Imagine that today you are going to do something different to earn money for the taxman. Instead of driving your truck you are going to ride The Wall of Death, a motorcycle stunt once common at fair grounds. Spectators would stand on a platform at the top of a large, upturned cylinder, like an enormous bucket, inside which a motorcycle was ridden round and round, rider and machine horizontal, as if stuck to the wall. It may not be too different from what you are used to: certainly, the person who owns the machine and who sets you off on your journey will be more than happy that they are staying behind. But that’s not the only similarity, the laws of nature that will keep you and the motorcycle from falling to the bottom of the bucket are the same as those that keep your truck on the road.
About 300 years ago, Sir Isaac Newton discovered that when an apple becomes detached from a tree it falls to the ground. Not much of a revelation you might think but Sir Isaac went on to describe three basic laws of motion that are still used today. Briefly, Newton stated that a body in motion would continue in a straight line unless acted on by an external force; that acceleration will be in the same direction as any force applied; and that every action has an equal and opposite reaction. These laws are true for all bodies: planets and people, rockets and trains, trucks and motorcycles.
So, as you ride the motorcycle round The Wall of Death, it is Newton’s Laws of Motion that should provide a description of what’s happening; and by climbing on the motorcycle, you are going to put Newton – and yourself - to the test. You start by riding round the small ramp at the bottom of the bucket until your speed is high enough for you to ride up the wall. As the speed of the motorcycle increases, the affect of the force working to the side gradually catches up that of the force that is trying to pull you down to the ground (your weight). Once the effect of the side force overcomes that of your weight – and, of course, that of the motorcycle – you are stuck to the wall. And you ride round as if suspended in mid air, marvelling at nature and Newton.
You are now travelling at a constant height from the base of the bucket and at a constant speed. To you, riding at 90 degrees to the wall, as if it was a road, is like climbing a hill that never ends. You feel a force acting on you, pressing through the seat of the motorcycle. You remember what Newton said: that you will continue in a straight line unless acted on by an external force, and that any force applied will have acceleration in the direction of that force. The external force provided by the wall is continually changing your direction by pushing you toward the centre of the bucket. It’s like what happens with a hammer thrower at the Olympics. The athlete spins round and round with the hammer on the end of a cord. The hammer is kept in circular motion about the athlete by a force transmitted through the cord, which, like the acceleration, acts in the direction of the athlete. The hammer wants to go off at a tangent but cannot until the athlete let’s go.
Back on the wall, the acceleration and force may be acting towards the centre of the bucket but you also feel a reaction, pushing you into the seat of the motorcycle. This is no surprise; Newton has told you that every action has an equal and opposite reaction. (It’s this reaction that is sometimes called centrifugal force, a pseudo force that in reality doesn’t exist. The real force, as we have seen, acts towards the centre of the circle, and is the centripetal force). One thing that does surprise you, however, is how much the force increases with little increase in speed. It seems to you that with only a small twist of the throttle you are pressed against the wall with such force that the two cannot be directly proportional to one another – and you are right. Speed has a squared relationship with side force: double the speed and the force increases fourfold.
Surviving the wall you’ll be happy to be back in the safety and comfort of your truck. But don’t forget, the laws of motion that applied in the bucket apply everywhere. When attempting to negotiate a bend, Newton tells you that it will take a force to alter the original course, and if you want that direction to continue to change, and you will as long as you are in the bend, the force must remain. Now, instead of the wall creating this change in direction, the truck’s tyres apply the necessary force, accelerating you towards the centre of the circle. If the side force becomes too great, then just like in the bucket, it will overcome the effect of the weight of the vehicle. This time, however, it doesn’t provide stability; it destroys it and the truck rolls over.
In the days when no self-respecting Leyland Marathon or Ford Transcontinental would be seen without a set of furry dice hanging down the inside of the windscreen, the driver had an instant indication of the effects of Newton’s laws. As the tyres forced the truck into a curved path, the dice were the last things to follow on, appearing to swing in the opposite direction to the truck’s turn as they attempted, in reality, to travel straight ahead. The greater the side force, the greater the angle of swing. It’s hard to imagine how you could compare the forces acting on a pair of furry dice with those acting on a truck, until you remember your experiences in the bucket. When you increased speed, the side force increased, but there was no change in mass – you and the bike remained the same; no new material was added to either of you. The increase in force was purely down to an increase in its acceleration and the only things that affect this lateral acceleration are the radius of the curved path and the speed at which you travel round it.
This result is very useful: it means that when considering a vehicle’s stability, we can (in most areas) disregard its mass and just concentrate on accelerations. We know that a side force acts on the vehicle as it travels through a bend, and that there is acceleration in the same direction as the force. We also know that the vehicle’s weight is a force and that force has an acceleration; the acceleration due to gravity. So, as your truck travels through a bend, the lateral acceleration and how it compares with the acceleration due to gravity are all we need concern ourselves with. The dice will have the same accelerations acting on them, as they are attached to the truck, and although the force acting will be vastly different, the lateral acceleration and the acceleration due to gravity will be the same for a 44 tonne truck as they are for the 4 oz dice. All the driver need to do is watch the dice as the truck settles into a bend and see how far they swing to one side. This will give an indication of how much acceleration there is to the side compared with how much there is pointing downward.
It is actually similar in principle to how a tilt-test for vehicle stability is conducted. When a vehicle is placed on the platform, the coordinates of the resultant force are compared as the bed is gradully tilted. The component of lateral acceleration (a) can then be expressed in terms of the component of the acceleration due to gravity (g). This gives a static stability factor ‘a’ over ‘g’ (a/g). However, this figure will be reduced when the vehicle is on the road for reasons that will be mentioned shortly. In theory, you should be able find the a/g factor that the truck is actually experiencing by measuring the angle the dice make to the vertical as you drive it through the bend, and then find the tangent of that angle. How much could the dice lean before the truck becomes unstable? Unfortunately, it will depend on a number of things.
There’s an added complication with any road vehicle because of the position at which the lateral acceleration (and, therefore, the side force) acts. When you rode the motorcycle around the inside of the bucket, the lateral acceleration created by the wall worked straight through the centre of gravity of both rider and machine, and the point the motorcycle touched the wall. The reaction worked in the opposite direction along the same line. Now, the lateral acceleration created by the truck’s tyres at ground level is being transmitted to the vehicle’s centre of gravity, which will be at some height above, and something similar to a leverage forms. As the vehicle travels round a bend, this leverage is working on a pivot point at the outside tyres. It is being countered by the acceleration due to gravity trying to lever the truck downward, again acting at the centre of gravity and about the same pivot point. So, now it’s not just the size of these accelerations that is important, it’s also the size of their leverages. If the leverage of the lateral acceleration is greater than that of gravity, the vehicle will become unstable. In a car, which will have a wide track width compared to the height of its centre of gravity, the leverage of the lateral acceleration never manages to exceed that created by gravity. Lateral acceleration builds until the tyre friction limit is reached and the car slides sideways. In a truck, the leverage of the lateral acceleration will usually exceed that of gravity before the limit of tyre friction, resulting in rollover.
It’s not only the height of the centre of gravity that can have an affect on rollover. Anything that causes extra body roll will assist the lever trying to pull the vehicle over by reducing the righting affect of the vehicle’s weight. Soft tyres and weak suspension, or a heavy load, are prime candidates, as is an offset or shifting load. And, as with most things, it’s never that simple. Factor in rate of change in lateral acceleration associated with some manoeuvres, the resonance of steering input with suspension frequency during sudden lane changes; and the bucket and motorcycle job doesn’t seem that bad after all. But don’t give up on truck driving too soon; there’s plenty you can do to reduce the chances of rollover.
If the truck’s stability a/g drops during cornering or the a/g it is experiencing climbs, the two factors will converge. If they meet - or worse, the truck’s stability is exceeded – you’ll probably wish you were back in the bucket. So, the lateral acceleration it is experiencing needs to be kept as low as possible and the lateral acceleration it can withstand will need to be kept as high as possible. The former is down to speed and the importance of the squared relationship it has with side force (and, therefore, lateral accelleration). Whatever lateral acceleration your speed creates has to be resisted by the trucks stability and this will decrease for a number of reasons, the most important being the height of the centre of gravity. Ultimately, the probability of rollover will only be avoided completely by careful monitoring of a/g factors, either by you or, if you’re not too good with a protractor under conditions of extreme stress, a stability program. I think I know what the answer is.
About 300 years ago, Sir Isaac Newton discovered that when an apple becomes detached from a tree it falls to the ground. Not much of a revelation you might think but Sir Isaac went on to describe three basic laws of motion that are still used today. Briefly, Newton stated that a body in motion would continue in a straight line unless acted on by an external force; that acceleration will be in the same direction as any force applied; and that every action has an equal and opposite reaction. These laws are true for all bodies: planets and people, rockets and trains, trucks and motorcycles.
So, as you ride the motorcycle round The Wall of Death, it is Newton’s Laws of Motion that should provide a description of what’s happening; and by climbing on the motorcycle, you are going to put Newton – and yourself - to the test. You start by riding round the small ramp at the bottom of the bucket until your speed is high enough for you to ride up the wall. As the speed of the motorcycle increases, the affect of the force working to the side gradually catches up that of the force that is trying to pull you down to the ground (your weight). Once the effect of the side force overcomes that of your weight – and, of course, that of the motorcycle – you are stuck to the wall. And you ride round as if suspended in mid air, marvelling at nature and Newton.
You are now travelling at a constant height from the base of the bucket and at a constant speed. To you, riding at 90 degrees to the wall, as if it was a road, is like climbing a hill that never ends. You feel a force acting on you, pressing through the seat of the motorcycle. You remember what Newton said: that you will continue in a straight line unless acted on by an external force, and that any force applied will have acceleration in the direction of that force. The external force provided by the wall is continually changing your direction by pushing you toward the centre of the bucket. It’s like what happens with a hammer thrower at the Olympics. The athlete spins round and round with the hammer on the end of a cord. The hammer is kept in circular motion about the athlete by a force transmitted through the cord, which, like the acceleration, acts in the direction of the athlete. The hammer wants to go off at a tangent but cannot until the athlete let’s go.
Back on the wall, the acceleration and force may be acting towards the centre of the bucket but you also feel a reaction, pushing you into the seat of the motorcycle. This is no surprise; Newton has told you that every action has an equal and opposite reaction. (It’s this reaction that is sometimes called centrifugal force, a pseudo force that in reality doesn’t exist. The real force, as we have seen, acts towards the centre of the circle, and is the centripetal force). One thing that does surprise you, however, is how much the force increases with little increase in speed. It seems to you that with only a small twist of the throttle you are pressed against the wall with such force that the two cannot be directly proportional to one another – and you are right. Speed has a squared relationship with side force: double the speed and the force increases fourfold.
Surviving the wall you’ll be happy to be back in the safety and comfort of your truck. But don’t forget, the laws of motion that applied in the bucket apply everywhere. When attempting to negotiate a bend, Newton tells you that it will take a force to alter the original course, and if you want that direction to continue to change, and you will as long as you are in the bend, the force must remain. Now, instead of the wall creating this change in direction, the truck’s tyres apply the necessary force, accelerating you towards the centre of the circle. If the side force becomes too great, then just like in the bucket, it will overcome the effect of the weight of the vehicle. This time, however, it doesn’t provide stability; it destroys it and the truck rolls over.
In the days when no self-respecting Leyland Marathon or Ford Transcontinental would be seen without a set of furry dice hanging down the inside of the windscreen, the driver had an instant indication of the effects of Newton’s laws. As the tyres forced the truck into a curved path, the dice were the last things to follow on, appearing to swing in the opposite direction to the truck’s turn as they attempted, in reality, to travel straight ahead. The greater the side force, the greater the angle of swing. It’s hard to imagine how you could compare the forces acting on a pair of furry dice with those acting on a truck, until you remember your experiences in the bucket. When you increased speed, the side force increased, but there was no change in mass – you and the bike remained the same; no new material was added to either of you. The increase in force was purely down to an increase in its acceleration and the only things that affect this lateral acceleration are the radius of the curved path and the speed at which you travel round it.
This result is very useful: it means that when considering a vehicle’s stability, we can (in most areas) disregard its mass and just concentrate on accelerations. We know that a side force acts on the vehicle as it travels through a bend, and that there is acceleration in the same direction as the force. We also know that the vehicle’s weight is a force and that force has an acceleration; the acceleration due to gravity. So, as your truck travels through a bend, the lateral acceleration and how it compares with the acceleration due to gravity are all we need concern ourselves with. The dice will have the same accelerations acting on them, as they are attached to the truck, and although the force acting will be vastly different, the lateral acceleration and the acceleration due to gravity will be the same for a 44 tonne truck as they are for the 4 oz dice. All the driver need to do is watch the dice as the truck settles into a bend and see how far they swing to one side. This will give an indication of how much acceleration there is to the side compared with how much there is pointing downward.
It is actually similar in principle to how a tilt-test for vehicle stability is conducted. When a vehicle is placed on the platform, the coordinates of the resultant force are compared as the bed is gradully tilted. The component of lateral acceleration (a) can then be expressed in terms of the component of the acceleration due to gravity (g). This gives a static stability factor ‘a’ over ‘g’ (a/g). However, this figure will be reduced when the vehicle is on the road for reasons that will be mentioned shortly. In theory, you should be able find the a/g factor that the truck is actually experiencing by measuring the angle the dice make to the vertical as you drive it through the bend, and then find the tangent of that angle. How much could the dice lean before the truck becomes unstable? Unfortunately, it will depend on a number of things.
There’s an added complication with any road vehicle because of the position at which the lateral acceleration (and, therefore, the side force) acts. When you rode the motorcycle around the inside of the bucket, the lateral acceleration created by the wall worked straight through the centre of gravity of both rider and machine, and the point the motorcycle touched the wall. The reaction worked in the opposite direction along the same line. Now, the lateral acceleration created by the truck’s tyres at ground level is being transmitted to the vehicle’s centre of gravity, which will be at some height above, and something similar to a leverage forms. As the vehicle travels round a bend, this leverage is working on a pivot point at the outside tyres. It is being countered by the acceleration due to gravity trying to lever the truck downward, again acting at the centre of gravity and about the same pivot point. So, now it’s not just the size of these accelerations that is important, it’s also the size of their leverages. If the leverage of the lateral acceleration is greater than that of gravity, the vehicle will become unstable. In a car, which will have a wide track width compared to the height of its centre of gravity, the leverage of the lateral acceleration never manages to exceed that created by gravity. Lateral acceleration builds until the tyre friction limit is reached and the car slides sideways. In a truck, the leverage of the lateral acceleration will usually exceed that of gravity before the limit of tyre friction, resulting in rollover.
It’s not only the height of the centre of gravity that can have an affect on rollover. Anything that causes extra body roll will assist the lever trying to pull the vehicle over by reducing the righting affect of the vehicle’s weight. Soft tyres and weak suspension, or a heavy load, are prime candidates, as is an offset or shifting load. And, as with most things, it’s never that simple. Factor in rate of change in lateral acceleration associated with some manoeuvres, the resonance of steering input with suspension frequency during sudden lane changes; and the bucket and motorcycle job doesn’t seem that bad after all. But don’t give up on truck driving too soon; there’s plenty you can do to reduce the chances of rollover.
If the truck’s stability a/g drops during cornering or the a/g it is experiencing climbs, the two factors will converge. If they meet - or worse, the truck’s stability is exceeded – you’ll probably wish you were back in the bucket. So, the lateral acceleration it is experiencing needs to be kept as low as possible and the lateral acceleration it can withstand will need to be kept as high as possible. The former is down to speed and the importance of the squared relationship it has with side force (and, therefore, lateral accelleration). Whatever lateral acceleration your speed creates has to be resisted by the trucks stability and this will decrease for a number of reasons, the most important being the height of the centre of gravity. Ultimately, the probability of rollover will only be avoided completely by careful monitoring of a/g factors, either by you or, if you’re not too good with a protractor under conditions of extreme stress, a stability program. I think I know what the answer is.
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