

Expert
Posts: 3982
 They talkabout doing the math, will help you figure out the master cylinder you need. https://www.hotrod.com/articles/avoidingcommonmistakeshowtomakeyourstreetrodstop/ 



Expert
Posts: 1740
Location: Muskego, WI  Definitely worth reading. 



Expert 5K+
Posts: 6130
Location: So. California  I disagree. Not worth reading. According to their reasoning, you get more pressure with smaller bores, so we should all go to .05" bores so we can get the maximum line pressure possible. They did briefly mention the volume limitation, but didn't bother to show you how to calculate the other constraints that prevents you from going too small.
Also, who says 100 lbs is a good number for typical leg force? Where is the measured data? Men vs. women? How does this number change with a power brake booster in action?
What is the justification for a friction coefficient of .5 and how much does it vary depending on pad materials etc?
How did they calculate the effective radius that is essential for this final result? I do know how, but why go through the super easy part of the line pressure calculation in detail without giving the harder part of the calculations? Notice that their pad width is blank. That tells me that they just use a known or assumed value for the effective radius without actually calculating it out.
No mention anywhere of how drum brakes changes these calculations.
At the beginning they state that you need 9001200 psi line pressure for disc brakes to be effective, and yet, they show that with a relatively small bore 15/16" master, you can only get around 700800 psi. And their final calculation uses a pressure of only 600psi. One or more of their assumptions isn't true. This is why I stopped reading these magazines. I get tired of being treated like a kindergartner. You have to look elsewhere for real answers if you want to do this seriously.
We are unable to change the pedal ratio very easily on our cars. Has anyone measured it? It would be pretty easy to measure if you have a pedal assembly available that is removed from the car. 



Veteran
Posts: 286
Location: Newcastle Australia  I think you need to read the article again.
The 100lbs figure is a simple round number to make the calculations easier to understand. At no point does it mention that a human being (male or female) can only exert 100lbs force to a pedal. A typical person can exert their ideal body weight plus 20%. So a 200lb person can exert a pedal pressure of 240lbs.
And yes your statement that a .05" bore will give maximum pressure is correct but then you master cylinder would need to be 28 feet long, so not very logical. 



Expert 5K+
Posts: 6130
Location: So. California  I fully realize what you are saying. My point is that reading the article again won't answer any of this if you don't know it already by some other means. The article is nearly worthless. 



Expert
Posts: 1740
Location: Muskego, WI  Nathan,
The article is definitely very basic and aimed toward shadetree mechanics, not engineers. I think the point is to at least bring some attention to an often overlooked subject and provide some brake system fundamentals. Same applies to hydraulic clutch systems. 



Expert
Posts: 3982
 well the best thing they mention is simply measure the pressure Anyone know what the stock pressure is for the drums?
I think the problem is the amount of fluid you need to move and the amount of pressure you need to apply. They don't really mention about "how much" fluid you need to displace. 



Expert
Posts: 3318
Location: NorCal  If the MC diameter and pedal ratio are known you can compute the line pressure but the hard thing to determine is how much leg pressure is being applied to the pedal. 



Expert 5K+
Posts: 6130
Location: So. California  Since I made a mockery of their article, I feel some responsibility to illustrate the answers to the things that I brought up as much as possible.
1. Volume calculation:
They really should have went through a realistic volume calculation to determine if a 15/16" bore would be adequate for their needs or not. Some of the numbers are not well known to me, but others are very well known. In the calculation I am doing, I am considering a disc/drum car using the front Scarebird conversion with a stock Chrysler rear axle since that's what I am generally interested in, and many people here are too. The article seemed to be building a disc/disc car, which will have a little different requirements.
Assumptions: Disc pad gap  The allknowing internet claims a gap of .45mm to .60mm. I chose to use 0.5mm. Using the high number would be safer, but I suspect that isn't very close to reality unless you have a lot of runout (wobble) on your rotor.
Drum shoe gap  The problem with the stock axle is the lack of an automatic adjuster. So you have to be more diligent in adjusting it every now and then. Nevertheless, I am using a reasonably large number to account for a little bit of laziness. I chose to use .06" which is about 1.5mm.
Hose flex  I know that most reinforced rubbers will flex about 10%. This isn't backed up by data so it is more of an educated guess. I am also guessing that the ID of the hose is about 1/8". The hose flex doesn't add a lot to the total so getting more accurate numbers won't change the final result much.
Pedal ratio & pedal play: I don't know the correct numbers so I just made them up. This only affects the total pedal movement, not the stroke calculation.
You see that even with a large 1 1/8" bore master, that I still use up 56% of the stroke in overcoming all these gaps. That leaves 44% for doing the brake apply, which should be more than sufficient. The resulting freepedal movement is the stroke calculated, multiplied by the pedal ratio, with the play added afterward. If I change the bore size down to 15/16", the stroke percent comes out to 81%. That's too close for comfort for me. Only 19% left to account for inaccuracies and other possible issues. A good article would have given us more detail about what are the appropriate numbers to use in our assumptions and what minimum stroke percentage should be left after we are done.
Also, notice that the disc brake gap adds the most to the volume calculation. That's why disc brakes require bigger volume masters. If you are using an unequal volume master, you will need to do a separate calculation for both front & rear.
(Volume Calculation.jpg)
Attachments  Volume Calculation.jpg (73KB  40 downloads)




Expert 5K+
Posts: 6130
Location: So. California  3. Appropriate Friction coefficient
There are more types of brake pad materials now than I knew existed. Here is what I have found in order from lame to hightech:
Asbestos Organic: ?? (no longer produced)
NonAsbestos Organic: ?? (fades, wears fast)
SemiMetallic: .28.38 (higher rotor/drum wear)
Low Metallic: .38.5 (noisy)
Carbon Metallic: ?? (better thermal performance)
Ceramic: .33.4 (clean)
Carbon Fiber: ~ .6 (harsh transition, racing only)
Most of these numbers come from this link:
http://www.suscon.org/pdfs/bpp/pdfs/OEBrakePads.pdf
The asbestos & nonasbestos pad friction coefficients likely start near a value of 0.2. I would say that a much more realistic number to use would be .3 for standard pads, and maybe .35 for semimetallic & ceramic or .4 for low metallics. I can't see how you can justify using a value of .5 here since it is at the very top edge of what is possible.
Edited by Powerflite 20190724 9:53 PM




Expert 5K+
Posts: 6130
Location: So. California  4. Effective radius calculation.
For torque calculations, you need to multiply the applied force by the radial distance from the center of the wheel. The force is pressure times area. But you can't just multiply the total pressure by the total area, and some random radius because the radius changes as you go out to different parts of the brake pad. So you have to look at very small sections of area on the brake pad. If the area is very small, the radius in that small area is nearly the same and you can multiply that area by it's radius & pressure to get it's contribution. Do this over the entire pad and add them up. This is the work of calculus and more specifically; using calculus to do an integration over the pad area.
If the pad area looks like a simple annular sector (see picture), it is relatively easy to integrate over its area to find the resulting effective radius to use to calculate the torque.
The result is: Torque = u * Pad Area * Pad Pressure * [Ra + w^2/(12*Ra)]
Ra here is the average radius (R1+R2)/2, and w is the width R2R1. u is the friction coefficient. So you must add this other term to the average radius to get your proper effective radius. If the pad isn't a nice annular sector, you can still do the integration, but the math can get ugly.
We don't actually need to calculate the pad area and pad pressure because this is just the total force on the pad. That is given by the line pressure multiplied by the caliper piston area. So that's what we will use there instead. Keep in mind that the torque here is for one pad. You need to multiply it by 2 to get the total torque on one wheel, assuming that both pads are the same size & shape.
Wheel Torque = 2 * u * Line Pressure * Caliper Piston Area * [Ra + w^2/(12Ra)]
Edited by Powerflite 20190725 1:16 AM
(Annular Sector.png)
Attachments  Annular Sector.png (32KB  42 downloads)




Expert 5K+
Posts: 6130
Location: So. California  5. Drum brake torque
The torque calculation for disc brakes is quite easy once you figure out the proper effective radius to use, but drum brakes are more complicated because the shoes amplify the torque action by its movement. This action has been studied in detail many years ago and the calculation can be found in Mechanical Engineer's Data Handbook and other similar references. Refer to the picture below.
They use Tr for Torque from the right shoe. Assuming that the car is going forward, rename that one as the front shoe. Likewise the TL for left shoe torque should be renamed the rear shoe torque. K is the amplification factor, and the total torque on the wheel is given by Tfront + Trear. Of course the Force F here is the line pressure multiplied by the area of the wheel cylinder piston.
You can measure that angle theta easily by measuring the arc length of the pad and dividing it by the drum radius. This will be the double angle in radians. Divide this by 2 to get theta to use to calculate the amplification factor K. Notice that the torque doesn't depend on the width of the shoe. A little counterintuitive, but makes sense if you think about it.
Edited by Powerflite 20190724 11:59 PM
(drum_brake_torque_equation.png)
Attachments  drum_brake_torque_equation.png (164KB  45 downloads)




Expert 5K+
Posts: 6130
Location: So. California  6. Available line pressure
According to Jegs, the minimum line pressure you should see in your brakes is
Disc brakes minimum pressure: 800 psi.
Drum brakes minimum pressure: 400 psi.
and according to Mark Williams Enterprises, you should design your system with at least 1200 psi available during an emergency situation.
So for a disc brake system, it looks like there is good agreement on the 9001200 psi requirement. A disc/drum car should use a true proportioning valve to increase the front pressure while decreasing the rear pressure. The typical adjustable ones just reduce the rear pressure without affecting the front pressure. The only factor that isn't taken into account yet is how much force can you or your wife really apply during an emergency situation. 



Expert
Posts: 1435
Location: Alaska  A couple of comments, I have the pedal assembly out of my 58 Plymouth removed and setting on a shelf and the pedal ratio for manual brakes on this car is about 7.65 to 1. Way back in junior high we had an apparatus to measure leg strength. You would put on a heavy leather belt and stand on it, bend your knees and connect the belt to the machine with chains. When you straightened your legs with all your might it would read out the numbers. I was surprised that many of us boys could pull about 600 lb with our legs. Long story just to show that 100 lb is not much push with our legs. 



Expert 5K+
Posts: 6130
Location: So. California  Wow, I didn't realize the manual pedal had that large of a ratio on it. I just measured my Dodge/Chrysler manual & power pedals and found:
Pedal mounting bolt to pivot: 11" (same on both)
Bottom of Pedal to Pivot: 12" (same on both)
Manual Pivot to Push Rod: 1.375"
Power Pivot to Push Rod: 2.625"
I think measuring from the pedal bolt mount is a better number as that would give more of an average distance rather than from the bottom of the pedal. So that 11" value is what I am using. From this, I get:
Manual ratio: 8:1 (A little more than what you got, but close)
Power ratio: 4.2:1 (Much smaller than I expected!)
The maximum force that can be had from the booster can be calculated based on it's dimensions. measuring inner dimensions would be more accurate, but I don't want to take it apart so this will have to do. See picture for the dimensions that I measured. The 1.5" center is very approximate and should be remeasured once you take it apart. The area is one full 6" circle added to a 2.75" x 6" rectangle, with a 1.5" circle taken out. Assuming that the motor can make 16.5 in Hg of vacuum (which is 8.1 psi) I get:
Booster Area: 43 in^2 (This is the equivalent of a 7.5 diameter round booster  pretty small for a large car)
Max Booster Force: 348 lbs
This should help for doing line pressure calculations.
(Booster Dims From Outside.jpg)
Attachments  Booster Dims From Outside.jpg (30KB  43 downloads)




Expert
Posts: 3147
Location: Chestertown, NY ( near Lake George)  I've done a couple of ft disc brake conversions in my shop. The owners insisted they didn't need power brakes, I said we couldn't get better than about 5.5:1 ratio, they couldn't be convinced til they complained about the required pedal pressure to stop. Told em so!
Edited by Shep 20190727 4:21 PM




Expert
Posts: 3318
Location: NorCal  The typical FL MC has a 1 1/8" bore so the math says, with an 8:1 pedal ratio and 100 lbs on the pedal, you should have around 800 psi line pressure.
I'm still wondering how easy it is to apply 100 lbs to the pedal, especially for an old guy. All of my scales are too bulky to fit on a brake pedal.
Edited by 57chizler 20190727 4:42 PM




Expert
Posts: 1435
Location: Alaska  Nathan, I was measuring to about the center of the pedal pad but if you measure to the bottom of the pad it would be closer to 8 to 1. 57 chizler, think about this, every time you are walking, you are pushing your total weight on each leg against gravity. 



Veteran
Posts: 286
Location: Newcastle Australia  I'm still wondering how easy it is to apply 100 lbs to the pedal, especially for an old guy. All of my scales are too bulky to fit on a brake pedal.
Easy enough to find out with a common set of bathroom scales.
Sit down in a hallway with the scales against the wall and you back against the opposite wall. Push on the scales to see what you can achieve.
I achieved 71kg (156lbs) without too much effort. An emergency brake would be more. 

