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Old, Bold rider
2002 Honda 919, 1976 Yamaha XT500 cafe, TC-JAG TZ250
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Discussion Starter · #1 · (Edited)
Many have asked me to help with changing from a conventional axial front master cylinder (MC) to a radial, and in trying to give accurate information I came up with the following spreadsheet to help determine what piston size radial MC would be appropriate. The reason why there is so much confusion is the basic setups of the two types are quite a bit different: the axial units typically use a smaller piston size than the radials, and a lower mechanical leverage ratio at the lever than radials.

For example, my 2002 Honda 919 with stock master has a 14mm piston and the lever pivot to piston distance is 25mm, while the pivot to hand distance is ~ 90mm (When divided it is called the interaxis ratio). When the total area of all eight caliper pistons (30.15mm and 27mm) is divided by the area of the MC bore it gives a hydraulic ratio of 33.429:1, which when multiplied by the interaxis ratio produces an overall leverage ratio of 120.34:1. This is on the low side of typical for modern sintered brake pads. When I decided to switch to a radial MC for a variety of reasons, not the least of which being a desire for a slightly higher ratio for less effort at the lever and a wider engagement band to make holding the brake just this side of locking easier, I crunched the numbers for an overall ratio of ~130 - 135:1, and came up with a MC bore size of 17.5mm (actually it's 11/16ths, or 17.4625mm). Fortunately this is a size used by all years of the CBR1000, and a couple of Kawasakis. Installation of a MC obtained from a seller on EBAY confirmed the validity of the calculation -- slightly decreased lever effort, and better control near locking up.

On the subject of what ratio is desirable, and what to do if the ratio you want does not match up to an available master cylinder piston diameter: shoot for the next larger size piston and adjust the ratio using the only other parameter available to you -- the Master cylinder lever pivot to finger distance. For an example the numbers on the spreadsheet are for my 919. Change the master cylinder piston diameter to 18mm then go down to the pivot to finger parameter and change it until the overall ratio matches. Once you know approximately where to mount up the master cylinder it is easy to vary the feel on the road (well, parked next to the road) by moving the MC toward or away from the throttle.

Another factor to take into account is the coefficient of friction of the brake pads. Pad manufacturers do not make this information available for obvious reasons, so you have to go by feel here. If you are running brand X pads and like the feel they give with the stock MC enter the appropriate numbers in the spreadsheet for your system to get the stock ratio, then change the interaxis pivot to piston / pivot to finger and piston diameter numbers for the MC you want to run. If, however, the pads are too sensitive or "grabby", decrease the stock ratio by about 5% to start. Conversely, if they have adequate power but take too much effort at the lever increase the ratio by 5%. Then vary the pivot to finger number to obtain the desired ratio. You get the idea.

FYI: The typical range of ratios for modern brakes are from ~115:1 to 145:1 or a little more. Lower than 115 will give a lever that pulls back a short distance then feels rock hard, but takes too much effort at the lever to stop. Higher than 145 to 150 will take more lever travel to engage the brakes, but will require less force at the lever, usually feeling too sensitive when braking.

The spreadsheet: written in MS works, will also open in Excel.

It will work for up to 6 pistons. It will also work for single acting calipers as while there are pistons on only one side, the rear wall of the bore the pistons operate in acts as a second piston, moving the entire caliper body to apply force to the inside pads. They are calculated in the same manner as the double acting calipers.

Link: Master cylinder calculator updated 4 Mar 2021.xlr
Rob
 

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McTavish
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Frankly, given the number of threads and posts re what master to use with what caliper set I've seen here over the years, I'm shocked that virtually no one is bothering to even comment on Rob's thread.
 

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Made it a "Sticky Thread" so whenever someone does need to use the calculator, it will be easier to find. Thanks Rob for taking the time to put it together.
 

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TEXAN
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I like the comment about sliding calipers, and how both sides of the hydraulic cavity are doing work (and therefore the calc is the same as for a fixed caliper with pistons on both sides). Easy to visualize that way.
 

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Awesome. Glad we got these smart guys around.
 

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I trying to use the spreadsheet but I have a few question.

If I am using 2 calipers with 2 x 27mm pistons do I use 22 for caliper large diameter and mid ?

also, I'm not quite sure what to measure for Master cylinder lever pivot to finger and Master cylinder lever pivot to piston ???

Can someone help me out ?

this is the Nissin Brake master cyl 14mm that I plan of using replacing a 11mm MC with a single 2 x 27mm pistons caliper
 

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Old, Bold rider
2002 Honda 919, 1976 Yamaha XT500 cafe, TC-JAG TZ250
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Discussion Starter · #10 ·
The pivot to piston distance can be found amongst the measurements on the illustration on the left (that's 25mm). The pivot to finger distance is the one that you have to determine: the 174mm distance on the illustration on the right only gives the total length of the lever. The distance you need is from the center of the lever pivot bolt to the midpoint of the finger(s) on the lever. Usually the length I use is 90mm as a starting point. The pistons, if all are 27mm, are entered in the large diameter line, and the mid and small piston lines set to zero. The number of calipers should be set to the number of pistons of a particular size, in this case four. I will be updating the spreadsheet to reflect the change.

Now let's get the original setup nailed down. When crunching the numbers for the single caliper setup the only way they make any sense is if the caliper is a single acting type (pistons on only one side of the disc), which when coupled to an 11mm master cylinder makes an overall ratio of ~86:1. All you have to do then is enter the size master cylinder (14mm), and the number of pistons and you should get the answer you are looking for.

To check your work, the ratio I got when entering the pertinent numbers was 107.1184 : 1. If you want to get closer to the original ratio increase the master cylinder diameter.

Out of curiosity, what motorcycle is this?

Rob
 

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Thank you very much.

The bike is a 2017 Triumph Street Twin, with a single 2 piston (Single acting type) caliper (27mm each) with a 11mm Master Cylinder

I have added another caliper, same setup and changed the MC with a Nissin 14mm one.

It is still winter here and can't do a road test but it looks promising.

The parts came from the Triumph T120 parts bin and this bike uses a 14mm MC. So hopefully all will be good! Thanks for your input
 

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There are another important parameter - brake disc effective radius and wheel radius. Brake disc effective radius = (disc_diameter-pad_width)/2. Common pad width ~30mm.
For 320mm disc its (320-30)/2 = 145mm. for 296mm - 133mm
For example 320mm disc produces 9% more braking force than 296mm disc on the same setup and the same force applied to the lever.

And the same rule works for wheel radius. R18 wheel produces about 5% more braking force on the same brake setup.
 

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McTavish
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There are another important parameter - brake disc effective radius and wheel radius. Brake disc effective radius = (disc_diameter-pad_width)/2. Common pad width ~30mm.
For 320mm disc its (320-30)/2 = 145mm. for 296mm - 133mm
For example 320mm disc produces 9% more braking force than 296mm disc on the same setup and the same force applied to the lever.

And the same rule works for wheel radius. R18 wheel produces about 5% more braking force on the same brake setup.
Yes, there are lots of complexities involved beyond the pure hydraulics, leverage ratios at the master, and accounting for the few and very basic friction pad classes.
My sense is that the total math is more complex than you have described, thus making it even more complicated.
For example, there is surely at least some factor involved that accounts for the increased pad:disc velocity of the larger disc diameter, as well as the longer path line which increases the swept area.
Yes, there are two moment arms that can help or hinder, axle CL to tire contact patch and axle CL to the effective rotor diameter. Ideally is larger rotors whose edge is closer to the contact patch, thus also explaining why so called "ring brakes" are so powerful, to the point that sometimes a designer can substitute one ring rotor instead of two classic rotors.
All good stuff, indeed!
 

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OK, I new here but not to bikes and braking.

I couldn't agree more to the benefits of using a radial master cylinder.

I'd like to offer the ones that I prefer to use in my builds. They're used on the Kawasaki Concours 1400, and have a matching clutch m/c if you want to go with a hydraulic clutch system.

Made by Nissin, this part features the reservoir, adjustable lever and has a built-in bleeder at the top to purge those pesky air bubbles.

I find them on eBay for around $75 to $100. See here in my blown GL:
 

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I think I'm being a bit dim, here...

First question: cell B11 (single or double acting) isn't referenced in the formula for overall ratio (B12)?

Second question: if I want to find the appropriate diameter of a radial master cylinder to replace an axial - no changes to any other part of the braking system - I would assume the master cylinder lever pivot to piston measurement is now zero, but that gives a divide by zero error?

The specific application is a single-disc Yamaha SRX600. Axial master cylinder 12.7mm diameter, 25mm lever pivot to piston. Four-piston double acting caliper with, I think, 27mm pistons. This gives a believable-sounding overall ration of 130.17. Obviously, if I punch in a new master cylinder diameter with a typical radial diameter of, say, 20mm, without changing any other field, the overall ratio is wildly different. Help...
 

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Old, Bold rider
2002 Honda 919, 1976 Yamaha XT500 cafe, TC-JAG TZ250
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2,480 Posts
Discussion Starter · #16 · (Edited)
I think I'm being a bit dim, here...

First question: cell B11 (single or double acting) isn't referenced in the formula for overall ratio (B12)?

Second question: if I want to find the appropriate diameter of a radial master cylinder to replace an axial - no changes to any other part of the braking system - I would assume the master cylinder lever pivot to piston measurement is now zero, but that gives a divide by zero error?

The specific application is a single-disc Yamaha SRX600. Axial master cylinder 12.7mm diameter, 25mm lever pivot to piston. Four-piston double acting caliper with, I think, 27mm pistons. This gives a believable-sounding overall ration of 130.17. Obviously, if I punch in a new master cylinder diameter with a typical radial diameter of, say, 20mm, without changing any other field, the overall ratio is wildly different. Help...
Updated and corrected the spreadsheet and added a second section that calculates the master cylinder piston diameter from the desired ratio. The parameters populate independently.
It's pretty simple to use, and calculating the radial MC from your parameters it looks like a 5/8 inch bore (15.875mm) combined with a pivot to finger distance of 101mm would give a ratio in the 130:1 range.

Keep in mind that regardless of the type of caliper (pistons on both sides or on only one side) the number of similarly sized pistons is the same. Read the last section of the OP for the explanation.

Link: Master cylinder calculator updated 4 Mar 2021.xlr

Rob
 

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Many have asked me to help with changing from a conventional axial front master cylinder (MC) to a radial, and in trying to give accurate information I came up with the following spreadsheet to help determine what piston size radial MC would be appropriate. The reason why there is so much confusion is the basic setups of the two types are quite a bit different: the axial units typically use a smaller piston size than the radials, and a lower mechanical leverage ratio at the lever than radials.

For example, my 2002 Honda 919 with stock master has a 14mm piston and the lever pivot to piston distance is 25mm, while the pivot to hand distance is ~ 90mm (When divided it is called the interaxis ratio). When the total area of all eight caliper pistons (30.15mm and 27mm) is divided by the area of the MC bore it gives a hydraulic ratio of 33.429:1, which when multiplied by the interaxis ratio produces an overall leverage ratio of 120.34:1. This is on the low side of typical for modern sintered brake pads. When I decided to switch to a radial MC for a variety of reasons, not the least of which being a desire for a slightly higher ratio for less effort at the lever and a wider engagement band to make holding the brake just this side of locking easier, I crunched the numbers for an overall ratio of ~130 - 135:1, and came up with a MC bore size of 17.5mm (actually it's 11/16ths, or 17.4625mm). Fortunately this is a size used by all years of the CBR1000, and a couple of Kawasakis. Installation of a MC obtained from a seller on EBAY confirmed the validity of the calculation -- slightly decreased lever effort, and better control near locking up.

On the subject of what ratio is desirable, and what to do if the ratio you want does not match up to an available master cylinder piston diameter: shoot for the next larger size piston and adjust the ratio using the only other parameter available to you -- the Master cylinder lever pivot to finger distance. For an example the numbers on the spreadsheet are for my 919. Change the master cylinder piston diameter to 18mm then go down to the pivot to finger parameter and change it until the overall ratio matches. Once you know approximately where to mount up the master cylinder it is easy to vary the feel on the road (well, parked next to the road) by moving the MC toward or away from the throttle.

Another factor to take into account is the coefficient of friction of the brake pads. Pad manufacturers do not make this information available for obvious reasons, so you have to go by feel here. If you are running brand X pads and like the feel they give with the stock MC enter the appropriate numbers in the spreadsheet for your system to get the stock ratio, then change the interaxis pivot to piston / pivot to finger and piston diameter numbers for the MC you want to run. If, however, the pads are too sensitive or "grabby", decrease the stock ratio by about 5% to start. Conversely, if they have adequate power but take too much effort at the lever increase the ratio by 5%. Then vary the pivot to finger number to obtain the desired ratio. You get the idea.

FYI: The typical range of ratios for modern brakes are from ~115:1 to 145:1 or a little more. Lower than 115 will give a lever that pulls back a short distance then feels rock hard, but takes too much effort at the lever to stop. Higher than 145 to 150 will take more lever travel to engage the brakes, but will require less force at the lever, usually feeling too sensitive when braking.

The spreadsheet: written in MS works, will also open in Excel.

It will work for up to 6 pistons. It will also work for single acting calipers as while there are pistons on only one side, the rear wall of the bore the pistons operate in acts as a second piston, moving the entire caliper body to apply force to the inside pads. They are calculated in the same manner as the double acting calipers.

Link: Master cylinder calculator updated 4 Mar 2021.xlr
Rob
Hello Rob and thank you for the calculation sheet.

I am currently upgrading the brakes on my Ducati S2R 800. The previous owner had installed new 4 piston calipers and 320mm disks but had left the 15mm axial MC on which feels mushy.
So i am upgrading the master cylinder. As far as i know the calipers have 2x34mm pistons and 2x30mm pistons ( btw the spreadsheet has a minor mistake, if you have one diameter of pistons and you put zero on the lines for mid and small piston it calculates like you have only 2piston calipers, so i guess someone should also change the number of big pistons to 8? or maybe an if loop in the spreadsheet). Nevertheless back to the subject. For my setup and with a RCS19 MC from Brembo i get an overall ratio of 126.6 with the pivot adjustment to 18mm and i am worried that this is maybe a little firm for road use and might block the front wheel. With the RCS17 i go up to 158 for the 18mm pivot and 142 with the 20mm pivot it will be more progressive but i guess i should lock it to 18mm?
Overall i am trying to replicate the feel of the braking system of a Triumph Daytona 675 2008 which I rode for some time a while back and loved the brakes. Anyone knw the stock ratios of this bike? Thank you in advance.
 

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Old, Bold rider
2002 Honda 919, 1976 Yamaha XT500 cafe, TC-JAG TZ250
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Discussion Starter · #18 · (Edited)
From the dimensions you gave the RCS19 with pivot at 18mm would give an overall ratio of 126.6:1, reasonable for the street, but not what you are looking for. Moving the pivot to 20mm decreases the ratio to ~114:1 which will give a rock hard lever but very high effort. The worst part of that is the feedback is masked by the excessive pull at the lever, creating a "wooden" feel, and it is very difficult to modulate near lockup, particularly when trail braking where a small mistake will put the rider on the ground. As is stated in the original post a ratio exceeding 150:1 is only suitable for track use and even then it requires a carefully fettled system and very experienced hand at the lever.

I took screenshots of the updated spreadsheet with the pertinent data so you can see the results. My numbers were higher than yours. It made sense when I changed the pivot from 109.22mm (my preferred) to 100mm and the numbers fell right into place with yours. I also double checked the numbers with my TI-86 graphing calculator, which is where the original equation was first worked up and tested. They always matched your numbers. From these a combination of 17mm piston and 20mm pivot (142.3:1) will get you in the ballpark as regards feel vs. effort on the street. Remember that moving the master cylinder toward / away from the throttle is a good way to vary the feel somewhat, depending on how much room you have on the handlebar.

FYI, if you haven't already looked at the equation here it is: Ratio =(1/B4^2)((B5^2+B6^2+B7^2)*B8)(B9/B10). Notice that it does not do a full area calculation for the pistons which in this case is unnecessary. All that's needed is the final numbers. And yes, I did the whole area calculations just to double check the simplified equation and got exactly the same numbers. As to the piston count: you are correct that if you are using calipers with all pistons the same size the "Number of large pistons" line has to reflect the actual number of pistons.

Interesting note: When Lockheed double acting calipers were first introduced in the '70s the ratio that would loft the rear wheel was in the low 60:1 range. I chalk that up to the much softer organic pads common for that era.
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Rob
 

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Many have asked me to help with changing from a conventional axial front master cylinder (MC) to a radial, and in trying to give accurate information I came up with the following spreadsheet to help determine what piston size radial MC would be appropriate. The reason why there is so much confusion is the basic setups of the two types are quite a bit different: the axial units typically use a smaller piston size than the radials, and a lower mechanical leverage ratio at the lever than radials.

For example, my 2002 Honda 919 with stock master has a 14mm piston and the lever pivot to piston distance is 25mm, while the pivot to hand distance is ~ 90mm (When divided it is called the interaxis ratio). When the total area of all eight caliper pistons (30.15mm and 27mm) is divided by the area of the MC bore it gives a hydraulic ratio of 33.429:1, which when multiplied by the interaxis ratio produces an overall leverage ratio of 120.34:1. This is on the low side of typical for modern sintered brake pads. When I decided to switch to a radial MC for a variety of reasons, not the least of which being a desire for a slightly higher ratio for less effort at the lever and a wider engagement band to make holding the brake just this side of locking easier, I crunched the numbers for an overall ratio of ~130 - 135:1, and came up with a MC bore size of 17.5mm (actually it's 11/16ths, or 17.4625mm). Fortunately this is a size used by all years of the CBR1000, and a couple of Kawasakis. Installation of a MC obtained from a seller on EBAY confirmed the validity of the calculation -- slightly decreased lever effort, and better control near locking up.

On the subject of what ratio is desirable, and what to do if the ratio you want does not match up to an available master cylinder piston diameter: shoot for the next larger size piston and adjust the ratio using the only other parameter available to you -- the Master cylinder lever pivot to finger distance. For an example the numbers on the spreadsheet are for my 919. Change the master cylinder piston diameter to 18mm then go down to the pivot to finger parameter and change it until the overall ratio matches. Once you know approximately where to mount up the master cylinder it is easy to vary the feel on the road (well, parked next to the road) by moving the MC toward or away from the throttle.

Another factor to take into account is the coefficient of friction of the brake pads. Pad manufacturers do not make this information available for obvious reasons, so you have to go by feel here. If you are running brand X pads and like the feel they give with the stock MC enter the appropriate numbers in the spreadsheet for your system to get the stock ratio, then change the interaxis pivot to piston / pivot to finger and piston diameter numbers for the MC you want to run. If, however, the pads are too sensitive or "grabby", decrease the stock ratio by about 5% to start. Conversely, if they have adequate power but take too much effort at the lever increase the ratio by 5%. Then vary the pivot to finger number to obtain the desired ratio. You get the idea.

FYI: The typical range of ratios for modern brakes are from ~115:1 to 145:1 or a little more. Lower than 115 will give a lever that pulls back a short distance then feels rock hard, but takes too much effort at the lever to stop. Higher than 145 to 150 will take more lever travel to engage the brakes, but will require less force at the lever, usually feeling too sensitive when braking.

The spreadsheet: written in MS works, will also open in Excel.

It will work for up to 6 pistons. It will also work for single acting calipers as while there are pistons on only one side, the rear wall of the bore the pistons operate in acts as a second piston, moving the entire caliper body to apply force to the inside pads. They are calculated in the same manner as the double acting calipers.

Link: Master cylinder calculator updated 4 Mar 2021.xlr
Rob
Hi Rob,
I have read with interest your article and would love to use the calculator but have had no luck opening it. Any thoughts would be greatly appreciated. I`m running windows 10.
Cheers Bill.
 

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McTavish
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Hi Rob,
I have read with interest your article and would love to use the calculator but have had no luck opening it. Any thoughts would be greatly appreciated. I`m running windows 10.
Cheers Bill.
Did you change the file extension so it's xls instead of xlr (to dodge blocking)?
That worked for me, noting I'm on 8.1
 
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