Bike Science: Trigonometry and carbon fiber help Paralympian win
Posted by Shawn Small (Columnist) on April 4th, 2011 at 12:09 pm
[After a hiatus, our Bike Science column is back. Below, carbon fiber master and engineer Shawn Small shares the science behind one of his recent projects.
Steven Peace was a Lieutenant Commander in the Navy in his early 30s when he suffered a massive stroke while lying alone one night in his apartment. He was found 14 hours later when EMT’s broke down his door. When he came to, he was paralyzed on his right side and suffered from severe aphasia.
Only 6 months after leaving the hospital Steven quickly defied all odds by riding a Catrike Trail (recumbent) in the Soldier Ride which goes from Phoenix, AZ to Las Vegas, NV. Here’s how Steven described that first ride; “..the ride was unbelievable, and life-changing. After the first ride, I knew I had to do another one, and another, and another.”
After a few years on the Catrike recumbent, Steven decided to make the transition to an upright trike for competition. The stroke had left him with poor balance, so a standard two-wheeled bicycle was out of the question. With an upright trike he would then be able to compete on the National and International Para-Cycling levels.
Steven recently received a new carbon fiber Specialized Roubaix Pro as his race bike. Steven uses a custom solution to help stabilize him while racing. Similar to stabilizer systems used for heavy front racks he has two strong springs that attach his fork to his frame. The springs are then attached to the frame onto a carbon fiber post that Ruckus Components (my company) installed. This helps keep the fork and bike pointed forward and absorb the turning forces generated by road and rider forces.
Now for the nerdier (fun) side of it, we will use some basic trigonometry and Hooke’s Law to approximate the spring force. Hooke’s law states that:
Where x is the displacement of the spring (how far you pull it), F is the restoring force generated by the spring, and k is the spring constant of the spring chosen. We know the k value from the spring manufacturer (91 pounds-force/inch), so we need to compute the distance (x) that the spring is stretched when he turns.
To determine the distance (x) we use our rusty but trusty high-school trigonometry skills (SOH-CAH-TOA), to calculate (x):
Since Ruckus Components attached the system I know the (a) value is 1.5 inches, so for a turn of the fork by 10 degrees we can calculate the following:
x = 1.5 (inch) tan (10 degrees)
x = 0.264 inch
Using this value with Hooke’s Law and our spring constant:
F = – 91 (pounds-force/inch) * .264 (inch)
F = -24.1 pounds-force
Note: the negative value denotes the direction of the force.
Using our close friends the spreadsheet we then can tabulate a quick range of values for different turning angles:
I know all these numbers might seem like they have nothing to do with bicycling, but in Steven’s case, they do.
With his modified trike, Steven won his first National Championship race and led to placing 8th in the road race and 9th in the time trial at the World Championships. In 2011, Steven will be competing with the U.S. National team in Sydney, Australia. We wish him the best of luck with his new race set-up and were honored to build it for him.
— Read more about Steven in this article in his hometown newspaper.
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