# Why is a cart with swiveling casters in front stable, but not if the swiveling casters are in back?

Consider a four-wheeled cart that has swiveling casters for the two front wheels, and has wheels that don't swivel in back. For example, a common shopping cart, or trolley if you prefer. If such a cart is pushed and let go, it will continue to roll in the same general direction, and so I'll call it stable.

On the other hand, if the same cart is turned around, pushed, and let go, then the cart won't continue in the same direction for long; it has a tendency to spin around, so I'll call it unstable.

Why is a cart with swiveling casters in front stable, but is unstable when the same cart is turned around?

Consider what happens in front wheel steering, such as an automobile:

• Turn the steering wheel slightly clockwise.
• The front wheels each turn slightly clockwise.
• Their rolling action causes the wheels to pull the front end of the vehicle slightly to the right.
• The back wheels follow the track of the front wheels, but in a slightly tighter turn.
• Holding the steering wheel in that position will cause the vehicle to continuously turn in a circle.
• The wheels' caster makes them try to return to a neutral position.

The wheels are mounted with "caster", meaning that the almost vertical axis about which the wheels rotate when steered doesn't meet the ground at the same position as where the wheels meet the ground. This causes sideways friction when the wheels are not in a straight-forward position (negative feedback).

This is a very stable arrangement:

• Turns are circular.
• The sharper the desired turn, the more the steering wheel must be turned.
• Releasing control causes the steering to automatically return to a neutral position.

Now consider what happens in rear wheel steering, such as a fork-lift (or when driving a car in reverse):

• Turn the steering wheel slightly clockwise.
• The back wheels each turn slightly counter-clockwise.
• Their rolling action causes the wheels to push the back end of the vehicle slightly to the left.
• The front wheels continue forward, turning to the right, but in a slightly tighter turn.
• Holding the steering wheel in that position will cause the back wheels to steer more and more widely around the front wheels, which make an increasingly tighter turn.
• Depending on the caster, the wheels might have a tendency to steer even more when released.

This is a very unstable arrangement:

• To drive a circular path, the driver must initiate the turn by swinging the back end out to the left, and then must continuously reduce the amount of steering to avoid following a spiral path.
• Releasing control does not return the steering to neutral, and will likely result in a very tight spiral.

Rear wheel steering is very handy at slow speed. A fork-lift for example can position the front end, push it into place, and adjust the back end to line up square. Similarly, it is easier to back a car into a parking spot than to drive in forward, and much easier to drive out forward.

But at higher speed, rear wheel steering is inherently unsafe. With front wheel steering, if something goes wrong, the vehicle ends up going straight. With rear wheel steering, if something goes wrong, the vehicle ends up spiraling out of control.

## Edit: a simpler explanation:

The OP commented: "Shopping carts have no caster, but they do have trail. But I don't see how trail can be responsible, seeing as the same swiveling casters are stable if in front, but unstable if in the back. There must be another explanation.", and yes, there is another explanation. I mentioned negative feedback, but failed to expand on the idea.

Imagine what happens when a vehicle turns to the right. As a passenger, you feel yourself pulled to the left by a force (some physicists say a virtual force) known as centrifugal force.

This same force acts on the vehicle itself, though because it is a rigid object you don't notice it except perhaps for a slight tip to the left.

Now consider how the vehicle's wheels react to this force, looking at three different types of vehicles:

• On a railroad car, the wheels are not steerable and are attached to a fixed axle. This means that both wheels must roll at the same rate, even though when going around a curve one wheel has to travel a greater distance. Centrifugal force behaves as if it acts on the car's center of gravity and pushes all the wheels to the left. The track, and the surface of the wheels themselves are not, as one might think, perfectly level. Instead they slope to the inside so that the part of the wheel that hangs over the inside of the rail has a larger diameter than the part of the wheel that hangs over the outside of the rail. When the car turns, and is pushed to the left, the left wheels end up rolling on their larger diameter section while the right wheels run on their smaller diameter section. In effect, the car has larger wheels on the left and smaller wheels on the right, and it naturally turns to the right, following the track. (At slow speed this effect doesn't happen, hence the loud squealing of slipping wheels in shunting yards.)

• On a vehicle with front-wheel steering, the centrifugal force also acts on the center of gravity and pushes all the wheels to the left. The rear wheels are fixed and so continue following the vehicle. The front wheels can turn, so as they push to the left against the ground, the ground pushes them to the right. With caster, or trail, this force provides negative feedback that makes the wheels return to their normal straight-forward position unless a steering wheel is forcing them to stay in a turned position.

• On a vehicle with rear-wheel steering, it is the front wheels that are relatively unaffected by the sideways force, and the rear wheels that react to it. The force of the road on the wheels makes them want to turn to the left. But the vehicle is turning because the rear wheels were already turned to the left, so in this case the centrifugal force provides positive feedback. The more the vehicle turns, the more the wheels tend to make it turn. Rather than forcing the vehicle to turn, the steering wheel must be used to prevent the vehicle from turning.

The rail car is symmetric front to back, asymmetric side to side, and steers by a very different mechanism using both front and rear wheels.

The front-steering vehicle's front wheels are affected by negative feedback, which forces the steering back to a neutral position.

The rear-steering vehicle's rear wheels are affected by positive feedback, which forces the steering into ever increasing turn positions.

Negative feedback is generally a good thing, enforcing stability (e.g. thermostats).

Positive feedback is generally a bad thing, causing rapid unrestricted growth (e.g. explosions, PA system howling).

## Historical side notes:

Since they don't use rolling wheels, ships and planes steer from the rear because in that situation, rear steering is more stable. It's no longer done this way, but the traditional ship steering wheel used to be turned the opposite way to how it is turned in a car. (Notice in the description above how steering clockwise caused the rear wheels to turn counter-clockwise. Having the steering wheel turn the same way as the rudder made sense.) One would move the top of the steering wheel to the left in order to turn the ship to the right.

Planes on the other hand do still use this "backward" steering. When steering, the pilot pushes on the right rudder pedal in order to yaw to the right. This is the exact opposite of how anyone that has used a soap-box car with single axle front steering would expect it to work.

Bureaucrats and social idealists are often ignorant of the laws of physics, which tend to conflict with their world-view.

In the 1970s Joan Claybrook, as head of the US National Highway Transportation and Safety Administration, somehow discovered that motorcycles were more dangerous to their drivers than were cars. As a result, she commissioned, at great expense to the taxpayers, the design of a "safe" motorcycle.

Naturally it had a steel-pipe roll-cage to protect the driver.

And since her friend Ralph Nader had already killed the Chevrolet Corvair because he incorrectly believed that rear-engine vehicles were "unsafe at any speed", she had the motorcycle's engine mounted at the front.

This of course meant that the steering had to go at the back.

Anyone that has ever walked along, pushing a bicycle without holding the handlebars, knows that it's easy to go forward and impossible to go backward. The engineers and other professionals working on the project pointed out that her design wouldn't work, but she dismissed negative "opinions" of the naysayers, her ideals of highway safety taking precedence over reality.

Eventually it was given a pair of outrigger wheels (effectively the same as training wheels on a child's first bicycle), because no one was able to drive it without it almost immediately tipping over.

Here's an image of the prototype (the driver would sit facing the right):

• "Depending on the caster, the wheels might have a tendency to steer even more when released." (You were speaking of swiveling casters in the rear.) I think you've hit on the crux of the problem, but I don't think that the tendency to steer even more can be attributed to caster. Shopping carts have no caster, but they do have trail. But I don't see how trail can be responsible, seeing as the same swiveling casters are stable if in front, but unstable if in the back. There must be another explanation. Jul 8, 2019 at 13:48
• By the way, I love the bit about Claybrook's "safe" motorcycle, the perfect example of why bureaucrats shouldn't be allowed to design things. Jul 9, 2019 at 1:24
• @rclocher3 says "There must be another explanation.", and yes, there is, and I've now added it. Jul 11, 2019 at 16:37
• Great answer! Thank you sir! Jul 15, 2019 at 18:44

Your release doesn't need to be perfectly inline with motion with swivel casters on the front. The single direction casters in the rear make any left/right force upon release irrelevant because they are constrained. Flipped around with swivels on the rear and your release has to be perfectly inline for straight movement. Any left/right force upon release and it'll turn the casters.

• Please explain what you mean by constrained. Jul 3, 2019 at 20:22
• The non swiveling casters are constrained to only forward/backward motion. They don't swivel. Jul 4, 2019 at 13:29
• You seem to be saying that whether or not the rear wheels swivel is the only factor. I don't think that you've proved your case, because I could turn your argument on its head and say that any left/right force on release of a cart with rear swiveling casters is irrelevant because the front wheels are constrained. Clearly my false argument is contradicted by experiment, but I don't think you've explained why unconstrained wheels are stable if in front, but unstable if in the rear. (If you think your argument makes sense then maybe you just need to break it down more for me, ha ha!) Jul 8, 2019 at 13:54
• To clarify, imagine using a single point attachment to provide force to push the cart. The force would be supplied in the center of the cart from left to right. Assuming the force was supplied normal to the L/R plane then the cart would move straight regardless of where the swiveling casters were located. It's the variability of using your two hands to provide the force that causes the cart to turn when the casters are on the rear. It is almost impossible for you to provide a perfect normal force to the cart. Jul 8, 2019 at 15:30
• Right, I get that a human pushing a cart and then letting it go causes a perturbation. The crux of the matter is that such a perturbation with the swiveling casters to the rear causes the cart to spin out, but a perturbation like that with the swiveling casters to the front merely causes the cart to turn slightly, and then the cart returns to stability. Why? Jul 9, 2019 at 1:22

Wikipedia mentions shopping carts, explicitly:https://en.wikipedia.org/wiki/Caster_angle

In the extreme case, such as the caster wheel on a shopping cart, the system is undamped but stable, as the wheel oscillates around the 'correct' path.

The shopping cart wheels are not normally/ever casted, so the beginning of @ray-butterworth's effort is wasted in this case. He also mentions driving wheel a lot, which is unrelated to the question at hand.

Where I think he hits the nail is these two paragraphs (with regard that the cart's swiveling wheels have trail):

• On a vehicle with front-wheel steering, the centrifugal force also acts on the center of gravity and pushes all the wheels to the left. The rear wheels are fixed and so continue following the vehicle. The front wheels can turn, so as they push to the left against the ground, the ground pushes them to the right. With caster, or trail, this force provides negative feedback that makes the wheels return to their normal straight-forward position unless a steering wheel is forcing them to stay in a turned position.

• On a vehicle with rear-wheel steering, it is the front wheels that are relatively unaffected by the sideways force, and the rear wheels that react to it. The force of the road on the wheels makes them want to turn to the left. But the vehicle is turning because the rear wheels were already turned to the left, so in this case the centrifugal force provides positive feedback. The more the vehicle turns, the more the wheels tend to make it turn. Rather than forcing the vehicle to turn, the steering wheel must be used to prevent the vehicle from turning.

I wish he had made those two paragraphs the answer. But I also appreciate the deeper tour I got about how steering works with automobiles, fork lifts, trains, boats and airplanes.

Meta note: In the eyes of the Engineering SE tour, the shorter and precise answers - maybe with links to blogs or articles that provide the full story - would be preferred.

• "I wish he had made those two paragraphs the answer." One of the problems with SE is that people often respond right away, and only later realize that they have a better answer. I don't know why (perhaps from seeing so many other posts with "EDIT:"), but it feels right to add the better answer, and wrong to remove the original answer. If I were to answer this all over again from scratch, the answer would be significantly different. Perhaps someone with a lot more experience here could convince me of what the "right" thing to do is. Jul 14, 2019 at 0:44
• @RayButterworth I hope you don’t take my writing as a criticism - please also observe that I appreciated your longer answer. :) I have used StackOverflow intensively on the software side and know how well the concept suits there. This is more about the general fitting of the Q&A concept also to other areas, such as engineering here. Maybe the domain is by nature more complex and the tool will struggle to make a good fit. Jul 14, 2019 at 6:56
• I agree with your "criticism". Had it been in a comment, I'd have upvoted it. Jul 14, 2019 at 13:55