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CoP v's CoF

Discussion in 'Biomechanics, Sports and Foot orthoses' started by Cpod, Jun 8, 2009.

  1. Cpod

    Cpod Welcome New Poster

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    I have been reading some literature about inversion sprains. I'm a little confused regarding the use of terminology when discussing foot biomechanics. I understand what Centre of Pressure is, however some literature refer to Centre of Force. Does this mean the same thing?

    Thanks for your help.
  2. David Smith

    David Smith Well-Known Member


    Strictly speaking no it does not, however some literature uses it interchangeably.

    Force = mass * Acceleration and Pressure = unit force / area, so you can see that pressure is not force. This would be like saying apples and apple pie are basically the same. Apple = a certain fruit and apple pie = a certain fruit covered with pastry. It doesn't work.

    Now specifically, pressure is the force over an area and therefore since area is 2 dimensional and scalar you cannot measure pressure in 3 dimensions and pressure does not have direction. If you do not believe this then imagine pressure inside a spherical vessel the pressure of a gas inside will act in all directions but not just in one defined direction.

    Force is in fact a vector it has magnitude and direction, force always has direction and in the real world total force is, by convention, the summation of force in 3 dimensions. (forget about time)

    Therefore generally the pressure and C.o.P is focused on some 2 dimensional plane of reference and the force that acts perpendicular to it, I.E the floor with a pressure mat on it and characterised as the vertical ground reaction force.

    And so the pressure is a measure of force / area in a specified plane e.g. the vertical pressure applied to a pressure mat characterised as pressure on the foot by the software in the computer.

    The Centre of Pressure is the summation of all the discreet forces, e.g. as measured by each force cell in a pressure mat, acting in on point of interest that balances all those forces in the plane of reference and about the 2D axes of that reference plane.

    Now, you can change the orientation of that plane but the equation then becomes (force cos theta)/area and once you do that you need to consider the trigonometrical function of the other planar forces since they to will have some influence on the total force/area or pressure. You might see that this makes using pressure insoles on an orthosis as a reference for applied pressure a little difficult to consider in terms of what force is being measured and where it is coming from.

    Centre of Force on the other hand is the summation of all forces, with direction since force is a vector, So therefore CoF has a 3D vector and is the direction is the cross product of all three forces in each plane, the force magnitude is the cube root of the sum of the cube of forces on the other three sides (extended Pythagoras).

    So therefore to define that summed force vector in terms of pressure your plane of reference would need to be rotated to be perpendicular to the summed force vector. This, clearly would not be the same reference as the normal plane of reference, which is usually the floor.

    So you see that pressure is normal (perpendicular) to the plane of reference and force has a vector. Applying this directly to the foot then:

    The CoP might have a magnitude of 500N acting vertically at say 1cm lateral to the STJ (sub talar joint) and 2cm distal to the STJ. Therefore to find the moment acting about the joint (the STJ) of interest we find:

    500 * 0.01 = 5N/m everting

    500 * 0.02 = 10N/m dorsiflexing

    Now imagine that we have a Centre of Force acting at the same location with the same magnitude but the direction is not simply vertical.

    The force has 3 components x, front - back, y, vertical and z lateral to medial (referenced to the foot of interest) x = 2N y = 50N and z = 500N then the centre of force is 500.166N (near enough to 500N). Without boring you to death with the maths the resultant force vector is directed at 5.5 dgs from the z axis and 2.5 dgs from the x axis and so the projection is well below the STJ in the x and z axis and therefore produces inverting and plantarflexing moments about the STJ. Completely the opposite in direction to the CoP action.

    So I hope you can see that CoP is definentely NOT the same as CoF. :confused::wacko:

    Cheers Dave
  3. Further to Dave's answer: whether pressure is a vector or scalar quantity is a common subject of debate.

    See here:

    The third link is probably the most interesting: "In order for a quantity to be a vector quantity there must be a unique direction for that quantity at any specific location. Consider a point in the center of a tank of compressed gas under a pressure of 100 Pascals. The pressure at that point has a magnitude, 100 Pascals, but it has NO particular direction - that makes it a scalar quantity! When that pressure, however, is applied to a surface, the result will be a vector quantity because the direction of the force that results from the pressure being applied to that surface will always be exerted perpendicularly to the surface [Pascal's Law]."

    So when pressure is applied to the surface of an orthosis, it's a vector (pressure force)?

    All yours Dave...
    Last edited: Jun 8, 2009
  4. Cpod:

    The terms "center of force" and "center of pressure" are used interchangeably within the biomechanics literature to describe the point location of force occurring on the plantar foot from ground reaction force. Center of pressure seems to be much more commonly used, but they are basically used to describe the same measurement. These are important measures in pressure mat, pressure insole and force plate studies.

    Hope this helps.
  5. Cpod

    Cpod Welcome New Poster


    That it of great help, many thanks.

  6. Cpod

    Cpod Welcome New Poster

    Many thanks for your helpful reply.

  7. David Smith

    David Smith Well-Known Member

    Pressure is scalar but when you define its plane of action it can be described as vector. This is done when using a pressure mat and the CoP at any given time is described in terms of that plane.

    However a scalar is defined as a quantity that is not changed by a change of reference frame. Therefore pressure itself is scalar but the special case of defining its direction with a reference plane makes it vector, like 20mph is a speed and a scalar but 20mph west is a velocity, which is a vector because the direction is defined by locating it in a reference frame and defining its direction.

    Now, when you change the reference frame the pressure as a vector becomes meaningless because a vector must be defined by its direction, which therefore must have a fixed reference frame.

  8. David Smith

    David Smith Well-Known Member

    Can't entirely agree with that Kevin.

    This statement is true but in my opinion not a valid protocol.


    GRF perpendicular to the load cell embedded in the pressure measuring device

    The individual load cell measures a change in voltage or resistance or capacitance differential that is a result of some known deformation reaction to a force. Therefore force is characterised but not measured and this characterisation can be displayed in anyway that the manufacturer of the equipment feels might be an intuitive display that communicates the force action.

    Pressure is a further characterisation of force in that the software determines how it will characterise discreet force in terms of an area.

    So while it is true to say that they are descriptions of the same measurement, i.e. some electrical differential, they are not characterisations representing the same thing.

    The perpendicular force applied to a load cell is absolute the pressure is not. It relies on the resolution of the hardware and software. So the force on one cell may be 10N. The pressure as characterised by the equipment could be anywhere on a scale from infinitely high to infinitely low. Could be 1 pascal or 10,000 Giga Pascals. What the actual characterisation is displayed at is dependent on convention, size of cell, resolution of software, precision of hardware, limitations of display medium etc.

    As an example:
    If you put a drawing pin sharp end on a pressure mat load cell and pressed on it with a force of 10N then the force displayed should be 10N.

    What will be the pressure? Ideally it would be 10N/area of the pin point. Lets say that area is 0.01mm then the pressure is equivalent to 1000N/mm or 100,000N/cm square square or 1giga pascal. (I pascal = 1N/mtr square)

    However, in this case the cell is actually 1cm square and so this is its highest resolution available and this is how the software characterises the force into pressure I.E. according to the display the pressure is only 10N/cm square, which is 100kilo pascals or 0.001giga pascal. Usually there are up to four cells per squ centimetre and the software will use some proprietory algorithm to sensibly characterise pressure distribution about the four cells and the gaps between the four cells and the eight sets of four cell around it. (Could be confusing eh?)

    So even tho the same data is used to characterise both parameters, the processing and evaluation protocols are different and so CoP and CoF are definentely are not the same and it is important to recognise this.

    Cheers Dave
  9. David:

    Just stating fact. Maybe you should put a post up on Biomech-L to see what the consensus is among biomechanics researchers and offer your suggestions to them as to why you think they are wrong in using these terms interchangeably. From my reading of the biomechanics literature over the past quarter century, CoP and CoF are still used interchangeably to describe the same measurement parameter.
  10. Cpod

    Cpod Welcome New Poster

    I have been looking at tools/equipment to measure CoP e.g. the MatScan, RsScan etc. When looking at ways to analyse the data, the equipment has CoF measurements, however when looking at the literature which uses these tools they present the data in CoP. Confusing?
  11. David Smith

    David Smith Well-Known Member

    Yes it is but in these cases there is a tacit agreement that force characterised by the equipment used, e.g. the pressure mat, is equal to - that force which is applied perpendicular to the plane of reference and so is the same as pressure in terms of a central point location but only on a scale that is greater than at least the area of 2 load cells.

    Kevin wrote
    Yes I will do that, just to make sure I'm not getting mixed up some where along the line. But, I ask, if they are the same then how do you find 3D applied moments about a point of interest using CoP. Isn't this is exactly what you can do using CoF.

  12. Dave:

    Think of the biomechanics terms of "CoP" and "CoF" being analogous to the automobile terms of "boot" and "trunk" or "bonnet" and "hood". Both terms describe the same things. This is the essence of the evolution of language. Maybe you can change it, but my guess you won't be able to, no matter how hard you try.
  13. Or, "fanny pack" and "bum bag" :D
  14. David Smith

    David Smith Well-Known Member

    Re: CoP v's CoF (the Biomech-L thread so far)

    Dave Smith - Original Post
    What opinions do you have regarding the use and interchangeability of the terms Centre of Force (CoF) and Centre of Pressure (CoP) especially when applied to analysing data from a pressure mat system or pressure insole system where one might be interested in pressure or force plantar to the human foot during ambulatory activities.
    Replies so far
    I'd assume that they mean the same thing, but I see COP used more often
    and that's the one I'd go with. Now if only you guys would spell
    "center" correctly! ;)

    Seriously, as a grad student I missed half of the papers on locating the
    hip center for the longest time because I didn't realize that half of
    the English-speaking world uses a different spelling!

    Brian Schulz, Ph.D.
    I'm sure I'm not shining any new light on the subject, but force is a
    vector quantity and by definition a force distributed over a surface
    becomes a pressure. To me, this means that "center of force" is
    somewhat incorrect as there is no "center", just the point origin of
    the force. Since pressure is distributed on a surface it can have a
    center. That is just my opinion, so take it for what it's worth...

    I would have two quick concerns with using COF instead of COP.

    (1) force is a vector and already classified with a single point of application/origin, so there really isn't a centre to it. Pressure (a scalar quantity) is force over an area (the plantar surface of the foot in this case), so there can be a centre to it.

    (2) COF is commonly used to abbreviate "coefficient of friction" in similar research. So it may be confusing to use it to abbreviate a different term.

    Robert D. Catena, Ph.D.

    Centre of pressure is the traditional name (e.g., Elftman, H., A
    cinematic study of the distribution of pressure in the human foot. The
    Anatomical Record, 59:481-491, 1934) and especially allies to pressure
    mapping systems but has also been used for force platform systems.
    Centre of force is not a common name and might be better replaced by
    "point of force application". In any case a force does not have a

    Gordon Robertson

    What you have to consider is how pressure mats/insoles actually work. They measure the normal force over and area, from which you can derive pressure. So to consider these two terms as representative of the outcome measure is unfair really as both force plates and pressure systems essentially measure force. The term centre of force really isn't used that frequently simply because it refers to a point of force application, which whilst it may be theoretical is a point. By the very nature of this point we should discuss this as centre of pressure.

    Hope this helps


    Dr Dominic Thewlis
    Lecturer In Biomechanics

    So the general consensus appears to be 3 things –
    1) That CoP is preferable to CoF since when considering force applied over an area it really becomes pressure by definition.
    2) CoF cannot be the same as CoP since force is a vector and pressure is scalar.
    3) Force is a point application and so cannot have a centre (or center for Brian)

    1) I can see the logic of that but as Dominic pointed out “What you have to consider is how pressure mats/insoles actually work.”

    They characterise normal force or rather discreet force locations perpendicular to a reference plane e.g. the pressure mat on the floor. The area that each force point is spread over is relative to the size of the sensor cell and nothing about the centre of pressure can be known until we have data from more than one cell.

    2) Isn’t the pressure mat scenario a special case? Doesn’t pressure become a vector when defined by a reference plane? i.e. it is given direction. Similar to speed (mph) becomes velocity when a direction is specified.
    3) Can one not consider the many force points defined by the multiple cells of a pressure mat as having a central location that is the CoF?
    So each load cell of the pressure mat only characterises normal force. If it were possible to have load cells that also characterised horizontal or shear forces then the resultant force vector for each cell would have a 3D nature and the summation of all these vectors would result in a single point 3D force vector that would be similar to the 3D force vector characterised by a force plate software output. So isn’t it fair to say that, in terms of a pressure mat or insole system, the summation of all forces, normal and shear, can be described as the Centre of Force and the summation of all normal forces the Centre of Pressure? Therefore since we do not have systems that characterise discreet force locations in 3D, only those that characterise normal force, then the only sensible term to use would be CoP.

    Dave Smith Podiatrist, MSc App Biomechanics

    Replies to second post
    From a mechanics viewpoint, the term center of force is not good. A force is a vector quantity, with a magnitude, a direction and a line of action, which means that its center is a questionable aspect. Center of pressure is from that viewpoint better, even if it assumes some things about the pressure. The crossing of the resultant contact force with the surface would be most mechanically correct, or perhaps CRP, contact resultant point. But note that this would include also the tangential component, not only the transversal as I assume is the case in the 'pressure'.

    Anders Eriksson
    KTH Mechanics

    As mentioned by some other guys, Force is vector quantity and is supposed to act on a predefined point. Thus, there can't be really a center for it. When you consider force distributed over an area you are considering pressure. Thus, as pressure is distributed quantity it can have center.
    But, there is a point of discussion here. If you have several forces applied at different points.Then, there could be a point where you can apply resultant force which could create similar effect as that of the individual forces. You can call this point as COF.
    Correct me if am wrong some where.
    Sarang Dalne
    ANSYS, Inc.

    I am much more accustomed to seeing CoP used in the literature. I would expect that CoP and CoF should be one and the same, but "pressure" implies a force distributed over an area (which I believe to be correct when talking about standing), where as "force" is simply a vector quantity that has a magnitude and a direction. Thus, I think it is technically more correct to refer to the location at which the resultant force acts under the feet as CoP.

    Hope this helps,
    Karen Troy

    Sarang (and other responders) suggested that force is a vector and acts on a predefined point. However, there are many cases of distributed forces, of which pressure is one example. Gravity is another force that is distributed (over a volume, or mass, rather than an area). When we speak of the location of the resultant force of gravity, we call it the center of gravity, but this is a special case of center of force. (Note that center of gravity is not nesasarily co-located with the center of mass, but that doesn't typically come up in biomechanics).

    So I would question the assertion that a force must act on a predefined point. We model them a such, because it makes the math simpler. However, since a force can be distributed, either continuously (pressure, gravity, etc.) or discretely (as suggested by Sarang), then the point of application of the resultant, net force could certainly be called a center of force. So, as Sarang says, I think that center of force is valid.

    I would suggest this: for insole pressure measurement, or any resultant derrived from measuring pressure over a region, center of pressure is more useful as it is more descriptive. If, however, you are using a force plate where the location of the resultant applied force is determined from discrete load cells, it is reasonable and arguably more relevant to call it a center of force.

    Is that reasonable?

    Ian Wright.
    TaylorMade Golf.


    Yes thats pretty much how I would see it, although I hadn't considered the gravity example.

    Cheers Dave Smith

    PS. Is that Ian Wright MBE Crystal Palace, Arsenal and England cap television star and now engineering boff ? :) http://www.talkfootball.co.uk/guides/football_legends_ian_wright.html
  15. Let me recap, to make sure I'm getting this right: we should use centre of pressure; pressure is a scalar; when pressure acts against a surface its action is normal to that surface. So, if we know where the centre of pressure is and we know the angulation of that point on the supporting surface, the pressure force "vector" for want of a better term will be normal to that surface? So how does friction influence the angulation of this pressure force?

    If centre of pressure is a single point, with point of application and with a line of action etc. Isn't that a vector? Indeed, isn't that a force? ;)
  16. David Smith

    David Smith Well-Known Member


    Careful now, That's almost philisophical, but sure I would agree that the vector summation of all the discreet normal force applications would represent a force application at a single point. Therefore, I here you say, might this not be defined as the centre of force? No - Because only in this special case can CoP be equated with CoF because there is no obliquity of the force to the plane of reference.
    However to avoid confusion I would prefer that the two terms are not seen as equivalent and that only CoP is applied to the centralised characterisation of the
    discreet forces applied to a pressure mat.


    More from Biomech-L

    Dear Dave,

    I'd like to add a couple of points to the discussion.

    1. Personally, I think center of pressure and center of force
    essentially mean the same thing (the point of application of the overall
    force applied to the surface). Pressure (or stress) has a direction,
    just like force (e.g., tensile stress vs. compressive stress are in
    opposite directions just like tensile force vs. compressive force).
    Think of it as the center of the force distribution. I agree that center
    of pressure is the more common term.

    2. When you are looking at a force platform the normal direction and
    shear directions have their own center of force (or center of pressure)
    and these don't have to be the same point. For example, take two point
    forces applied to a horizontally-mounted force platform (so that normal
    and vertical are the same direction for simplicity). One force is
    applied directly down on the center of the platform. A second force is
    applied diagonally downward with a vertical component equal to the first
    force. The center of normal force (and center of normal pressure
    registered by the platform) is half way between the points of
    application of the two vertical forces. The center of shear force (and
    center of shear pressure) is at the point of application of the second
    force (since the first force has no shear component. This center of
    shear pressure cannot be calculated precisely on a standard force
    platform. The platform would register a moment about the vertical axis
    as a result of this shear force and knowing the magnitude of the shear
    force one could calculate a moment arm of the shear force about the
    center of the platform. Knowing the direction of the shear force one
    could calculate a line of application of the shear force but would not
    be able to narrow it down to one particular point of application.

    Concerning #2 above, I'm pretty sure most researchers have ignored the
    center of shear pressure over the years. Any "center of pressure"
    reported in the literature has been "center of normal pressure" as far
    as I know and that is not necessarily the same thing as "center of shear
    pressure". I'd be interested in hearing what others think.



    Richard N. Hinrichs, Ph.D.
    Department of Kinesiology
    Arizona State University


    Nice reply, these are my thoughts;

    1) I agree with this if one only considers the normal force and I agree that pressure is a vector when a direction is defined by its plane of application i.e. pressure (or stress) is perpendicular to a surface of interest.

    2) CoP on a force plate is not quite the same as CoP on a pressure mat. The former is the CoP relative to the whole plate and in terms of equilibrium of moments about the plate axes from convenient single point forces in 3 dimensions. CoP of the latter is relative to the area in contact with the object applying the force, e.g. usually a foot, and a product of all the discreet perpendicular forces at each load cell site.

    In your example it would still be possible to calculate a vector product of both force points that was the single force action equivalent of the two force actions. This could be the result of two feet appling force to a plate simultaneously and the resultant vector product of the forces from both feet would be some where between the two feet and usually have some direction oblique to the plane of the force plate surface. This therefore would contain the shear and normal forces and would be, by my way of thinking, the Centre of Force.The Centre of pressure however would only ever have a product that was normal to the force plate surface and this would be similar to the pressure mat. Therefore, in this case, the CoF is distinctly different from the CoP and so when using a pressure mat the correct term for the characterisation of the central point of application of all normal discreet forces, in my opinion, is CoP.

    I see you point about the seperate CoP of the shear forces, however, it seems to me that of course there can be no CoP defined in terms of the horizontal plane, but theoretically there could be a characterisation of horizontal forces if a vertical plane was visualised.

    Regards Dave Smith

  17. Yeah, that's why I've got a PhD, Dave :rolleyes:. So in this "special case" when it is equated to the centre of force, is it a vector quantity? Is it the same as CoF?
  18. David Smith

    David Smith Well-Known Member

    Touchee! -- On balance, yes. (Damn!:mad:) But with the qualifier that it is only the centre of force as is characterised by the equpiment and not the actual centre of all the forces applied to the foot / mat interface.:cool:

    LoL Dave
  19. Never mind. :D
  20. David Smith

    David Smith Well-Known Member

    I blame CPod, he started it:butcher: Hey an argument resolved - not a bad outcome by any standard. :dizzy:

  21. Dave, you'll still be my first port of call with my physics problems.
  22. David Smith

    David Smith Well-Known Member

    Last of Biomech-L replies


    Pressure doesn't always have to be perpendicular to a given surface.
    That is only the normal pressure (or normal stress). There is also shear
    pressure (or shear stress). The problem is that pressure mats typically
    don't measure that shear stress.

    regards Rick


    How would you define the area acted on by a shear force? wouldn't you
    need to define a new plane of action perpendicular to the shear. Surely
    a shear force has a line of action not a point of action, relative to
    the plane of the the normal force action. So how would one define the
    area of a shear force. Would it be the shear force divided by the area
    of contact between two surfaces of interest?
    Never come across that concept before in terms of pressure. I suppose in
    tribology one considers the shear force and the surface area of contact
    to predict wear rates, is this increase in surface area contact termed
    as a reduction in shear pressure?

    Good thoughts Rick

    Cheers Dave


    Imagine you have a stick with a 1 cm by 1 cm square cross section. The
    very bottom of the stick has been nicely sawed off to reveal the nice 1
    cm^2 area. Now you push the stick against the floor so that the entire 1
    cm^2 area touches the ground. In addition to pushing down on the stick,
    you pull back on the stick to elicit a frictional force. The frictional
    (shear) force applied to the ground by the stick divided by the 1 cm^2
    area of contact is the average shear pressure (or shear stress). Another
    example is friction between tires and the ground for racing cars. This
    is all about shear pressures between the tire and the ground (and of
    course normal pressures as well because without the normal pressure you
    would not have contact between the tire and the ground in the first


    Yes I completely understand your contention but I have never heard of shear
    force expressed as a function of the area of contact before i.e. => shear
    pressure.Can you give some examples of this from publications?
    This brings in considerations of apparent contact area V's actual surface
    area, which is not a problem when considering shear force and friction in
    terms of a coeffient of the normal force but pressure on the contact
    interface would be highly variable and always higher at the real points of
    contact than the estimated overall pressure.

    Good discussion

  23. David Smith

    David Smith Well-Known Member


    Just some new thoughts

    Consider that we use a pressure insole that characterises force applied normal (perpendicular) to the load cell. That insole is sitting on the *variably curved surface* (**there is a correct term for that but it won't come to mind) of an orthosis, then we characterise the normal forces in terms of pressure and display it in terms of a flat surface i.e. the computer screen. I consider that the resultant estimation of CoP would be highly ambiguous in its location or even direction. The forces that are normal to the load cell are then oblique to the reference plane of the floor which is intuitively represented by the PC screen.

    Imagine having a sphere with and internal gas pressure. The CoP would be in the centre of the sphere and not on any inner surface of it. Now represent that sphere in a flat plane and try to characterise the CoP. It would make no sense if you did do this and yet this is what the pressure insole software must do. It unravells the curved surfaces and makes some algorithmic judgement about the centre of pressue location in a flat plane with reference to the PC screen.

    Consider the sphere example again and imagine how many ways it might be possible to lay out the inner sphere as a flat plane, Would the CoP be in the same relative position for each unravelled pattern. I think not. Is there an international standard formula for unravelling the orthosis shape into a flat plane? I think probably not! even if there were every orthosis is not analogous to a sphere since they are not regular or consistent shapes.

    The orthosis does not have even pressure at any one point of time of interest and the forces characterised by the load cell are a combination of horizontal and vetical force in the global axis set. Now while this load might be a good approximation of the force that could contribute to plantar pressure it may not be a good (accurate or precise) characterisation of the location or direction of those forces especially in terms of CoP.

    It would be good if there were a manufacturers reprsentative reading this who could give us a better explanation of how they cope with all these confounding error potentials.

    Cheers Dave

    And more from Biomech -L


    That is my point. I don't think many people have even considered shear
    pressure because the technology to measure it hasn't been there.
    Everyone is so busy measuring normal pressure with pressure mats that
    they have ignored the shear pressures. Force platforms can measure shear
    forces, but not shear pressures, so people don't ask the next set of
    questions and things don't get published. When I was working with Peter
    Cavanagh 30 years ago at Penn State we first talked about this in the
    context of running shoe design, wear on the soles of the shoes, etc.,
    but we never took it any further because we didn't have any device to
    measure these shear pressures on the bottoms of shoes. I imagine the
    race car industry must know something about this since wear on tires is
    such an important issue as is getting as much traction as possible out
    of the tires.

    The topic of shear stress, however, has been written about extensively
    in the mechanics of deformable bodies literature. I teach about this in
    my "Biomechanics of the Skeletal System" course at ASU. The textbook by
    Nordin and Frankel is a good place to start. I have not done a good
    literature search for original articles on shear stress, but I'm sure
    they are out there. Since stress and pressure mean essentially the same
    thing, perhaps looking in to the stress literature is a good place to



    OK I can see that,so if your willing, let's run with that idea of shear
    pressure. This is a very important consideration in podiatry since it is
    thought that shear forces / shear pressure are more responsible for the
    pathogenisis of ulceration, rather than normal pressure, in neuropathic feet
    e.g. diabetic neuropathy, and especially those with partial foot

    There is a system, which I have read about that can characterise shear
    forces - In Shoe Biaxial Shear Force Measurement: The Kent Shear System.
    Medical and Biological Engineering and Computing July 95 34 315-317
    Akhalaghi F. Pepper MG.

    Actually if you put a pressure mat on a force plate and used the two
    simultaneously as a subject walked oner them then you would have a good idea
    about shear forces and their location on the plantar foot. The area, and
    therefore the shear pressure, would depend on the contact area of the foot
    but would this be discreet enough? Could we assume that the discreet areas
    of highest normal pressure as defined by the pressure mat can be
    proportionaly assigned the highest shear force? So, for instance, if an area
    of 1cm square bears 40% of the total normal pressure, can we then assume
    that 40% of the total shear pressure can be assigned to that area (assuming
    that there is no slippage involved or that slippage is uniform across all

    Hmmm! How would that work? At some point slippage will occur between two
    surfaces as the contact points under the interface surface area break down
    and the coefficient of friction is reduced. If this happened on a foot, say
    a prominent metatarsal joint results in high local pressure and so therefore
    one assumed a proportional amount of shear force can be assigned
    here,wouldn't that indicate that slippage would more likely occur here than
    on a less loaded area. However one part of the foot cannot slip on its own
    since it is attached to the rest of the foot. Would the skin continue to
    breakdown in terms of coeffcient of friction unti the shear forces equalised
    across the foot? Would thisd be the pathogenisis of ulceration?

    Just thinking out loud, perhaps you can throw some light here Rick.

    Thanks for your participation, regards Dave

    Dear Dave,

    For me CoF also makes some sense. In physics you often have Force fields:
    every point (3D) has it's own force value (3D). Eg. an electic force field
    or a gravity force field. Now if you calculate the total resulting force
    over an certain area (integral force over volume) than this should lead to a
    effective force. It will also need a point where it is applied - imho this
    would be the CoF.

    @making a force vektor out of pressure and orientation: You will have to be
    careful here - mathematically this is correct, but your calculation will
    lead to a force vektor which incorporates only the normal forces of the
    specified surface. All shear forces will not be considered by this



    Thanks for your thoughts ( especially since you agre with mine :))

    There seems to be three camps emerging here one supporting our point of
    view, i.e. that CoF and CoP are not really interchangeable, and one saying
    that CoF and CoP are the same if you consider that the pressure mat data is
    a special case and we are always only talking about normal force, and
    another supporting the usefulness of using the concept of CoP in a
    horizontal plane, I.E. (the normal force * the coefficient of friction) /
    area of interface contact = shear pressure. I am discussing this latter
    consideration with another Bimech-L user (Richard Hinrichs) since it may be
    a useful concept for consideration in Podiatry where we are concerened about
    shear forces causing ulceration of the skin in diabetic subjects for

    Regards Dave

    Hey Dave,

    Good if there is some sort of agreement :)

    Concerning you last point: If you calculate the normalforce*coff of
    friction/area = shear pressure: this calculation does not really calculate
    the shear pressure, it simply calculates the maximal possible shear pressure
    until slippage will occur.



    Yes, and ideally this equation would be the shear force / interface contact
    area but at present wer can't measure or characterise discreet shear force
    on its own. Then of course there is the problem that even if you can measure
    discreet shear force for a certain adrea of interest, how does this actually
    relate to even more discreet areas of contact i.e. the contact curfaces are
    not 100% smooth, they have irregularites that will have high peak forces /

    Do you think trying to define shear pressure would be useful or would there
    be to many assumptions made to make the definition useful?

    Thanks Dave
  24. Agreed. Nice work fella.

    We are now entering the realms of Riemannian geometry! Yippee (not).

    Spooner's health warning: Unless you like mathematics; REALLY, REALLY like mathematics, don't even bother to look at these links or your brain will turn to jam.:wacko:

    I suspect that's its not good in terms of CoP and that the manufactures have no strategy to deal with this- could be wrong, could be something to do with differentiable adjacent manifolds, but I doubt it since the pressure measurement system has no data regarding the surface geometry it is upon. Good discussion.
    Last edited: Jun 17, 2009
  25. David Smith

    David Smith Well-Known Member


    The maths of Riennman geometry is beyond me but hats off if you have a handle on it. The concept is worth explaining tho.

    If you imagine the earth globe made into a chart i.e. a flat map of the world. Now imagine if the world were a hollow cylinder, making a chart (flat map) would be easy because a cylinder's surface is in one dimension i.e. the distance from point A to Point B about its circumference or latitude is the same at any point along its longitude or a line parallel to its height. Or to put it another way draw two parallel lines of longitude and the distance between then is always equal even if we flatten out the cylinder

    This is not so on a sphere or globe this is what is known as a two dimensional manifold. This because the surface of interest bends in two planes and not one like the cylinder. Therefore 'parallel' lines of longitude are not equidistant apart at any point along their latitude. However if you now flattened the globe out into a chart then the parallel lines of longitude would be equidistant but this would be an illusion in terms of real distance between two objects of interest along lines of latitude on the topography of the globe. Therefore to make the correct distance calculatable from the lines of longitude, mathematical equations must be employed. On a real chart the positions of the countries are adjusted to take account of this fact. So if you look at the flight plan of a jet going from London to New York it goes west toward Iceland and Newfoundland Canada and then down the U.S. coast to New York, which on a chart looks like the long way round but projected onto a globe will be the straightest line (ish).

    So if we take the heel cup of an orthosis as a segment of a shpere then plotting the distance and dislaying that as a real equivalent distance on a flat screen or chart of the heel cup, becomes the same problem as the global topography to chart one. This further complicated by the fact that there are multiple 3D curved surfaces on an orthosis, which is a problem of differential adjacent manifolds as Simon points out. This would still be possible to do if we had a common reference from orthosis to orthosis chart, which was known by the software of the pressure mapping system. Of course we dont since each foot and orthosis interface is different. So the question is how do we know where the pressure, indicated on the pressure chart, is actually located on the real foot - orthosis interface. Until we do this and know the exact location of each discreet force area application, how can we unambiguously chart a centre of pressure from ambiguously positioned discreet areas of force application?

    Would you say this a reasonable explanation and summary Simon?

    Cheers Dave
  26. David Smith

    David Smith Well-Known Member

    Simon and all

    Lets consider the inserted diagram.


    The diagram A) shows the force or pressure applied by a truncated cone shape to a flat pressure measuring system. Diagram B) shows the same shape applying force to an inverted cup in a cone shape. This might be analogous to a heel in a heel cup.

    In the B) diagram the pressure is measured by a flexible inlay system like an insole system. The pressure characterised by A) is the force dived by 1 cm square. Lets say 500N/1cm = 500N/cm^2. B) has two sensors and each characterises the normal or perpendicular force applied to it. This is a trigonometrical function of the sloping surfaces and it works out that each sensor indicates a force of 125N and is therefore a pressure of 125N/cm^2. The sensor that is under the flat area has no force applied and so the pressure is zero. And yet there is still 500N of force applied but the two sensors only indicate a total of 250N force, is this reasonable?? Have we managed to lower the total applied force, it might appear so.

    Now calculate the centre of pressure on A) -- easy its 500N/cm^2 at the area of the sensor which we we call point Y.

    Now calculate the B) centre of pressure as charactersied by the pressure chart display on a flat pc screen. So that 250N/3cm^2 = 83.33N/cm^2. And the centre of pressure will indicate that it is applied at point Y. ?????

    Clearly this would be a great error by itself.

    Now consider the shear forces, in A) there are none but in B) they are introduce to two new areas and the magnitude of these forces are not characterised by the pressure sensors. Therefore the shear pressure (if I can introduce that term as the horizontal force divided by the interface contact area) is unknown and ignored but may be a significant consideration in tissue pathology or in estimating changes in moments about a certain joint of interest.

    As far as our interest in the change of local pressure at point y goes, our reliance on the characterisation and display, in a flat 2D plane, of the relevant pressure gives us a false impression, I would say.

    Cheers Dave
    Last edited: Jun 18, 2009
  27. Not really, I looked at it some years ago when I was studying Demp's work. Like you, I found the maths beyond me.
    Nice work.

    At the University I used to work at they used to use the domed surface of the inside of the planetarium to teach this stuff- in the days when marine navigation was a skill, and not down to GPS.

    This reminds me of the classic question: how many degrees do the internal angles of a triangle add up to?

    I do think it is important to point out that the problems Dave and I are discussing here are result of the limitation of the technology available. That is the concept of centre of pressure per se is not flawed, merely that in-shoe pressure sensor equipment, when placed on non-flat surfaces will provide erroneous results. Like Dave said, it would be nice to get comment from some of the representatives of the manufacturers of such products.
    Last edited: Jun 18, 2009
  28. OK, so where does this leave us? It appears that the results of research which have reported CoP based data, collected using in-shoe sensors placed over non-flat surfaces may well be fundamentally flawed and erroneous (that includes one of my papers BTW :D:bash:).
  29. David Smith

    David Smith Well-Known Member

    Ok, so these are only my assumptions, which appear to me to be quite reasonable, about the possible limitations and errors of pressure insoles. There may be some reasonable explanation as to how these are overcome. However I have long held these beliefs and have yet to find any answers to contradict them.

    Further investigation might reveal if these limitations and errors are significant in clinical terms. ;)

    Cheers Dave
  30. I'm not sure how you would overcome these problems without a knowledge of the topology of the orthosis-pressure sensor interface. So I can't see how the software could deal with this other than to "fudge it". It seems to me the greater the deviation of the surface from the horizontal and the more complex the curvature the greater the potential for error. So instinctively propulsive phase should be less erroneous than midstance.
  31. Does anyone have a copy of this paper they could PM me please?: http://www.iop.org/EJ/abstract/0957-0233/10/1/017
    £50 for one paper btw??????????? madness

    BTW2 this fella, with his cue-ball noggin is really starting to annoy me: http://happyabout.info/foolosophy.php, this twat keeps appearing at the side of my posts, one version I can deal with, but four copies down the side of the page? Is this a subliminal message you're trying to send to me, Craig? How is this a relevant advert that has been linked to key words in this thread....... Rhetoric question.
    Last edited: Jun 22, 2009
  32. markjohconley

    markjohconley Well-Known Member


    I'm revisiting a biomechanics terminology webpage.
    The website notes that there's a difference but only relevant for astrophysicists etc.
    Could someone explain the difference, please. So when I read COG or COM in a podiatry article should I get particular? Thanks, mark c
  33. admin

    admin Administrator Staff Member

    Mark - I merged your question to this thread. Its probably better answered here.
  34. markjohconley

    markjohconley Well-Known Member

    From perusing through some biomechanical terminology webpages and physics forums I now accept that for all practical purposes COG = COM.
    But in fact they are only coincident for "spheres in constant gravity fields". Haven't had one of them come in for a biom. assessment yet.
    Enough of the physics for one day, I'm off to bed, mark c
  35. Re: COG V COM


    While there is good agreement on the term center of mass (CoM), unfortunately, there is not good agreement on the term center of gravity (CoG).

    CoM refers to the point location within an object where the mass of the object can be thought to be concentrated. CoM is quite useful to know when we want to analyze the kinematics and kinetics of objects.

    CoG, on the other hand, is also used within the literature as a synonymous term for CoM. However, one of the legends of biomechanics, David Winter, has also used the term CoG to also describe the point on the ground which lies directly underneath the CoM of a standing individual in order to better understand how the interchange of positioning between center of pressure (CoP) and CoG can accelerate or decelerate the motion of the CoM during standing (Winter DA: A.B.C. (Anatomy, Biomechanics and Control) of Balance during Standing and Walking. Waterloo Biomechanics, 1995).

    I use the term, center of mass, when I need the term to better describe the kinetics and kinematics of the human body, as do most other modern biomechanists within the international biomechanics community.

    Hope this helps.
  36. efuller

    efuller MVP

    To add to Kevin's post.

    Center of gravity as Winter describes it is the point on the ground toward which the force vector acting on the center of mass is acting. This is helpful for figuring out what ground reaction force will do to the whole body. For example, when the center of mass (and center of gravity) is anterior to the center of pressure the body will tend to rotate forward. The center of gravity gives an easy transverse plane understanding of the above. Where as the sagittal plane description gives a better picture with the center of mass (if you include the force vector of gravity and ground reaction foce.) Those vectors create the force couple that causes the forward rotation.

    Center of mass is much more useful in a situation where a person is jumping up in the air and another person pushes on them. The further the vector of force is from the center of mass the more the person will rotate when pushed. So, yes there is more application in space travel, but it can also be applied in sports like American football. (Reciever jumps to catch a ball and defender hits their legs and sends the receiver spinning



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