# Cyclist moving up a hill

1. Sep 18, 2011

### IEVaibhov

Consider a cyclist going up an inclined plane.
Will going in a zigzag path make it easier for the cyclist to go up the hill?

(Assume that there IS friction on the incline)

2. Sep 18, 2011

### rcgldr

It will take less torque to follow a zigzag pattern, except for the parts of the path where the cycle goes straight up the hill. Momentum (speed) could be built up on the other parts of the path to compensate. The amount of work done is the same, but there's some optimal combination of force versus distance, or torque versus revolultions for a human to produce some fixed amount of work. If lower gearing was an option, that could be used instead of zig-zagging.

Last edited: Sep 18, 2011
3. Sep 19, 2011

### IEVaibhov

Ok, that is interesting. How does low gearing help?

4. Sep 19, 2011

### Staff: Mentor

How do you think? What are your thoughts on this question? Do you have a bike with gears, and a nearby hill where you could do some experiments?

5. Sep 19, 2011

### rcgldr

Lower gearing reduces the amount of torque required at the pedals it takes to produce some amount of torque on the rear tire. It also reduces the speed of the rear tire. It ends up being easier to pedal but at a lower speed, so it will take less effort (because of the reduced torque at the pedals), but a longer time (because of the reduced speed) to climb a hill using lower gearing.

wiki article:

http://en.wikipedia.org/wiki/Bicycle_gearing

6. Sep 19, 2011

### Gnosis

Respectfully Berkeman, a teacher who fails to answer a question, but asks a question in its stead has failed to teach or convey anything of any value. Such is not helpful to the OP nor is it helpful to many others that will visit this forum and this particular bicycle related thread whom are not disciplined in physics.

Though I’m now on the ancient side of life, I’m not irritated by poorly articulated questions especially realizing they oft times emanate from those lacking a fundamental comprehension of physics principles however, I do deem it entirely inappropriate that those formally disciplined in physics who typically deem themselves virtual masters of their field respond with a question rather than any manner of valued answer.

Subsequently, if you’re easily irritated by such questions and cannot find it within your means to respond with a helpful answer, then I respectfully suggest that you refrain from responding altogether and allow others who are willing to assist the OP in this area of applied physics. This isn’t meant in any demeaning manner rather, it is meant in the spirit of promoting open discussion without a sense of “who disturbed the bear from his sleep”.

7. Sep 19, 2011

### Staff: Mentor

This is most likely a misplaced schoolwork question. And it is against the PF rules to give answers to homework/schoolwork questions. My questions were meant to 1) try to see if it was schoolwork related, and 2) to get the OP to think a little on their own. We don't spoonfeed answers to students here on the PF. You have been here long enough that I think you would know that.

If you'd like to continue this discussion about the PF rules and our schoolwork philosophy here, please take it to PM with me.

8. Sep 20, 2011

### IEVaibhov

@berkeman :
I think that while going in a zigzag path, the frictional force acting on the tyres will be reduced. Suppose that the inclined plane makes an angle A with the horizontal, friction coefficient is u, and the cyclist is driving on a zigzag path. Consider a part of the zigzag path - if that part of the path is inclined at an angle (say B) to any line parallel to the inclined plane surface, the maximum frictional force will be u*((mgcosA)cosB). If the cyclist rode on a straight path, the maximum frictional force will be u*(mgcosA).
Thus, it will be easier for the cyclist to go uphill in a zigzag manner.

There is a temple in my native place, and to reach that temple you have to climb 300 steps from the ground. I once noticed a priest, almost 30-40 years elder me, walk uphill much easily. He was walking in a zigzag path, which for once seemed weird.

I asked this question because of the above observation + other observations near my residence. I have been warned before about 'schoolwork questions' and I know where to post them.

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9. Sep 20, 2011

### HallsofIvy

Staff Emeritus
I take it from this that you have never actually taught. A teacher does not just convey information. The most important thing a teacher does is teach a student to think for him or herself. And the way to do that is to ask question.

If you assume that such people are not capable of thinking for themselves, that would be true. However, that is not my experience on theis board.

I am also relatively ancient. And I am a bit surprised that in all those years you have never run across the "Socratic method" of teaching which was originated by Socrates himself! (No, I'm not that ancient!)

10. Sep 20, 2011

### DaveC426913

Gnosis, you are way off base, and I am impressed at berkeman's patience with your response.

Here is the relevant section in the PF rules, which the OP agreed to upon signing up to PF:

BTW, you agreed to them too. Maybe it's time for you to review them... : wink:

PF takes their rules quite seriously. It's one of the reasons why we're at 250,000 members and climbing.

That being said, getting back to the OP, and without trying to spoon feed feed him/her too much:

A zigzag pattern increases the length of the hill, lowering the rate of climb.

It is easier to go up a long hill with a shallow slope than a short steep one. (Consider a hill that's 100 ft high. You could do it if the hill were a mile long. Good luck doing it if the hill were only 100 ft long - a 45 degree angle).

While ultimately it takes same energy to do both, the human body can only expend energy at a certain rate. So doing it over time is easier.

Last edited: Sep 20, 2011
11. Sep 20, 2011

### Staff: Mentor

This is of topic, but you should read http://en.wikipedia.org/wiki/Socratic_method to understand what is going on.

12. Sep 20, 2011

### JeffKoch

Why do you think this road was built the way it was?

http://www.corbisimages.com/images/JL001835.jpg?size=67&uid=15f287f3-fb6e-4019-8866-79904e675783

13. Sep 20, 2011

### Staff: Mentor

As others have said, using a zigzag path up a hill lets you lower the peak effort, but it takes longer to make it up the hill. In the end you use a bit more energy using the zigzag method (to overcome the rolling resistnace for longer), but as Dave says you lower the peak effort required, which can help you make it up the hill.

And as another poster mentioned, you can use a rhythm to your pedaling in the zigzag pattern to ease the parts of the pattern where you are aimed up the hill as you change directions. I've used this technique at times when I'm close to bonking on a hill on my bike, and it can definitely help you out.

Perfect. Thanks.

14. Sep 23, 2011

### IEVaibhov

Thanks!

Last edited by a moderator: Sep 24, 2011