Dynamic Stability of
Robert Q. Riley
with tilting three-wheeler contributions by Tony Foale
Revised September 2014
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.
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.
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 with the lay driver. 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. Consequently, the single rear wheel layout is usually considered the preferred platform for a high-performance consumer vehicle in the hands of the non-professional driver. But racecar drivers often prefer slight oversteer to understeer. Oversteer gives the skilled driver the ability to perform extreme maneuvers that an understeering vehicle would simply mush through and refuse to perform. Moreover, by varying tire size and pressure, a single front wheel vehicle can be designed for neutral steer with oversteer present only at the limit of adhesion. Much depends on the details of the design, as well as driver preferences and skills.
The following will give the reader a better understanding of the center of gravity factors that determine the rollover stability of a three wheel platform. Obviously, this writer considers rollover stability perhaps the most important factor in the design of the three-wheel vehicle, but there are many other considerations as well. And within limits, a vehicle that lacks high rollover stability can be a safe one. A panel truck, for example, has a rollover threshold of only about 0.65-g lateral force. But one does not see the roadsides littered with overturned panel trucks. In general, drivers sense the limits of their vehicles and drive accordingly.
Trihawk is a good example of a well-designed three-wheeler, in terms of dynamic stabiltiy. It's a 2F1R design with power delivered to the two front side-by-side wheels. This means that more power can be delivered to the ground via the two powered front wheels. One typical problem with this layout, however, is that humans are built with legs that extend forward in a seated position. The feet therefore establish the forward limits of the occupants (the feet cannot extend through the drive axles), which forces the center of mass rearward toward the single rear wheel. This is exactly the opposite of the designer's need to locate the vehicle's center of gravity near the side-by-side wheels and away from the single-wheel end of the vehicle. Two occupants result in roughly 300 or more pounds located quite far from the front axle. Trihawk engineers solved much of this problem by locating the Citroen engine ahead of the front axle where it tends to offset the mass of the occupants. Additionally, Trihawk has a very low seating position and a wide track. As a result, the vehicle is among the best-handling three-wheelers around.
A number of 2F1R vehicles have used a motorcyle-plug-in as the basis of the design. T-Rex is a modern production vehicle built on this layout. Like our Tri-Magnum and Ron Will's Phantom, T-Rex uses an entire motorcycle, sans the front fork and wheel, to power the vehicle. The beauty of this approach is that it takes advantage of a well proven production motorcycle power train, already packaged in a frame. The down side is that large motorcycles are heavy and costly. But fortunately, much of a motorcycle's mass is well forward in the frame. And by locating the motorcycle as far forward as possible, and placing the occupants well forward and between the side-by-side wheels, it's possible to produce a vehicle that has excellent rollover stability. A wide and low design completes the formula. Our XR3, although not based on a motorcycle, has a front track that is wider than that of a Mustang, and it is a very low vehicle too.
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.
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.
TTWs With Only One Leaning Wheel
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