Brake theory: correct?

[Pete Biggs]

Below is a copy of an article posted to another forum. It is all correct and reasonable?

thanks ~PB

=================================

The only difference that there can ever be between two brakes operating from the same lever with the
same clearance is that due to progression. This is the amount that the mechanical advantage changes
as the brake moves through it's travel.

The simplest way this is done is to move the pivots so that the radius between the pad and pivot is
at about 45 degrees to the rim face. This is what V brakes (and cantis) do with their pivots on the
forks. Cantis would also be progressive like V brakes if it weren't for the straddle cable
undermining it all again. However even V brakes only exhibit about 15% improvement over a neutral
mechanism due to progression, the rest of their performance is due to the increased cable travel.

The ultimate force available is proportional to the square of the cable travel, so with double the
travel of a drop bar lever you could get up to four times the braking. In practice you wouldn't need
that much so I doubt that V brakes are optimised for maximum force. Either way, the 15% improvement
from progression looks pretty insignificant. All of this argument ignores friction, if you include
the effect of friction you gain even more with extra cable travel, because cable tension, and hence
friction is reduced.

Cable stretch: All materials stretch/deform by a amount proportional to the load applied, whilst the
load remains within the elastic limit. Beyond the elastic limit the structure takes a permanent set.
The stretch on the cable is well within the elastic limit, but with 1.3m of cable and only 10mm of
travel, it doesn't take much force to soak up half the travel. The front cable is half the length
and so requires twice the force to stretch the same amount of course. The amount of stretch (S) is:
S=FL/(AE) where L is the unstretched length F is the force applied A is the cross sectional area of
the cable and E is the Youngs Modulus for stainless steel, a factor that defines how rigid a
material is.

 

[Sheldon Brown]

Pete Biggs wrote:

> Below is a copy of an article posted to another forum. It is all correct and reasonable?

No, it isn't.

The first three paragraphs are entirely wrong. The 4th paragraph is irrelevant.

The only good reason to operate two brakes with one lever is if they're side-by side wheels on a
tricycle or trailer.

For a bicycle, it's generally a Bad Idea to use both brakes at the same time, and if you have no way
of modulating them separately, it becomes a Very Bad Idea.

See: http://sheldonbrown.com/brakturn.html

Sheldon "Stop!" Brown +---------------------------------+
| If you understand everything, | you must be misinformed. | --Japanese Proverb |
+---------------------------------+

> thanks ~PB
>
> =================================
>
> The only difference that there can ever be between two brakes operating from the same lever with
> the same clearance is that due to progression. This is the amount that the mechanical advantage
> changes as the brake moves through it's travel.
>
> The simplest way this is done is to move the pivots so that the radius between the pad and pivot
> is at about 45 degrees to the rim face. This is what V brakes (and cantis) do with their pivots on
> the forks. Cantis would also be progressive like V brakes if it weren't for the straddle cable
> undermining it all again. However even V brakes only exhibit about 15% improvement over a neutral
> mechanism due to progression, the rest of their performance is due to the increased cable travel.
>
> The ultimate force available is proportional to the square of the cable travel, so with double the
> travel of a drop bar lever you could get up to four times the braking. In practice you wouldn't
> need that much so I doubt that V brakes are optimised for maximum force. Either way, the 15%
> improvement from progression looks pretty insignificant. All of this argument ignores friction, if
> you include the effect of friction you gain even more with extra cable travel, because cable
> tension, and hence friction is reduced.
>
> Cable stretch: All materials stretch/deform by a amount proportional to the load applied, whilst
> the load remains within the elastic limit. Beyond the elastic limit the structure takes a
> permanent set. The stretch on the cable is well within the elastic limit, but with 1.3m of cable
> and only 10mm of travel, it doesn't take much force to soak up half the travel. The front cable is
> half the length and so requires twice the force to stretch the same amount of course. The amount
> of stretch (S) is: S=FL/(AE) where L is the unstretched length F is the force applied A is the
> cross sectional area of the cable and E is the Youngs Modulus for stainless steel, a factor that
> defines how rigid a material is.
>
>

--
Sheldon "Insert Nickname Here" Brown
+-----------------------------------------------------------------+
| This message has been sent to you using recycled electrons | exclusively. Please do not discard
| them after use, | send them along and help conserve these irreplaceable | sub-atomic resources
| for future generations. |
+-----------------------------------------------------------------+ Harris Cyclery, West Newton,
Massachusetts Phone 617-244-9772 FAX 617-244-1041 http://harriscyclery.com Hard-to-find parts
shipped Worldwide http://captainbike.com http://sheldonbrown.com

 

[Jim Price]

Pete Biggs wrote:
> Below is a copy of an article posted to another forum. It is all correct and reasonable?

This is something I am personally paranoid about due to the number of times in my youth when lack of
available braking performance caused me bodily injury.

> The only difference that there can ever be between two brakes operating from the same lever with
> the same clearance is that due to progression. This is the amount that the mechanical advantage
> changes as the brake moves through it's travel.

Well, yes and no. The mechanical advantage while the brake is moving to close on the rim doesn't
affect anything but how much cable must be pulled to get the pad to the rim. Once the pad meets the
rim, the mechanical advantage change (in the calipers) between just touching and brakes hard on is
not going to change significantly, and it is this which is going to determine what your braking
performance is going to be like. The mechanical advantage in this range is not going to change much
in the brake levers either.

> The simplest way this is done is to move the pivots so that the radius between the pad and pivot
> is at about 45 degrees to the rim face. This is what V brakes (and cantis) do with their pivots on
> the forks. Cantis would also be progressive like V brakes if it weren't for the straddle cable
> undermining it all again. However even V brakes only exhibit about 15% improvement over a neutral
> mechanism due to progression, the rest of their performance is due to the increased cable travel.

I don't think that the "increased cable travel" is the cause of improved braking performance in V
brakes - I think that the design factor which causes the increased cable travel as one effect, has
another effect, which is to reduce the amount of cable stretch on transmission of effort from the
brake levers to the pads. This assumes other things like cable characteristics being equal between
different types of brakes, which they are not. I have some old cantis which have far thicker brake
cables than used on V brakes, presumably because of the effects I'm talking about.

As an intuitive illustration of what I'm getting at, here's a text diagram of two vertical rods
anchored with hinges with a string between them, meant to represent the lever type forces involved
in getting the finger force to the pads:

__ = string -- = ground
| = rod

| |
| |
| |
|__________|
| |
| |
| |
| |
------------

Pull on the top of one rod, and the other rod is pulled too. If someone tries to hold the other rod,
the force in the string increases. Now move the string.

| |
| |
| |
| |
| |
| |
|__________|
| |
------------

This time, the mechanical advantage is the same, but the tension in the string is a lot higher for a
given force from the puller. Thus the string will stretch more. I'm hoping this will illustrate my
point as clearly as possible, so on with the stuff I was commenting on:

> The ultimate force available is proportional to the square of the cable travel, so with double the
> travel of a drop bar lever you could get up to four times the braking. In practice you wouldn't
> need that much so I doubt that V brakes are optimised for maximum force. Either way, the 15%
> improvement from progression looks pretty insignificant. All of this argument ignores friction, if
> you include the effect of friction you gain even more with extra cable travel, because cable
> tension, and hence friction is reduced.

According to Keith Bontrager, the mechanical advantage of a canti brake tuned purely to optimise
mechanical advantage is about the same as a V brake. I have followed his instructions on how to
"trick" cantilevers, and I ended up with cantilevers which felt and performed extrordianrily like V
brakes. Here's a link: http://www.bontrager.com/keith/rants.asp?id=27&page=4 There's even graphs of
brake performance through the arc etc. for the really keen.

> Cable stretch: All materials stretch/deform by a amount proportional to the load applied, whilst
> the load remains within the elastic limit. Beyond the elastic limit the structure takes a
> permanent set. The stretch on the cable is well within the elastic limit, but with 1.3m of cable
> and only 10mm of travel, it doesn't take much force to soak up half the travel. The front cable is
> half the length and so requires twice the force to stretch the same amount of course. The amount
> of stretch (S) is: S=FL/(AE) where L is the unstretched length F is the force applied A is the
> cross sectional area of the cable and E is the Youngs Modulus for stainless steel, a factor that
> defines how rigid a material is.

So finally, to complete the yes and no bit I started off with, the cable stretch is going to mean
some more deflection at the brake lever end, but the force transmitted is actually the same as long
as you don't run out of brake lever travel. Everyone I know who adjusts brakes makes sure that they
have enough travel on the brake lever to apply the brakes without running out of travel at the
levers. In a matched set of brake levers and calipers, the amount of remaining pad clearance with
the brakes off is effectively determined by this adjustment. You can have more clearance with V
brakes, because the pads move further for a given cable travel in the early part of their arc of
movement. This makes them easy to adjust. The longer cable travel means you have options of using
thinner cable, balanced against how "stiff" a feel you want (because of lack of cable stretch).

Conclusions: I'd rather have an "increased cable travel" design, simply because it can be
mechanically stronger (i.e. cable less likely to break for a given thickness of cable). 1-0 to V
brakes. I'd rather have extra clearance at the pads if braking performance can be maintained. 2-0 to
V brakes. I'd like to be able to adjust how my brakes feel. (thats a point awarded to Avid speed
dial brake levers - can you get on-the-fly adjustable pull drop bar levers? With STI or Ergo?) I
actually like brakes you can apply maximum required force with light use of one finger, especially
on long descents.

If you've read this far, I suggest reading the Bontrager article.

Jim Price

 

[Jim Price]

Sheldon Brown wrote:
> Pete Biggs wrote:
>
>> Below is a copy of an article posted to another forum. It is all correct and reasonable?
>
>
> No, it isn't.
>
> The first three paragraphs are entirely wrong. The 4th paragraph is irrelevant.

Um, not irrelevant if you interpretted the question a completely different way like I did!

>> The only difference that there can ever be between two brakes operating from the same lever with
>> the same clearance is that due to progression.

I read this to mean a comparison of two different types of brakes (like a pair of cantis and a
pair of V brakes) being compared in use with the same _style_ of lever, and headed off in a
completely different direction. A direction that frankly was a little more flattering to the
original quoted article.

On the point of using one lever to operate more than one brake caliper, I would not do it on
anything two wheeled, although there are a few motorbikes which do this. They have hydraulic self
adjusting brakes, with brake balance set towards the front, which if you _have_ to do something like
this is the safest way to go. I do not know of anyone who makes a brake balance adjuster for bicycle
disk brake systems, though.

Jim Price

 

[Jobst Brandt]

Pete Biggs writes:

> Below is a copy of an article posted to another forum. It is all correct and reasonable?

It is neither correct nor reasonable and garnishing it with Young's Modulus doesn't do it any good
either. Besides, you ought to check your cable stretch ideas by hanging a 100lb weight on it and
measuring the "stretch". You'll be surprised how little there is.

Where do you get such BS? What is this speaking of yourself in the third person?

Jobst Brandt [email protected] Palo Alto CA

 

[Steve Palincsar]

On Wed, 04 Jun 2003 11:36:56 -0400, Sheldon Brown wrote:

> The only good reason to operate two brakes with one lever is if they're side-by side wheels on a
> tricycle or trailer.

and yet this is or was very common with tandems, to allow a third drum or disk brake to be run off
one brake lever whilw the other operated the main braking system. on a tandem. this works fine.

> For a bicycle, it's generally a Bad Idea to use both brakes at the same time, and if you have no
> way of modulating them separately, it becomes a Very Bad Idea.

again, in practice with a tandem, where pitchover is essentially impossible, this seems to work out
just fine.

 

[Pete Biggs]

[email protected] wrote:
> Pete Biggs writes:
>
>> Below is a copy of an article posted to another forum. It is all correct and reasonable?

That was a typo. I meant to ask: "Is it all correct?". Personally, I do NOT think it is all correct
but am not sure about the details.

> It is neither correct nor reasonable and garnishing it with Young's Modulus doesn't do it any good
> either. Besides, you ought to check your cable stretch ideas by hanging a 100lb weight on it and
> measuring the "stretch". You'll be surprised how little there is.
>
> Where do you get such BS? What is this speaking of yourself in the third person?

Thankyou. I did not write the "article". It was a message posted to the public Cycling Plus web
forum and I was arguing against the poster! I realised I didn't have sufficient understanding of the
maths and physics involved to do the job properly so I came here for some help. Any more details
would be appreciated.

~PB

 

[Sheldon Brown]

I pontificated:

>>The only good reason to operate two brakes with one lever is if they're side-by side wheels on a
>>tricycle or trailer.

Steve Palincsar wrote:

> and yet this is or was very common with tandems, to allow a third drum or disk brake to be run off
> one brake lever whilw the other operated the main braking system. on a tandem. this works fine.

Not always, and I strenuously advise against it in my article on Tandem Brakes
http://sheldonbrown.com/tandem-brakes.html

>>For a bicycle, it's generally a Bad Idea to use both brakes at the same time, and if you have no
>>way of modulating them separately, it becomes a Very Bad Idea.
>
> again, in practice with a tandem, where pitchover is essentially impossible, this seems to work
> out just fine.

Pitchover has nothing to do with using both brakes at once.

The great danger of this setup is fishtailing. It is especially dangerous for tandems, if they ever
get ridden with a child stoker or with no stoker.

The Tandem list has reported a number of grisly accidents resulting from this practice.

It is also "common" to see bikes with only a rear brake, but it doesn't mean it's actually _safe_.

Sheldon "Especially Not Tandems!" Brown +-----------------------------------------------------+
| If a little knowledge is dangerous, where is | the man who has so much as to be out of danger? |
| --T.H. Huxley |
+-----------------------------------------------------+ Harris Cyclery, West Newton, Massachusetts
Phone 617-244-9772 FAX 617-244-1041 http://harriscyclery.com Hard-to-find parts shipped Worldwide
http://captainbike.com http://sheldonbrown.com

 

[Ryan Cousineau]

In article <[email protected]>,
Jim Price <[email protected]> wrote:

> Sheldon Brown wrote:

> >> The only difference that there can ever be between two brakes operating from the same lever
> >> with the same clearance is that due to progression.

> On the point of using one lever to operate more than one brake caliper, I would not do it on
> anything two wheeled, although there are a few motorbikes which do this. They have hydraulic self
> adjusting brakes, with brake balance set towards the front, which if you _have_ to do something
> like this is the safest way to go. I do not know of anyone who makes a brake balance adjuster for
> bicycle disk brake systems, though.

Among the motorcycles with linked braking systems, there are generally two systems in play. The
simplest has the usual brake lever and pedal, but each is biased towards its "natural" brake (lever
operates most of the front brake and a bit of the back brake, pedal operates most of the back brake
and a bit of the front brake). The purpose is to add back some of the natural brake balance that
most riders are not that adept at creating. This system apparently does wonders for settling most
bikes on corner entry.

The second system adds ABS to the mix. Once that happens, you hardly have to worry about anything
else, since the ABS can take care of any wheel-locking issues that might arise (in a straight line,
at least; ABS is not divine intervention).

--
Ryan Cousineau, [email protected] http://www.sfu.ca/~rcousine President, Fabrizio Mazzoleni Fan Club

 

[Jasper Janssen]

On Thu, 05 Jun 2003 00:14:26 GMT, Sheldon Brown <[email protected]> wrote:

>Pitchover has nothing to do with using both brakes at once.
>
>The great danger of this setup is fishtailing. It is especially

Fishtailing is when the rear wheel loses traction, the front is still getting braked, and the rear
continues its tendency to keep going in a straight line by 'breaking out' and making you end up
sideways (and on a tandem, I'd imagine generally on the ground) or worse, right?

On my commuter clunker, with my weight, using drum brakes, it seems the only way to stop in a
reasonable distance is by using both brakes. The front cannot get anywhere near enough leverage to
get close to getting my weight off the rear, unless I deliberately move my weight to the front.

That wouldn't help, it's not that the front hasn't got enough weight such that it loses traction
under heavy braking loads. It's just that the maximum force is used that the brake pads can get with
a reasonable force on the levers.

A clunker or two back, this was much, much worse (I still don't know what was wrong with the stupid
thing. It felt like the brakes had been oiled.), and I would break off the inner brake cables every
month or two because I pulled *hard* on those things to compensate. I would set them as close as I
could get them that did not involve more than a little drag while not engaged, and I'd very nearly
bottom out the levers on every stop, as well as on the more onerous ones flipping my front wheel
sideways. Kinda glad that one got stolen, in retrospect.

I see two factors contributing to these things: 1, my weight, which particularly nowadays requires
pretty substantial amounts of Newtons to slow down, and 2, that drum brakes are not all that good at
braking. Two of 'em are perfectly adequate, even for me, in the right setting (as long as they're in
good condition and not on the bike mentioned in paragraph
4), but I wouldn't want to go downhill with them much.

Jasper

 

[Sheldon Brown]

Jasper Janssen wrote:

I wrote:

>>Pitchover has nothing to do with using both brakes at once.
>>
>>The great danger of this setup [both brakes controlled by the same lever] is fishtailing.
>
> Fishtailing is when the rear wheel loses traction, the front is still getting braked, and the rear
> continues its tendency to keep going in a straight line by 'breaking out' and making you end up
> sideways (and on a tandem, I'd imagine generally on the ground) or worse, right?

Bingo.

> On my commuter clunker, with my weight, using drum brakes, it seems the only way to stop in a
> reasonable distance is by using both brakes. The front cannot get anywhere near enough leverage to
> get close to getting my weight off the rear, unless I deliberately move my weight to the front.
>
> That wouldn't help, it's not that the front hasn't got enough weight such that it loses traction
> under heavy braking loads. It's just that the maximum force is used that the brake pads can get
> with a reasonable force on the levers.

Your weight has nothing to do with it, the problem is that your front brake is inadequate/defective.

I was referring to bikes where the front brake was in good working order.

Sheldon "Better Get It Fixed!" Brown +----------------------------------------+
| All theory, dear friend, is grey, | but the golden tree of actual life | springs ever green.
| --Goethe |
+----------------------------------------+ Harris Cyclery, West Newton, Massachusetts Phone
617-244-9772 FAX 617-244-1041 http://harriscyclery.com Hard-to-find parts shipped Worldwide
http://captainbike.com http://sheldonbrown.com

 

[Jasper Janssen]

On Thu, 05 Jun 2003 16:27:41 -0400, Sheldon Brown <[email protected]> wrote:

>Your weight has nothing to do with it, the problem is that your front brake is
>inadequate/defective.

Not defective, just inadequate. I think. I'll have to get to a big parking lot sometime next week
and do some emergency stop tests, see how good they really are

Even with the cantis on my other old bike, though, with regular pads, they weren't quite good enough
to lift the rear wheel or get close to it. The one time I went over the bars, ever, was when my
front wheel encountered the side of a stationary car (stationary when I hit it, moving into position
for me to hit a second before). Different bike, BTW, which had a new fork after the incident. To get
me to be at .6 G or 5.9 m/sec^2 would require nearly 800 Newtons. The rim and spokes might be able
to withstand that, but that sounds like an awful lot of friction to make. It'd be 1.5 to 2 times as
much as most of the people here would need.

On my new to-be-built bike (which will have the frame of the old bike-with-cantis, and everything
else new and perfectly adjusted. Hopefully.), I intend to get/make/adjust brakes with a pretty high
mechanical advantage, but while I had it before, I never knew enough to mess with the adjustment
much. As far as the drum brakes are concerned.. maybe I could install brake levers with adjustable
mechanical advantage and adjust those to pull harder. Better compressionless cable housings might
make a difference. I'll experiment with it sometime.

Jasper

 

[Lee Bower]

Sheldon, While I understood your intentions, having dual brakes with one lever on a tricycle could
also be extremely dangerous. If one side worked better than the other, the trike would steer to the
side with the better brake. Turning brakes, as they are called, are common on off-road vehicles,
especially sand cars. I once had a truck with a warped front drum (remember, they had drums up
front?). When the brakes were pressed hard, the truck would steer uncontrollably in that direction.
I fixed that one quick!

Lee Bower

"Sheldon Brown" <[email protected]> wrote in message
news:[email protected]...
> Pete Biggs wrote:
>
> > Below is a copy of an article posted to another forum. It is all
correct
> > and reasonable?
>
> No, it isn't.
>
> The first three paragraphs are entirely wrong. The 4th paragraph is irrelevant.
>
> The only good reason to operate two brakes with one lever is if they're side-by side wheels on a
> tricycle or trailer.
>
> For a bicycle, it's generally a Bad Idea to use both brakes at the same time, and if you have no
> way of modulating them separately, it becomes a Very Bad Idea.
>
> See: http://sheldonbrown.com/brakturn.html
>
> Sheldon "Stop!" Brown +---------------------------------+
> | If you understand everything, | you must be misinformed. | --Japanese Proverb |
> +---------------------------------+
>
> > thanks ~PB
> >
> > =================================
> >
> > The only difference that there can ever be between two brakes operating from the same lever with
> > the same clearance is that due to progression. This is the amount that the mechanical advantage
> > changes as the brake moves through it's travel.
> >
> > The simplest way this is done is to move the pivots so that the radius between the pad and pivot
> > is at about 45 degrees to the rim face. This
is
> > what V brakes (and cantis) do with their pivots on the forks. Cantis
would
> > also be progressive like V brakes if it weren't for the straddle cable undermining it all again.
> > However even V brakes only exhibit about 15% improvement over a neutral mechanism due to
> > progression, the rest of
their
> > performance is due to the increased cable travel.
> >
> > The ultimate force available is proportional to the square of the cable travel, so with double
> > the travel of a drop bar lever you could get up
to
> > four times the braking. In practice you wouldn't need that much so I
doubt
> > that V brakes are optimised for maximum force. Either way, the 15% improvement from progression
> > looks pretty insignificant. All of this argument ignores friction, if you include the effect of
> > friction you
gain
> > even more with extra cable travel, because cable tension, and hence friction is reduced.
> >
> > Cable stretch: All materials stretch/deform by a amount proportional to the load
applied,
> > whilst the load remains within the elastic limit. Beyond the elastic
limit
> > the structure takes a permanent set. The stretch on the cable is well within the elastic limit,
> > but with 1.3m of cable and only 10mm of
travel,
> > it doesn't take much force to soak up half the travel. The front cable
is
> > half the length and so requires twice the force to stretch the same
amount
> > of course. The amount of stretch (S) is: S=FL/(AE) where L is the unstretched length F is the
> > force applied A is the cross sectional area of the cable and E is the Youngs Modulus for
> > stainless steel, a factor that defines how rigid a material is.
> >
> >
>
>
> --
> Sheldon "Insert Nickname Here" Brown
> +-----------------------------------------------------------------+
> | This message has been sent to you using recycled electrons | exclusively. Please do not
> | discard them after use, | send them along and help conserve these irreplaceable | sub-atomic
> | resources for future generations. |
> +-----------------------------------------------------------------+ Harris Cyclery, West Newton,
> Massachusetts Phone 617-244-9772 FAX 617-244-1041 http://harriscyclery.com Hard-to-find parts
> shipped Worldwide http://captainbike.com http://sheldonbrown.com

 

[Sheldon Brown]

Lee Bower wrote:
> Sheldon, While I understood your intentions, having dual brakes with one lever on a tricycle could
> also be extremely dangerous. If one side worked better than the other, the trike would steer to
> the side with the better brake.

That's also true of automobiles.

Back in the late '60s, I was a hippie cab driver in Boston, and not being one of the old timers, I
generally got the crummiest cabs.

A couple of times, though, I got lucky, and got a vehicle that had a bad front end, causing it to
pull to the right, and also bad brakes, causing it to pull to the left.

This was pretty cool, 'cause you didn't need to use the steering wheel except for actual turns. Just
a light pressure on the brake to go straight. Ease up on the brake to go right, brake a bit harder
(maybe with a bit more gas to keep up speed) to go left...

Sheldon "Serendipity" Brown +-----------------------------------------------------+
| We can complain because rose bushes have thorns, | or rejoice because thorn bushes have roses. |
| --Abraham Lincoln |
+-----------------------------------------------------+ Harris Cyclery, West Newton, Massachusetts
Phone 617-244-9772 FAX 617-244-1041 http://harriscyclery.com Hard-to-find parts shipped Worldwide
http://captainbike.com http://sheldonbrown.com

 

[Erik Brooks]

you ought to check
> your cable stretch ideas by hanging a 100lb weight on it and measuring the "stretch". You'll be
> surprised how little there is.

Regarding 'cable stretch' - in practice, would this actually be cable housing compression?

 

[Jobst Brandt]

Erik Brooks writes:

>> you ought to check your cable stretch ideas by hanging a 100lb weight on it and measuring the
>> "stretch". You'll be surprised how little there is.

> Regarding 'cable stretch' - in practice, would this actually be cable housing compression?

Not exactly. When a cable housing does not lie in circular arcs it does so under load and this makes
a length change. Of course if the cable housing is damaged (kinks) then these also change position
and length. There are two common brake cable housings, ones with square wire have a "keystone" wire
cross section so that it has a greater contact area when the housing is curved. I don't know whether
this is better on the average than the round wire coils but it seems to be. I haven't measured it.

Jobst Brandt [email protected] Palo Alto CA