Simple Machines

This is likely to be a very meandering post. Forgive me. I'll try to make it worth the read.

I'm a teacher at a public high school (my blog has yet to hit big enough to allow me to quit my job) and we have a custodian at my school who is a fount of all kinds of knowledge. There isn't much that Rob the janitor doesn't know, and very little that he can't do. If we ever find ourselves in some kind of post-apocalyptic nightmare scenario, or even just a season of Survivor, Rob is the guy everyone wants on their island.

So, the other day, Rob arrived at my classroom with a large flatbed pushcart loaded up with a couple hundred new textbooks. As he and I unloaded the cart, a thought occurred to me.
     I asked Rob, "How much do you suppose all these books weigh?"
     Rob considered the weight listed on a single case of books. He did a quick calculation in his head (a lot quicker than I could -- did I mention I'm an English teacher?), and replied, "A little over 1/2 ton."
     "Can you lift a half ton?" I asked.
     "Nope," he replied.
     "But you didn't have any trouble rolling this down the hall."
     He answered, "Nope, but I also can't lift a tree, but give me a big enough pry bar . . ."
     "Exactly," I said.
Rob then went on to remind me that it was Archimedes who said, "Give me a long enough lever and a fulcrum and I can move the world." Rob and I agreed: that's the beauty of simple machines.

Image from Mechanic's Magazine, Vol. II, 1824 

Wheels and axles. Levers and pulleys. Inclined planes, wedges, and screws. These simple devices don't defy the laws of physics and gravity, but they do help us use the laws to our advantage. Mechanical advantage. To do more work with less effort, for example.

Think about that cartload of books. I don't know anybody who could lift that kind of weight, but put a big lever under it, or hook that weight up to some pulleys and lifting it becomes easy. Put the load onto a cart with wheels, and moving it around is no problem. Allow me to get a little hypothetical on this subject. Pick up one of those books and you'll know you're lifting about five pounds (textbooks just keep getting heavier!). But if someone added that book to the cart (or removed one from it), would you be able to tell the difference? What if they added or removed two or three of them? Would the cart suddenly get noticeably harder or easier to push? How many pounds would someone have to add or subtract from the load before the difference could be felt? Without lining up a bunch of test subjects, I'm going to take a guess and say that it would take at least 10 books, or 50 pounds, to be noticed -- maybe more -- it's just guess, but it's a guess that feels right. The same mechanical advantage that allows us to easily move hundreds or even thousands of pounds makes a difference of only a few pounds seem inconsequential.

What got me thinking about that cartload of textbooks was an ongoing "friendly disagreement" I have with other cyclists about the importance of the weight of a bicycle. Not too long ago I was out for a ride with a friend. At one point we had to "portage" our bikes around a road blockage and my friend picked up my bike and remarked (with shock!) how heavy it was. I knew my lugged steel-framed bike weighed more than my friend's carbon machine, but in actuality, I doubt the difference was more than three or four pounds. We can of course detect that kind of weight difference when we lift a bike up, but the thing is, that isn't how we ride a bike. And considering the way a bike is actually ridden, a few pounds don't really make much difference. Keep in mind, a bicycle is far more efficient a machine than a basic flatbed pushcart. With pneumatic tires and high-quality bearings in the hubs, the friction and rolling resistance are incredibly low. The leverage gained from cranks and gears makes the weight difference of a few pounds almost meaningless.

Also keep in mind that we can't just talk about the weight of the bike. We have to consider the weight of the rider, too. So it isn't a question of a 17 lb. bike vs. a 21 lb. bike. If the rider weighs, for example, 150 lbs., then we're really comparing 167 to 171 lbs. making the difference even less significant and therefore harder to discern while riding. Here's another fun thing to consider: carrying a pair of 24 oz. water bottles adds roughly three pounds to a bike. But how many people honestly can say they feel faster when they've emptied their water bottles? Most of us probably don't notice that difference except when we're carrying the bike up or down stairs, or putting the bike up on the roof rack of a car. Or posing for post-ride photos with our bikes held triumphantly in the air.

What about climbing? We're definitely going to notice extra weight when climbing, right? Actually, even that isn't so simple. Even a steep climb -- say, something like 18% grade -- is still 82% horizontal if you look at it differently. The steepest climb I've ever ridden was 25% grade, but roads that steep are rare. One of the toughest, most famous climbs in the Tour de France is Alpe d'Huez, and that has a maximum gradient of "only" 13% (it averages about 8%, but it goes on for over eight miles). But what is a hill, if not an inclined plane? We might have difficulty dead-lifting a certain amount of weight vertically, but rolling up an inclined plane allows us to easily raise weight that we couldn't otherwise lift, so again, a small difference in weight really doesn't make as big of a difference as we tend to believe.

So does weight make a difference on a ride? Does it affect our speed or make us work harder? Sure it does. But you really need to be talking about pounds, not grams -- and more than a couple pounds, at that. In Grant Petersen's book Just Ride, he cites a Cornell Aeronautical Lab study (commissioned by Schwinn) that found a difference of only 1 mph in average speed for every 12 pounds added to or subtracted from a bike. Now, a lighter bike definitely feels faster. But I think the perceived difference is a lot greater than the actual difference. Accelerating from a standstill will be quicker, especially if it's the wheels that are lighter, and one can really feel that difference. But once the bike is rolling, it doesn't take extra effort to keep a heavier bike going, so the overall effect is minimal. When we're riding out of the saddle, like on a climb or a sprint, and rocking the bike beneath us, a lighter bike will feel different (we perceive it to be faster) because we're essentially tossing less weight side to side -- but again, I expect that the actual difference in forward progress is less than what it feels like. When I ride a heavier bike uphill, I feel that weight being shifted left to right -- but it doesn't feel like I'm dragging an anchor behind me.

My commuter -- pushing almost 40 lbs, fully loaded.

I ride my bike to work as much as possible. The bike I commute on has a lugged steel frame and is fully equipped with racks, fenders, lights, and bags. Fully loaded for work, it easily tips the scales at nearly 40 lbs. My morning commute is 13 miles and takes me about 50 minutes: an average of 15 mph. I take a different route in the afternoon -- 15 miles, with a couple moderate climbs. It takes me about one hour: again, an average 15 mph. On occasion, if the weather forecast is really good and I don't have to carry much to work, I'll ride one of my lighter bikes -- about 23 lbs. I'm easily dropping 15 pounds or more, so one would expect that the commute would be faster. And it does feel faster. But in actuality, the morning ride takes barely less than 50 minutes. The ride home takes barely less than an hour. Any gain I get with the lighter bike is so minor that it is easily wiped out by a poorly timed traffic light. In other words, those traffic lights probably make a bigger difference in my commute time than the weight of the bike.

Cyclists obsess about bicycle weight. Some spend huge sums of money to shed a few grams. And sometimes the quest to shed grams throws all the other priorities out of whack, like strength, durability, comfort, or convenience. The way I look at it, bicycle components can be light -- or they can be stupid-light. Too many components today are stupid-light. And then I have cycling friends who smirk at my fendered bikes -- too much weight, they'll say. But when the roads are wet, I figure those fenders are worth every ounce in keeping me comfortable. But ultimately, the quest to shed grams yields much smaller gains than what people perceive, or what they'd like to believe. Remember: pounds, not grams.

Bicycles are, at their heart, simple machines -- or really, a combination of several simple machines working in harmony. A "compound machine" consisting of wheels, levers, and pulleys. The simple machine transforms our energy and makes us much more efficient than we can be on our own. We go farther and faster using less energy. High quality, supple-casing tires lower our rolling resistance, and high quality bearings lower our friction losses. Gears give us the leverage -- the mechanical advantage -- to move effortlessly. And all of that advantage combined makes a few grams, or even a few pounds, a fairly minor factor in our speed or our enjoyment of the ride.