View Full Version : CoP v's CoF

06-09-2009, 06:59 PM
Dave Smith -

I'de like to make this a discussion if possible, so Ive posted the replies so far and added my own reply to them.

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! ;)

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

My Reply

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