For step by step photos of the project, check out the audio slide show: "An E-Bike Potpourri."

When I ride with serious cyclists, they give me endless grief about the plastic milk crate attached to my bike rack. No doubt they’re right that it adds considerably to the bike’s drag coefficient. Still, it’s awfully handy for holding a coat, groceries, or an impulsive garage-sale purchase. So what if the crate detracts from the Lance Armstrong look?

Such purist riders—and the bike shop owners who cater to them—also find other practical modifications anathema. They particularly despise electric motors, which you might use to commute to the office without arriving drenched in sweat, getting your workout on the ride home instead.

Being the practical, crate-toting cyclist I am, I was inspired by a recent encounter with Elise Giddings, an entrepreneur who two years ago helped found Cycle 9 (http://cycle9.com), a bike shop in Carrboro, N.C., devoted to helping people use their bicycles as practical transportation—often by outfitting them with electric-assist motors.

Giddings told me that with a standard hub-motor kit, the conversion might take about an hour. That seemed too easy—and pricey. A good kit (meaning one with decent batteries and a powerful motor) would set me back more than US $1000. So I started scanning the Web in the hope of making the classic DIY trade-off of time for money.

Sure enough, others had ridden this road before me. The design I settled on was shaped by the several generations of electric-bike conversions that Eric Peltzer, a sculptor and inventor in Altadena, Calif., describes at http://www.electricycle.com. It’s a mash-up of bicycle, electric scooter, and kart-racing hardware.

My starting point was an old mountain bike. Its frame was beefy enough to stand up to the extra 8 kilograms (17 pounds) or so in hardware, much of it from a 24-volt, 400-watt brushless DC motor. The one I bought, which includes an internal controller, came from Superkids Online and cost a mere $75.

This motor is normally sold for electric-scooter use. In order to retain pedal power, I needed to attach it to the rear wheel in a way that provided adequate speed reduction without interfering with the bike’s leg-powered drivetrain. That meant I had to equip the motor with a very small drive sprocket. Searching for one steered me into the world of karting—a sport that involves miniature gasoline-powered race cars that use chains with a smaller pitch than bicycles normally have. I bought a tiny nine-tooth sprocket from Margay Products, of St. Louis, for the motor and a 92-tooth Kevlar-composite sprocket from Precision Karting Technologies, of Wixom, Mich., for the rear wheel. Together they gave my e-bike a reduction ratio of just over 10:1.

Attaching the rear sprocket to the left side of the hub was by far the biggest challenge. I wanted to coast without feeling cogging torque, the drag that a motor’s magnets impose as it rotates without power. So I included a freewheel—something almost all bikes have in their rear hubs to make sure that the wheel never turns the pedals.

I started with a bicycle hub designed to accept a disk-brake rotor on the left side. Using a lathe, I removed much of the metal from the left side of the hub and cut left-hand threads in it to accept an ACS Southpaw freewheel, which is made for bicyclists who prefer to have the chain on the left side. (Believe it or not, for some people this feature is important.) That tactic allowed me to screw a second freewheel on the side opposite the normal freewheel mechanism, which remains in place to serve the standard pedal-powered drivetrain on the right side of the bike. The folks at Cycle 9 sold me a sturdy rim and spokes to go along with the modified hub, and they laced it all together into a wheel. Total cost of the highly modded wheel: about $200.

I got more lathe practice fabricating an aluminum disk to connect the added freewheel with the much larger 92-tooth sprocket, and more still when it came to attaching the nine-tooth drive sprocket to the motor. That involved machining down an adapter I had purchased with the motor to a diameter just 0.001 inch (0.0254 millimeters) bigger than the inner diameter of the drive sprocket. For me, a mere Sunday machinist, that proved a delicate operation: I must have taken dozens of micrometer measurements along the way. I then heated the sprocket with a propane torch, expanding its diameter temporarily, and inserted the adapter, driving it home with a sledgehammer after temperatures equilibrated.