Does contact area affect friction?
Thomas Morrow
In friction climbing, you are told to smear as much rubber as you can
on the rock in order to increase your holding force. But this goes against
my high school physics, which says that the holding force is the
friction coefficient times the normal force. Since contact area
doesn't affect either the coef or the normal force, it shouldn't make
any difference.
But physics definitely goes against my experience. If I try footholds
on 70-80 degree sandstone, I slip when just my toe contacts, but if I
smear the ball of my foot, I stick.
I am sure this question has been discussed before, but I am interested
in the answer.
-Tom
--
-Tom
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Shane Jensen
>In friction climbing, you are told to smear as much rubber as you can
>on the rock in order to increase your holding force. But this goes against
>my high school physics, which says that the holding force is the
>friction coefficient times the normal force. Since contact area
>doesn't affect either the coef or the normal force, it shouldn't make
>any difference.
>
>But physics definitely goes against my experience. If I try footholds
>on 70-80 degree sandstone, I slip when just my toe contacts, but if I
>smear the ball of my foot, I stick.
In the perfect world of physics the "force of friction" is equal to
the "coefficient of friction" times the "force" that is creating the
contact between the two objects. This "friction force" does not vary
by changing the contact surface area(keeping the "force" the same).
This is the high school version, assuming we live in a perfect world.
Now off to the real world. On many(almost all) objects the
"coefficients of friction" changes as the surface contact
area does. This effective coefficient increases as the area
increases. So by increasing the contact area, you increase
the "coefficient of friction" therefore increasing the "force
of friction".
Imaging holding an object in one finger, now let another finger help,
and then another, until all fingers are holding on. It has
become easier to hold and requires less force to hold. Something
similar for the shoes. The rubber acts as the fingers(pushing itself
into the irregular surface of the rock), the more
rubber making contact the more friction that is created.
Hope this was understandable. My students seem to follow a similar
explanation but then they could be lying 8-).
Shane
--
/------------------------------------------------------------------\
| Shane Jensen(INFP) uph...@gemini.oscs.montana.edu |
| "Imagination is more important than knowledge" Albert Einstein |
\------------------------------------------------------------------/
Andrew Butterfield
uph...@gemini.oscs.montana.edu (Shane Jensen) wrote:
WARNING - for technophile climbers only !!!
>
> Now off to the real world. On many(almost all) objects the
> "coefficients of friction" changes as the surface contact area
^^^^^^^^^^^^
> does.
pressure - surely
> Imaging holding an object in one finger, now let another finger help,
> and then another, until all fingers are holding on. It has
> become easier to hold and requires less force (*) to hold.
force *PER FINGER* --- the total force applied by all your fingers
will have risen.
>Something
> similar for the shoes. The rubber acts as the fingers(pushing itself
> into the irregular surface of the rock), the more
> rubber making contact the more friction that is created.
High school physics is wrong, but in the wy you have stated
Andrew Butterfield, butr...@cs.tcd.ie
Dept. of Computer Science, Trinity College, Dublin 2, IRELAND
Philip S Sidel
>mor...@oracle.com (Thomas Morrow) writes:
>> ...
>>my high school physics, which says that the holding force is the
>>friction coefficient times the normal force. Since contact area
>>doesn't affect either the coef or the normal force, it shouldn't make
>>any difference.
>>
>>But physics definitely goes against my experience.
>> ... I slip when just my toe contacts, but if I
>>smear the ball of my foot, I stick.
>
> ....
>Now off to the real world. On many(almost all) objects the
>"coefficients of friction" changes as the surface contact
>area does. This effective coefficient increases as the area
>increases. So by increasing the contact area, you increase
>the "coefficient of friction" therefore increasing the "force
>of friction".
>
>Imaging holding an object in one finger, now let another finger help,
>and then another, until all fingers are holding on. It has
>become easier to hold and requires less force to hold. Something
>similar for the shoes. The rubber acts as the fingers(pushing itself
>into the irregular surface of the rock), the more
>rubber making contact the more friction that is created.
>
> ....
I'm no physicist (high school or otherwise), but Shane's illustration
brings to mind another possible factor. I believe that it is easier
(less painful to the body parts in contact with the rock and less
demanding on the muscles and tendons applying the pressure) to apply
greater pressure or force against the rock when a larger body area
(say the ball of the foot as contrasted with just a toe) is in contact
with the rock. Aside from the greater surface provided by a smear,
the smear also involves a shorter (and stronger) set of linked
appendages.
On the other side of the balance is the contortion involved in getting
the foot into a smear position compared with the more natural foot
position of edging on a toe. This negative factor can be reduced by
stretching and practice to increase foot flexibility and "naturalness"
of smearing. (I still have a long way to go to maximize the foot
surface I get onto the rock and the pressure I get onto my feet to
hold them on -- part of it is also learning to direct the pressure
more against the rock and less in the "sliding off" direction -- that's
mostly getting my body weight properly distributed above my feet, but
also some pressing with legs and feet).
Phil Sidel
--
Philip S. Sidel, T.Dir., CIS/SSCRCC | Phone: (412)648-7384
2R26 Forbes Quad | Bitnet: SI...@PITTVMS.BITNET
The University of Pittsburgh | Internet: Si...@VMS.CIS.PITT.EDU
Pittsburgh, PA 15260 | sid...@pitt.edu
Michael S Hood
>In article <TMORROW.93...@ap215sun.oracle.com> tmo...@oracle.com (Thomas Morrow) writes:
>>In friction climbing, you are told to smear as much rubber as you can
>>on the rock in order to increase your holding force. But this goes against
>>my high school physics, which says that the holding force is the
>>friction coefficient times the normal force. Since contact area
>>doesn't affect either the coef or the normal force, it shouldn't make
>>any difference.
>
>Now off to the real world. On many(almost all) objects the
>"coefficients of friction" changes as the surface contact
>area does. This effective coefficient increases as the area
>increases. So by increasing the contact area, you increase
>the "coefficient of friction" therefore increasing the "force
>of friction".
I disagree.
Leonardo da Vinci wrote, "Friction made by the same weight will be of
equal resistance at the beginning of the movement though the contact
may be of DIFFERENT BREADTHS or LENGTHS" (emphasis mine).
If a large area supporting a certain load is in contact with the surface,
there are a large number of small area contacts supporting the load. If
a small area supports the same load, there are fewer contacts (due to the
smaller area available), each of which is larger than the contacts on the
large area.
The total microscopic contact area, which produces the frictional force,
is the same for both areas. The frictional force is proportional to
the normal force (as in the equation) due to the phenomenon just illustrated.
Michael Hood
This is not necessarily the opinion of the Hillenbrand Biomedical Engineering
Center at Purdue.
Michael S Hood
friction:
The total microscopic contact area increases with increasing normal force.
Conceptually, the previous poster (the one whom I answered) is partially
correct; the coefficient of friction is influenced by MICROSCOPIC contact
area (not the actual area in "contact" with the surface).
I hope this physics stuff makes sense to many. I will be happy to provide
further explanation.
Michael Hood
This is not necessarily the opinion of Hillenbrand Biomedical Engineering
Center at Purdue.
Michael S Hood
that "contact area" affects the frictional force.
I have a suggestion (just brainstorming input) for
why more friction is present when the foot is firmly set on the rock
as opposed to just applying the toe edge:
The normal force is the component of applied force which is ORTHOGONAL
(at right angles or perpendicular) to the surface. Perhaps this
component is greater when the foot is more firmly set, thus producing a
higher frictional force through the greater normal force (not the greater
surface area).
Michael Hood
This is not necessarily the opinion of the Hillenbrand Biomedical Engineering
Center at Purdue.
jim bowers
(Thomas Morrow) says:
>
>In friction climbing, you are told to smear as much rubber as you can
>on the rock in order to increase your holding force. But this goes against
>my high school physics, which says that the holding force is the
>friction coefficient times the normal force. Since contact area
>doesn't affect either the coef or the normal force, it shouldn't make
>any difference.
>
>But physics definitely goes against my experience. If I try footholds
>on 70-80 degree sandstone, I slip when just my toe contacts, but if I
>smear the ball of my foot, I stick.
>
>I am sure this question has been discussed before, but I am interested
>in the answer.
>
In rock climbing it is not a standard coef of friction scenereo.
There are two differences.
1) interlocking - this is like two pieces of velcro stuck to each other.
The rock acts like a velcro hook to grab the rubber and the more
velcro the better.
2) deformation - a small piece of rubber in contact will tend to deform
and move more than a large piece of rubber. As soon as the rubber
starts to deform and move than you are talking about dynamic friction
which is less than static friction.
Therefore the more rubber on the rock the better which is why slippers
are so awesome on friction.
Jim Bowers
Michael
>uph...@gemini.oscs.montana.edu (Shane Jensen) writes:
>>mor...@oracle.com (Thomas Morrow) writes:
>
>>Now off to the real world. On many(almost all) objects the
>>"coefficients of friction" changes as the surface contact
>>area does. This effective coefficient increases as the area
>>increases. So by increasing the contact area, you increase
>>the "coefficient of friction" therefore increasing the "force
>>of friction".
>>
>>Imaging holding an object in one finger, now let another finger help,
>>and then another, until all fingers are holding on. It has
>>become easier to hold and requires less force to hold. Something
>>similar for the shoes. The rubber acts as the fingers(pushing itself
>>into the irregular surface of the rock), the more
>>rubber making contact the more friction that is created.
Whoever you are all i can say is go back to PHYS101, or better yet, high-school.
This is inane. Your example contradicts itself. This is stupid.
Coming from someone who knows, you have made some mistakes here. These posts
simply mislead people who otherwise would be learning the truth. Please
check your facts before you post. Read Mike hood's article (ho...@niblick.ecn.
purdue.edu) a few (10 or so) posts back. This is correct.
What increased surface area does is decrease the likelihood of shear.
Teeth will not change this area in smooth rock dependably though. The odds
are just as good of decreasing the area. On rough rock it will possibly
change things, but what changes is the relative transmission angle, and thus
the normal force, NOT THE COEFF OF FRICTION!!!
>brings to mind another possible factor. I believe that it is easier
>(less painful to the body parts in contact with the rock and less
What you are feeling on the skin is SHEAR which is related to area.
>demanding on the muscles and tendons applying the pressure) to apply
Pressure is not applied, force is.
>greater pressure or force against the rock when a larger body area
>(say the ball of the foot as contrasted with just a toe) is in contact
>with the rock. Aside from the greater surface provided by a smear,
>the smear also involves a shorter (and stronger) set of linked
>appendages.
True
Eric Hirst
The coefficient of friction f is defined as:
Max. tangential force / unit area Max. shear stress
f = -------------------------------- = --------------
Normal force per unit area Pressure
If the maximum shear stress were a linear function of pressure, f
would be a constant. (High school model.) But there is no reason
to expect that it should be a linear function, particularly over a
wide range of pressures. In particular, previous posters have noted
that the maximum shear stress is limited by the tendency for chunklets
of rubber to spooge clear off the shoe.
At least one other poster noted that the actual pressures and shear stresses
will vary somewhat over the contact area. I recommend imbedding an array
of strain gauges into each shoe and wiring them to a small personal computer
which can numerically integrate the stresses and resolve the net force
components. All the top climbers are using these nowadays.
Eric Hirst
er...@u.washington.edu
Maybe next time, I'll post something good.
k...@onan.jhuapl.edu
you all would have flunked. Prior to being nuc'd by the bb at large, I'd like
to paraphrase Socrates (actually Plato, in Phaedro I think) and observe that
people who're wise in one limited respect tend to believe that they know
everything. You don't need to know any physics to climb. Monkeys do a fine job
of it. Being able to climb 14d XXXX doesn't imply that you're Dirac, Feynman,
etc.
BTW, if anyone is interested in a REAL (read quantitative) dialogue about the
physics of a fall, shoe friction, the (human) kinematics and dynamics of
climbing, dissipation (vs storage) in dynamic ropes, whether catastrophes are
possible, new materials for climbing, etc,etc,etc should email me. Maybe we
could revisit some of the original work at a leisurely pace and come up with
useable quantitative tools for the (physics) laypeople. Maybe even some
simulation of kinematics. Could be fun...
Kim
Edward Pavelchek
> In rock climbing it is not a standard coef of friction scenereo.
> starts to deform and move than you are talking about dynamic friction
> which is less than static friction.
I know this is textbook learning for standard materials, but it seems
contrary to a typical experience, which is slowly smearing off extreme
friction foot placements. One counter argument is that your motions as
you rock back and forth are 'walking' the rubber off the hold, but I
have tried standing as still as possible on extreme friction angles
(bouldering) and have still found that my feet slide slowly.
This implies that static friction si the same or lower than dynamic
friction, at least for Stealth and some other rubbers on granite.
For car tires, having similar static and dynamic friction would seem to
be a safety advantage, as loss of control would not be as drastic.
--
Ed Pavelchek e...@mcnc.org
"...but that is another story. As far as we knew, we were
living happily everafter." Royal Robbins
Shane Jensen
>I know this is textbook learning for standard materials, but it seems
>contrary to a typical experience, which is slowly smearing off extreme
>friction foot placements. One counter argument is that your motions as
>you rock back and forth are 'walking' the rubber off the hold, but I
>have tried standing as still as possible on extreme friction angles
>(bouldering) and have still found that my feet slide slowly.
>
>This implies that static friction si the same or lower than dynamic
>friction, at least for Stealth and some other rubbers on granite.
Static friction is always greater than dynamic friction.
On extreme angles the force pulling you down is greater than the
static frictional force. Since you are sliding, dynamic frictional
forces are now in control.
Let u=coefficient of friction(u(static) > u(dynamic))
m=mass of object
g=gravitational acceleration
angle=steepness of ramp(0=horizontal,90=vertical)
The two equations below are the forces that are parallel to
the surface. It is these forces that determine whether you
will slip or won't.
The first equation shows that friction decreases as the angle
increases. The second equation shows that the force pulling
an object along the surface increases as the angle increases.
Friction=u*m*g*cos(angle)
Force=m*g*sin(angle)
When "Force" becomes greater than than "Friction(static)", the object
begins to move. Now "Friction" decreases because we must
consider dynamical friction(u(dynamic) < u(static)).
In the case of climbing shoes u(dyn) is close to u(stat) but
u(dyn) is still less than u(stat).
>For car tires, having similar static and dynamic friction would seem to
>be a safety advantage, as loss of control would not be as drastic.
Tire manufactorers consider this when designing tires. As of right
now, having u(dynamic) close to u(static) means creating tires out
of rubber compounds like our climbing shoes. These tires would be
expensive, and would not last very long. Not a cost effective
option.
Let's see how many disagree with me this time 8-)
Shane
BTW, I do have references available for those who are interested.
Edward Pavelchek
>In article <1993Apr12.1...@mcnc.org> e...@mcnc.org (Edward Pavelchek) writes:
>>have tried standing as still as possible on extreme friction angles
>>(bouldering) and have still found that my feet slide slowly.
>>
>>This implies that static friction si the same or lower than dynamic
>>friction, at least for Stealth and some other rubbers on granite.
>
>Static friction is always greater than dynamic friction.
>
>On extreme angles the force pulling you down is greater than the
>static frictional force. Since you are sliding, dynamic frictional
>forces are now in control.
>When "Force" becomes greater than than "Friction(static)", the object
>begins to move. Now "Friction" decreases because we must
>consider dynamical friction(u(dynamic) < u(static)).
>In the case of climbing shoes u(dyn) is close to u(stat) but
>u(dyn) is still less than u(stat).
This is classically correct, but not always descriptive of reality.
Hasn't everyone s l o w l y greased off friction smears?
If the dynamic friction is sizably
less than the static friction, *which was insufficient to support me at
a particular angle*, then I should accelerate downwards. Conditions can
be found where the foot moves inexorably a whole inch or so in 60+
seconds. Constant motion, not increasing speed.
Are you going to model shoe rubber as a solid under static
friction, but as a viscous fluid under dynamic friction? That's
probably pretty useful, but the fact that no appreciable speed picks
up still means that the static friction and the viscous drag are
identical.