# The Physics of Baby Carriers

This is something I have thought about for some time. It is also something I (as a father of 4) have a lot of experience with. The problem is these infant car carriers. In the car they are not a problem. The problem is out of the car. Not sure what I am talking about? Here is a picture:

I don’t mean to attack the infant carrier industry. I am sure some people really like these things. For me, there is only two situations that are good for taking the seat out of the car.

• In a restaurant. The infant seat works well with those toddler high chairs. Most of the current infant seat models are designed to fit on top of the high chair (you know -those wooden ones).
• In a grocery store. Again, the infant seat fits well with the standard grocery cart.

In both of the two cases, it is useful to be able to use both hands. For other cases, I find it to be much easier to just carry the baby. So, what is my problem? What is wrong with these modern devices? It is all about physics and center of mass.

Center of Mass and Not falling over

This may seem straight forward, but if the center of mass of an object is outside its supports, it will fall over. What is center of mass? Gravity is a force between objects with mass. If I take an object, every piece of that object will have a gravitational force on it from the interaction with the Earth. This would be a pain to deal with the forces on all these pieces (or impossible). The center of mass is the point that you (or I) could apply the gravitational force for the whole object and get the same result as the force on all the pieces. Here is a simple example:

This will only work if all the “pieces” that make up the object are connected together.

How to make something NOT fall over

Suppose I have the following two objects.

The object on the left would clearly fall over while the one on the right would not. I drew some vectors on the objects to represent the gravitational force (from the center of mass – the red dot) and the force of the floor pushing up. Assume both of these objects have the same mass and same center of mass. Note that the net force on both of these objects is zero (vector). To understand why one falls over and the other doesn’t, you need more than the net force, you need to look at the torque. What is torque? The simplest answer is that torque is the “rotational force”. It is like force, except for rotations. There are several definitions of torque:

The first equation shows torque as a vector. That usually makes people a little uncomfortable, so I wrote the second equation with just the magnitude of the torque. F is the force that is applied. r is the vector from the point about which you want to calculate the torque and ? is the angle between the force and the line from the where the force is applied to the point about which you want to calculate the torque.

Why do I call torque “rotational force”? Well, what does a force do? A force changes the momentum of an object (net force that is). A rotational force changes the angular momentum. If the mass distribution of an object does not change, then the torque changes the rotational velocity. I know this seems sort of confusing, but it really isn’t the point of this post. The point I WANT to make is that if the torque about any point is zero, the object will not change its rotational speed – and thus not tip over.

For the two case above, the torque about the point at the bottom is clearly not zero. The force of the floor pushing up has zero torque about that point (because the r is zero). The torque due to the gravitational force (exerted at the center of mass) is clearly not zero. It tips over.

For the other case, the torque IS zero (about any point). Suppose I take the left “leg”. The force from the floor on that leg exerts no torque about that point since r is zero. The torque from gravity has a much larger force than the remaining force from the floor. However, the other force (though half the magnitude) is twice as far away from the point of interest. Also, these two forces create torques in opposite rotational directions. The result is that there is no net torque about that point. It turns out that the net torque about any point on that object is zero. So, that object does not tip over.

Back to carrying the car seat

So, what does this have to do with the baby seat? The picture above does not show this too well (because that guy is quite large), but in order to not fall over a person needs to make sure his or her center of mass is in between his or her feet. Here is a diagram.

The baby seat has mass and therefore a gravitational force on it. Since the seat can not be directly over the feet, it will contribute a non-zero torque. This torque is countered by shifting the body torso in the other direction. I know you have seen people do this, especially smaller people (because they need to move the torso over even further to create an equal and opposite torque). I know what you are thinking, that picture does not look realistic. You are correct, the person should not be smiling. Maybe you can see the main problem with carrying this baby seat. How are you supposed to walk like that? What if you carried the car seat in front of you with two hands?

If the guy doesn’t want to fall forward, he needs to lean back to keep the center of mass over his feet.

So, I have used these things and they are just silly. If you want to be hands free and carry a baby, use one of these

Why are these better? They just look cool. Plus, how far away is the baby from the feet? Not far at all. Much less torque, much less compensating lean needed. Really, the best place would be on your head. This would be directly over your feet. I have never seen this though.

Notes:

• I found pictures on Flickr.
• Please do not carry your baby on your head, someone could get hurt and blame me.
• Remember that I said that there were some good situations to use the car seat as a carrier – like the grocery store and at a restaurant.
• When I first started using these things I would just end up carrying the baby AND the car seat separately.
• Maybe this works for you, then please – I mean no disrespect.

1. #1 tushar
December 3, 2008

hey man, nice article however i wanted to point out a mistake in your article. the formula for torque is actually Torque=(Distance)(cross)(Force) and not Torque=(Force)(Cross)(distance) as mentioned in your post. Other than that excellent article

2. #2 Rhett
December 3, 2008

@tushar,

Thanks for pointing out that error (I fixed it). This is what happens when you start a post at the beginning of a vacation and finish it at the end.

3. #3 Pat
February 15, 2009

Guaranteed if men carried around babies of different weights 8-12 hours/day trying to go out and about, or trying to do things, they would use all that engineering training to develop ergonomically, simple, and safe solutions for baby carrying of any age, from infant to toddler.

In fact, I would bet that hasn’t yet been done by men to test what the demands are for infant and child carriers. Since women’s are even less strong than men, it’s probable that there are carriers for men and carriers for women that is required – due to the gravity factors, etc.

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