Applied Bicycle Science

From Texaco to Moe's

The air feels like it did when we used to buy outrageously fruit-flavored gum whose scent made it to the end of the short gas station aisle where we would go after school with change from my dad's sock drawer change cup. It afforded us the flirt before our parents were home from work in the strange interval before we knew how to kiss and after we’d become addicted.
That gas station, where my buddies and I would hide our bikes behind the dumpster and wait for cars to not use all of the time allotted by the automated car wash blow dryers so we could run toward them and jump, be blown back, or lean our faces in to feel our cheeks morph as if on high speed missions, that gas station, where the repetition of pulling into pump two from Candelaria taught me what side of the car my gas cap was on sold itself, and Moe's Bagel World put in a new and out-of-place sign that featured a torus with continents and sea.
It was there, at Moe's that I stood behind you with my fingers tucked into the pocket of your tight jeans, you reaching back to tuck your thumbs in mine as we looked at the menu hanging over the counter, and you asked me, "How can a bagel world not have cinnamon-raisin?"

Transition

Then later I became someone else and sailed small arcs of the earth to meet people I didn’t recognize.

Sexual Chess and the Dam of Inhibition

Her eyes paused on my socks. They were yellow socks under Birkenstocks. They were orange—pumpkin really, but it was October—almost October. I wondered what she thought, but was forced to plow confidently through. She had a bowl of—green beans? lima beans? some podded bean, and she was sitting outside, plastic chair and table, reading and watching people in the street. I was one of them. I stopped to talk. Pant rolled up to bike, I walked the silver Schwinn across the street. That’s when she saw the sock. Then she offered to share her beans. My pod—the one she handed me—had two. I ate one smoothly, and one shot sideways, landed on the walk. I felt for a third. It wasn’t there. “Not a pro,” she said. “Not even good,” I returned. Well, she was sure she’d see me around. “Two for Tuesdays at the pub,” I advertised, “I’m probably gonna head over there later.” I shied from the formal invite, and cranked away anxiously. Should I play? I have longings. I want to connect. I guess I have to. He looks at her, gets the eye contact. His smile and "hi" are a knight on the board. Quick, I need a strategy. I don’t want a fu*king strategy. Clothes off is not mate in two. In a room, a town, a planet of others thirsty for love, I can feel how we could be mutual veins, but inhibitions construct dams that transform rivers into reservoirs, pools to evaporate.

Bicycle Physics

Aristotle, Galileo, Newton, and the First Two Laws of Motion

Aristotle asked the question, “Why do things move?” and it seemed obvious that forces give objects motion. Then he asked, “What keeps them moving?” In the case of the cart it was the ox, but what about the arrow? Two thousand years later, Galileo said, “The question needs no answer. Moving objects have an intrinsic quality of motion.” Late that century, Newton set that thought in stone as his first law of motion.

A body in motion retains its motion, and a body at rest remains at rest unless acted on by a force.

Each body in motion, the way Newton tells it, has mass and velocity. We call the product of these two momentum:

\begin{equation} \mathbf{p} = m\mathbf{v}. \end{equation}

A vector is a quantity with magnitude and direction. The arrows indicate vectors. Mass is just a number, just something sitting there. But velocity is defined as speed with direction, therefore it’s a vector. A vector doesn’t change until it feels a force.

\begin{equation} \mathbf{F} = \frac{d\mathbf{p}}{dt} \end{equation}

Force is the time derivative of momentum. This is Newton’s second law. A force capable of twisting is called a torque. On a bike this could be wind, gravity, or the rider's own tendency to lean.

Momentum and the Steering Trail

The diagram shows the main concept:

Schematic of bike with geometry labeled to identify the steering trail.
We’re concerned with the steering trail and the head tube angle. Here’s a quick derivation relating the two. \begin{equation} a+b = r \end{equation} \begin{equation} \mathrm{cos}\,\theta = \frac{R}{a}; \;\; \mathrm{tan}\,\theta = \frac{b}{s} \end{equation} \begin{equation} a = R\,\mathrm{sec}\,\theta; \;\; b = S\,\mathrm{tan}\,\theta \end{equation} \begin{equation} S = \frac{r\mathrm{cos}\,\theta-R}{\mathrm{sin}\,\theta} \end{equation} We see that the steering trail varies with the headtube offset, known as the rake, and the headtube angle. At the limit where the steering trail goes to zero, the bike has the greatest tendency to respond to torque in a way that balances. But as the steering trail vanishes, the rider loses the ability to communicate with the bike. An intermediate angle and a moderate rake lets us roll into our momentum, while maintaining the ability to curve and corner. Engineers apply this. Most bikes have a head tube angle around seventy degrees, and rake of a few centimeters.

Conservative Fields

A force field is a region of space inside which a particle feels a force. We live in a force field. The earth’s gravity pulls us in. A force field is said to be conservative if work done against it can be returned as work done by it. Mathematically, \begin{equation} \oint \mathbf{F}\cdot d\mathbf{r} = 0. \end{equation} The net work required to move an object around a closed loop is zero. Gravity has this property. Work to get up a hill is returned as acceleration back down. At the top it pushes us, and on the geometry of the bike we glide smoothly.

Conclusion

Get going and the rest is taken care of. Anyone who’s tried knows that inhibition is a waste of time.

The Story of the Silver Schwinn

I went to the sports recycler to check out used bikes. There was a Schwinn, circa nineteen seventy—giant, silver, classic. I took it for a test ride. The frame was too big, but with the seat low, as it had been adjusted by the rider before me, it fit well. The price was right, so I rode it home. Not until later did I find out that the steering trail on this jewel allowed for all out no hands pedaling, confident hill bombing, and even turns from one street to another perpendicular without a touch of the bars.

When gravity is working for me, I let go of the bike, stand on the pedals with hands out, and let the cold air rush my layers. But staring at the point of perspective, I still see the handlebars. I don’t want to know they’re there.

It’s the evening of my eating the bean, and on my ride home I realize it was edamame, of course—the coolest podded bean around. I climb to the top of Pleasant St., turn onto fifth, then let the hill lead me to speed. I hop onto the frame and stand full height on the bike to spread my arms as if the axis to the wheels.

That’s where I am now. Head back under stars, I float in an effortless orbit around the last night of September, where I am a streak to the lamp lit red leaves who are themselves on a ride they need not control.