An analysis of supermarket spinal injury

by Mike

Overview

Trolleys with four wheels can be made in various ways. The rear (US shopping carts) or front wheels (Heavy Load trolleys in UK DIY superstores) may be constrained to point forwards ('fixed'), or neither (most UK supermarkets - unfortunately for my poor back). There may be a braking handle (as with airport luggage trolleys) - and this may either release or apply the brake. A brake may also be present on one of the wheels, operated by foot (UK supermarkets).

I shall examine the physics of each type of wheel configuration, and suggest an alternative design.

About Wheels

The problem with trolley wheels is that, while fixed ones experience lateral friction, freely-rotating ('free') ones do not. Why is this a problem? Because the amount of lateral friction has a direct effect on the amount of torque required to be applied to the handle in order to manoeuvre the trolley. Large required torque is my main enemy here: speaking as someone who has suffered from back disorders, I can say from personal experience that it is the main cause of pain and injury while shopping [footnote: For those who are young and healthy, I want to say: YES, I actually MEAN that! When your body gets older, it's less sturdy. You may think that this doesn't happen until you are about 70 years old, but I'm 39, and I've had back trouble for about 5 years now. It could happen to YOU!]

Let's take a look at what happens with the three main types of wheel configuration:

No Fixed Wheels / No F***g Way (NFW) trolleys

Very common in the UK supermarket, these are the worst kind. Because there is negligible lateral wheel friction, the centre of rotation (COR) of the trolley can be almost anywhere. This is great from a manoeuvrability point of view, but it makes it very hard to go around corners, because the COR is free to move, and so it tends to stay on the line of travel. Think about this for a moment. If you want to corner, you need the trolley to change orientation. Once the orientation has changed, you can push on the handle and begin changing the direction. This is not ideal. It means that you are at the mercy of vector algebra. If your trolley is proceeding in a Northerly direction and you want to go East, you must adopt one of the following strategies:

1. Pull on the right side of the handle and push on the left to change the trolley's orientation, then follow it round so that you are standing behind it, and push forwards. The resulting trajectory is a curve, not a sharp corner, so you'd better make sure you have room to swing around, and watch out for the lateral inertia, which exerts terrible punishment on your poor back!

2. Stop completely, make your hips the COR (ouch!) and pull the handle to the right using both hands, so that the front of the trolley swings around too. You use your feet to provide the lateral friction so that you get maximum force. This gives a better turning circle, but is VERY bad for the body. Any kind of torque on the spine like this can cause damage.

3. Stop completely, walk around the trolley, pulling it around with you, then push forwards again. This is probably the best approach, giving a perfect 'square' cornering trajectory with minimum back damage. However, you will getted 'tutted' at by irritated shoppers who wonder why you have stopped in their path.

If you've been following this so far, you'll be thinking “why would they inflict this kind of nonsense on the British public? Especially when the Americans don't have to put up with it (see later)?” I can't tell you the answer to that question. I suspect that somebody somewhere decided that manoeuverability was more important than cornering. This is obviously (to me) incorrect. There are occasions when you need to get your trolley out of a tight corner, perhaps when it is stuck between two others, or has ended up with its nose in the bread boat - but at the same time, supermarkets are arranged in a pattern of rectangular displays with a grid of aisles between them, necessitating a large number of cornering operations while traversing the grid. Even on a busy Saturday before the football match starts, I submit that the cornering count is always much greater than the 'manoeuvering out of a tight spot' count. Therefore, the cornering capabilities of the trolleys should have been given priority in the design. They were not. Shame on you, ASDA, Sainsbury, and all the rest!

OK, rant over. On to the other types:

Fixed Rear Wheels (FRW) trolleys

I am told that these are what you get in America. I think I'll emigrate. They are much better for your back. Let's take a look at the physics again.

The COR is always on or near the rear axle line. First of all, taking the trolley and the human driver as a unit, this is fairly close to the centre of the whole unit. So the turning circle is always good. But also, because the handle is close to the COR, this means you need more force to turn the trolley. At first glance this is a bad thing; however, there are two other factors that make it a good thing: (a) the lateral friction on the fixed rear wheels keeps the COR roughly in the right place, so there are no unexpected movements, and (b) you can push with one hand and pull with the other. You can of course do (b) with a NFW trolley, but because the COR is much freer to move, you lose a lot of control.

Another factor is the positioning of heavy goods in the trolley. If you happen to place heavy goods near the front of a NFW trolley, it is hard to turn because they make the COR stay near the front. In a FRW trolley, this is not so important, because the lateral friction on the rear wheels counteracts this effect and keeps the COR near the rear, giving you more control. It is still better, of course, to put heavy goods near the back of the trolley, but it's just that FRW trolleys can cope better if you can't, or don't, do this.

Fixed Front Wheels (FFW) trolleys

These are notoriously hard to manoeuvre. This is because the COR is on or near the front axle line, so, taking the trolley and human driver as a unit again (as above), this results in the maximum possible radius when turning, and you need a huge turning circle. If you have never seen this, go and watch the performances of people buying bags of compost or sand in B&Q!

So, if these trolleys are so hard to turn, why make them? Actually, there's a good reason. The goods they must carry can be very heavy indeed, and keeping the COR near the front means that the handle is at a maximum distance from the COR. This implies that the amount of handle force required to turn the trolley is reduced, because the same force results in a greater moment (torque) the further it is from the COR. It's the same principle as a lever. Stand far enough away from the pivot, and you can lift ten times your own weight. If you tried to transport ten bags of sand on a FRW trolley, you'd have a hard time turning it, because all the sand would be on one side of the COR, and you'd be on the other, with your feeble, puny pushing moment unable to do much at all without the strength of an olympic weight-lifter.

So, FFW trolleys have their place, and so do FRW trolleys. However, NFW trolleys do NOT have a place anywhere except for the lightest of loads in environments where space is limited, or an unusual shape, and they often need to be manoeuvered out of tight spaces. This applies much more to a catering trolley in a restaurant, for example (where it has to negotiate all those tables, and only has food on it, which isn't too heavy), NOT to a supermarket trolley! I submit that ALL supermarket trolleys should be FRW.

A new kind of trolley

In order to implement the following idea, you'd need a way of altering the lateral resistance of each wheel (i.e. the degree to which it were constrained to point forward). This is an engineering challenge that is probably beyond my ability! However, here it is anyway:

When the trolley is at rest, moving at low speeds, or moving in reverse at any speed at all, it is in NFW mode (all wheels completely free to turn), so that it can easily be manoeuvered out of tight spaces.

As the forward speed increases, the rear wheels become more fixed, to reduce the lateral force needed to keep going in a straight line. We are now in 'American mode'.

If a turning force is applied while moving at significant speed, the COR moves toward the front of the trolley to a degree that depends on the angular speed (this is done by making the rear wheels gradually freer and the front ones gradually more fixed - hence the engineering challenge!). The effect of this would be that the trolley would respond to your 'turn left' command by first moving its nose to the left and starting to bend the trajectory into a curve, then, as the angular momentum increased, it would tend to allow the back end to swing out (with your good self attached!), while keeping the front wheels steady in order to follow a nice tight cornering curve. Once it was pointing in the correct direction, you would apply force to stop the rotation, and this would make the COR move back to the rear again. The effect of this would be that the trolley would stop 'cornering' and start 'tending to go straight' again.

To me, this sounds like shopping heaven, and the first supermarket to implement it will have my custom for ever.

As a closing thought, I'd like British supermarkets to consider this. Which is easier to manoeuvre accurately - a car (with a good tight turning-circle), or a boat?