Questions to Ask About That Bizarre Prong Collar Diagram

Dear Dog Owner,

I’m writing to let you know of some really dreadful misinformation going around.

But first, here’s the truth.

It’s very simple. Prong collars hurt dogs. They can hurt a lot, depending on how tightly they are fastened and the handler’s behavior. Sometimes the sensation may be as low as mild discomfort. But make no mistake: if wearing a prong collar gets your dog to stop pulling on the leash, it’s because it becomes uncomfortable to do so.

If you take a good look at a prong collar, your intuition will be correct. Ouch! Even though those prongs are blunt, they transfer a lot of pressure into a tiny area.

Unfortunately, some trainers who use prong collars will go to great lengths to defend them, often by making stuff up. It’d be one thing if they would say, “Right, I know the collar hurts this dog, but it’s the best thing I know how to do. I’m willing to consult a professional for other ideas on how to handle this case.” But humans hold on to our biases. So instead, against what we can directly perceive with our own senses, prong defenders make up fairytales about how beneficial such collars are for the dog. They are getting more and more agitated and come up with more and more absurd defenses.

If a trainer has told you that prong collars are good for dogs because they “distribute pressure” around the neck or “protect the trachea,” please know that this is not the case.

Here are some of the many holes in the silly claims about prong collars.

The Diagram

I am going to critique a certain diagram (and a few other arguments about prong collars) I have seen online. But I won’t link to the diagram. I hate vague-posting, but I can’t see another ethical way through this swamp. I feel bound to say something about the misinformation, but I know that linking to it, even for criticism, will promulgate it. So I am in this weird position.

If you haven’t run across the diagram (I’ll describe it in a moment) or heard these arguments, great. Just bookmark this post and go on your way. If you come across weird claims about prong collars in the future, you can come back and read this article.

If you have seen the diagram and arguments, and maybe even been persuaded by them, this post is for you.

The diagram has a drawing of a prong collar with forces drawn on it to supposedly “prove” that prong collars do not put any pressure on the front of a dog’s throat. This is incorrect, and it’s easy to verify on yourself in real life if you want to wear a prong collar attached to a leash, then have someone pull steadily against it. Or you could use ballistic gel to create a model to test this on, which would be safer. This is a real-life case of the Emperor’s New Clothes. The purveyors of these myths are asking you to go against what you can perceive with your senses and instead, believe a fairytale.

I’m going to give you some basic critical thinking points for this diagram and others like it through the lens of basic engineering mechanics. I’m suggesting what questions to ask when you see diagrams that purport to portray the forces on prong collars.

Note that the people who post diagrams like this put on the mantle of science and accuse anyone who disagrees with them of “being emotional.” Ya know, if “being emotional” makes you realize that what your trainer recommended is hurting your dog, then more power to emotions. But here, empathy and science agree. The prong users’ attempts to apply science to support their bias are absurdly wrong.

The diagram in question appears impressively science-y, with its vectors and arrows and cosines. But it wouldn’t get a passing grade in a high school statics/dynamics course. It lacks required definitions, descriptions, and disclosures of approximations and assumptions. It uses the wrong kind of diagram for the information it purports to present. It’s the opposite of impressive; it’s desperate.

So here’s what to do if you encounter this diagram. Ask the person who is posting some questions. The questions follow here in much detail. You can, if you like, skip all this and download the one-page PDF with the questions on it. But the more of the details you can understand, the more you will realize how ridiculous the diagram is.

Questions to Ask about the Prong Collar Diagram and Claims

l. Which of the four primary force scenarios involving a prong collar does this diagram illustrate?

There are at least four possibilities. My explanations of them include some technical details, but you can definitely get the gist of it without a strong math background.

Force Scenario A. The pressure of the prongs themselves on the dog’s neck with no leash attached. The prongs are creating pressure inward while the dog’s body is pushing outward in a state of static equilibrium. The pressure exerted by the prongs of the tightly fitted collar (as per the fitting instructions) is always ignored when people claim prong collars “protect the trachea.” Whatever the orientation of the collar—whether the chains and attachment area are at the back of the dog’s neck or the right side of the neck, some of those prongs are in the front of the dog’s throat, pressing inward.

The formula for this is ΣF = Σ(ma) = m1a1 + m2a2 +m3a3 + • • • + mnan = 0.

In plain English, that means that the sum of all the different forces comes to zero. That’s because the collar is stationary. It doesn’t mean there aren’t any forces. It means they balance each other. Imagine a tight belt. It can exert pressure on your abdomen without being attached to anything else. It gets uncomfortable fast. Now imagine it with prongs on the inner surface. There is much less surface area on prongs than on a belt (or flat collar), so the pressure is concentrated. It likely causes pain or at least discomfort. On a prong collar, the inward pressure will be distributed around the neck and be roughly equal for all the prongs. But that’s when there is no external pressure on it. Remember—we haven’t attached a leash to it, yet.

A prong collar not attached to a leash is still exerting plenty of concentrated pressure on a dog’s neck.

Force Scenario B. The steady-state force when a leash is attached and it is taut between the dog and handler (i.e., the dog is pulling). The force of the leash pulling backward balances with the force of the dog’s body tissues and other physical elements pushing roughly forward. The collar tightens because of the movement of the chain through the holes. But even after it is tight, the pressure exerted by the different prongs will not all be the same. They will depend on the direction the dog is pulling and the orientation of the collar.

Think of the belt again. If you are wearing a tight belt and someone grabs a part of it and pulls you toward them, the belt no longer has equal pressure all around your waist. If they pull on the right side of your belt and you resist, there will be increased pressure on the left side of your belt. Likewise, if they pull on the back, there will be increased pressure on the front. The prong promoters argue that the prongs, because of their angles, somehow magically direct the pressure away from certain areas. Even if that were true in the way they argue it (it’s not), decreased pressure in one area means increased pressure in another. Force doesn’t just go **poof** into thin air. It has to go somewhere. So depending on the orientation of the collar on the dog’s neck and the direction of the force, there is no area of the neck that is magically protected from pressure from the prongs 100% of the time.

I understand why people buy the idea that the prong collar “protects” the dog’s neck, even though that’s an incredibly deceptive thing that prong trainers say. Imagine a dog wearing a flat collar pulling on leash for all they are worth—pulling and gasping. Not great for their neck and throat. If one used a prong collar instead, the dog **might** pull less. You might see less pulling and gasping. That’s why people use them. Pulling less decreases the type of force described in this scenario (but not necessarily the other three). But to then call that “protecting” the dog’s neck is doublespeak at its finest. There are much better ways to protect a dog’s neck than to poke things into it if they pull. And remember, plenty of dogs do pull when wearing prong collars. Mine did, the few times many years ago that I used one.

OK, back to the math. The forces are vectors, with both magnitude and direction, but if the dog and handler are moving as a unit, the sum of the forces is approximately 0. Let me emphasize that this is an approximation. The dog and the handler will always make minute changes in direction, which create acceleration. The acceleration creates a sum of forces that is nonzero. But for an approximation, we can assume the pulling is steady and in the same direction, and the sum of the forces = 0.

The formula is the same, but the numbers in it will be different: ΣF = Σ(ma) = m1a1 + m2a2 + m3a3 + • • • + mnan ≈ 0.

The prong is tighter and exerting more pressure into the dog’s neck asymmetrically when the leash is applying force

Force Scenario C. The dynamic force of a correction (jerk on the leash) when the leash is attached to the “live ring” of the prong collar. The live ring is the one that allows the collar to tighten when there is force transmitted by the leash. With this type of correction, the force is instantaneous and dynamic and the sum of the forces does not likely equal zero; it will equal mass times acceleration. The tightening of the chain part of the collar directs some of the force to close and tighten the rest of the collar via a pulley, then the rest of the non-symmetrical force can move the dog off balance. The formula is ΣF = Σ(ma) = m1a1 + m2a2 + m3a3 + • • • + mnan = ma.

A jerk of the leash, when it’s attached to live ring, causes an instantaneous, dynamic tightening of the collar

Force Scenario D. The dynamic force of a correction when the leash is attached to the “dead ring.” The dead ring holds the collar at a constant tightness. With this type of correction, the force is also instantaneous and dynamic and does not likely equal zero. Again, it will equal mass times acceleration. There is no pulley action and less or no tightening in this case because the configuration of the chain is fixed. A forceful correction of this type will have forces that differ from (C) above, and may be more likely to pull the dog off balance. But the formula is also ΣF = Σ(ma) = m1a1 + m2a2 + m3a3 + • • • + mnan = ma.

A jerk of the leash attached to the dead ring (both rings) causes an instantaneous, dynamic jerk on the dog’s neck and may pull the dog off balance



Even if you don’t care to follow all that, know that there are different forces involved with prong collars, and some can go on at the same time.

Of the forces above, A is a static force, B can be approximated as static, and C and D are dynamic forces. Static and dynamic forces are computed differently. And remember that B, C, and D always add to the baseline force of A. If you ask which force is being discussed or represented in a drawing, prong enthusiasts usually won’t answer this, because doing so reveals that their one drawing is only a tiny part of the big picture (besides being wrong). They are not presenting the true mathematical picture at all.

2. If they tell you which of the four force scenarios the drawing illustrates, ask them to post diagrams of the other three force scenariosAsk them to discuss how these forces combine and interact, and whether there might be even more scenarios. Posting one diagram when there are multiple forces that work differently is unethical.

3. Ask them what orientation of the collar on the dog’s neck their diagram represents. Is the leash attachment area on the right side of the dog’s neck, as directed by many paid trainers who use prongs, or on the back of the neck, as many lay people use it?

Leash attachment portion of the prong collar on right side of dog’s neck as directed by some trainers
Leash attachment portion of prong collar on the back of dog’s neck, as commonly used by lay people

This question will also show that they are not presenting an accurate picture. They will not want to answer it.

If you want to see real-life photos of the right-side attachment, search for “How to Fit a Prong Collar.” Ed Frawley has a post on the Leerburg site. (I won’t link it here, but it’s easy to find.) He states that one should place the attachment section of the prong collar on the right side of the dog’s neck, not the back of the neck. The photos of the Doberman and the Malinois on that page show the right side attachment and will also give you an idea of how tightly the collars are fastened (see section A above).

If they do answer the question about the orientation of the collar, ask them to provide a force analysis that applies to the other orientation. All the elements will rotate by 90 degrees, and the leash angles will probably change. Ask them how these two orientations affect any claims about the pressure of the prongs going to zero at certain parts of the dog’s neck. It can’t be the same part in both cases (if that claim were even true to begin with).

4. On any diagram, ask whether it represents a statics problem or a dynamics problem. Why did they not make the distinction? (Another instant fail in our high school mechanics class.) Most seem to be drawn as statics problems, but they also seem to represent the forces of a correction, which is a dynamics problem. Do you see how it is to the prong collar defender’s benefit to leave that part vague?

5. If the drawing is a two-dimensional rendering, ask them what margin of error this approximation introduces, since leashes attached to collars create forces in three dimensions. Leash pressure is rarely exactly coplanar (on the same plane) as the collar orientation, which is the assumption behind using a two-dimensional drawing. The following photos show the direction of the leash force (black leash) and its relationship to the plane of the collar (yellow line).

Figure 1. Force of the leash is approximately coplanar with the collar. On a real dog, the orientation of the collar would be closer to vertical since it is usually placed close behind the dog’s ears, but that doesn’t work on my stuffed dog.
Figure 2. Force of the leash is not coplanar with the collar
Figure 3. Force of the leash is not coplanar with the collar

If a diagram is two-dimensional, this assumes that the force of the leash is coplanar with the collar. This is rarely the case in real life.

It’s defensible to use a two-dimensional approximation of the problem, but only if the creator discloses the approximation and includes a discussion of the ways this could skew results. When the force is not coplanar with the collar, for instance, the upper and lower prongs in the pairs do not exert force equally. In the image directly above, where the leash is taut and being held higher than the plane of the collar, the lower prongs of the front pairs will exert more force into the dog’s neck than the upper ones.

Again, this would be a permissible simplification, but only if the diagram creator acknowledged it and discussed the effects it had on the accuracy.

Other Problems with the Diagram

The diagram I’m discussing has some other obvious errors. Again, I will not link to it, but these are general principles you can apply in the future if you see such diagrams.

The diagram has a two-dimensional problem drawn onto a three-dimensional perspective rendering of the collar. This creates errors in the angles. To accurately draw the angles they are trying to represent, you need a view looking straight down on the collar. The image on the left immediately below approaches that. Notice how the upper prong of each pair almost obscures the lower. I shot that photo almost straight down. Now, look at the upper and lower prongs in the image on the right. Drawing angles onto an image like that one and claiming that they are valid would be an instant failure in any mechanics course.

To represent an object such as this type of collar accurately, a top view and side view should be provided. A three-dimensional rendering could be included to show readers better visualize the object. This is not where you draw your angles, though.

In another terrible error, the creator of the drawing drew the angles on parts of prongs that were not connected to each other. They used the top prong for one section of each angle drawn, but then used the bottom link on the collar, the part that does not connect to the top prong, for reference for the other part of the angle. The first image below shows the section that is operating as a unit and should be the basis of any angles computed.

These parts of the prong collar are part of one functional unit

The second image shows how parts of the collar that are not directly connected were used for computing angles.

These parts of the prong collar are not directly connected to each other

This may be a subtle point to follow, but it is an egregious error.

A final problem is that the drawing doesn’t account for the change in direction of the force resulting from the pulley effect of the chain that tightens at the attachment area of the collar during a correction. A pulley changes the direction of a force. This is an especially interesting omission because if the creator had noticed it, they could’ve used it to support their argument (which would still be erroneous, though). That they missed this shows that we may be dealing with more ignorance than deception. But the end effect is still the same: they are using fallacious math to support a biased and incorrect conclusion.

When force is applied to the live ring, that force changes direction as the chain pulls through elements of the collar that act as pulleys

Bonus Fallacious Argument

This argument may not accompany any particular diagram. But it is common, and so demonstrably wrong.

If someone states that the prong units are acting as levers, ask for details about this. Levers are machines that magnify (increase) force. Ask what class of lever it is: 1, 2, or 3? (That one, at least, is a simple question—if there is a lever function going on here at all.) Ask for an approximation of the mechanical advantage of the levers (ratio of load and effort). How much do the levers increase the pressure from the prongs on the dog’s neck? Increasing force is the function of a lever. So prong users who claim that the prong units have a lever function are shooting themselves in the foot. Levers increase force.

A true lever has a load that is normal (at a right angle) to the lever itself. Think of a seesaw (a class 1 lever). We put loads (children) on top of the seesaw; we don’t apply a force horizontally and push it from end to end. If we did, it wouldn’t be functioning as a lever. Ask for a diagram showing a detail of a prong acting as a lever and the forces applied by it, including the ratio of effort to force. Ask how much the lever is increasing the force on the dog’s neck. Because that’s what levers do: increase force.

Succinct Printable Document with the Questions

I know this is awfully long. So here is a one-page document that has the key questions to ask when you encounter a prong collar diagram that purports to show beneficial effects.

Questions to Ask About Prong Collar Claims

Conclusion

It never seems to go well when defenders of prong collars try to appeal to science. It would be funny if it weren’t tragic that people can make stuff up, take shortcuts, refuse to define their terms, and won’t disclose approximations—and convince many people that they are producing good science merely by drawing some arrows.

Not to mention that they convince many people, who in their hearts may suspect otherwise, that they are doing a good thing for their dog when they use a prong collar. People do desperate things when their dog has a behavior problem they don’t know how to fix. I certainly did.

Some may ask why I didn’t provide my own diagram of the forces. I think I’ve made it pretty clear that it would take more than one diagram. The interaction of forces on a prong collar is not a simple problem. It needs to be addressed with the more sophisticated mathematical modeling tools we have now, such as the finite element method.

Take-home message: One drawing can’t represent all the force scenarios on a prong collar. It’s a cheap deception. Trainers who use pain or discomfort to train or manage dogs need to own it. They need to stop making up stories about protecting the dog’s throat when instead they are painfully concentrating force into tiny areas.

Copyright 2021 Eileen Anderson

P.S. I am keeping comments closed for now. I have been working on this off and on for months and am tired of the whole thing.

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