Wonders of Science, pt. 2, brakes this time Options

[lapuwali]

The recent revival of the 4-lug vented rotor thread (which I also look on with interest) has revived some more old equations I fooled with in my motorcycling days.

Back then, I had a pair of Hondas with terrible brakes, which had brake parts very similar to other models with excellent braking. Puzzled, I did some investigation.

The two bikes had different kinds of bad brakes. One felt squishy no matter how much bleeding one did, and had a "long" lever, sometimes coming all the way back to the bar. The other felt wooden, with underpowered brakes. One chief difference was the "wooden" feeling bike had a 0.5in diameter master cylinder with one two-piston caliper, while the other, squishy-feeling one had a 10mm master cylinder (don't ask why one was metric and the other not, that was just Honda's way) with two of the very same two-piston calipers. (Talking just front brakes here).

Apparent brake power is easily described by the ratio of the areas of the master cylinder piston and the brake caliper piston. Doing the math, I found that the "wooden" feeling bike had a ratio of 13:1 (total caliper piston area was 13 times the master cylinder piston area). The "squishy" bike had a ratio of 40:1. The standard explanation is that a larger ratio will give more force at the calipers for a given lever force, at the expense of more lever travel. With a ratio that's way too high, the lever can't move far enough (that is the master cylinder piston can't move far enough) to move enough fluid to even press the pads firmly against the rotors. With a smaller ratio, you get less lever travel, but more force is required at the lever for a given force at the calipers.

Looking at some of the other bikes with excellent brake feel showed that their ratios all clustered around 20:1. Higher ratios felt a tad more powerful, lower ratios had better "feel". By "higher", I mean "higher numerically", so 20:1 is higher than 18:1. Doing the numbers on the two "bad" bikes, I found if I simply swapped master cylinders between them, the ratios would move to closer to 20:1 (one exactly, the other to 25:1). Did that, and the results were a significant improvement according to everyone that tested them.

Now, there are many other factors in brake feel and power; things like: caliper flex, the mechanical advantage provided by the lever ratio of the foot pedal, front-rear proportional split, the mechanical advantage of rotor diameter, etc. Cars are different enough that I didn't think these "magic" ratios from the bike world would make any sense. Didn't stop me from running the numbers, anyway.

914s have unservo'd brakes, and a straight front/rear split, so there's some chance...

914/4 calipers have 42mm pistons, and there are four of them in the front braking system, so that's 5540 sq. mm of total area. With a 17mm master cylinder (227 sq. mm), the ratio is 24:1. Hm. With a 19mm master cylinder (283sq.mm), it's 20:1. Very interesting. These numbers are very close to the magic ratio. Personally, I find a 19mm MC with stock /4 calipers to be "too hard", so it's possible the magic ratio for cars is higher than 20:1. I've never managed to drive a 914 with a 17mm MC, so I can't say if that's "squishy", or "just right", or "still too hard'. The exact number near 20:1 is mostly a matter of taste, but ratios far away from 20:1 are likely to be universally disliked.

The two most commonly (it seems) "other" front calipers fitted to these cars (BMW 320i and the 911 M) both have 48mm pistons, four total for both calipers. That's 7236 sq. mm of total area, and they produce these ratios: 17mm 32:1, 19mm 26:1. Both should be "too squishy" by the magic ratio standard, although the 19mm seems to be within the "magic tolerance". They'll certainly provide a LOT more braking force for a given pedal force, but the pedal will be pretty long with the 17mm MC. To reach the magic ratio, an MC of 21mm would be required.

So, despite the apparent vast difference between car and bike brake setups, the same ratios seem to follow, at least for non-servo brakes with a proper front/rear split.

[McMark]

Thanks for the info. Very interesting read.