Additional Math Pages & Resources

Wednesday, August 25, 2010

Double-butted when you spoke? Part II


We're continuing to investigate the math of bicycle spokes today.

In the following discussion, I am assuming standard-sized (700c or 27 inch) wheels on road bicycles. Let's say we want to get some new wheels for our bicycle.

To gather data, I relied on several bikes I own, the website of DT Swiss (a major spoke manufacturer) and a great website operated by Sheldon Brown. Sheldon has been into bicycles for a long, long time. When I started working at a bicycle shop in 1972, Sheldon was already an authority in the business.

Here are the numbers we will start with:
  • Spoke thickness can range from 1.6-2.3 mm diameter
  • Spoke length can range from 215-310 mm from the bend to the tip of the threaded end
  • Spoke weights - about 4-7 grams per spoke
  • Spoke nipple weights - range from 0.3-1.1 grams per spoke
  • Front Hub weights range from 70-230 grams
  • Rear Hub weights range from 200-600 grams
  • Quick Release skewers (hold hub to frame) weigh 50-200 grams per pair
  • Front hubs widths range from 125-135 mm
  • Rear hub widths range from 125-140 mm
  • Wheel rims weigh 300-600 grams each (per rim)
  • Rim tape (covers the spoke tips and nipples) weighs 30 grams per wheel
  • Inner tubes weigh 50-110 grams
  • Tires weigh from 160-400 grams per tire
OK, now it's time for some math. Let's just focus on weight today.

Q1. Using these numbers, calculate the weight of an imaginary pair of wheels of your choice.

Ignore the gears on the rear wheel and any hub-mounted brakes, generators or reflectors. Otherwise your weight calculation must be complete with skewers, hubs, spokes, rims, nipples, tape, inner tubes and tires. Include both wheels. Round off any sums or products to reasonable numbers. Do the work in your head for each component, show your work, and add it all up without a calculator. Convert to pounds at the end.

A1. Here's how I would weigh my set of wheels:

140 g = Quick Release; one pair
200 g = Front hub
300 g = Rear hub
360 g = Spokes @ 36 front, 36 back = 72 x 5 g
70 g = Nipples @ 72 x 1 g, rounded  off
800 g = Rims; one pair 2 x 400 g
60 g = Rim tape; one pair 2 x 30 g
160 g = Tubes; one pair 2 x 80 g
600 g = Tires; one pair 2 x 300 g
2690 g = 2.7 kilos x 2.2 lbs/kilo = 2.2 + 2.2 + 1.5 = 6 lbs rounded off
or
2690 / 454 g/lb = 2700 g / 450 g = 6 lbs

Click here to see your wheel spinning