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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.
CAMBER GAIN AND RECOVERY, AND DESIGN OF TRICYCLES
How critical is camber gain in suspension? I am considering converting a BMW motorcycle to a trike using the two front forks set wide apart, one on each side. The standard sliding system would be used for suspension and the wheels would turn with the sliding pillar for steering. I could use a lower link to provide caster gain with the tube pivoting at the top. However, it would be far easier to fix the fork tube solid to the chassis and set the KPI and caster by location of the fork tube. Has this system ever been used, to your knowledge? There is/was an English Morgan sports car that used sliding pillar suspension but I have not seen a schematic of it. I have not determined just what this would do to lead, though I can set caster, camber, scrub anywhere necessary.
I will offer some comments later about the general vehicle concept the questioner has in mind, but first I will address his actual question regarding importance of camber gain.
For those new to the term, camber gain is the rate of camber change with respect to suspension displacement, as measured with the sprung structure (frame) held stationary. Typically, the measurement is done in the shop, with the wheel replaced by a bump steer plate with inch or millimeter graduations on it, and a caster/camber gauge or an angle finder. To really be precise, however, displacement should be measured at the contact patch, or where the contact patch would be if the wheel were in place.
In English units, camber gain is expressed in degrees per inch. It is positive when camber goes toward negative (top of tire inboard) as the suspension compresses and toward positive as the suspension extends.
In most suspensions, camber gain is not a constant. It has an instantaneous value at any given point in the range of suspension displacement, and this changes as the suspension moves. For short and long arm (SLA) suspensions, where the upper arm is the shorter one, camber gain increases (goes toward positive) as the suspension compresses and decreases (goes toward negative) as the suspension extends. If the arms are similar length, camber gain stays nearly constant as the
suspension moves. With MacPherson strut suspension, camber gain changes the opposite way: decreases as the suspension compresses and increases as the suspension extends. With sliding pillar or pure trailing arm suspension, camber gain is zero throughout the suspension travel.
It isn’t customary, but we could speak of camber gain gain, or perhaps camber acceleration: the rate of change of camber gain with respect to displacement – in other words, the second derivative of camber with respect to displacement, or the first derivative of camber gain with respect to displacement. This would be expressed in degrees per inch squared. It would be positive in most SLA suspension, zero for sliding pillar, and negative for MacPherson strut. For swing axle suspension, it would be slightly negative but close to zero, provided that we measure displacement at the contact patch as suggested above. Camber acceleration would also not be a constant for most systems, but would have an identifiable instantaneous value at any point in the travel.
Camber recovery in roll is related to camber gain. It is the reason we generally want some camber gain. With independent suspension, if camber gain is zero the wheels lean with the frame in cornering. This is undesirable; we would like the wheels to stay upright.
Camber recovery is expressed in percent. If the wheels lean 75% as much as the body, we have 25% camber recovery. If the wheels don’t lean at all, we have 100% camber recovery. If the wheels lean the same as the body, we have zero camber recovery. If the wheels lean into the turn, we have more than 100% camber recovery. If the wheels lean more than the body, we have negative camber recovery.
There are certain rules that govern the relationships among camber gain, camber recovery, front view swing arm length, and track width. (Note that these simple rules do not account for compliance effects or jacking.)
Camber gain in degrees per inch equals 180/π (approximately 57.3) divided by front view swing arm length in inches. This also works with any other units of length, provided we use matching ones for suspension displacement and front view swing arm length. An FVSA of 57.3” gives one degree per inch of camber gain.
Camber recovery in percent equals camber gain times track width divided by 360/π (approximately 114.6, or twice 57.3), this quantity multiplied by 100%. Camber gain of one degree per inch gives 50% camber recovery with a track width of 57.3”. Camber gain of 2 degrees per inch gives 100% camber recovery with that track. Any given amount of camber gain gives more camber recovery as we widen the track.
For a single wheel, track width is zero or undefined, and there is no way to get camber recovery in roll. This is the situation at the rear of a tadpole trike (one with two front wheels) or the front of a delta trike (one front wheel).
So, returning to the questioner’s proposed vehicle, if there’s no camber gain and hence no camber recovery at the front, it’s no worse than the rear.
In fact, the first Morgans to use sliding pillar suspension were trikes. For about the first decade of the company’s existence, trikes were all they made. When they decided to build cars, they adapted the front suspension concept from the trikes. An image search for “Morgan front suspension” will turn up lots of pictures, including exploded views.
However, I strongly advise against all attempts to convert a motorcycle into an upright-cornering trike, regardless of the suspension and steering geometry. All such vehicles are death traps. They cannot be made stable enough for the speeds they’re capable of. They will all flip at half a g lateral acceleration or less. The c.g. is too high and too close to a line connecting either front contact patch center and the rear one, or either rear contact patch center and the front one. Both tadpole and delta variations have this problem.
The only way to make an upright-cornering trike that’s reasonably safe is to spread out the wheels both laterally and longitudinally, get the c.g. very low, and put the c.g. well toward the two-wheeled end. The Morgan trike design illustrates this approach. The track is wider than most English cars of the time. Everything in the vehicle is as low as possible. They came with a variety of engines, but the best known versions had a big Matchless V-twin about at the front axle line or a little ahead. Road & Track tested one years ago. I was interested to see what they’d get when they measured the weight distribution. As I recall, it was around 60% front. I don’t recall any skid pad results being mentioned. I think this was before they adopted that as part of their road test procedure. The tires are narrow and run at high pressures. I doubt that they’ll generate a µy above .75. Yet on dry asphalt that vehicle will bicycle before it will slide, based on videos of these trikes competing in hill climbs.
So anything with the proportions of a motorcycle trike conversion is really tippy. That doesn’t keep them from being fairly popular, unfortunately. I see such conversions on the road all the time, both with two rear wheels and two fronts. Some of them are based on really powerful motorcycles that will do well over 100mph. I’ve also seen some lately based on scooters. Evidently, there are a lot of people who know nothing of physics and who suppose that if other people do something it must be safe.
Some ostensibly forward-looking manufacturers in recent years have been equally oblivious to the requirements for stability in a 3-wheeler. Designers of the Corbin Sparrow (now being marketed under the NMG moniker) and the Aptera both got it wrong. They failed to put the weight at the wide end. Yes, they incorporated rollover protection systems. But that’s no substitute for building a vehicle that slides before it flips.
Somebody did get it right, though, about three decades ago. The vehicle was called the Trihawk. It used a boxer 4 engine from a front-drive Panhard, hung out ahead of the front axle and driving the front wheels through the original car transaxle. Car and Driver tested one of those. They got
around .85g on the skid pad on something like 185/60-14 street tires, with no wheel lift. An image search will turn up pictures of this car too.
I have been talking so far about trikes that corner upright. There is an alternative way of building a 3-wheeler, especially if the operator sits astride it, as in a motorcycle conversion. You can make it lean like a 2-wheeler. You either let it lean completely freely, or spring it very softly in roll. Optionally, you incorporate a roll brake or roll lock to hold the vehicle upright on slippery surfaces and when parked.
There will of course be some limit to how far the vehicle can tilt, but that can be upwards of 45 degrees to either side. We then have a vehicle that can corner about like a motorcycle, but if it loses traction when cornering hard it is caught by the inside wheel rather than falling on the ground. This would offer advantages over both 2-wheelers and upright-cornering trikes. It could also be fairly narrow, preserving some of the cornering line advantages of a single-track vehicle.
If I were to try something like that using motorcycle front forks and head tubes, I’d connect these with a pair of beams pivoted in the middle at the original motorcycle head tube. I’d keep the original 2-wheeler’s steering geometry at each of the two front wheels.
Leaner trikes (and also leaner 4-wheelers) are an old idea, with potential still unrealized. I am attaching a picture I recently got from Chris Beebe in Madison, Wisconsin. It shows dirt oval sidecar racing using leaner sidecar rigs. I don’t know much about the history of these, and Chris doesn’t either. Any readers with knowledge of this bizarre niche of motorsports history are invited to share what they know.
The sidecar monkeys (passengers) are not climbing all over the rig to keep it right side up. They have a steering wheel that they are working. It doesn’t appear to steer any wheels, though. It appears to work a rack and pinion mechanism that controls the tilt of the rig. The driver also appears to be controlling tilt with his right foot.
Again, anybody who knows anything about these rigs or the history of this class is invited to educate me.