Let's do some simple math and see what the difference in pressure will be between a 111/416 (1.0625 inches) and a 71/48 (0.875 inch) master cylinder. We're going to assume 50 pounds of brake-pedal effort, a brake-pedal ratio of 6:1, and a front-brake caliper with two pistons, each with a diameter of 1.5 inches.
First we have to calculate the area of the two different master-cylinder pistons. We have to convert these piston diameters into square inches of area. The formula is as follows:* Area = radius squared x pi (3.1417)-let's simplify that to:* Area = diameter x diameter x 0.7854* 1.0625 x 1.0625 x 0.7854 = 0.887 square inches of piston area* 0.875 x 0.875 x 0.7854 = 0.601 square inches of piston area
We also have to calculate the area of two, 1.5-inch-diameter caliper pistons used in our typical two-piston brake caliper. The formula here is to calculate the area of each piston and add them together.* 1.5 x 1.5 x 0.7854 = 1.77 square inches of area for one piston plus another 1.77 square inches for the second piston, which equals a total of 3.54 square inches of caliper piston area.
To calculate the line pressure created by the master-cylinder piston area, we'll use this formula:* Pedal force x pedal ratio / piston area = line pressure (psi)* Big piston master = 50 pounds X 6 / 0.887 = 338 psi* Small piston master = 50 pounds x 6 / 0.601 = 499 psi
From line pressure alone, you can see the advantage of the smaller piston. But now that advantage is multiplied by the diameter of the caliper piston. The larger the caliper piston, the more pressure is multiplied. In our example, the two-caliper pistons generate a total of 3.54 square inches. Hydraulic pressure (in psi) created by the master-cylinder piston now multiplies the pressure times the area of the brake-caliper piston.* Big-piston master cylinder = 338 psi x 3.54 sq. in. = 1,196 psi of pad force* Small-piston master cylinder = 499 psi x 3.54 sq. in. = 1,767 psi of pad force
The force difference on the caliper pad between the big and small master-cylinder pistons is 47.6 percent! The smaller master-cylinder piston creates almost half again as much caliper force. With the larger 111/48-inch-diameter master-cylinder piston, your car won't stop without a ton of pressure on the brake pedal. It's possible a 1-inch master cylinder will also work well in your application. Either way, you can see it's critically important to properly match brake components.
I can't take credit for the math involved with this answer (if you saw my high school algebra grades, you'd know why). For this information, I referenced the HP Trade title Brake Handbook by Fred Puhn that unfortunately is out of print. If you're interested, used copies of this book are still available at amazon.com, but the prices are a bit steep at around $50 a copy. HP does have a current book titled Brake Systems by Mike Mavrigian and Larry Carley that sells on amazon.com for cheap.