How to Slow Down Faster: The Math behind Brakes. Part 6, Tuning It

brake2

Part 1 is here.

Part 2 is here.

Part 2b is here.

Part 3 is here.

Part 4 is here.

Part 4b is here.

Part 5 is here.

     Ok so last time we figured out that with a .9 deceleration, our front tires produce .970 gs of friction, while our rear tires produce .942 gs of friction.  That’s nearly perfect.  Now, with a 1.2 g deceleration we get 1.310 gs and 1.632 gs respectively.  Our goal now is to further balance them out so the gap between the front and rear frictions are almost the same.  I stated last time that since we’re dealing here with semi-race cars, the brake pads we’ll use will be limited.  I’ll upgrade here to the EBC Yellowstuffs, with a coefficient of friction of .55 instead of our old .50 and then install 99 spec Brakes and then compare that to AP Racing’s 6 Pot Caliper Big Brake Kit.

     Let’s start with Mazda’s 99 spec brakes (they offer an increase in both front and rear rotor sizing, as well as front caliper piston sizing) and see if they balance/unbalance both a .9 and 1.2 decelerations (I won’t show the whole process again, only the changes and results for comparison) :

Front Caliper Piston Diameter (in): [1.33464 in] + [1.50000 in] (actual value)

Rear Caliper Piston Diameter (in): [1.42124 in]. (actual value)

Mu of Brake Pad (unitless): [0.55] (EBC Yellowstuffs) (actual value)

Front Rotor Diameter (in): [12.3622 in]. (actual value)

Rear Rotor Diameter (in): [12.3622 in]. (actual value)

     As you can see, there are changes to the front and rear rotor size, as well as the front caliper piston diameters.  Instead of two piston of the same size, we have one smaller piston before the larger one to prevent brake tapering.  Also, with the upping of the rotor size, we have an increase in brake capacity, as well as thermal capacity.  So lets start:

= [1.399 in^2] + [1.767 in^2] for the Front Inboard Caliper Piston Area  (in^2).

= [1.586 in^2] for the Rear Inboard Caliper Piston Area  (in^2).

= [5.431 in] for the Front Rotor Effective Radius (in).

= [5.470 in] for the Rear Rotor Effective Radius (in).

= [2210.612 lb] for the Front Brake Force (lb) (per axle). vs [1887.219 lb]

= [1115.353 lb] for the Rear Brake Force (lb) (per axle). vs [943.609 lb]

     As we can see, the upgrades to the brake system for the 1999 rx7 increased its brake force, both in front and back.  And just looking at the rear, even though we didn’t change the calipers, just by increasing the rotor size we get an increase in brake force (even though I upgraded to better brake pads, if you use the previous brake pads, we still get an increase in brake force).  That proves that just by increasing rotor size without even changing brake pads or increasing the number of caliper pistons, we can get an increase in brake force.  Now lets plug in those numbers and factor in weight transfer to find our deceleration/Mu.

     First for a .9 g deceleration:

= [2.270 g] for the Front Coefficient of Friction. vs [1.938 gs]

= [1.135 g] per front tire. vs [.970 gs]

= [2.225 g] for the Rear Coefficient of Friction. vs [1.883 gs]

= [1.113 g] per rear tire. vs [.942 gs]

     Now with a 1.2 g deceleration:

= [2.100 g] for the Front Coefficient of Friction. vs [1.793 gs]

= [1.050 g] per front tire. vs [.897 gs]

= [2.640 g] for the Rear Coefficient of Friction. vs [2.234 gs]

= [1.320 g] per rear tire. vs [1.117 gs]

     Here we can see that our upgraded brake system outputs more brake force and thus increases our deceleration, although if the tire can put that to use is a different question.  Our previous decelerations at .9 gs were .970 gs of friction for the front and .942 gs of friction for the rear.  They have both been increased about 10-15% each, to 1.135 gs and 1.113 gs.  You see the same with the 1.2 gs of deceleration, although there the front and rear still aren’t balanced out.  We’ll try out our new AP Racing Brake Kit (which only offer an upgrade for the front brakes) next, leaving the rears as stock and seeing what that does for out braking system.

Front Caliper Piston Diameter (in): [1.060 in] + [1.250 in] + [1.500 in] (actual value)

Rear Caliper Piston Diameter (in): [1.42124 in]. (actual value)

Mu of Brake Pad (unitless): [0.55] (EBC Yellowstuffs) (actual value)

Front Rotor Diameter (in): [12.992 in]. (actual value)

Rear Rotor Diameter (in): [11.6 in]. (actual value)

     Here our Big Brake Kit upgrades only the front brakes, leaving the rears as stock.  I’ll be reverting back to our normal stock rear brakes, and not use the 99 spec brakes.  I’ll also use the EBC Yellowstuffs as well.  You can see here that we’ve increased the number of caliper pistons to 3, with the smallest being 1.06 inches, and the largest being 1.5 inches.

= [.882 in^2] + [1.227 in^2] + [1.767 in^2] for the Front Inboard Caliper Piston Area  (in^2).

[1.586 in^2] for the Rear Inboard Caliper Piston Area  (in^2).

[5.746 in] for the Front Rotor Effective Radius (in).

[5.089 in] for the Rear Rotor Effective Radius (in).

[2863.329 lb] for the Front Brake Force (lb) (per axle). vs [2210.612 lb] vs [1887.219 lb]

= [943.609 lb] for the Rear Brake Force (lb) (per axle)

     Once again, our Front Brake Force(lb) is upped by the massive brake kit.  The only questio now is if it actually works:

     .9 Deceleration:

= [2.940 g] for the Front Coefficient of Frictionvs [2.270 gs] vs [1.938 gs]

= [1.470 g] per front tire. vs [ 1.135 gs] vs [.970 gs]

= [1.883 g] for the Rear Coefficient of Frictionvs [2.225 gs] vs [1.883 gs]

= [.942 g] per rear tire. vs [1.113 gs] vs [.942 gs]

     1.2 g deceleration:

= [2.720 g] for the Front Coefficient of Friction. vs [2.100 gs] vs [1.793 gs]

= [1.360 g] per front tire. vs [1.050 gs] vs [.897 gs]

= [2.234 g] for the Rear Coefficient of Frictionvs [2.640 gs] vs [2.234 gs]

= [1.117 g] per rear tire. vs [1.320 gs] vs [1.117 gs]

     These brake kits are made mainly for the track, and not everyday driving, so our deceleration of “only” .9 gs is going to suffer.  Here we see that our front friction is almost 50% more than the rear ones, making our brake balance out of whack.  But for our track days where we use grippier tires, and suffer 1.2 gs of deceleration, our front brakes are finally up to par with our rear ones.  Except by a bit too much.  But we can always use a prop valve and adjust the balancing between the front and rear brakes.  What bigger brakes are mainly made for is to offer more thermal capacity so the brakes don’t catch on fire and cause the driver to crash.  But we also don’t want brakes that can’t use the full capacity of the tires and cause our stopping distances to be a mile long either.  So we try to balance out our tire grip with our brake force, as well as our brake balance between the front and rear brakes.  Causing one to have too much bias will obviously overwork one tire, and underuse another tire resulting in worse braking distances.  Next, we’ll try to work backwards, and try to create our own braking system which will offer a better balance between the front and rears while braking at 1.2 gs.  Stay tuned.

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1 Response to “How to Slow Down Faster: The Math behind Brakes. Part 6, Tuning It”



  1. 1 How to Slow Down Faster: The Math behind Brakes. Part 6, Tuning It Trackback on March 24, 2009 at 4:32 pm

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