Hydraulic brake basics

[starspangled]

Hi folks,

I've just been in a spirited argument with several folks regarding hydraulic drum brakes and the relationships of master cylinder and wheel cylinder bore diameters and brakeline diameters.

It is my belief that changing to a larger or smaller master cylinder bore will have a direct effect on braking pedal pressure, and that a change in bore diameter of wheel cylinders will also have a direct effect, and that larger or smaller diameter brakelines can have a direct effect on the sensitivity or 'felt' pedal pressure in the system.

Their primary argument is that the brakeline diameter has absolutely no effect whatsoever, and that master cylinder to wheel cylinder bore relationships are not much of a consideration in a braking system.

The final consensus was that there may or may not be a difference due to master cylinder bore changes, and that there is virtually no effect in wheel cylinder bore changes, and no agreement was reached on brakeline diameter's effect on a braking system except that I was probably wrong.

So, I request some opinion and feedback from you engineers who have been involved in this area of the trade. Thanks for any assistance in this and also for any relevant formulae you may contribute.

Starspangled

 

[patprimmer]

Don't use this group of friends to help you do brake work.

Cross sectional area of master cylinder vs cross sectional area of wheel cylinder has a directly proportional effect on pedal effort. End of story.

Pipe diameter is a slightly more complex situation. If the pipe was already very small, a reduction might have an instantaneous effect, but would quickly equalise. The restriction to flow might have a very slight effect as the pedal is pushed, but once the brake linings are being firmly pressed to the drum, the pressure will equalise to what it would be with a bigger pipe. This presumes the pipe has more than a few thou dia.

The co-efficient of friction of the linings on the drum also has a significant effect, and the rigidity of the system can effect the feel. ie rubber hose vs steel pipe.

Regards

eng-tips, by professional engineers for professional engineers
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[MikeHalloran]

I'm not a 'braking system' engineer, but I've been messing with hydraulic systems for a while, and I've always serviced my own brakes. It's not that I'm not a trusting person ... Oh. Yeah. It is.

A capillary brakeline would raise the pedal pressure for a time. A garden hose brakeline would expand under pressure, as do the hoses in any system, but _minor_ changes in brakeline diameter would not be detectable by the ordinary driver.

Changing either cylinder diameter affects the ratio between force applied to the pedal and force applied to the braking mechanism.

There are a lot of different kinds of drum brakes. So- called 'trailing shoe' brakes require a lot of force to work, but have a 'feel' rather like disc brakes, given power assist on both. Until you back up; then they become leading shoe brakes, and are self- energizing, meaning they require a lot less force to generate a given braking torque, as do 'leading shoe' brakes, and the more common regenerative (read 'turbo self- energizing) combination, 'duo servo' in my old Chevy books.

I get the impression that Mercedes' new 'brake assist' is an electronic implementation of 'self- energizing' brakes. Maybe they should go back to drums...

Oh. With the 'due servo' brakes, the reaction force generated by one shoe adds to the braking force applied to the other shoe, so the friction behavior of the shoes themselves gets involved in the pedal response, in a fairly complex way.



Mike Halloran
NOT speaking for
DeAngelo Marine Exhaust Inc.
Ft. Lauderdale, FL, USA

 

[starspangled]

Thanks Pat and Mike! I might be more specific: I am thinking that to a person that is very familiar with a single particular vehicle, as their own race or street car, the changing of brakelines by 1/16" or 1/8" would noticeably change the pedal feel when braking.

I am convinced that to double the diameter, say from 1/4" to 1/2" would cause a dramatic change in pedal feel. I don't know if it would change the reaction time of master cylinder to wheel cylinder, as the speed or elapsed time until wheel cylinder expands from pedal being depressed, but I can't imagine that it would be otherwise.

The actual numbers I used were to halve the diameter of a .250 brakeline, and halve again, and halve again, and halve agin until .015625 diameter. This exaggerated example was to refute the claim that brakeline diameter has absolutely zero effect on the system.

The assumption is that if this had an effect on the system, and if the opposite of progressive increases was achieved until brakeline is 16 times as large also has a dramatic effect, then any increment in between of large or smaller must have an effect, whether it can be sensed or not.

Unfortunately in this case fluid dynamics is not my specialty.

Starspangled

 

[MintJulep]

In theory, hydraulic fluid is incompressible. Therefore pressure changes are transmitted nearly instantaneously throughout the system, with no associated flow.

In a real brake system there is a small amount of flow associated with the volume that the brake cylinder piston sweeps as it moves.

Assuming perfectly rigid brake lines, there is a direct relationship between the stroke of the brake cylinder and the stroke of the master cylinder - proportional to the square of the radii. Assuming that we are operating at reasonable temperatures, and reasonably constant temperatures we can ignore any changes in fluid density. Thus the MC needs to displace a mass of fluid into the brake line, and that same mass comes out the other end of the brake line to fill the BC.

Divide the line into think slices. The mass of fluid in each slice is proportional to the square of the radius.

Now, assume that the brake application time is independent of line diameter.

For a small diameter line any given mass of fluid must pass through more slices than for a large diameter line (remember, the mass the must move is determined by the BC size). The fluid in a small line will need to accelerate and decelerate more than in a large line, and will have a higher average velocity.

Thus I conclude that there will be higher inertia and fluid friction forces within the small line system than in a big line system.

I'm not going to work through any actual numbers, but my feeling is that these forces will be small in comparison to the total forces involved, and that the effect would be imperceptible.

 

[ntsqd]

Anyone contending that the bores ratio isn't much of a consideration has obviously never driven a vehicle where the ratio was off. In a non power system you can have a pedal effort that ranges from rock hard with minimal stopping power to an excessively spongy, air in the lines kind of feel. That range of total leverage ratios is surprisingly narrow.

Do a simple area calc for the ID of the 3/16" tube used in most brake plumbing. Use some arbitrary length like 10 feet. Now do that same calc for the ID of 1/4" tube. If you want you could also do Hoop Stress' on each, but I think you'll see my point b4 then.

So the trade-off is expansion under pressure vs. volume transfer rate.

 

[GregLocock]

I agree that brake feel is affected by the line construction, for practical systems. For a given wall thickness smaller diameter is better. However, line losses will be greater due to wall friction, and smaller due to reduced inertia. I don't know about those two in practice, I do know about the elasticity issue.





Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[Warpspeed]

Another factor that comes into this is that some drum brakes are designed with at least one leading shoe that will have a self servo action. That can dramatically effect pedal pressures and brake feel.

I all brings back memories. I have not dirtied my hands on a drum brake for at least twenty years, hehehe.

 

[patprimmer]

The las time I dirtied my hands on a drum brake was to correct a very bad job by the factory engineers in selecting the wheel cylinder bore size.

I am not prone to criticising factory engineers as they normally have far greater resources and experience than hot rodders, but for some reason in this case they used a very large bore wheel cylinder on the back drums, and a proportioning valve to prevent rear wheel lock. This was an E/W engine Front WD setup.

The rears locked before the proportioning valve could act under slippery or high speed conditions. This was extremely disconcerting, as the rears locked when the fronts were only about 30% or less effective. It actually caused me to crash the car in an emergency in a situation I would easily have avoided with good brakes.

As a consequence, I removed the proportioning valve, then reduced the wheel cylinder to the smallest I could get, which was only 40% of the original CSA.

It still locked rears first, but at least there was reasonable stopping power from the fronts when this happened.

I then reinstalled the proportioning valve.

I never crashed it again.

Wheel cylinder size does have a noticeable effect. Leading trailing shoe does have a noticeable effect. Friction compound does have a noticeable effect. Any reasonable brake line diameter will have a negligible effect.

Brake line material can have a significant or even dangerous effect as pedal travel can be lost to elasticity in the lines.

Rigidity of drums, shoe backing etc can, but normally don't have a noticeable effect.

Regards

eng-tips, by professional engineers for professional engineers
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[Warpspeed]

Probably the best modification to drum brakes, is to remove them, and chuck them in the big dumpster bin. Fit discs instead.

To anyone thinking of trying larger bore wheel cylinders or calipers, just make absolutely sure the master cylinder can displace enough fluid so the dual system still works properly. Having the pedal unexpectedly hit the floor can spoil your whole day.

 

[starspangled]

Great advice, gentlemen, and much appreciated. I'm aware of the relationships of large bore to small bore and of the potential for a change in pedal feel and force of appliation at the brake lining dependent on the particular bore combination. I have customized my own brakes, first on the advice and authority of a well known automotive engineer. The results were dramatic and just as promised.

Carrying that a step further as decribed above it seemed there must be a following relationship of greater or lesser pedal feel and actual apply time of force at the wheel cylinder dependent on the volume of fluid in motion, which would seemingly be more or less restricted dependent on brakeline diameter.

Of course my example was extreme bordering on ludicrous of a ratio of 16:1 change in diamter. However you seem to agree overall that there would indeed be at least some difference due to varying line diameter. It seems in a real world application a difference of changing from 1/4 steel line to 5/16 might be noticeable, and to 3/8 might be dramatically noticeable. There is a time factor due to restriction and friction as mentioned for the pressures to equalize. It is in that relationship that responsiveness might be notable. Further a considerably higher volume of fluid in motion in a larger line would apprently cause the brakes to at least intially apply much more quickly, with pressures then equalizing in the system.

So far it seeems I'm on the right track in general. The bottom line of the other side's argument was untenable: that there would be no difference whatsoever, period. Though there are many related factors I believe we agree that their viewpoint is incorrect.

I very much appreciate your hearty response and clarifications of the deper issues involved. I am always and continually amazed at how such seemingly inconsequential factors can have some many effects within a system.
Thanks.

Starspangled

 

[Tmoose]

My GM cars of the 60s had big brake lines leaving the dual master cylinder.
Volvo 240s, at least until 1989 (my 8th, newest and present) have tiny lines right off the master. I believe I notice a "delay" when applying them fast. I suspect it >>might<< even help prevent wheel lock-up "jamming" on the brakes.

 

[starspangled]

Thanks Tmoose! That brings it into clear perspective. It seems obvious that there cannot be a condition of 'NO DIFFERENCE' from up-sizing or down-sizing the lines connecting a master to a slave. Yes, I would think that with a sophisticated system such as your Volvos, as opposed to an old yard truck with drum brakes, it would be far more noticeable.