## Friday, June 29, 2012

### The Fourth Wheel

A few days ago I went for a walk with my baby daughter. To be more precise I had an errand in town 30 min walking distance from our home. Slowly pushing the bulky stroller, I reached the destination, accomplished the errand and already quite tired turned back toward home. Just as I was crossing the street one of my stroller's wheels broke off and fell on the ground.
My first thought was lifting the stroller with the baby, grabbing everything into my hands and running away from the street. But I am no giant. Then, I tucked the fallen wheel in the stroller basket and tried pushing the stroller. To my amazement, it worked. The stroller rolled on the 3 remaining wheels almost as good (or almost as bad) as it was on 4 wheels. Two wheels were on the left and only one on the right - the back one. It looked strange not only to me. A few passer-byes looked in surprise and made sure I know that one wheel is missing. But we reached home in the same 30 min we walked there and my daughter managed to fall asleep along the way.  My question is, how is it possible for a 4--wheel creation to continue functioning even when one wheel is missing. Think about it - car requires a jack and will lean in one corner if one wheel is missing. A dog with 3 legs wont go far...So why did my stroller ?

I didn't get a picture of a stroller with the broken wheel. Here is the stroller, with all 4 wheels on.
Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Anonymous said...

the reason a car won't work is because with 4 wheels the weight is evenly distributed, and that is how it is supposed to work. But when 1/4 of the weight is hanging over, it fails. However, on the stroller the back wheels are taking more force so the front wheels are less necessary, and If the person is holding it, the stroller will be stable.

I am 11 and I figured this out!

Jerome said...

It is going to seem like I am not answering the question at all by my beginning remarks, but it will lead me into my assumptions.

Background remaraks.
=====================
I read somewhere that parents seem to prefer to carry small children on their (the parents') left hip. That was certainly true of both my wife and I which would seem odd because both of us are dominantly right handed. There are all sorts of reasons offered for this odd behavior, but I cannot find a reference for it. Here however is a picture of a woman constructing a wrap which puts the child on her left hip, just the way I would do it.

http://www.wrapyourbaby.com/hipcrosscarry.html

Introduction
============
By the same token, I would imagine that most people would put the child in the lower middle of the carriage flat bed so the baby is closest to you. Instinctively you would not want to have to reach a great distance if you suddenly had to pick the baby up. I'm thinking of those old style baby carriages, the kind used when my kids were young. (Read many years ago).

Center of Gravity
=================
What I'm trying to say is that the center of gravity of the load is closest to the parent and is not dead centered.

Most of the weight is closest to you, the mother (or sometimes the father).

When the wheel fell off, the center of gravity shifted, or the center of gravity sort of redefined itself.It would be better to think of two smaller centers of gravity.

The one of most interest would be the front left.

The center of gravity of the remaining wheels has now awkwardly shifted mostly on a line connecting the lower left and the upper right wheels. What you are doing (my guess) is pushing down slightly on the right side to get the lower right wheel to hit the ground.

You are making up for the mass that would normally be on the upper left wheel that is now missing. Because the wheel is meant more for balance than weight (remember baby is closest to you), you may not even notice that you are putting that extra push on the right side.

You cannot do that with a car. The mass is so extensive that mere mortals cannot compensate for it. Maybe if you put a cube of lead on the trunk on the oppose side of the (front) wheel that fell off, you might be able to get the vehicle to move, but it's much easier to use a spare.

Ilya said...

Factors that make it easier with the stroller:
1. Weight distribution. If the baby is sleeping with the back reclined, that puts more weight on the back wheels that are both there.
2. Absolute weight involved. Compared to a car you don't need as much to compensate for the missing wheel in the case of the stroller. Certainly enough that human arms can supply.
3. Lever. Since the handles are levers, that makes it easier to apply the necessary force to compensate for the missing front wheel.

Dennis (of Dennis and Katrina) said...

Knowing, from experience, the situation you found yourself in, I had two thoughts:

The first was that with a stroller, the parent pushing from the rear of the stroller can create a downward force on the rear left, keeping the (missing) right-front wheel clear of the ground. Creating enough force to do this in a car isn't easily possible - the car is more massive and I would guess that the dog can't figure out how to balance.

My second thought was that this is related to a previous puzzle, asking why a stool with 4 legs is LESS stable than one with three legs. The answer to that puzzle was that three points define a plane - when you add the 4th leg, you're creating four planes that the chair can move between. I wonder if the stroller still moves well because there's still a plane? Under this theory, the car wouldn't still be a plane because of the effect of the suspension. And the dog is still out of luck!

If the center of gravity of the stroller is not outside the triangle formed by the three wheels of the stroller, it will balance. There are some additional factors to consider, such as the angle of the force you are pushing it with, but the location of the center of gravity being within the triangle of the wheels is the basic idea.

Anonymous said...

I think the stroller still worked with one front wheel missing because the center of gravity for the stroller, with your baby and with you pushing it, was towards the back of the stroller not the front. Especially if your baby is lying down in the stroller as in the picture, I would think her center of gravity would be right near the back of the stroller seat, just above and slightly in front of the back wheels.

This problem reminded me of how parents with strollers often get onto sidewalks with no curb cuts: bt pushing down on the back of the stroller to lift the front wheels up over the curb.

I don't think that your stroller still would have worked quite as well without one of its front wheels if:
(1) If your walking trip home involved big downhill(s) because that would have put more force and weight on the front of the stroller. I am assuming your trip home was mainly flat or maybe uphill (in the latter situation, the 3-wheeled stroller would work the best I think);
(2)If there were heavy items in the basket below the stroller, unless they were near the back of the basket near the back wheels
(3) If your baby was positioned rear facing in the stroller so that her center of gravity was closer to the front of the stroller
(4) If your child was older and heavier, and/or sitting up in the stroller, since those characteristics too would move her center of gravity (and that of the stroller and child combined) closer to the front of the stroller.

An aside, regarding (2) above, when my children were younger, I often walked with a stroller to the grocery store, bought more than I had intended to, and came home with the stroller's basket full of heavy food items. I think that even though my walk home from the store is uphill, if one of my front wheels had come off (sometimes the weight of the food was so much, I thought the stroller might be able to take it), I would have been out-of-luck... though even then I would have made it home eventually. :)

TracyZ

Annie said...

I think the weight in your stroller was distributed so more weight was in the rear and/or right side....it's center of gravity was over the remaining three wheels. If the weight had shifted to the front left I think you might have had a harder time getting home!

Maria said...

You all are terrifically smart, no matter what age you are. There is one 11-year old, very impressive!
I am glad to hear this had happen to you as well. Jerome - very interesting observation about left hip/side preferences. I also place my baby on my left hip much more naturally than on the right. And I am a righty.

I agree with you that this a a matter of Center of Mass and here is a picture that I made to demonstrate what you are describing with your words above. Because baby is in the back of the stroller, the center of mass is not in the center of the rectangle between the wheels but closer to the back, inside the triangle created by the functioning wheels. If center of mass would be outside, the stroller would flip.

Click to see the image, the use Back button

Stephanie said...

It is quite simple really. The mother acted like a jack to a car. Also unlike cars, the font wheels of a stroller typically swivel and are thinner than the rear tires that. Most often roll in the forward and reverse positions. In addition, a strollers weight is not equally distibuted. The rear of the stroller holds the handle bars and steering, easily explaining how when empty they have been known to flip over with a diaper bag suspended off the handle.