (how it would jack weight when turning each direction)? I know that different oval track chassis builders
are playing a lot with spindle inclination.
The basics of this are simple. However, it gets a bit more complex when you try to be really exact about it.
First of all, the terminology is a bit confused. I prefer to call the front-view angle of the steering axis with respect to the spindle pin the spindle inclination, and call the angle of the steering axis with respect to ground vertical the front-view steering axis inclination, or SAI. The term kingpin inclination can mean either of those, which means that it has to be interpreted in context and can sometimes be ambiguous.
When we buy a spindle for an oval track car, we are usually buying a single piece comprising the stub axle or spindle pin (which by itself is sometimes called a spindle, especially if itís a separate piece) and the upright. The inclination then is the front view angularity of the steering axis relative to the pin axis, or more precisely to a perpendicular to the pin axis.
When caster and camber are zero, the SAI equals the spindle inclination. When we add some caster, it still almost does. When the upright leans back, it is slightly foreshortened in front view, so the actual inclination in a front view projection increases very slightly. However, this effect is very small and we usually ignore it.
When we adjust in some camber, the steering axis tilts with the wheel. Camber is conventionally negative when the tilt is inward at the top; SAI is conventionally positive top-in. Therefore SAI is approximately equal to spindle inclination minus camber.
For oval track we generally tilt both front wheels to the left: negative camber on the right wheel, positive on the left. Depending on the class of car and the track, camber can be three degrees or more. If the right and left spindles are the same, that means the SAI can easily be different on the right and left by six degrees or more. So the most common reason for running unequal spindle inclinations is simply to get the left and right SAIís more nearly equal. Common spindle inclination angles are 5, 8, and 11 degrees. With 3 degrees of tilt on both wheels, and a 5 degree spindle on the right and an 11 degree on the left, you get about 8 degrees SAI on both sides.
But suppose we want to be a bit more creative and ambitious, and consciously use SAI split to produce specific weight jacking effects. How would we understand how it all works and what to expect?
Assuming the wheel has a positive scrub radius or front-view steering offset (contact patch center outboard of the point where the steering axis intercepts the ground plane), with zero caster but some SAI the geometry jacks the car up when we steer either direction from center. When thereís some caster, things get a bit more complex, but basically adding SAI makes the corner of the car at issue jack up when we steer either way. Caster, in contrast, makes the corner jack down when the wheel toes in and up when the wheel toes out.
Other things being equal, making one corner of the car jack up loads that wheel and the diagonally opposite one, and unloads the other two. If we jack more than one corner up or down at once, the effect depends on the relationship between them. If we jack both front corners up or down equally, it does essentially nothing to the wheel loads.
If we add caster to the right front, the car de-wedges more (loses percentage on the outside front and inside rear) when the wheels steer left and wedges more (gains percentage on the outside front and inside rear) when the wheels steer right. If we add SAI to the right front instead, the effect is similar when the wheels steer right but opposite when the wheels steer left. The car wedges more when we steer either way.
If we add caster to the left front, the effect is similar to adding it to the right front: the car de-wedges more when we steer into the turn and wedges more when we counter steer. If we add left front SAI instead, the car de-wedges more when we steer either way.
There are also effects on camber. When we add caster, the wheel leans more in the direction we steer it. When we add SAI, the wheel goes toward positive camber more when we steer either way.
There are effects on steering feel. When we add caster on both sides, we increase the steeringís tendency to seek inertial center. When we add caster on just one side, we create a pull in the steering toward the opposite side. Adding SAI on just one side does not do that. Adding SAI on either or both sides just makes the steering seek car centerline center more.
The weight jacking effects from caster and SAI increase as we add scrub radius.
CANCELLING DRIVESHAFT TORQUE WITH TIGHT PACKAGING CONSTRAINTS
Just read your latest article in Racecar Engineering on live rear axles which I note I have found in one of your newsletters. I run an MG V8, 477 rwhp, in circuit racing and we are currently upgrading roll cage and chassis stiffness, and putting in a 9Ē live axle with a Trutrac LSD. Space and packaging in an MG is fairly tight to say the least, so your comments on having a four link with birdcage one side are intriguing from the point of eliminating all of the negative forces, but I donít have the room. Over the last couple of evenings I have been digging into all the books and info I have on the three link I was planning and I find reference to torque steer and wedge etc. in roll. The offset design of the C Type Jaguar, though, seems to even this out and some are reporting it eliminates these forces in acceleration. I found two references to the system having problems with braking, so it seem there is an issue with inducing forces in that direction. My question is: if I ran a three link, top link offset to the right from the rear of the car (I presume when you talk of right and left it is looking from rear of car) with the brake caliper on the left attached on a floating birdcage which has a link to the chassis, would I be achieving the same result as your four link? Or do I have to have a decoupling top link to allow the freedom for the floating brake side to work?
My issues with packaging are that the MG has very narrow chassis, rails converging from bottom side rails in front of wheels to inside of wheels. Distance between rails at wheel centreline is 800 mm. Attached is a photo & a picture I have drawn what could work if a birdcage with such a long tube in it would be acceptable(at 380 mm long I would have to use thin wall chrome moly tube to keep weight down). The lower links are 1000 mm apart and the top links would be 630 mm apart. Rear track is 1480 mm with 335 x 660 x 18 tyres and 3.7 gears. Also I have already put some steel in the chassis to stiffen, but I can cut that out and revise.
The questioner sent a nice .pdf of a cad model, which I will attach when sending this newsletter. The axle is shown, with a Panhard bar and provision for four trailing links. The links themselves are not shown but the brackets for them on the axle are shown, and so is one of the unibody rails. The top two links are indeed much closer together than the lowers, and they have to be to clear the rails. A long birdcage on the left is shown, per my recommendation in other articles. This allows the system to compensate for driveshaft torque without creating roll and wedge in braking, by functioning as a three-link under power and a four-link under braking.
The weight of the birdcage shown is probably not a major concern. Compared to a layout with a shorter piece of tubing, the weight penalty is perhaps three pounds. A nine-inch rear axle with wheels and brakes weighs at least 250 pounds, so the difference is not highly significant. The real problem is the amount of anti-squat the system would have to have in order to get full driveshaft torque cancellation and also minimal roll steer.
For minimal roll steer with the axle configuration shown, the side view instant centers need to be around axle height. The tire loaded radius is just over a foot. The lower link pivots are about half a foot above the ground, or half a tire radius below the axle centerline. The uppers are about half a foot, or half a tire radius above the axle centerline. So for every 100 pounds of thrust at the tires,
thereís about 150 pounds of compression on the lower links and about 50 pounds of tension on the right upper link, which is a little more than a foot off center. Axle torque is just a little more than 100 lb ft, so driveshaft torque is about 28 lb ft. To counter that, the upper link needs to make around 25 pounds of lift with a tension of 50 pounds. It therefore needs a slope of about 1 in 2. In side view, the upper linkís centerline reaches axle height about two feet ahead of the axle. If the instant center is at axle height, and the side view swing arm length is only two feet, the car has something like 300% anti-squat. Thatís likely to create wheel hop problems.
If the left upper link is on a brake floater (birdcage with only one link, as described by the questioner) instead, and the left lower link is welded to the axle tube, then the lower links need to be close to horizontal, and the side view instant center ends up being only about half as high, and twice as far forward of the axle. Thatís much better. The anti-squat is now only about 75%. The upper link is still at the same angle and under the same tension, but the heavily loaded lower links arenít making lift force.
The problem would be how to have a brake floater that reaches in to the upper link bracket, while still allowing the lower link bracket to be rigidly attached to the axle tube. Thatís not necessarily an insurmountable challenge, but it would call for a two-piece floater of some kind, to permit installation and removal.
A brake floater usually has a trailing link above the axle, but it might be possible to have the link be the lower one instead Ė that is, have two upper links rigidly attached to the axle housing and only one rigidly attached lower. That single lower link would see some big loads under power, but it could be made strong enough, and it wouldnít need a lot of inclination, while the upper links would need to be roughly horizontal for minimal roll steer. This upside down three-link isnít as good structurally, but it would fit, and the floater could be one piece.
Rules permitting, one other approach is to have a compliant pull bar for the right upper link, as used in some dirt oval track cars. Such a member can only react tension forces, and goes slack in compression. Braking is then reacted by a separate member. In oval track cars with a pull bar, the usual thing is to have a shock with a rubber snubber for that. The shock also damps the compliance of the pull bar. In oval track cars, the pull bar is not usually offset to the right, but for road racing that would be the way to do it. The shock would be centered, mounted to the top of the center section of the axle. The left upper link would be omitted, and no birdcage or brake floater would be needed.
This design has one other advantage: it can be used on a steered axle. A variation of it could be used on the front of a four wheel drive off-road vehicle, where the links would probably need to be leading links rather than trailing. The shock would be offset to the left, sloping down toward the rear, or to the right, sloping up toward the rear. The pull bar would be centered. The shock would be in compression under power, and the pull bar would be in tension under braking.