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The idea of smaller, energy-efficient
vehicles for personal transportation seems to naturally introduce the three wheel
platform. Opinions normally run either strongly against or strongly in favor of the
three wheel layout. Advocates point to a mechanically simplified chassis, lower
manufacturing costs, and superior handling characteristics. Opponents decry the
three-wheeler's propensity to overturn. Both opinions have merit.
Three-wheelers are lighter and less costly to manufacture. But when poorly designed
or in the wrong application, a three wheel platform is the less forgiving layout.
When correctly designed, however, a three wheel car can light new fires of enthusiasm
under tired and routine driving experiences. And today's tilting three-wheelers,
vehicles that lean into turns like motorcycles, point the way to a new category of
personal transportation products of much lower mass, far greater fuel economy, and
superior cornering power.
Inherently Responsive Design
Designing to the three-wheeler's inherent characteristics can produce a
high-performance machine that will out corner many four-wheelers. A well designed
three-wheeler is likely to be one of the most responsive machines one will ever experience
over a winding road. Superior responsiveness is primarily due to the three-wheeler's rapid
yaw response time.
Yaw response time is the time it takes for a vehicle to reach steady-state cornering
after a quick steering input. A softly sprung four-wheeler will have a yaw response time
of about 0.30 seconds, and a four wheel sports car will respond in about half that time. A
well designed three-wheeler can reach steady-state cornering in as little as 0.10 seconds,
or about 33 percent quicker than a high-performance four wheel car.
Quick steering response has nothing to do with the number of wheels or how they are
configured. It is a byproduct of reduced mass and low polar moment of inertia. A typical
three-wheeler is lighter and has approximately 30 percent less polar moment than a
comparable four wheel design.
Rollover Stability of Conventional Non-Tilting Three-Wheeler
A conventional, non-tilting three wheel car can equal the rollover resistance of a four
wheel car, provided the location of the center-of-gravity (cg) is low and near the
side-by-side wheels. Like a four wheel vehicle, a three-wheeler's margin of safety against
rollover is determined by its L/H ratio, or the half-tread (L) in relation to the cg
height (H). Unlike a four-wheeler, however, a three-wheeler's half-tread is determined by
the relationship between the actual tread (distance between the side-by-side wheels) and
the longitudinal location of the cg, which translates into an "effective"
half-tread. The effective half-tread can be increased by placing the side-by-side wheels
farther apart, by locating the cg closer to the side-by-side wheels, and to a lesser
degree by increasing the wheelbase. Rollover resistance increases when the effective
half-tread is increased and when the cg lowered, both of which increase the L/H ratio.
A simple way to model a three-wheeler's margin of safety against rollover is to
construct a base cone using the cg height, its location along the wheelbase, and the
effective half-tread of the vehicle. Maximum lateral g-loads are determined by the tire's
friction coefficient. Projecting the maximum turn-force resultant toward the ground forms
the base of the cone. A one-g load acting across the vehicle's cg, for example, would
result in a 45 degree projection toward the ground plane. If the base of the cone falls
outside the effective half-tread, the vehicle will overturn before it skids. If it falls
inside the effective half-tread, the vehicle will skid before it overturns. To see a
drawing showing a base-cone illustration of single front wheel (1F2R) and single rear
wheel (2F1R) vehicles, click on: Single Front & Single
Rear Wheel Comparison (23k).
The single front wheel layout naturally oversteers and the single rear wheel layout
naturally understeers. Because some degree of understeer is preferred in consumer
vehicles, the single rear wheel layout has the advantage in this department. Another
consideration is the effect of braking and accelerating turns. A braking turn tends to
destabilize a single front wheel vehicle, whereas an accelerating turn tends to
destabilize a single rear wheel vehicle. Because braking forces can reach greater
magnitudes than acceleration forces (maximum braking force is determined by the adhesion
limit of all three wheels, rather than two or one wheel in the case of acceleration), the
single rear wheel design has the advantage on this count as well. Consequently, the single
rear wheel layout is usually considered the superior platform for a high-performance
consumer automobile. But much depends on the details of the design.
Tilting Three-Wheelers (TTWs)
Tilting three-wheelers, vehicles that lean into turns like motorcycles, offer increased
resistance to rollover and much greater cornering power - often exceeding that of a four
wheel vehicle. And designers are no longer limited to a wide, low layout in
order to obtain high rollover stability. Allowing the vehicle to lean into
turns provides a much greater latitude in the selection of a cg location and the
separation between opposing wheels.
 Consider that a motorcycle has no side-by-side wheels, yet it does not
overturn when going around corners. A motorcycle negotiates turns by assuming a lean
angle that balances the vector of forces resulting from the turn rate. The rider
leans the motorcycle into the turn so it remains in balance with the forces that are
acting on it. As long as the motorcycle's lean angle matches the vector of forces in
a turn (resultant), it will not overturn. In order to stay in balance with turn
forces under all possible conditions, however, a motorcycle must be able to lean at an
angle of 50-55 degrees before any part of the machine contacts the ground.
Three and four wheel vehicles can also be made to lean into turns.
But with tilting vehicles equipped with side-by-side wheels, other physical and geometric
realities come into play. For example, a vehicle having a wide body may contact the
ground even at moderate lean angles, which will make it impossible to stay in balance with
turn forces at the upper extremes. In addition, the greater the separation between
the side-by-side wheels, the greater the wheel movement at equivalent lean angles.
The movement of the side-by-side wheels can become excessive even at relatively small
angles of lean in vehicles having a track approaching that of conventional automobiles.
And the mechanical challenges of accommodating steering, bounce, and tilting, along
with the angular limitations of CV joints on powered axles, places additional limitations
on the lean angle of tilting multi-track vehicles. As a result, much of the
recent work on tilting suspension systems has concentrated the three wheel platform.
The Project 32 Slalom (1F2R) and the Mercedes F300 Life-Jet (2F1R) are excellent examples of
modern tilting three wheel designs.
Free-Leaning versus Active Lean Control
Tilting three-wheelers can be free-leaning and controlled by the rider,
just like ordinary motorcycles. However, if the mechanical limit of lean is less
than is necessary to balance turn forces under all possible conditions, then some form of
active (forced) lean control must be used to account for turns that exceed the lean limit.
This is usually accomplished by hydraulic or electro-mechanical actuators operating
on signals from an electronic control unit (ECU). Normally, the ECU processes
signals from sensors that monitor lateral acceleration, vehicle yaw and lean angle,
steering angle, and other relevant factors, then provides control output to the lean
actuators. Another advantage of active lean control is that the operator is no
longer required to balance the vehicle, as when operating a motorcycle. With active
lean control, the vehicle is driven just like an ordinary automobile, and the lean control
system takes care of the rest.
Rollover Threshold of TTWs
The rollover threshold of a TTW is determined by the same dynamic forces
and geometric relationships that determine the rollover threshold of conventional
vehicles, except that the effects of leaning become a part of the equation. As long
as the lean angle matches the vector of forces in a turn, then, just like a
motorcycle, the vehicle has no meaningful rollover threshold. In other words, there
will be no outboard projection of the resultant in turns, as is the case with non-tilting
vehicles. In a steadily increasing turn, the vehicle will lean at greater and
greater angles, as needed to remain in balance with turn forces. Consequently, the
width of the track is largely irrelevant to rollover stability under free-leaning
conditions. With vehicles having a lean limit, however, the resultant will begin to
migrate outboard when the turn rate increases above the rate that can be balanced by the
maximum lean angle. Above lean limit, loads are transferred to the outboard wheel,
as in a conventional vehicle.
 Tony Foale, author of Motorcycle Chassis Design,
explains the behavior of an all-leaning-wheels TTW in terms of a virtual motorcycle wheel
located between the two opposing real wheels. In a balanced turn, the resultant
remains in line with the virtual motorcycle wheel. But in turns taken above the
limit of lean, the resultant projects to the outside of the virtual wheel (vehicle
centerline), according to the magnitude of turn forces in excess of those at lean
limit. It's also important to note that the vehicle cg moves inboard as the vehicle
leans into a turn.
When calculating the rollover threshold of a TTW having a lean limit, one
must consider the inboard migration of the cg due to the angle of lean, the outboard
projection of forces at the friction limit of the tires, and the traditional relationships
between the cg height, the effective half-tread (at lean limit), and the wheelbase.
TTWs With Only One Leaning Wheel
 Another
interesting category of TTWs includes vehicles having only a single leaning wheel, such as
the Lean Machine developed at General Motors in the late '70s and early '80s. GM's
Lean Machine is a 1F2R design wherein the single front wheel and passenger compartment
lean into turns, while the rear section, which carries the two side-by-side wheels and the
power train, does not lean. The two sections are connected by a mechanical
pivot.
The rollover threshold of this type of vehicle depends on the rollover
threshold of each of the two sections taken independently. The non-leaning
section behaves according to the traditional base cone analysis. Its
length-to-height ratio determines its rollover threshold. Assuming there is no lean
limit on the leaning section, it would behave as a motorcycle and lean to the angle
necessary for balanced turns. The height of the center of gravity of the leaning
section is unimportant, as long as there is no effective lean limit.
The rollover threshold of a vehicle without an effective lean limit will
be largely determined by the rollover threshold of the non-leaning section. But the
leaning section can have a positive or negative effect, depending on the elevation of the
pivot axis at the point of intersection with the centerline of the side-by-side wheels.
If the pivot axis (the roll axis of the leaning section) projects to the axle
centerline at a point higher than the center of the wheels, then it will reduce the
rollover threshold established by the non-leaning section. If it projects to a
point that is lower than the center of the side-by-side wheels, then the rollover
threshold will actually increase as the turn rate increases. In other words, the
vehicle will become more resistant to overturn in sharper turns. If the pivot axis
projects to the centerline of the axle, then the leaning section has no effect on the
rollover threshold established by the non-leaning section.
In vehicles of this type that have a limit on the degree of lean, rollover
threshold would be calculated as with an all-tilting-wheels vehicle operating at or above
its limit of lean. In this case, the cg height of the leaning section would have an
important effect on the behavior of the vehicle as a whole. Once a tilting vehicle
reaches its limit of lean and locks against its limit stops, it can be analyzed as a
non-tilting vehicle having the geometric configuration of the tilting vehicle at lean
limit.
The front-to-rear incline of the roll axis of the leaning section is an
important consideration with this type of vehicle. With free-leaning designs, the
roll axis should project to the ground at the front (leaning) wheel. This is done to avoid
a roll/lean couple, which could result in roll inputs during acceleration and braking.
This is not as important in vehicles equipped with active lean control.
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