Minimum weight for the car is 560kg and I'm currently working with a wheelbase of 2.2 metre. We're going to be mid-engined, so I wouldn't be too surprised is we have a weight distribution somewhat towards the rear, say around 45% Front : 55% Rear. Centre of gravity height is unknown. The only useful figures I've got (I've only ever done testing of military vehicles, which probably doesn't help much) are for a Toyota MR2 at 0.485m above ground. We'll be a smidgin lower and the absence of a roof on the car will take that lower still, so I'd estimate (in finest sticking a finger in the air fashion) a centre of gravity around the 0.42m mark.
The tyres for the formula (Yokohama A048R) can produce a static coefficient of friction of around 1.2-1.3, but we may well have plenty of downforce, so it's not entirely inconceivable that we could be producing around 1.5g under braking. So, a quick spurt of calculation gives the following weight distribution:
| Front | Rear | |
| Nearside | 123.75 kg | 151.25 kg |
| Offside | 123.75 kg | 151.25 kg |
Let's now look at the weight distribution under braking. When you brake, weight is taken off the rear wheels and put on the front wheels. The amount of weight transferred is a function of mass, rate of deceleration, wheelbase and centre of gravity height. The governing equation is:
Weight Transfer = Mass x Deceleration x Centre of Gravity Height / Wheelbase
So with 1.5g deceleration, we get just under 1.6 kN of weight transferred (or 160.3 kg of mass). That's a fair chunk of mass - we end up with just 71.1 kg of mass on each rear wheel when braking, which wouldn't give me huge confidence under braking unless there was a nice, healthy chunk of downforce to screw the rear wheels down. We also have 203.9 kg on each front wheel.
At 1.5g of braking, and assuming we've wound the bias adjusters to the perfect position, each front wheel has to provide 203.9x9.81x1.5 = 3 kN of deceleration force. George Polley's website suggests that the overall diameter of a 13" A048R tyre is 550 mm, which gives us a torque produced by the braking system of 3x0.55/2 = 0.825 kNm.
I've been looking at two different brake callipers - both can use a 276mm diameter disc (that's 10.5" in old money give or take a gnat's chuff). The bigger, 4-piston, calliper uses a 46.1mm high brake pad and 4 1.25" diameter pistons and the smaller, 2-piston, calliper uses a 38.4mm high brake pad and two 1 5/8" diameter pistons. The coefficient of a brake pad varies a bit, but Ferodo DS2500 compound (I know a lot of racers use Mintex, but Mintex don't publish their mu values and Ferodo do) has a mu value of 0.5, so effectively the deceleration force at the rotor needs to be doubled to give a force at the piston.
I'm going to assume an even distribution of force across the whole of the brake pad so that the centroid of that force is in its centre. So the effective radius for the application of the braking force is going to be (disc diameter - pad height) / 2, or 110.45mm for the 4-piston callipers and 114.3mm for the 2-piston callipers. Torque = Force x Distance, so the piston force = torque / distance (x 2 to allow for the pad friction coefficient). Running with the values earlier, we get the following numbers: 7.2 kN for the 2-piston callipers and 7.5 kN for the 4 piston callipers.
Pressure = Force / Area, so we can now calculate the pressure required in the braking lines at the front. It comes out at 24 Bar for the 4 piston design and 27 Bar for the 2 piston design. The callipers are rated at 30 Bar, so they're man enough for the job and all we need to do now is sort out whether our poor race will actually be able to apply enough pressure at the brakes to get that level of deceleration. The ECE braking regulations mandate a brake pedal force of around 500N for stopping with the engine disengaged. So if we assume this is our pedal force and a pedal ratio (amplification by the lever action) of around 5, we have a pedal force of 2.5 kN. This means we need an area ratio of around 3, i.e. the area of the calliper pistons needs to be no more than three times the area of the master cylinder piston. For our 4 piston calliper we get a piston diameter of 36mm and for our 2 piston callipers we get a maximum diameter of 58 mm. These comfortably fit within the bounds of what is available and give plenty of options for fine tuning by having a smaller pedal force ratio.
So, in summary, the 2 piston callipers and 13" wheels will be fine, and in a desire to make as many people happy as possible, I'll engineer the uprights and suspension to fit under 13" rims. I've got a nice steel rim handy - I'll measure that if this rain ever stops falling.
At 1.5g of braking, and assuming we've wound the bias adjusters to the perfect position, each front wheel has to provide 203.9x9.81x1.5 = 3 kN of deceleration force. George Polley's website suggests that the overall diameter of a 13" A048R tyre is 550 mm, which gives us a torque produced by the braking system of 3x0.55/2 = 0.825 kNm.
I've been looking at two different brake callipers - both can use a 276mm diameter disc (that's 10.5" in old money give or take a gnat's chuff). The bigger, 4-piston, calliper uses a 46.1mm high brake pad and 4 1.25" diameter pistons and the smaller, 2-piston, calliper uses a 38.4mm high brake pad and two 1 5/8" diameter pistons. The coefficient of a brake pad varies a bit, but Ferodo DS2500 compound (I know a lot of racers use Mintex, but Mintex don't publish their mu values and Ferodo do) has a mu value of 0.5, so effectively the deceleration force at the rotor needs to be doubled to give a force at the piston.
I'm going to assume an even distribution of force across the whole of the brake pad so that the centroid of that force is in its centre. So the effective radius for the application of the braking force is going to be (disc diameter - pad height) / 2, or 110.45mm for the 4-piston callipers and 114.3mm for the 2-piston callipers. Torque = Force x Distance, so the piston force = torque / distance (x 2 to allow for the pad friction coefficient). Running with the values earlier, we get the following numbers: 7.2 kN for the 2-piston callipers and 7.5 kN for the 4 piston callipers.
Pressure = Force / Area, so we can now calculate the pressure required in the braking lines at the front. It comes out at 24 Bar for the 4 piston design and 27 Bar for the 2 piston design. The callipers are rated at 30 Bar, so they're man enough for the job and all we need to do now is sort out whether our poor race will actually be able to apply enough pressure at the brakes to get that level of deceleration. The ECE braking regulations mandate a brake pedal force of around 500N for stopping with the engine disengaged. So if we assume this is our pedal force and a pedal ratio (amplification by the lever action) of around 5, we have a pedal force of 2.5 kN. This means we need an area ratio of around 3, i.e. the area of the calliper pistons needs to be no more than three times the area of the master cylinder piston. For our 4 piston calliper we get a piston diameter of 36mm and for our 2 piston callipers we get a maximum diameter of 58 mm. These comfortably fit within the bounds of what is available and give plenty of options for fine tuning by having a smaller pedal force ratio.
So, in summary, the 2 piston callipers and 13" wheels will be fine, and in a desire to make as many people happy as possible, I'll engineer the uprights and suspension to fit under 13" rims. I've got a nice steel rim handy - I'll measure that if this rain ever stops falling.
1 comment:
You ask for mintex mu values I give you mintex mu values:
http://www.toyotaimportsforum.co.uk/articles/article.php?cat=&id=11
Current pick of the bunch for the wilwood powerlite calipers is the polymatrix A compound:
http://brakepads.wilwood.com/02-graphs/a.gif
And for pagid pads:
http://keith.maddock.com/bremsen/pagid-compound.jpg
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