How to select a proper hand brake.
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Joined: Sep 2006
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From: Vancouver, BC, Canada
How to select a proper hand brake.
I don't know how much help this will be to someone. I am pretty sure that I am correct but if you know better let me know.
So I was bored today and decided to see if I can figure out the whole idea behind different bore sizes of master cylinders and calipers. After an exhaustive search on-line and being unable to find anything satisfactory from one source I've decided to write this little article. I don't know how true it is but this is what I came up with. If any of you know something else and want to contribute please let me know.
We all know that brake master cylinders come in various bore sizes and brake calipers come with different number of pistons as well as different bore sizes. The question is how do you match up the master cylinder with the right caliper to get the result that you are looking for. What bore sizes do master cylinder and caliper have to be to achieve smooth gentle braking, two finger lock-up, or a long endo.
To figure what combination of master cylinder and caliper we want we need first need to revisit the internal structure of the master cylinder and the caliper as well as grade 12 physics. The entire brake assembly is nothing but a hydraulic system and is pictured bellow:
Fig. 1: Internal design of a hydraulic braking system. [1]
When you apply pressure on the brake lever it pushes a piston into the master cylinder and increases the pressure on the brake fluid. The fluid itself hardly moves, but the pressure increase is transmitted to the brake caliper's piston which pushes the brake pad onto the spinning rotor and slows down the motorcycle.
We know that the harder you squeeze the brake lever the higher the pressure inside the brake line and the harder the brakes bite. If you squeeze the brake lever and the brake bites too hard you will lock up the tire. If you squeeze the lever and the brakes bite very “gently” or not at all you won't be able to stop in time or control your balance in a wheelie. The effectiveness of the pressure that you apply and the time and manner in which you stop depends on the ratio of the surface area of the master cylinder and the surface area of the caliper's piston and is described by Pascal's principle. Basic description of the principle is such: If you increase the pressure at one point in a liquid by pushing a piston in, that pressure increase is transmitted to all points in the liquid. A second piston at some other point in the fluid can then push outward and do useful work. [2]. The usefulness of this work is what we are trying to determine.
One advantage of the hydraulic system over simple mechanical linkages is the possibility of force multiplication [2]. Force multiplication can also be described as the ratio between the surface area of the master cylinder piston and the surface area of the caliper piston. Let's see how this force multiplication applies to our braking system. As an example I am going to use the stock specifications for an 03 Honda CBR F4i rear brake caliper and master cylinder. According to Honda USA the diameter of the rear brake caliper is: IN-38.180mm to 38.230mm and OUT-38.098mm to 38.148mm and for the master cylinder IN is 14.000mm to 14.043mm and OUT is 13.957mm-13.984mm. The difference between the IN and OUT pistons won't be described as it is not relevant to our calculations. In reality of the structure of the master cylinder on the motorcycle is much more complicated so for our purposes we'll be using the simplified version to demonstrate the principle.
We'll assume that our braking system has a brake caliper with the diameter of 38mm and master cylinder of 14mm. The surface area is π(radius)2 and radius is diameter devided by 2.
Brake caliper surface area is: π(19) 2= 1134.11mm2.
The master cylinder surface area is: π(7) 2= 153.94mm2.
The force multiplication is 1134.11/153.94 and is equal to 7.36.
This means that if you apply pressure on the master cylinder of 1kg/mm2 it will translate to 7.36kg/mm2 at the caliper piston. The more pistons you add the higher is the force multiplication. So if you have a 2 piston caliper the total force multiplication will be 14.72, and 4 pistons will be 29.44. Manufactures increase the number of pistons in the brake calipers to help the motorcycle stop faster with less force applied to the brake lever. This table provides relative reference numbers to the force multiplication of various diameters of brake caliper pistons and master cylinder pistons.
Table 1: Force multiplication number based of different master cylinder and caliper bore sizes. [3]
Once you know the diameter of your caliper piston and the result you'd like to achive you can find out what bore diameter of the master cylinder should be. If you want a brake that will grab instantly look for the highest force of multiplication number. If you want the brake to barely grab then look for the lowest force of multiplication number.
Before you decide what bore size your hand brake should be find out the diameter of the rear caliper as well as how many pistons it has. This is what ultimately determine the feel and effectiveness of the brake. Same concept applies for the front brakes and can be used as a guide for track setup on race bikes.
[1].Tim Remus et al. “A Guide To Hydraulic Ratios And Picking Master Cylinders How To Match Masters And Calipers”. www.bikernet.com/wolfgang/PageViewer.asp?PageID=911, (Nov. 2, 2007)
[2]. Randal D. Knight, “Physics for Scientists and Engineers”, Vol. 1 pg.457 (2004)
[3]. http://www.vintagebrake.com/mastercylinder.htm (Nov. 2, 2007)
So I was bored today and decided to see if I can figure out the whole idea behind different bore sizes of master cylinders and calipers. After an exhaustive search on-line and being unable to find anything satisfactory from one source I've decided to write this little article. I don't know how true it is but this is what I came up with. If any of you know something else and want to contribute please let me know.
We all know that brake master cylinders come in various bore sizes and brake calipers come with different number of pistons as well as different bore sizes. The question is how do you match up the master cylinder with the right caliper to get the result that you are looking for. What bore sizes do master cylinder and caliper have to be to achieve smooth gentle braking, two finger lock-up, or a long endo.
To figure what combination of master cylinder and caliper we want we need first need to revisit the internal structure of the master cylinder and the caliper as well as grade 12 physics. The entire brake assembly is nothing but a hydraulic system and is pictured bellow:
Fig. 1: Internal design of a hydraulic braking system. [1]
When you apply pressure on the brake lever it pushes a piston into the master cylinder and increases the pressure on the brake fluid. The fluid itself hardly moves, but the pressure increase is transmitted to the brake caliper's piston which pushes the brake pad onto the spinning rotor and slows down the motorcycle.
We know that the harder you squeeze the brake lever the higher the pressure inside the brake line and the harder the brakes bite. If you squeeze the brake lever and the brake bites too hard you will lock up the tire. If you squeeze the lever and the brakes bite very “gently” or not at all you won't be able to stop in time or control your balance in a wheelie. The effectiveness of the pressure that you apply and the time and manner in which you stop depends on the ratio of the surface area of the master cylinder and the surface area of the caliper's piston and is described by Pascal's principle. Basic description of the principle is such: If you increase the pressure at one point in a liquid by pushing a piston in, that pressure increase is transmitted to all points in the liquid. A second piston at some other point in the fluid can then push outward and do useful work. [2]. The usefulness of this work is what we are trying to determine.
One advantage of the hydraulic system over simple mechanical linkages is the possibility of force multiplication [2]. Force multiplication can also be described as the ratio between the surface area of the master cylinder piston and the surface area of the caliper piston. Let's see how this force multiplication applies to our braking system. As an example I am going to use the stock specifications for an 03 Honda CBR F4i rear brake caliper and master cylinder. According to Honda USA the diameter of the rear brake caliper is: IN-38.180mm to 38.230mm and OUT-38.098mm to 38.148mm and for the master cylinder IN is 14.000mm to 14.043mm and OUT is 13.957mm-13.984mm. The difference between the IN and OUT pistons won't be described as it is not relevant to our calculations. In reality of the structure of the master cylinder on the motorcycle is much more complicated so for our purposes we'll be using the simplified version to demonstrate the principle.
We'll assume that our braking system has a brake caliper with the diameter of 38mm and master cylinder of 14mm. The surface area is π(radius)2 and radius is diameter devided by 2.
Brake caliper surface area is: π(19) 2= 1134.11mm2.
The master cylinder surface area is: π(7) 2= 153.94mm2.
The force multiplication is 1134.11/153.94 and is equal to 7.36.
This means that if you apply pressure on the master cylinder of 1kg/mm2 it will translate to 7.36kg/mm2 at the caliper piston. The more pistons you add the higher is the force multiplication. So if you have a 2 piston caliper the total force multiplication will be 14.72, and 4 pistons will be 29.44. Manufactures increase the number of pistons in the brake calipers to help the motorcycle stop faster with less force applied to the brake lever. This table provides relative reference numbers to the force multiplication of various diameters of brake caliper pistons and master cylinder pistons.
Table 1: Force multiplication number based of different master cylinder and caliper bore sizes. [3]
Once you know the diameter of your caliper piston and the result you'd like to achive you can find out what bore diameter of the master cylinder should be. If you want a brake that will grab instantly look for the highest force of multiplication number. If you want the brake to barely grab then look for the lowest force of multiplication number.
Before you decide what bore size your hand brake should be find out the diameter of the rear caliper as well as how many pistons it has. This is what ultimately determine the feel and effectiveness of the brake. Same concept applies for the front brakes and can be used as a guide for track setup on race bikes.
[1].Tim Remus et al. “A Guide To Hydraulic Ratios And Picking Master Cylinders How To Match Masters And Calipers”. www.bikernet.com/wolfgang/PageViewer.asp?PageID=911, (Nov. 2, 2007)
[2]. Randal D. Knight, “Physics for Scientists and Engineers”, Vol. 1 pg.457 (2004)
[3]. http://www.vintagebrake.com/mastercylinder.htm (Nov. 2, 2007)
Registered User
Joined: Feb 2005
Posts: 1,156
From: mechanicsburg PA
Re: How to select a proper hand brake.
BREMBO 16X18 RADIAL MASTER!!!! on any stuntbike....no matter if ur running dual caliper or adapter style junction valve....u cant go wrong with the brembo...so smooth and progressive and lots of stopping power!!! woo hoo
Registered User
Joined: Jun 2022
Posts: 1
Re: How to select a proper hand brake.
OP: Lay's down the science
brembo fan boi: *shïts and pisses*
Hahahaha just had to say it. I thought it was hilarious. Anyways, SOLID post my friend. You're a life saver. You can now commit one crime and have legal immunity as a reward for your contributions.
But I will add that in the calculations for the simplified version the pie is unnecessary as the proportions still measure out the same. Aka 19squared/7squared still equals 7.367
brembo fan boi: *shïts and pisses*
Hahahaha just had to say it. I thought it was hilarious. Anyways, SOLID post my friend. You're a life saver. You can now commit one crime and have legal immunity as a reward for your contributions.
But I will add that in the calculations for the simplified version the pie is unnecessary as the proportions still measure out the same. Aka 19squared/7squared still equals 7.367
Last edited by Blahhahablah; Jun 1, 2022 at 11:33 AM.
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