How many degrees of slope can you climb?
This is a topic that is prone to bragging solitaire, and the fact that people frequently confuse two different units of slope measurement makes this topic contentious.
We join Rhett Allen, a physics professor at Southeastern Louisiana University, in this article to discover the limits of bicycle climbing.
The first definition of slope is the steepness of the surface unit; typically, the slope I is the ratio of vertical height h to horizontal distance l. Both percentage and degree are expressions of slope; the percentage formula is vertical height / horizontal distance * 100 percent, and the degree formula is tanα = vertical height / horizontal distance.
Consider the following examples.
A highway has a maximum slope of 5%, 3°.
The maximum slope of a parking garage is 15%, 8°.
The climbing capacity of a car is 36%, 20°. Certain off-road vehicles can climb 60%, almost 30°, which is the slope of stairs in an ordinary building.
100% slope is 45 °, almost a cliff feeling.
How steep a hill can be climbed does not depend on power.
“If you don’t care about the speed of climbing, say a fraction of a meter per second, you can keep climbing with very little friction. It’s like lifting a heavy object with a pulley that only requires a small motor.”
Rhett Allain is a physics professor at Southeastern Louisiana University who writes a physics science column for Wired magazine.
In theory, as long as the right gear ratio is found, a very small amount of power is sufficient to sustain the climb.
However, a very small gear ratio requires the rider to turn his legs like crazy, maintain a very high pedaling frequency, and if he is not careful, he will fall off the bike because it is too slow.
When combined with the actual situation, the climb’s speed could not be too slow, so Professor Allan set the climb’s minimum speed to walking speed, 2 meters per second. Then he performed extremely complex calculations in a very professional physics manner, eventually determining that 40 percent gradient is the maximum gradient that the bike can challenge, at which point it must do 422 watts of work, a power value that professional cyclists almost always achieve.
If you want to split hairs and see how far the slope goes, no matter how much power we output or what gear ratio the bike has, we can’t go up another meter, and the center of gravity becomes a keyword.
The only thing you can’t get past is the center of gravity.
We all know that when the slope steepens to a certain point, we fall backward.
We fall back when the vertical extension of the rider’s center of gravity with the ground is not between the contact points of the two wheels and the ground.
And, more specifically, where is the cyclist’s center of gravity?
Keith Bontrager, an elite-level Bikefitting mechanic, says this is difficult to explain conceptually, but he generally sets the center of gravity 3 to 4 cm behind the pedals when the crank is at the nine-o’clock position on the cassette side.
To determine the point at which the cyclist falls back, we must perform a trigonometric calculation: Tilt angle = 90° – [Tan-1 (height of the center of gravity horizontal distance from where the rear wheel lands to the center of gravity)]
This formula yields a critical point of 25.8°, corresponding to a 48 percent gradient. Of course, this is true if the rider remains seated in the car seat throughout the climb.
When the angle becomes too steep, we all have to leave the cushion and rock up to two steps.
If the center of gravity for this stance rocker is recalculated, a new critical point of 41°, or 86.9 percent, is obtained. This appears to allow the rider to conquer any crag, putting off-road jeeps to shame.
However, one factor, the friction between the tires and the ground, is significantly underestimated in this set of calculations. Anyone who drives knows that when the slope is too steep, the tires slip, and bicycles are no exception.
The first disappointment is always the tire friction.
Hristian Wurmbäck, a product manager for Maersk tires, states unequivocally that tire friction will be the first thing to fail when climbing steep hills.
“The coefficient of friction of a complex compound such as rubber is difficult to predict: is it dry, is it wet, how dry is it, how wet is it… You’ll never find the perfect one that can be used in every situation.”
“From asphalt to wet mixed soil surfaces, the coefficient of friction performance of the tires ranged from 0.3 to 0.9.”
Professor Allan optimistically set the coefficient of friction at 0.8, but after applying his complex formula, the friction of the tires could only support a 38.7° climb, or roughly 80% of the grade.
However, the estimate of 0.8 is always too optimistic, considering that 30% of road construction ramps are made of concrete, not asphalt gravel roads, and the coefficient of friction of rubber drops to 0.6 during movement and applying Professor Alain’s formula, the slope obtained is approximately 60%.
Even if you’re confident you have enough power, the right sizing ratio, and exceptional center of gravity control, you’ll be beaten by a 60% steeper grade because your tires will let you down unless you keep a bottle of 502 in your cycling suit at all times.
The good news is that an HC climb (short for hors CATégorie in French, meaning “outside the class” and denoting the most difficult climb) is only a 10km or more climb with an average gradient of 7.5 percent, according to the UCI.