All things being equal (object LxWxD, centre of gravity, etc), which object would be more stable? One with a four wheels (roughly a wheel in each corner), or one with three wheels (two at the back and one at the front, in the middle)?
To my amazement, everyone I have spoken to about this (only a dozen or so people) have said that three wheels would be more stable.
Surely, four wheels are?
There are pros and cons.
Three wheeled vehicles are more stable in the sense that they can manage an uneven road without rocking as much.
They are less stable in the sense that cornering can sometimes be rough.
Reliant Robins have a reputation for tipping over under extreme circumstances. I have no idea how much of a concern this is – or even if it’s merely an urban legend.
A three wheeled vehicle will always have all three on the ground, but that’s not very relevant.
What is relevant for a trike is whether the single wheel is at the front or back. A “tadpole trike” (two wheels at the front) is OK.
A trike with two wheels at the rear is (all else being equal) godawful for stability compared to a four wheeler. The problem is that when you steer, inertia is trying to tip the trike around the axis between the front wheel and one of the rear wheels. There are two problems with this. Firstly, the CG of a trike is much nearer to that axis than the CG of a four wheeler would be to the axis around which it might flip. Secondly, the tipping axis of a trike with a single front wheel is angled across in front of you. If you start to tip, the natural reaction is to brake, but if you do that, then you are just adding to the amount of inertia trying to tip you around the relevant axis.
Some high performance FWD cars (like the Peugeot 106 GTI) are notorious for lifting the rear inner wheel when cornering. FWIW, I read at another forum that this behaviour was incorporated intentionaly while designing the suspension geometry. Somehow lifting the rear wheel allows the car to take tighter turns.
The lack of comparative stability is one of the reasons that the ATV industry has, in general moved away from tricycle designs to quadracycle designs.
“Always” may be a bit strong here - under hard enough cornering the number may be two, one or even zero.
I don’t think it’s so much a question of number of wheels, as it is the wheelbase area over which the centre of mass/gravity can sit; once the centre of mass leaves this boundary, the vehicle is going to tip. Generally, this is easier to do with a triangular base than a rectangular one.
As a teenager I grew up with 3 wheel ATV’s, (even have the broken collarbone to show for it.) For turning, you leaned into the inside of corners or else. You could really whip them around and have a lot of fun.
In my late 20’s I could finally afford toys again and bought a 4 wheel ATV. What a difference in steering. You have to push the handlebars a lot more. Very few if any moments can I recall feeling like I’m tipping over in corners.
That is unless I’m doing something dumb involving mud, steep inclines and excessive speed.
Fans of Mr. Bean have seen multiple demonstrations of this phenomenon.
Mangetout has the underlying reason correct.
Three-wheelers have been banned for years in the US.
What Princhester said. Trikes with two front wheels (tadpole trikes) are very stable. Centrifugal force + braking force tends to tip a vehicle forward during a turn, and you need the 2 front wheels to resist these forces. But it’s not very crucial to have 2 rear wheels. Tadpole trikes seem to be just as stable as 4-wheel vehicles.
One disadvantage of a trike is that no two wheels are in line. Four-wheel vehicles only make 2 tracks on the ground, but trikes make 3. You straddle a pothole with the two front wheels of a trike, and the rear wheel hits the pothole. This is more crucial when riding off-road, which is the main reason this off-road HPV* has 4 wheels. For road use, tadpole trikes are good enough.
*HPV=Human Powered Vehicle
To be more explicit about this, there are two different classes of vehicle stability; static or quasistatic stability (which relies upon a balance of forces including the “implied” D’Alembert force to account for inertial loads) and dynamic stability.
Static stability is simple; if the applied forces, including the inertial (D’Alembert) force, friction between wheels and tires, and whatever other forces (forward traction, rocket/jet propulsion, aerodynamic forces, et cetera) are in balance and don’t result in a net “overturning force”, then the vehicle is stable. (It helps if you know what a freebody diagram is and how to cast one, but you can convince yourself by playing with Tinkertoy models of this, too, which is honestly more fun.) What is an overturning force? Imagine all the forces being summed at the center of gravity (CG) of the vehicle. If the forces stay within a box (or, for a tri-wheeled vehicle, a triangle) defined by the contact points of the tires, then the vehicle is stable. Otherwise, it is unstable and will begin to overturn and unless the overturning moment is countered (by leaning into the turn or slowing down) it will roll. For comparable speeds this is largely a function of the mass of the vehicle, the height of the CG with respect to ground, and the distance from the CG to the edge of the envelope in the general direction of the applied inertial force. For any given area, an equilateral triangle has a greater moment arm (distance from CG to nearest point on the envelope perimeter) than a square; hence, for a regular polyhedron (tetrahedral pyramid versus a cube) the tet is more stable.
However, a few points have to be bourne in mind. First, virtually no vehicle footprint is a regular (equal length side) shape. Cars and quadrunners are longer than they are wider; hence, the wheelbase is their controlling static dimension. With tricycle vehicles, the forward (or rearward, for “tadpoles”) single wheel is generally further away than the other two are to each other; hence, it will tend to tip in a direction more perpendicular to that long axis (between the single wheel and then CG) than across the two-wheel axle. (This assumes that the mass is well centered inside the envelope; if you’re hanging off the back of your three-wheeler or riding up a steep hill, the proximity of the mass to the rear axle will make overturning more likely.)
Height of the CG is also a consideration. The higher the CG, the greater the “vertical arm” is, and the less of an incline or enbankment is required to push the CG outside the evelope, as seen looking down from above. On triwheel ORVs, the rider sits quite high out of necessary clearance for the engine and transmission, making them unstable in turns. The same is true for quadrunner ORVs but the two front wheels give a greater footprint; plus, the inertial force directed primarily forward (while in motion) and sideways (while turning). For triwheel vehicles, this is toward the closest point on the stability envelope; for quads, the distance is greater, and hence they are somewhat more stable. (A tri-bike with two wheels in the front and one in the rear would be more quasistatically stable but would be dynamically less stable, as we’ll see in a minute.) A car is more stable yet, as the engine and driver sit lower to the ground and the wheels are pushed further out. In the extreme case of high performance racing cars (like F1 cars), the engine, driver, and tranny are scant inches from the ground and the wheels are pushed as far outboard as mechanically possible; when these things come off the track they usually don’t just tip over; the forces to make them do such are so large than they often become airborne or cartwheel.
One also need bear in mind that we are discussing highly simplified mechanics here; we’re assuming rigid body motion and point contact. The reality is that tires, suspensions, and road material all have flexibility; friction can be suddenly lost or applied, changing the state; and that the tires contact the road in patches rather than points, and this contact area changes with speed, balance, pavement material, et cetera. All of this adds a great deal of uncertainty which typically has to be accounted for empiracally (by testing and observation), though advanced structural simulation via analytical “codes” (finite element analysis) has come a long way in predicting real world behavior of flexible, time-varying mechanical conditions.
That sneaks us up to dynamic stability, which is the stability of the system with respect to time-varying conditions. Essentially, dynamic stability accounts for the fact that when a system undergoes some kind of change the properties and responses of the system may change, and so a vehicle that may be statically unstable can still be controlled via feedback; either mechanical feedback (suspension which flexes to slant the car into a turn, countering the centrifugal force) or applied feedback (a driver or traction control system that responds by steering out of a skid or applying the brakes). Many systems are only stable dynamically or nearly so; a motorcycle or bicycle, for instance, is almost always on the edge of being unstable; as every rider knows, you have to constantly shift your weight when cornering or handling a bike at low speeds, and a unicycle is always statically unstable–and yet, an experienced rider can ride one for hours without falling down.
Dynamic stability is a really complicated topic which gets into controls theory (and nonlinear structural dynamics) and is so far beyond the scope OP’s question that there’s no point in going into any great detail, but a few points are worth mentioning:
[ul]
[li]For wheeled vehicles which are steered at either the front or the rear all suffer from what is called Ackermann error; this is the difference between the turning radii of the steering wheels, i.e. the distance between the points where the axis of each of the wheels intersects with the axis of the non-steering axis. (Lamentedly, I can’t find any diagram of this online, though there has to be one somewhere, but there’s plenty of discussion about it among car enthusiasts.) This is a result of the having the wheels mounted on a steering knuckle and connected to the steering wheel by a rack-and-pinion or worm-gear system rather than a single pivoting axle, as with a quadrunner. However, it would take an incredible amount of force to turn a full solid axle; your steering wheel would be wider than the car, and you’ve have to design the car to allow clearance for the rotation of the whole axle, so we live with the compromise. Many well-designed modern cars have a passive steering linkage for the rear wheels to reduce the amount of error as well as compensate for body roll (often called a parallel-link or multi-beam link), and a few manufacturers have offered active steering (Nissan’s HICAS, as an option to some models of the 300ZX and 240SX), but all cars have a slight tendancy to “drag” one or both of the rear wheels in a turn, which is accounted for by the give of the tire.[/li][li]Triwheel vehicles, by definition, don’t suffer from error at all. However, because most trikes are direct steer with no mechanical reduction, a slight turn of the handles translates into a large response. On a bike, most steering at speed is done by shifting weight rather than turning the handlebars. A car, on the other hand, uses gearing to reduce the angular motion of the steering wheel by a large factor to reduce the turning angle (and simultaneously multiplies the force).[/li][li]Rear steer vehicles and especially rear tri-wheels then to be very maneuverable at low speeds but highly unstable at high speeds. The reasons for this are kind of difficult to explain without drawing Bode plots and mumbling about poles and zeros but are readily observable in a grocery cart or industrial lawn mower. Essentially, front steer vehicles tend to be more forgiving while rear steering is amplified because the CG tends to swing out from behind the front wheels. The drive axle–front, rear, or both–also contributes to this. [/li][li]R. Buckminster Fuller once designed a series of “tadpole” (two wheel front axle, rear steer) cars (Dymaxion Car) that he claimed would be very stable and efficient. The cars looked a lot like a modern helicopter fuselage sans rotor or tail. High speed stability was provided by aerodynamic forces (shape of the vehicle plus one or more deployed stabilizers) to counter the inherent instability of a rear-steer configuration. This resulted in a teardrop-like design that had a large interior area, was stable and yet very maneuverable at low speeds, and allegedly very fuel efficient. Unfortunately, it was also aerodynamically unstable at high speeds; the rounded underbody, while reducing drag, also produced lift, and the car was subject to void-induced vibration and forces in the rear. The design still has its adherents who insist that these problems can be negated by improved design, but triwheel cars have failed to take the automotive world by storm; save for the Messerschmitt KR200 commuter car (as seen in the film Brazil), no production cars have been built in this configuration.[/ul] [/li]So, to much belatedly answer the question of the OP, all things being “equal”, four wheels are generally more stable, as they offer a greater envelope of stability, despite the greater mechanical complexity and inherent misalignment of the steering gear. Three wheels are more maneuverable, especially at low speed, but are less able to resist overturning in a curve, espeically with a forward single wheel.
Unfortunately, I don’t have my copy here at the office right now so I can’t cite directly from it, but Gillespie’s Fundamentals of Vehicle Dynamics is the standard reference for vehicle dynamics in the automotive and agricultural/construction equipment industries. I haven’t read through it but Pacejka’s Tire and Vehicle Dynamics seems to be the most widely used reference with regard to pneumatic tires. This is actually a very incomplete area of engineering knowledge; while most people just think of tires as being black blogs of rubber that just hold up the car, the pneumatic tire is one of the most complex, advanced, and poorly understood components of your powertrain, despite having no moving parts. Weird, huh?
Stranger
Heh…try taking that down some San Gabriel singletrack with a fifty foot drop on one side and a sheer wall on the other. :o
I’ve always had an urge to get into 'bents, and the trikes look a lot easier to manage and carry some cargo than recumbant two-wheelers (which generally don’t have any place to stick a rack or bottle cage and prevent you from wearing a backpack) but aren’t the trikes significantly heavier? Is there a good quality manufacturer of tri-bents? Most of the bi-bents I’ve seen have some fairly questionable components and construction, though in all fairness I’m comparing them to mountain bikes, not road bikes.
Stranger
Take it from someone who’s daily driver is a sidecar rig: Three wheels is less stable, and feels even more unstable than it actually is. The asymetrical motorcycle/sidecar combiniation is omitted from the above discussion.
This one of the advantages of a sidecar/motorcycle combination over a trike. Junk like nails and such tends to stay put once it reaches the middle of a traffic lane, and grease tends to accumulate there as well. Potholes that are straddled by normal traffic are not repaired with the same urgancy as those in the tire tracks. With a trike you have your steering wheel running on the slickest part of the lane. With a tadpole configuration, you have your rear wheel in it, which requires traction to maintain stability. Also, there are plenty of two-track dirt roads, but no three track roads.
The only advantage this gives a trike is reduced likelyhood of a punctured tire. Nails and such tend to lay flat on the road, where they do not puncture the first tire that runs over them. The first tire, however, tumbles the object so that it has a fair chance of puncturing the following tire.
Think of all the flats you’ve ever had on car, bicycle, or motorcycle. Odds are that the the frequency is biased about 75% to the rear tire(s).
Thank you all very much for the informative replies!
Cheers
Fantastic post, Stranger.
There isn’t a big difference there. Most two-wheel recumbents can be fitted with a luggage rack and/or a seat bag. Some can be configured with two racks for loaded touring. (example 1, example 2).
My Catrike Pocket weighs 26 lb, and is probably the lightest recumbent in its price range. This company has a good reptuation, and I’m happy with the quality. WizWheelz is another good US trike manufacturer. There are good imported trikes as well (Greenspeed, and ICE being the best known), but I find the US companies provide a better value for the money, at least for purchase in the US.
Some 'bent trikes are heavy though. My SO rides a Sun EZ-3 AX which tips the scale at 50 lb. (She likes the higher seat.)
I’m not sure which bikes you’ve seen, but in my experience, recumbents from major manufactuers (RANS, Burley, Bacchetta, etc) are all very well built. They do have cheaper components than MTBs of the same price, but that’s because the recumbent bike frame and seat cost more to produce. Almost all components are standard MTB components and can be upgraded later.
My biggest concerns about frame is that most of the bi-bents I’ve seen are not as well-reinforced in the joints as I’d like; on the other hand, they’re probably seeing lower stresses. It’s also been a few years since I’ve looked at bents.
I like your CATRIKE, 'cept the placement of the brakes looks uncomfortable and I wonder about grip shifters; but I like the orientation of the grips–much more natural than an upright bike. They’re a bit pricey but if I could ride a bike to work I’d consider it. How the heck do you park it, though? You can’t exactly portage the thing up the stairs and into a corner of the office. 
/end hijack.
Stranger
Why would TIG-welded joints need to be reinforced at all? As long as the frame tubes have enough wall thickness to withstand the stresses, there shouldn’t be a problem.
Yeah, grip shifters aren’t the best choice, though it’s not as bad as you might imagine. Bar-cons (bar-end shifters) work better for this type of handlebar, and Catrike’s more expensive models come with bar-cons standard.
As for parking, it’s about the width of a standard wheelchair so you can easily pull it through doorways and office hallways. (The “correct” way is to lift the rear of the trike by the luggage rack and pull the trike behind you.) Of course it’s a bit longer than a wheelchair, so elevators might be a bit tricky - my office is on the 1st floor so I’ve never tried it.
Sorry for continuing the hijack. I’d be happy to talk more about recumbents if you want to start a new thread about it.
There’s so little weight on that wheel in a corner that it makes it largely redundant. However, it isnt really relevant to this discussion.