disc brake system mechanical advantage (MA)

For discussions about bikes and equipment.
Brucey
Posts: 31989
Joined: 4 Jan 2012, 6:25pm

disc brake system mechanical advantage (MA)

Postby Brucey » 3 Jan 2019, 8:11pm

Some notes on disc brake system mechanical advantage (MA):

With rim brakes the notional system MA comprises four elements

a) - lever MA (set by the geometry of the lever but can be measured as the ratio of 'finger pull' to 'cable movement')
b) - caliper MA (set by the geometry of the brake arms, but can be measured by the ratio of 'cable pull' to 'brake block push')
c) - wheel MA (the ratio of the diameter of the brake track to the rolling diameter of the wheel)
d) - brake block coefficient of friction

which multiply to give an overall system MA.

However in practice it isn't as complicated as that: In the first place we need not concern ourselves overly with d) because the value is about 1 anyway and the brake blocks can easily be changed for a different sort if necessary, so it is really more of a 'fine tuning' parameter. Similarly c) can be assumed to be about 1 also in most cases, (although fat tyres on small wheels may be an exception).

On the other hand in reality there are also cable losses; cables are of variable quality, have friction in them and the losses increase as the tension in the cable increases. So in practice a system MA of (say) 5:1 with 4:1 levers isn't going to be quite as good (or at least will be more sensitive to cable condition) vs a 5:1 system which uses 3:1 levers, because the cable tension (for any given braking effort) is less in the latter case.

It is easy to go wrong with a rim brake system; levers vary from over 4:1 (many old dropped bar levers with exposed cables) to about 2:1 (for some V brakes) and caliper MAs vary from less than 1:1 to over 1.75:1. A good system MA to aim for (on an unladen bike) is between 5:1 and 6:1. On a laden bike a higher system MA may be a better idea, but there will inevitably be reduced brake running clearance at the wheel rim.

With mechanical disc brakes the same overall logic applies, but the caliper MA is a lot higher and the wheel MA is a lot lower. The main point to note is that brake calipers are sold as being one of two types 'road' or 'MTN' but may vary slightly in MA within each category; no-one has published any data on this, and I have only carried out a few measurements myself (*). So the four categories are;

a) lever MA; most systems are designed for lever MAs which vary from about 3.5:1 (road) to about 2:1 (MTN)
b) caliper MA; this is likely to be either ~10:1 (road) or ~17.5:1 (MTN)
c) Wheel MA; this is the ratio of the working diameter (WD) of the disc to the rolling diameter of the wheel
d) the friction coefficient of the brake pads

Note that the majority of 'road' disc calipers on the market even today owe their origins to designs which date from prior to 2008, when lever MAs were about 3.5:1 (as required for first generation dual pivot brakes). It is not clear to me which models have a higher caliper MA to work optimally with the current levers (NSSLR type which are nearer 3.0 :1).

Again d) can be assumed to be about 1 and this can be used as a fine tuning parameter. The wheel MA is greatly affected by the size of the brake disc and its design; to a first approximation the working diameter (WD) of the disc is the overall diameter of the disc less the brake track width. So a 160mm disc with a 20mm track has a 140mm WD but a 165mm disc with a 15mm track has a 150mm WD.

The rolling diameter (RD) of the wheel can be assumed to be the bead seat diameter of the rim (BSD) plus twice the tyre section width, so a 25-622 tyre has an RD of about 672mm, and (with the 165mm disc) a wheel MA of ~0.22. If a wider tyre and (say) the aformentioned 160mm disc is used then the wheel MA could be sigificantly lower, ~0.195. Obviously wheels can vary in diameter and so can brake discs. Brake discs vary from ~140mm (~125mm WD) to ~200mm (~180mm WD). With the same size wheel this might mean wheel MA values that vary from about 0.18 to 0.27.

Thus a typical road bike based system might have lever MA of 3:1 (for NSSLR levers as per most new shimano STI models 2008-), a caliper MA of ~10:1, a wheel MA of ~0.2, giving a system MA of 3 x 10 x 0.2 = 6.
A typical MTN based system may have a lever MA of 2.25:1, a caliper MA of 17.5:1, and a wheel MA of 0.2, giving a system MA of 2.25 x 17.5 x 0.2 = 7.74

A 'road' system with better matched levers and calipers might have 3.5:1 lever MA so system MA would be 3.5 x 10 x 0.2 = 7.

This is still not quite as good as a MTB based system and of course the cable tension will be higher in the 'road' case too, so the usual result is that a 'road' system isn't quite as powerful as an 'MTN' based system. System MA values are not wildy different from those of rim brakes so it boils down to friction coefficient (i.e. what pads/conditions you use) and (at any given MA value with typical wheels and discs) whether maintaining a small clearance to a disc without rubbing is really any easier than maintaining a (~x5) larger clearance at the rim.

With hydraulic systems the overall MA can be calculated similarly but the lever MA can be the mechanical lever MA value and the caliper MA can be the ratio of the slave piston area (on one side of the caliper) to the master cylinder piston area. Efficiency is likely to be better (at the same MA value) because cable friction is absent in a hydraulic system.

(*) If anyone would like to measure their caliper MAs and contribute them to this thread it may prove to be a useful pool of data. Measuring caliper MA values with some mechanical calipers (eg all Avid BB series AFAICT) is made easy by the fact that the FPA has a 1.0mm pitch thread; a whole turn of the FPA is worth 1.0mm of pad movement and the difference in cable pull for that is simply the caliper MA. Hence for a BB5 (road) caliper the cable pull for 1mm of pad movement is ~9.5mm and MA measures ~9.5:1. Since the MA sometimes varies (more with some calipers than others) through the stroke it is best if the measurement is taken mid-stroke if possible.

cheers
-------------------------------------------------------------------------------
~~~~~~~~~~~~~~~~~~~~~~Brucey~~~~~~~~~~~~~~~~~~~~~~~~

thelawnet
Posts: 1525
Joined: 27 Aug 2010, 12:56am

Re: disc brake system mechanical advantage (MA)

Postby thelawnet » 6 Jan 2019, 11:54pm

I have a Shimano hydraulic disc brake database here

https://docs.google.com/spreadsheets/d/ ... 57g8HR29c/

It is my understanding that Shimano use 10mm lever pistons. Caliper pistons are generally 22mm.

In addition, there are different lever lengths.

These are 'T' series Deore/XT length (T6000)

Image

And these are the more common M series Deore/XT length (M6000)

Image

This is the very cheapest MT200 lever

Image

It appears to be quite similar to the T6000, though there is a difference in that T6000/T8000 are alu and MT200 is steel (MT201 is the same but alu).

It is my understanding that the M6000 calipers (there is no T6000 caliper) use 22mm pistons, while MT200 use 21mm pistons.

MT400 is similar to the M6000 lever, and likewise the calipers are 22mm.

There is intended usage difference between T and M brakes, in that the M brakes are for MTBing, whereas the T brakes are for touring/trekking.

It is generally intended therefore that the MTB brake usage is one-fingered to allow more control over rough ground. A shorter lever makes more sense as such.

Note that there are some combinations of short levers and 21mm pistons. The difference in braking power from the pistons is 10% between 21mm and 22mm, which is not IMO especially significant, so this is a bit of a detail. However there is in general some correspondence between the short levers & larger pistons. The longer levers on the T brakes is presumably more of an ergonomic thing.

Note also that the M series brake levers from Deore and up feature Servowave

Image

This is absent, by design, from the T brakes.

Shimano have fiddled about with including it on their road brakes, but it is not clear if they are ending this, as it's missing from the most recent road groupset, 105.

User avatar
NATURAL ANKLING
Posts: 9464
Joined: 24 Oct 2012, 10:43pm
Location: English Riviera

Re: disc brake system mechanical advantage (MA)

Postby NATURAL ANKLING » 8 Jan 2019, 1:14am

Hi,
So how do you think they go about arriving at the ratios of lever and slave, when the in-between bits can have a dramatic effect on performance.
Cables especially going round bends.
Long or short cable travel.
Deflection /bending of parts including forks.
Hydraulics are a bit simpler as loss is zilch.
Priority Is Still 500K In 24..Just Dreaming...Stay Focused Guys And Keep Sharp...
You'll Find Me At The Top Of a Hill...............Somewhere

Brucey
Posts: 31989
Joined: 4 Jan 2012, 6:25pm

Re: disc brake system mechanical advantage (MA)

Postby Brucey » 8 Jan 2019, 9:00am

establishing MA values is described upthread. I also mentioned that cable losses vary with type, condition and installation.

It is well worth spending time and effort when installing cables simply because if you do, they will usually work adequately for longer before they need to be fiddled with again.

cheers
-------------------------------------------------------------------------------
~~~~~~~~~~~~~~~~~~~~~~Brucey~~~~~~~~~~~~~~~~~~~~~~~~

User avatar
NATURAL ANKLING
Posts: 9464
Joined: 24 Oct 2012, 10:43pm
Location: English Riviera

Re: disc brake system mechanical advantage (MA)

Postby NATURAL ANKLING » 8 Jan 2019, 8:16pm

Hi,
Brucey wrote:establishing MA values is described upthread. I also mentioned that cable losses vary with type, condition and installation.

It is well worth spending time and effort when installing cables simply because if you do, they will usually work adequately for longer before they need to be fiddled with again.

cheers

Yeh sorry, I did not read your post slowly enough :oops:
Priority Is Still 500K In 24..Just Dreaming...Stay Focused Guys And Keep Sharp...
You'll Find Me At The Top Of a Hill...............Somewhere