if you wanted maximum braking, where would you sit?

Omitted assumtion: the tires are at or near the limits of adhesion.

Hence, the equal load on the front and rear tires, since optima
traction occurs when both tires are equally loaded


-

Nemo wrote: “I believe that a standard road bike can has a maximu
deceleration rate to the tune of about .6g's.

That’s in accord with the .57g figure the article I later cite
indicated as a strong braking level

”Because quality tires now have coefficients of friction around .9 t
1.5, in almost all situations involving a traditional bike on clean, dr
pavement, the deceleration rate is limited by the bike's tendency t
roll over the front tire. As previously stated in the thread, this roll
over tendency is a function of the angle of the CG relative to the fron
contact patch and the ground.

I initially though the coefficient of friction might be that high, bu
when I calculated rollovers at those levels, I though it might be of
since I remember skidding fronts on road bikes on occasion without doin
endos. So the presented tabulations were for lower decel rates assumin
the adhesion limits were close to the .6G. Apparently, we need plug i
higher decel rates into the optimal seat placement formula I derived fo
more realistic seat placement on the braking specialized bike

Assuming that it is possible to locate the CG anywhere we like, it i
possible to use the maximum available traction between the tires and th
road. If the coefficient of friction of tires is assumed to be constan
regardless of load, weight distribution is a null factor

“Unfortunately, real tires have a coefficient of friction that drops a
load increases.” Yep, that’s why I calculated seat placement spreadin
load over both tires equally under decel

“(I believe this has something to do with the thermal properties o
rubber.)” Nope, it has to do with the flexibility and distortion of th
rubber letting the tire embed itself into small irregular contours i
the pavement and then increasing tractions due the tires horizonta
abutting of those irregularities

“It thus becomes evident that ideal weight distribution minimize
weight on both tires, implying that they each carry half of th
constant load. The easiest way to do this on paper is to simply cente
the CG between the tires and put it at ground level. We all know tha
the CG will always be some distance above ground level. In that case
it must be located further back to compensate for the forward weigh
shift while braking. In fact, the CG location can be determined by th
following formula

Df= h*CF+WB/

Where, Df is the horizontal distance of the CG from the front contac
patch, h is the CG height above the ground, CF is the coefficient o
friction between the tires and the road, and WB is the distance betwee
the front and rear contact patches

Having said all that, it may be true that the drop of the CF for
bicycle with unequally loaded tires is so small that it is not wort
considering. In that case, the weight must only be shifted back to
distance of

Df=h*C

to achieve maximum braking.

I made bike and rider cg independent variables

Since the OP was interested in the maximum braking position,
calculated optimal seat position premised upon the even weigh
distribution under decel, independent of whether deviations from tha
position might be small or large. The non-linear coefficient of frictio
not trivial with automobile, although I’m not sure whether the round to
profile of the bike tire reduces or enhances this effect relative th
flat top profile of a car tire or if the lighter weight of the bike tir
would place the function of coefficient of friction as a function o
weight in a flatter curve

Obviously, positioning a seat for maximum braking means ignoring idea
handling positioning, so this is a braking purpose only solutio
equation, and except for the low cg recumbents, is so poorly weigh
distributed outside of decel as to be a very poor handling bike. A roa
bike optimized for a coefficient of friction of 1, will be doomed t
wheelies when seated and not braking


Changing the decel rate to 1G, gives the following seat positions fo
the previously posted bikes

Road bike 77.11 inches behind patch Second lowracer (9” seat height
35.38 behind patch (that puts us in the rear tire). LWB recumbent 53.2
“behind patch (that also puts us in the rear tire). MWB recumbent 56.14”
behind patch (above the rear, 2” back of axle, so no wheelies.) Carbon
Prone 61.11” behind patch.



--

meb wrote:

...
Changing the decel rate to 1G, gives the following seat positions for
the previously posted bikes:

Road bike 77.11 inches behind patch Second lowracer (9?seat height)
35.38 behind patch (that puts us in the rear tire)....

On my recumbent lowracer, the (estimated) combined CG is about 24"
behind the front tire contact patch.

Tom Sherman - Quad Cities

On Sun, 11 Jan 2004 22:55:58 GMT, meb
wrote:
clipped
In fact, the CG location can be determined by the
following formula:

Df= h*CF+WB/2

Where, Df is the horizontal distance of the CG from the front contact
patch, h is the CG height above the ground, CF is the coefficient of
friction between the tires and the road, and WB is the distance between
the front and rear contact patches.

Having said all that, it may be true that the drop of the CF for a
bicycle with unequally loaded tires is so small that it is not worth
considering. In that case, the weight must only be shifted back to a
distance of:

Df=h*CF

to achieve maximum braking. “

I made bike and rider cg independent variables.

Since the OP was interested in the maximum braking position, I
calculated optimal seat position premised upon the even weight
distribution under decel, independent of whether deviations from that
position might be small or large. The non-linear coefficient of friction
not trivial with automobile, although I’m not sure whether the round top
profile of the bike tire reduces or enhances this effect relative the
flat top profile of a car tire or if the lighter weight of the bike tire
would place the function of coefficient of friction as a function of
weight in a flatter curve.


Obviously, positioning a seat for maximum braking means ignoring ideal
handling positioning, so this is a braking purpose only solution
equation, and except for the low cg recumbents, is so poorly weight
distributed outside of decel as to be a very poor handling bike. A road
bike optimized for a coefficient of friction of 1, will be doomed to
wheelies when seated and not braking.



Changing the decel rate to 1G, gives the following seat positions for
the previously posted bikes:

Road bike 77.11 inches behind patch Second lowracer (9” seat height)
35.38 behind patch (that puts us in the rear tire). LWB recumbent 53.28
“behind patch (that also puts us in the rear tire). MWB recumbent 56.14”
behind patch (above the rear, 2” back of axle, so no wheelies.) Carbon
Prone 61.11” behind patch.

CG is approximately at the navel I've read, so the lowracer with 9
inch would have a CG at 16 to 18 inches high or 16-18 inches behind
the contact patch for 1 G braking. Practically, the front wheel can
do 100% of the braking without changing the CF much, using automobiles
(front or rear engine) as an example.

Tom Schneider

Tom Sherman wrote:
meb wrote:
... Changing the decel rate to 1G, gives the following seat positions
for the previously posted bikes:

Road bike 77.11 inches behind patch Second lowracer (9?seat height)
35.38 behind patch (that puts us in the rear tire)....
On my recumbent lowracer, the (estimated) combined CG is about 24"
behind the front tire contact patch.
Tom Sherman - Quad Cities


The equation I derived had seperate bike and rider cg premised upon th
rider location being adjustable

If the 24" coincides with the bike cg position, the optimal braking sea
position would shift rearwards

Obviously, the designer of your lowracer was not focussing on bes
braking as the ultimate design objective to sacrifice all othe
attributes in hopes of achieving the optimal braking bike. :


-

ZeeExSixAre wrote:
"David Damerell" wrote in message
ZeeExSixAre wrote:
True, but braking on a road bike isn't usually as nearly effective as on an
MTB because you can't really pull big leverage while on the hoods.
Bunk. I can lift the rear wheel from the hoods. How much more braking can
I have?
I can too, but I have to lean way forward. I was thinking more of the
insta-endo that most people can do with flat bars.

Er, if I can lift the rear wheel from the hoods in a controlled fashion,
but getting a free flying lesson is easier from flat bars, I think I would
describe the road bicycle's braking as more effective.
--
David Damerell flcl?

David Damerell wrote:

ZeeExSixAre wrote:
"David Damerell" wrote in message
ZeeExSixAre wrote:
True, but braking on a road bike isn't usually as nearly effective as
on an MTB because you can't really pull big leverage while on the
hoods.
Bunk. I can lift the rear wheel from the hoods. How much more braking
can I have?
I can too, but I have to lean way forward. I was thinking more of the
insta-endo that most people can do with flat bars.

Er, if I can lift the rear wheel from the hoods in a controlled fashion,
but getting a free flying lesson is easier from flat bars, I think I
would describe the road bicycle's braking as more effective.

That's just because you've defined effective as "easily able to stop as
quickly as possible" rather than "easily able to brake so hard I can kill
myself." What on earth are you thinking?

--
Benjamin Lewis

Everything that can be invented has been invented.
-- Charles Duell, Director of U.S. Patent Office, 1899

(wle) writes:

if you could position your center of gravity anywhere, to ensure
maximum braking power, where would it be?

obviously over the front wheel is no good, you would flip.

there is a point, leaning either ahead of the front wheel, or
behind the back wheel, that the opposite wheel is off the ground.

clearly those are 2 limits, the answer must lie between them.

if there were very little friction, it would hardly matter.

assume a level road, brakes that can cause a skid no matter what.

ok, so where do you sit?

When you brake, you decelerate; this causes the net vector of force on
each of the masses which make up the bike and rider to swing forward,
so it is equivalent to going down a hill. Essentially you need your
body weight as far aft and as low down as possible consistent with

(a) maintaining control of the bike - so your hands have to stay on
the grips and your feet on the pedals;

(b) not doing your posterior a severe mischief - so your arse has to
stay off the back tyre.

Generally this means sliding off the back of the saddle and lowering
yourself behind it which in my case at the limit equates to resting my
sternum on the sadde.

Note that, on a normal 26", 27" or 700c wheeled diamond frame bicycle
it is impossible on level ground for a normal rider to get their
weight so far aft as to tip the bicycle over backwards while
maintaining grip on the bars and feet on the pedals, still less when
braking or descending; so that's a non-issue.

state assumptions, like coefficient of friction between tire and road,
weight of bike and rider.

It really doesn't matter. On wet roots the coefficient is nearly
nil. On dry, course-grained sandstone it's effectively infinite. In
order to keep the wheels rolling (which you need to do to get most
efficient stopping power) you obviously need much less braking force
on the former than on the latter, but it still does no harm to get
your weight back in an 'oh-****-I-need-to-stop-NOW' situation.

Of course in an 'oh-****-this-one's-going-to-hurt' situation it often
makes sense to get off the bike... *before* it hits whatever's going
to stop it dead. Less damage to you and usually less damage to the
bike. Note that if you are in mid air at the time this may not be
relevent...

--
(Simon Brooke) http://www.jasmine.org.uk/~simon/

;; Want to know what SCO stands for?
;; http://ars.userfriendly.org/cartoons/?id=20030605

Sheldon Brown wrote in message
I think you are correct because the OP misstated the problem. In
reality however Tim M is correct. In practice, when we go over
the bars it is not [usually] because the front wheel stops and
the bike and rider pivot around the contact patch. More often
we go over the bars because the frame and fork and rider and rear
wheel pivot around the front axle.

'Fraid not. For that to happen, the front wheel would have to stop
moving forward, while the frame and fork did the endo.

I don't think the wheel has to stop - so every nose wheelie is
preceeded by a wheel locking? A relative slowing would suffice,
presuming the necessary rotation got it's start somehow...

...Such a scenario
would actually involve the front hub bearing reversing direction, so the
wheel would be rolling backward with respect to the frame. Where is
there a force that would cause the front wheel to rotate backwards?

From rider movement. The same way that riders do nose wheelies, or
"stoppies" -- by throwing ones weight forward into the bars, or by
picking up the rear wheel by lifting one's feet -- except unintentionally
-- an accident of rapid deceleration.

Surface irregularities in the road could do it as well.

In a case where the front wheel is forcibly stopped by falling into a
deep pothole or hitting a high curb, it _is_ possible for the bike to
pivot around the front axle, but there's no way this can happen under
the influence of the brake alone.

Agreed. There has to be something else there to get it started.

Doug

On Fri, 09 Jan 2004 19:33:12 -0600, Tom Sherman
wrote:
The following website will be instructive to mechanically inclined
people interested in trike construction details.

That is so cool, it makes me want to go and build one right now.
Unfortunately, there are any number of limiting factors, such as my
lack of equipment, supplies, knowledge, ability, money, and time.
I've got the enthusiasm, although with my short attention span I
don't know if it would last long enough to finish the project.

In
http://www.ihpva.org/com/PracticalInnovations/weld.html
under the section titled "Trike steering geometry", sub-title
"Ackerman steering compensation", steering is treated as if there
was a live axle with no differential for the front wheels. I think
such trikes are nearly all rear wheel drive, leaving no need for a
live axle; why would there be front wheel scrubbing?

Does your trike use Ackerman steering compensation?

Tom Sherman - Quad Cities
--
Rick Onanian