scr4: Not in my experience. Standing on a hill is easy. A track stand is hard. The difference, as I said, is friction. On foot, you don’t slide down the hill. On wheels, you do.
Chronos: Of course they’re different. Gaining elevation is simply a matter of motivating a certain mass though x feet of height. Holding your position on the hill is a continuous task - a function of mass and inclination. It’s true is that if you “attack” the hill, the percentage of effort expended on this task declines, but I was addressing the more-usual scenario of low gearing, low speed and more effort dedicated to holding-the-hill.
Princhester: No, in walking, one uses no effort resisting sliding down the hill. Friction of feet/shoes-on-pavement does that.
Wrong. In a perfectly balanced trackstand facing uphill you have just enough weight on your front foot to balance the tendency of the bike to roll back. You are not moving. You are not going up, you are not going down, and no energy is expended at all. If any is being expended it is because holding your weight with one knee out in front of you in such an awkward fashion may of itself cause a degree of exertion, as will the need to adjust your balance. But this is an artifact introduced by your example and is not relevant to the question at issue.
If you need a way to envisage this, perform this thought experiment: instead of a bike, imagine a four wheel pedal car (so balance is not an issue). Imagine that the “pedals” are supersize so you can if you want stand on them comfortably with with both feet.
Now, you take this vehicle and you go try it out on a series of increasingly steep hills until you find one in which your whole weight, on the front pedal, will perfectly balance gravity trying to roll you backwards down the hill so that you go neither up nor down. You put both feet on the front pedal and stand up straight, perfectly still. You are expending no effort at all. You are standing upright and still on a pedal in a wheeled vehicle on a hill which, according to you, should take effort to keep in one place above that which it would take to just stand on the hill.
And yet you are in precisely the same posture, expending precisely the same posture, either way.
No, the only difference is that a bike requires more concentratio to balance.
As I said, standing is exactly the same situation: you are using your muscles to resist gravity, otherwise you’d fall on your butt.
On a track stand (or tricycle), to stay still on a hill of angle A, your leg must excert a constant force F = (Mh + Mb) g sin(A) / R, where Mh: mass of person, Mb: mass of bike, g: gravitational acceleration, and R: gain ratio (inches of forward movement for inch of pedal movement). When standing still (on your legs), on a hill or otherwise, your leg(s) must exert a constant force of F=Mh g.
Granted, if you’re merely standing still, that allows the legs to be stretched straight, while your legs are bent during a bike/trike track stand. So if you take into account that physiological factor, standing on a hill might be easier. But this doesn’t apply to the situation where you’re moving up the hill.
I understand your point completely.
Once a force is applied to a mass it moves. The only thing that will stop it is another force (in this case friction). So when you propel yourself forward with one foot to walk the only thing stopping you from contiuing to float foward is the friction between your next foot and the ground. If you get rid of this friction or reduce it (i.e. stepping out onto ice or stepping onto a skateboard) that friction is reduced and you can contiue moving forward with less resistance.
On a bike that resistance is reduced using a wheel on an axel. Where that axel rests on the bike fork is fairly frictionless (compared to a rubber sneaker sole against pavement).
You’re getting warm. Let’s rephrase that. Tell me it’s as easy as holding the cart on level ground.
BTW, I’ve actually done the tricycle-on-a-hill experiment. To be specific, it was a pedicab. Passengers sit in the back and pay to be squired about. On a hill, to rest, I had to use the brake.
Good grief indeed. Maybe you need to restate your claim because I think we’ve lost sight of what it is.
The fact is, given a sufficiently low gearing, climbing a hill on a bike is more efficient than walking up that same hill. I explained the reasons in my first post to this thread. There are no energy loss mechanisms which exist for bicycles but are missing for walking.
I already gave the caveat that a bicycle needs sufficiently low gearing to be as easy as walking. Pedicabs don’t have such low gearing, at least for something that carries that kind of weight. I used to own a Greenspeed tricycle with a 72-speed drivetrain, and it was very easy to pause on a steep hill without using brakes. Of course it’s even easier if I apply the brakes, but I never said otherwise.
I’d like to offer my perspective on the issue. A simple way to think about a bicycle travelling up a hill is with a free body diagram approach. When the rider turns the pedals, this ends up generating a force between the bottom of the rear tire and the ground, in the direction parallel to the hill (tangential). The only other force is gravity, acting vertically downward. The gravitational force can be divided into a component perpendicular to the ground (normal), which holds the bike against the road, and a component tangential to the ground which propels the bicycle up the hill. In order to maintain a constant speed up the hill, the rider must provide enough force to match the tangential component of gravity, plus overcome the losses in the system (similar to those on flat ground).
Walking is less efficient because the hiker’s centre of gravity will bob and down unnecessarily, and the speed will be increasing and decreasing during each step.
On a bike, if the hill is too steep you may not be able to sustain enough power to overcome the forces discussed above, due to lactic acid buildup in the muscles. It is still possible to slowly walk up the hill because when walking, the muscles can rest for as long as need be between steps. While resting, gravity pushes you down with sufficient force that your shoes will not slip, so you only have to remain standing, which uses about the same amount of exertion as doing so on level ground (the only difference is the angle of your feet).
A similar strategy can be used to bike up the hill by standing and placing your weight over the front pedal to keep the bike from rolling backwards between “steps” (pedal pushes). The problem with this is that depending on the gearing, the amount of force needed for each step may be more than you can generate using your weight and your muscles combined. The other problem is that if you are going very slowly, plus periodically stopping, it becomes very difficult to balance.