GrahamFountain wrote:tom16v wrote:I am not a qualified engineer and have only A level physics to call on, so need this explaining in lay mans terms if possible please.
I've had a go at an explanation of what changes the effectiveness of the brakes, if not exactly in layman's terms, at least with nothing above 'A' level physics involved:
The increase in brake effort for a front brake upgrade is simply the increase in piston area multiplied by the increase in the distance between the hub and the pressure centre of the pad, i.e. the increase in force on the pad, for a given hydraulic pressure, times the increase in leverage.
The area of tha pad isn't relevant to the increase in effort (Amontons' second law), and only affects the way the pad heats up, for a given amount of braking effort, and thus only affects the way the brakes fade – bigger pads will fade less quickly. Similarly, venting the discs only affects the way the disc and the pads heat, and thus reduces fade, but does not change the brake effort (well it will reduce it very, very slightly in normal use, because the pads will run a bit cooler and thus have a very slightly lower coefficient of friction; up to the point where the unvented ones fade). The effect of moving the pressure centre further out is only the increased leverage, even though the pads are running on a faster part of the disc (Coulomb's Law of friction).
It is also true that bigger pistons affect the "length" of the pedal, i.e. how far you have to press the pedal to get the same pressure on the pad, but that has no significant effect on ratio between the hydraulic pressures at the front and rear brakes once everything has stopped moving. I do need to look closely at how the load sensing valve works, and if anyone has a proper description anywhere, that would be interesting. I know how the brake balance pressure reducing valve on the TR7 works, but I guess that's quite different.
There is a bit of a problem with calculating the increase from moving the pressure centre, in that it's not obvious where the pressure centre of a brake pad is. However, the pressure centre should be close to the geometric centre of area (centroid) of the pad, or the pad would wear funny. So, the ratio between the distances of the centroids from the hub should be very, very close to the ratio between the distances to the pressure centres.
Increasing the effort by increasing the piston size also changes the length of the pedal, how much further you have to push it to get the same hydraulic pressure as before. Increasing the effort from the front brakes by either means obviously changes the brake balance, biasing them more to the front.
Biasing the brakes to the front is important if you are also increasing the grip from the tires, as the perfect balance – where front and back wheels lock at the same time – moves forward with increasing grip. That's just because the better tires let you decelerate more quickly, before the wheels lock, and the better brakes let you take advantage of that better grip. And as you decelerate more quickly, there's more weight transfer - more dive at the front and more lift at the back. So if the perfect balance moves forward, which means the back wheels are more likely to lock, you need to move the actual balance forward to keep the car the same safe distance in front of where the back wheels might lock first.
As said, upgrading the front brakes does move the actual balance forward, but how much the change is needed depends on where the centre of gravity is, specifically how high off the road. So a given brake upgrade may or may not change it enough for a given tire upgrade.
One of the big problems in doing a proper analysis is that I don't know where to set the CofG for the worst case – the situation that moves the perfect brake balance forward the most. I also have limited information on tire grip. There's some info in text books, research papers, and general web pages, but to do the job properly, what's needed is the change in coefficient of friction between the tires fitted as standard in the 70s and 80s and the sort of tires we might fit today. There's also a question of what tires Triumph might have allowed for owners fitting when they set the safety margin between the actual and perfect brake balance.
As an aside, that issue of tire grip includes the effects of wider tires as well. While Amontons' second law says the apparent area of contact between solid surfaces does not affect the ratio between the forces – i.e. doesn't affect the coefficient of friction – rubber isn't a solid in that sense. Hence, wider tires give better grip, and worn treaded tires give more grip than new ones. Why that should be is a bit beyond A level physics, but there is some research available on the internet that discusses it.
Graham
