Hello again Allan,
You have made several references to Newtons Laws. To be clear on what we are saying I quote published texts:
First law:
Every body continues in its state of rest or of uniform motion in a straight line unless acted upon by some external force.
Second law
The rate of change of momentum of a body is proportional to the applied force and takes place in the direction in which the force acts.
Third Law:
To every action there is an equal and opposite reaction.
All three laws are relevant to the braking issue.
We accept that braking is a force, which acts against the velocity of a body. It does this by causing friction between the moving and non moving surfaces.
The degree of friction is controlled by modulating the pressure between the friction surfaces.
The amount of energy attributable to a moving mass is defined as the mass x its velocity otherwise known as momentum.
In the context of the arguments in this thread, we assume that the different vehicle masses are travelling at the same starting velocity before the brakes are applied.
if a laden vehicle has twice the mass of the unladen vehicle then from the laws above their respective momentums will be in the same ratio i.e 2:1.
If both vehicles had the same braking force applied, then the laden vehicle will take twice the distance to stop.
In the real world the braking efforts would not be the same, because, as has been stated else where the maximum braking effect occurs when the wheel is just about to loose grip (i.e skidding) So to achieve that operating point so the wheel does continue to turn, the pressure in the braking system is modulated either by an ABS system or by the driver.
It is now important to understand that the grip between the tyre and the ground is dependant on the down force pushing the wheel to the ground
For the unladen vehicle there is less mass for gravity to act on, thus grip quotient is less than for the laden vehicle.
So whilst the heavier vehicle has greater momentum, and will need to convert more energy to heat, it is also the case that because of the greater weight force, more braking effort can be applied, so the same vehicle both empty and laden can achieve the same stopping distances.
In addition to this, for most vehicles as the load is increased the centre of gravity is likely to rise. Under braking the mass tries to tip forward and the higher it is the great this effect is. It has the effect of transferring some of the weight to the forward axle, and this allows even more braking force to be applied thus improving retardation.
There are some riders to this:
All elements of the vehicle should be designed to cope with the maximum load and work duty.
The braking should be done in a straight line.
The driver should be able to apply sufficient force to the brake system to achieve the retardation rate.
The driver must be conscious of the load and the ability of the vehicle to contain the load under heavy breaking.
Clearly if a breaking system cannot cope with the mass, then stopping distances would increase, but also the vehicle is over loaded.
All this is fine in theory, and under ideal conditions the theory could be demonstrated, but most road conditions are not ideal, so it is sensible to give large vehicle more space for braking.
You have made several references to Newtons Laws. To be clear on what we are saying I quote published texts:
First law:
Every body continues in its state of rest or of uniform motion in a straight line unless acted upon by some external force.
Second law
The rate of change of momentum of a body is proportional to the applied force and takes place in the direction in which the force acts.
Third Law:
To every action there is an equal and opposite reaction.
All three laws are relevant to the braking issue.
We accept that braking is a force, which acts against the velocity of a body. It does this by causing friction between the moving and non moving surfaces.
The degree of friction is controlled by modulating the pressure between the friction surfaces.
The amount of energy attributable to a moving mass is defined as the mass x its velocity otherwise known as momentum.
In the context of the arguments in this thread, we assume that the different vehicle masses are travelling at the same starting velocity before the brakes are applied.
if a laden vehicle has twice the mass of the unladen vehicle then from the laws above their respective momentums will be in the same ratio i.e 2:1.
If both vehicles had the same braking force applied, then the laden vehicle will take twice the distance to stop.
In the real world the braking efforts would not be the same, because, as has been stated else where the maximum braking effect occurs when the wheel is just about to loose grip (i.e skidding) So to achieve that operating point so the wheel does continue to turn, the pressure in the braking system is modulated either by an ABS system or by the driver.
It is now important to understand that the grip between the tyre and the ground is dependant on the down force pushing the wheel to the ground
For the unladen vehicle there is less mass for gravity to act on, thus grip quotient is less than for the laden vehicle.
So whilst the heavier vehicle has greater momentum, and will need to convert more energy to heat, it is also the case that because of the greater weight force, more braking effort can be applied, so the same vehicle both empty and laden can achieve the same stopping distances.
In addition to this, for most vehicles as the load is increased the centre of gravity is likely to rise. Under braking the mass tries to tip forward and the higher it is the great this effect is. It has the effect of transferring some of the weight to the forward axle, and this allows even more braking force to be applied thus improving retardation.
There are some riders to this:
All elements of the vehicle should be designed to cope with the maximum load and work duty.
The braking should be done in a straight line.
The driver should be able to apply sufficient force to the brake system to achieve the retardation rate.
The driver must be conscious of the load and the ability of the vehicle to contain the load under heavy breaking.
Clearly if a breaking system cannot cope with the mass, then stopping distances would increase, but also the vehicle is over loaded.
All this is fine in theory, and under ideal conditions the theory could be demonstrated, but most road conditions are not ideal, so it is sensible to give large vehicle more space for braking.
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