Do you ever wonder how steep a hill your bicycle can conquer? This question often sparks debates, especially when considering different units of measurement for slope. Let’s delve into this topic with insights from Rhett Allen, a physics professor at Southeastern Louisiana University.
Firstly, let’s understand the definition of slope, measured as the ratio of the vertical height (h) to the horizontal distance (l). Slope can be expressed in both percentage and degrees, with the percentage calculated as (vertical height / horizontal distance) * 100%, and degrees represented by tanα = vertical height / horizontal distance.
Here are some examples:
- Highway maximum slope: 5%, equivalent to 3 degrees.
- Parking garage maximum slope: 15%, around 8 degrees.
- Car climbing ability: 36%, approximately 20 degrees. Some off-road vehicles can tackle slopes up to 60%, nearly 30 degrees, similar to the slope of typical stairs in buildings.
- 100% slope is 45 degrees, creating a cliff-like sensation.
Climbing Limits: Theoretical vs. Practical
Allen explains that theoretically, with an appropriate gear ratio, a small amount of power is sufficient for climbing, comparing it to lifting a weight with a small electric motor. However, in reality, a very small gear ratio would require cyclists to pedal rapidly, maintaining a high cadence, and risking a slow ascent that could lead to falls.
Considering a minimum climbing speed of walking pace (2 meters per second), Allen calculates that a 40% slope is the maximum challenge for bicycles. This requires an output of 422 watts, a power level achievable by many professional cyclists.
Beyond Physics: Center of Gravity
The critical factor determining how steep a slope can be conquered lies in the rider’s center of gravity. When the vertical line extending from the rider’s center of gravity doesn’t fall between the two wheels’ contact points on the ground, backward rolling occurs.
Keith Bontrager, an elite Bikefitting technician, places the center of gravity around the crankset side of the crank, positioned at 9 o’clock, 3 to 4 centimeters behind the footrest.
Considering both seated and standing riding positions, Allen calculates a critical point of 41 degrees or 86.9% slope, showcasing that riders could potentially conquer almost any hill.
Frictional Disappointment: Tire Traction
Christian Wurmbäck, the product manager for Continental tires, emphasizes that tire traction is the first factor to fail when climbing steep slopes. The coefficient of friction for rubber compounds varies under different conditions, making it challenging to provide precise data applicable to all scenarios.
Assuming an optimistic friction coefficient of 0.8, Allen’s calculations reveal that tire traction supports climbing up to approximately 38.7 degrees or 80%. However, considering real-world scenarios with a coefficient drop to 0.6 on concrete surfaces, the maximum slope becomes around 60%.
In conclusion, even with ample power, suitable gear ratios, and exceptional control over the center of gravity, tires become the limiting factor, exposing the rider’s climbing limits to be around 60%, a challenging feat that even the steepest hills in professional cycling don’t often reach.