# The CoP Does not exist: Validating Aerodynamic forces through a "line of action"

 Register Blogs Members List Search Today's Posts Mark Forums Read

 March 27, 2020, 09:52 #2 New Member   Dan Join Date: Feb 2020 Posts: 3 Rep Power: 6 Anyone have some input to this theory. Any help would be appreciated

April 1, 2020, 12:17
#3
Senior Member

Lucky
Join Date: Apr 2011
Location: Orlando, FL USA
Posts: 5,673
Rep Power: 65
What is your query? These are concepts we usually teach immediately after introducing force couples in mechanics, very basic mechanics stuff.

Any force acting at a point (we can call this the CoP) at some distance from a center (we'll call this the CoG) can be replaced by a force (now acting from anywhere you like) and a force-couple. This theorem is so prevalent, I'm not sure it can even be attributed to any name. So yes, you can always choose to take an arbitrary field of forces and turn it into a srewdriver acting somewhere. You could also have chosen to put this screwdriver at the CoP; and if you had done this, it wouldn't have had any twist to it.

Btw, the CoG also needs to be calculated by the interaction of a mass gravity field and the gravitational field. That is, the CoG is also a screwdriver.

Quote:
 Originally Posted by ds4719 While this is useful in telling us overall stability, it does not give us information on the forces at the locations that really matter, which is directly at the contact patches of the tires.
And??? You are doing overall stability analysis. If you wanted to know what's happening at the contact patches, that's not overall stability. If you wanted to get that information, don't consider the system as a single rigid body but a connected system of smaller bodies (i.e. multiple components). And you still can use either method.

Last edited by LuckyTran; April 2, 2020 at 08:02.

 April 1, 2020, 18:20 #4 Senior Member     Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,152 Blog Entries: 29 Rep Power: 39 Too long to actually grasp from the text what you're actually asking, also considering that wikipedia has this well sorted out in few lines here: https://en.wikipedia.org/wiki/Resultant_force Maybe reformulate the thing more succintly or wait for someone in the mood

April 4, 2020, 04:04
#5
New Member

Dan
Join Date: Feb 2020
Posts: 3
Rep Power: 6
LuckyTran thanks for your response. I havent gone that deep into mechanics so this topic was new for me. I have read a decent amount about aerodynamics and the CoP but NOT ONCE have i seen it related to this force-couple principle.

I made this post for another forum and copied it here because I felt it was necessary to understand this better with help from the experienced members here and for anyone else that has never heard of this relation.

Quote:
 So yes, you can always choose to take an arbitrary field of forces and turn it into a srewdriver acting somewhere. You could also have chosen to put this screwdriver at the CoP; and if you had done this, it wouldn't have had any twist to it.
This was the main point i wanted to understand. I can take a forces and moments measurement at any point in the simulation. I chose the CoG. The moment about this point should point towards this "Line of Action" and along this line there is no twist, as no moment just a pure force, got it. This concept was not to difficult to grasp.

Quote:
 And??? You are doing overall stability analysis. If you wanted to know what's happening at the contact patches, that's not overall stability. If you wanted to get that information, don't consider the system as a single rigid body but a connected system of smaller bodies (i.e. multiple components)
I agree that so far I am doing overall stability, weather measured from a point, the CoP, or forces on each axle. However I wanted to go a bit deeper into the relation to vehicle dynamics by calculating the force and force-couple at each contact patch. This is because front/rear tells us stability, but vertical forces at each tire can tell us how much extra travel the wheel has moved due to this force --> how much extra camber change has occurred --> how this effects slip angle --> leading to how much lateral force can be achieved.

The correct methodology and application of this concept is where i was looking for guidance.

sbaffini - i know its long and sorry for that. But thank you for the Wikipedia link, i also had trouble finding info on "force screw" probably because its not called that

-Dan

 April 4, 2020, 16:36 #6 Senior Member   Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,673 Rep Power: 65 You have to look in engineering mechanics bodies of text to find force couples, force wrenches, and force screws. Most formally it is called a force couple, but wrenches and screws are often mentioned for pedagogical purposes. In mathematics, these are just moments. The force-couple does not provide any new information that you couldn't have known by knowing the force at the CoP and the CoG. The principle of moving forces around in order to do any type of analysis goes back to free body diagrams. Knowing the CoP, the amount of the force, and the lever arm distance to the CoG, you can very quickly find the moment (the couple). Now you know the couple and can find the moment about any other point (such as the tires). You can then draw a free body diagram of your part, the tires, and expose the internal forces and very quickly find the "vertical forces" there. These are all concepts we teach in introductory statics courses, which is usually the first true engineering course (that isn't a basic science like physics, calculus) to engineering students. E.g. here is a bridge with a load on it. Find the resultant forces on the two supports.

February 9, 2022, 21:28
Very Insightful
#7
Senior Member

Claudio Boezio
Join Date: May 2020
Location: Europe
Posts: 137
Rep Power: 6
Thanks @ds4719 for your exhaustive post! You shed light on this topic and mention some key points that are essential to understanding this. I've seen many posts about people asking how to find the Centre of Pressure and most of them sadly remain unresolved.

1. There are force systems that cannot be further reduced than to a resultant force and a moment that are not perpendicular to each other, the so-called wrench that you mentioned. They rather reduce to a resultant force and two resultant moments, one of which is perpendicular to the force while the other is parallel to it. The perpendicular moment can also be zero in some cases. This in a way contradicts the common definition that a moment has to be perpendicular to the force that generates it. Out of about 10 mechanics textbooks I've consulted, only one vaguely touches this concept. This video shows how the resultant moment can be decomposed into these two components, if they are present. So knowing that a resultant moment can be parallel to a resultant force is crucial, because then no matter where the line of action of the resultant force passes through, that moment won't vanish.
2. Most definitions I saw for Centre of Pressure, mention that it is a point about which all moments become zero. However, these definitions fail to mention, like you on the other hand demonstrated, that there are force systems for which no such point exists, i.e. where there will still be a moment that cannot become zero. An axis can be found where the resultant force passes through where its perpendicular moment vanishes, but the parallel one still remains. Not knowing this makes people wonder why they can't seem to find the CofP, even by iteratively guessing and approximating the chosen Centre of Rotation, where at least one moment component never becomes zero.
Thanks also for these:
Quote:
 Tx(P) = Tx(0) + (-Fz*Py + Fy*Pz) Ty(P) = Ty(0) + (+Fz*Px - Fx*Pz) Tz(P) = Tz(0) + (+Fx*Py - Fy*Px)
Hopefully they can be useful for obtaining moments by translating the CofR without having to restart the CFD Software. I'll try them out.

Cheers, Claudio

 February 10, 2022, 01:02 #8 Senior Member   Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,673 Rep Power: 65 This is what we call fake news. All that plus the youtube video is literally the first two equations shown in the Wikipedia for https://en.wikipedia.org/wiki/Resultant_force No one has lied to you about calculating resultant forces and resultant moments.

February 11, 2022, 20:26
#9
Senior Member

Claudio Boezio
Join Date: May 2020
Location: Europe
Posts: 137
Rep Power: 6
Quote:
 Originally Posted by LuckyTran This is what we call fake news. All that plus the youtube video is literally the first two equations shown in the Wikipedia for https://en.wikipedia.org/wiki/Resultant_force No one has lied to you about calculating resultant forces and resultant moments.
I must have missed the Wikipedia article, thanks for that.

Where exactly is my post fake Sir, if I might ask?

 February 12, 2022, 15:06 #10 Senior Member   Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,673 Rep Power: 65 You are claiming that that I cannot compute a resultant force and moment for systems of forces yet present equations showing exactly how to do that. The screwdriver is a moment (and also a force couple). Depending on which area in the world you grew up in, you'll call it by one of these terms or other terms. It doesn't mean that it's not the exact same thing.

February 13, 2022, 14:48
#11
Senior Member

Claudio Boezio
Join Date: May 2020
Location: Europe
Posts: 137
Rep Power: 6
Quote:
 You are claiming that that I cannot compute a resultant force and moment for systems of forces yet present equations showing exactly how to do that.
I believe there's a misunderstanding. I stated that some force systems cannot be reduced further than to a wrench, i.e. a force and a moment parallel to it. I assume this is what you mean by screwdriver but please correct me if that's not the case.

 February 13, 2022, 20:35 #12 Senior Member   Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,673 Rep Power: 65 I think you are confusing the center of pressure with the center of rotation. They are not the same thing. Moments are always with respect to their moment centers. The moment center can be arbitrarily placed anywhere. You shouldn't ever talk about a moment without specifying what is the momentum center. A lot of people assume that this moment center is your center of "insert the name of your favorite animal here" when it can be anything.

 February 15, 2022, 02:34 #13 Senior Member   Claudio Boezio Join Date: May 2020 Location: Europe Posts: 137 Rep Power: 6 I believe I'm aware of the distinction between the two. It is my understanding that if the Centre of Rotation is placed at the Centre of Pressure, then the resultant moment component perpendicular to the resultant force becomes zero. The Centre of Gravity can very well be somewhere else.

 February 15, 2022, 09:18 #14 Senior Member   Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,673 Rep Power: 65 If the center of rotation and pressure coincide to the same location yes. But you don't get to put the center of rotation anywhere. The body or body collection moves according to the forces acting on it. What you choose is the moment center. The resultant force always has a line of action which is whatever it is. Moments are calculated about arbitrary moment centers which may or may not be on this line of action. Notice I've only used the word moment. There are an uncountable number moments than be calculated for any force system. They can be calculated w.r.t. to the center of pressure, w.r.t. the center of rotation, w.r.t. to the end of the universe. What you are referring to is torque, which is a very specific moment. The torque vector is the cross product of the force vector and the lever-arm vector. Maybe you didn't know that it was a cross product and thought that it was simply the product of the two magnitudes and left out the sin(theta) part, then I can see how it might be confusing. Otherwise, it's in the definition and the first equation that appears in the wikipedia article. You don't place the center of rotation or the center of pressure anywhere. They are whereever physics says they will be. You can pick and choose the moment center though.

 February 18, 2022, 18:05 #15 Senior Member   Claudio Boezio Join Date: May 2020 Location: Europe Posts: 137 Rep Power: 6 I wasn't aware of the distinction used in the US between torque and moment. I'm only talking about moments. Please allow me to clarify. The Centre of Rotation I was referring to, is an arbitrary point I have to define in the CFD software I use, about which the resultant moment is calculated for one or more boundary patches that I select. I've derived a formula to accurately calculate the Centre of Pressure only from the resultant force and moment. The expectation was for the case I'm working on, as a means of verifying this, that if I place that point at the Centre of Pressure calculated by me (the software doesn't calculate it), the software would output a zero (or very small) resultant moment for the patch in question. But it doesn't, because the force system has a resultant moment component parallel to the force. At first I didn't know that and suspected something might be wring with the software, now I know it's not. It works well though e.g. for a 2D Airfoil where the force system is planar. What I'm working on however is more complex than that. So that's what I meant by Centre of Rotation and I should have been more clear about this earlier. My apologies. You're right of course that the resultant forces and moments are what they are. But then it's my job to find out where they act and to make sure that they act at places that are appropriate for whatever it is that I'm designing. If I go the long way and extract data from post processing, I can calculate the forces via pressure, surface areas and normals and the resultant moment by forming the cross product and get very similar results to what the software outputs. However, the resultant moment I'm left with when evaluating the moments around the calculated Centre of Pressure are in my opinion still far too large and so I'm not sure if that point I've calculated is really correct. That's what I'm still investigating.