I play football at least 3 times a week. At least 3 times a week I cycle up from one side of the neighbourhood to the other to reach the court, and I say ‘up’ because there’s a constant slope along the entire neighbourhood, which slopes up as I cycle to the court, and slopes down as I cycle back home.
One repeated observation, one might find obvious, is that the difference between the difficulty in cycling downslope and upslope is significantly higher than the difference between running upslope and downslope.
While running upslope, sure, it may be a tad bit more difficult, but while cycling upslope, you’re already panting within 10 seconds!
What makes this rather uninteresting observation intriguing is that cycling is known to be more efficient; marathons are just about 47km long while cyclathons span over hundreds of kilometers. Any long distance can be covered easier and faster with cycles.
So then why is this so? Why is the difficulty more pronounced while cycling?
Upon reading this question, you may immediately think it’s obvious, turning to the fact that cycling has wheels and that obviously has something to do with it.
But the more you think along those lines, the more you realize you don’t get an actual concrete answer. U may feel the gravity pulls down the cycle with wheels a little more ‘smoothly’, or that while running, we don’t feel the gravity acting upon as directly.
It may make intuitive sense, but can we come up with a definitive physical answer? There just seem to be too many variables. How do we take into account the difference in friction - static and rolling friction? How do we calculate the work done with such complex movements? How exactly is our energy spent?
When there are too many moving parts within a system, often the best approach to take is in terms of power and energy. Why? Because we don’t care about the minutiae of each process, just the initial and final condition.
In both processes, we expend work to overcome friction to move forward. While moving upslope, however, we expend work to both overcome friction and overcome gravity. Specifically, while we’re moving upslope, the extra energy goes towards increasing our potential energy.
The increase of potential energy is easy to calculate - mass * acceleration due to gravity * change in height, or simply mgh. The time rate of change of potential energy, or power is
mgh / t = mgv*
where v* is the upward component of velocity, or vsinθ, where θ is the slope of.... well, the slope.
Where does the power - mgv*- come from? Our bodies. Our bodies getting tired is simply a result of giving out mgv* amount of energy every second.
So wether we’re on the cycle or on our feet, our body expends mgv* energy every second, and the more energy we expend every second, the more tired we get.
Does it seem obvious now? Since we move faster with our cycle, v* is greater in our cycle, so we expend more energy every second, and we get more tired every second.
Not only is the speed(v*) higher, but the mass(m) too, as we’re carrying the weight of the bike.
Let’s do some simple math.
Average running speed: 9 km/hr
Average cycling speed: 22 km/hr
Average weight of a bike: 15 kg
Average weight of a human(let’s take a man): 62kg
Thus, if the average man runs and cycles, the ratio of energy expended to over come gravity is: {22 * (62 + 15)} / (9 * 62), which approximates to 3 (g, and sin θ get cancelled).
So, to overcome gravity, we have to expend 3 times the energy while riding a bike upslope, and that’s why it’s easier to get tired and out of breath when in a cycle.