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  1. #1
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    hill efficiency, bike vs foot

    we all know that cycling is a hilarious amount more efficient than pedestrian travel. however, my introductory understanding of physics leads me to believe that there should be some hill grade at which walking is more efficient. my reasoning is that on level ground, a bicycle has to overcome air resistance, the inertia of the wheels, rolling resistance and the friction within the bike's components, but on a hill the bike also has to overcome gravity. when you're on foot, ironically its gravity that provides the normal force that opposes my sliding down the hill. i.e. on a steep hill, on foot i dont have to exert any force to stay put, whereas on a bike i do. this may be a completely skewed understanding of the physics of biking... but when i'm churning up a hill at a snail's pace, the only thing keeping me from walking is my road shoes. either way, i need to get in better shape (or get mountain shoes), but is my logic on the right track here?

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    The thing that counts is the speed at which you no longer can either pedal efficiently or balance the bike.
    Given a sufficiently low gear, it should be easier to pedal up any hill, provided you can keep the bike up...

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    It's so cold out there... scroz's Avatar
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    I bet you lay awake late at night a lot don't you...

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    It's so cold out there... scroz's Avatar
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    I suppose you would be right, due to the smaller amount of friction that must be overcome for a bike to roll backwards down a hill, there must be a finite point dependant on weight, resistance and angle etc. where being stationery on a hill must be more efficient on foot. However, when you add forward momentum and velocity into that, it is hard to say, because at some point it bcomes impossible to stay on a hill, whether it be on foot or bike or anything else as the gradient approaches 90 degrees

  5. #5
    Very Senior Member MikeR's Avatar
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    I know for a fact that I can't ride up a step ladder. . . Don't ask!
    It's better to cycle through life than to drive by it.

  6. #6
    Super Biker Mtn Mike's Avatar
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    Quote Originally Posted by pilar
    we all know that cycling is a hilarious amount more efficient than pedestrian travel. however, my introductory understanding of physics leads me to believe that there should be some hill grade at which walking is more efficient. my reasoning is that on level ground, a bicycle has to overcome air resistance, the inertia of the wheels, rolling resistance and the friction within the bike's components, but on a hill the bike also has to overcome gravity. when you're on foot, ironically its gravity that provides the normal force that opposes my sliding down the hill. i.e. on a steep hill, on foot i dont have to exert any force to stay put, whereas on a bike i do. this may be a completely skewed understanding of the physics of biking... but when i'm churning up a hill at a snail's pace, the only thing keeping me from walking is my road shoes. either way, i need to get in better shape (or get mountain shoes), but is my logic on the right track here?
    I'm pretty sure you are correct in this assumption, although I don't know the exact grade we would be talking about. I would say somewhere in th neighborhood of 45 degrees. Last night, as a matter of fact, a friend and I were mountain biking a loop that goes partially up a hill and then comes back down. One portion of the loop was practically strait up with about 1500 feet of elevation gained in about 2-3 miles (some parts were steeper, with about 45 degrees of incline, and some parts were slightly flater) I, being on my single speed, was walking and carrying my bike. My friend had all 27 speeds and was in his granny gear. We were going approximately the same speed, although I was breathing harder to keep up with him. I probably would have been able to pass him if I were walking without a bike. Any steeper of a hill, and I don't think one would be able to maintain forward momentum in granny gear.

    Why, you ask, would I bring my single speed on such a trail? Its because the way down is pretty technical and has lots of trees, roots, and brush to tear off deralliuers...but thats besides the point.

  7. #7
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    Speed does not equal efficiency...

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    Junior Member F=ma's Avatar
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    I think the bike is still more efficient. Gravity would exert the same force on both. (Gravity does not make walking up a hill easier and you do have to exert force to oppose gravity while standing, i.e. you can still fall down and roll to the bottom) Wind resistance would be less of a factor at slow speeds. And the bicycle uses levers, pulleys, and wheels which are all more efficient than feet alone -- whether on hill or a flat plane.

    Remember kids: Physics is Phun.

  9. #9
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    Yep.

    Efficiency is the ratio of input to (useful) output.

    If you had a three-wheeled bike, but otherwise as efficient as a two-wheeler, balance would no longer be an issue.
    That leaves the pedalling.
    Let's aim for a cadence of 80, a combined weight of 100 kg and a power of 0.33 kW (a reasonable maximum effort, and apply this to a 100 %, or 45-degree, "perfect" slope. That gives a speed uphill of around 0.85 km/h, or 0.53 mph.
    It would require a reversed 56-11 gear, with an additional 2:1 converter somewhere, giving 2.4 gear inches.
    But I'm positive that the bike would be more efficient at climbing the hill than walking it would be.

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    When walking you have to expend energy just to hold yourself up. Sitting on a bike, all your energy goes into propelling yourself and the bike forward. The bike is therefore more efficient when the energy required to move the bike up the hill is less than the energy required to keep yourself standing still.

  11. #11
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    Quote Originally Posted by CdCf
    Speed does not equal efficiency...
    Yes to this. Due to osteoarthritis in my knees I cannot comfortably walk up the hills around here for any but short distances, but I can cycle up them longer distances (like 1-1/2 to 3 miles and longer). I don't go fast; my hill speed is around 5mph, but I do roll up them and I roll faster than I could walk them.
    I . . can . . . doooo . . . it

  12. #12
    Wood Licker Maelstrom's Avatar
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    I don't know about on a road bike, but on really technical trails I will hop off and run/walk instead of bike. IT just isn't worth my time to keep pedalling

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    Quote Originally Posted by foehn
    Yes to this. Due to osteoarthritis in my knees I cannot comfortably walk up the hills around here for any but short distances, but I can cycle up them longer distances (like 1-1/2 to 3 miles and longer). I don't go fast; my hill speed is around 5mph, but I do roll up them and I roll faster than I could walk them.
    Sounds a lot like my granddad a couple of years ago.
    He could barely use the stairs in his house, and walked slowly with a cane, but he could easily ride his bike faster than most people run!
    He's 82 now, and just yesterday had his second knee joint replaced.
    I expect him to be back on his bike this summer!

  14. #14
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    It is interesting what you say. I live on a hill so I experience the delights in going down it in the morning. About 4 minutes to get to work (handy) and twelve coming home.

    The other day as I was coming up the hill in underdrive, two kids walked passed me, walking their BMX bikes. For me it's a question of fitness still but one day I'll be able to slip up to second and then I'll faster. Certainly though, in underdrive, the gradient of the hill doesn't seem to make a difference to the work level.
    School years were the best days of my life. I used to get caned by middle aged women wearing high heels, stocking and glasses. Now I have to pay for it.

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  15. #15
    Super Biker Mtn Mike's Avatar
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    Quote Originally Posted by CdCf
    Yep.

    Efficiency is the ratio of input to (useful) output.

    If you had a three-wheeled bike, but otherwise as efficient as a two-wheeler, balance would no longer be an issue.
    That leaves the pedalling.
    Let's aim for a cadence of 80, a combined weight of 100 kg and a power of 0.33 kW (a reasonable maximum effort, and apply this to a 100 %, or 45-degree, "perfect" slope. That gives a speed uphill of around 0.85 km/h, or 0.53 mph.
    It would require a reversed 56-11 gear, with an additional 2:1 converter somewhere, giving 2.4 gear inches.
    But I'm positive that the bike would be more efficient at climbing the hill than walking it would be.
    You give some conversion factors here, but I see nothing to compare the efficiency of biking to walking. The actual comparison in wattage output for both would be helpfull, if anyone knows it. However, no matter how efficient a bike might be going up hill, there comes a point when it's just imposible to ride up a hill. And in my mind, THAT is truly when walking is more "efficient". Sure the required wattage output on a bike might always be less, but how efficient are you in reality when you fall backwards on your rear, or spin your tires out?

  16. #16
    Toyota Racing Dev. PWRDbyTRD's Avatar
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    I have yet to find a grade I can walk up faster than I can pedal up...and I'm talking about even when using a 22/32 gearing
    Linkage...My 2004 Kona Hoss Dee-Lux My Mindless Banter
    Disclaimer: I'm 425lb...I put unnormal loads on my bike. This should help you in answering any of my questions.

  17. #17
    Wood Licker Maelstrom's Avatar
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    You talking on the road or trail?

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    i mean road... perhaps none of us is well versed enough in physics to really answer this question, and even if there is an answer, it may not even be applicable to hills that people actually ride anyway. perhaps just for my given fitness level, if you put me on a bike next to me in some running shoes at the bottom of the same steep hill, perhaps i would make it to the top faster in a bike and a tad less "winded," but bikes have been touted as the most efficient human powered locomotion out there and leaps and bounds over foot travel, but in this scenario i think that the benefit is very slim.

  19. #19
    Dog is my co-pilot 2manybikes's Avatar
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    When you are walking a bike up a hill, you are still moving all the weight you were when you were riding. But now you are spending calories to hold up your body weight too. This is very important. This is a big factor in why a bike goes farther than a runner or walker, when the pedestrian can't hold up body weight they have to stop.
    The cyclist can go a long way after being too tired to even stand, because he is sitting and the bike is supporting him.
    At some point, the gear ratio of pedal speed to wheel speed is just to hard to push. Then it's easier to walk. Not much easier than on a lightweight mountain bike with a 24 x 34 low gear for example, but a little.

    You can go a little slower, this means less work. You have changed the speed. And you can balance at a stop. Short stops mean a lot too.

    I think I have this right........ Work = mass (weight) x velocity (speed).

    The gear reduction moves the pedals more than the wheel too. The benefit of the bike is twofold, gear reduction and it supports your weight.

  20. #20
    Super Biker Mtn Mike's Avatar
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    Quote Originally Posted by 2manybikes
    When you are walking a bike up a hill, you are still moving all the weight you were when you were riding. But now you are spending calories to hold up your body weight too. This is very important. This is a big factor in why a bike goes farther than a runner or walker, when the pedestrian can't hold up body weight they have to stop.
    The cyclist can go a long way after being too tired to even stand, because he is sitting and the bike is supporting him.
    At some point, the gear ratio of pedal speed to wheel speed is just to hard to push. Then it's easier to walk. Not much easier than on a lightweight mountain bike with a 24 x 34 low gear for example, but a little.

    You can go a little slower, this means less work. You have changed the speed. And you can balance at a stop. Short stops mean a lot too.

    I think I have this right........ Work = mass (weight) x velocity (speed).

    The gear reduction moves the pedals more than the wheel too. The benefit of the bike is twofold, gear reduction and it supports your weight.
    I think everyone is correct in the basic physics involved with motion, but the biomechanics that come into play in both cycling and walking get pretty complicated. In a typical situation, a bicycle is definitely the most efficient form of transportation, due to a lot of factors including, gear reduction and the ability to coast. However, there comes a point (when going up an imposibly steep hill) when the mechanics change.

  21. #21
    Dog is my co-pilot 2manybikes's Avatar
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    Quote Originally Posted by Mtn Mike
    I think everyone is correct in the basic physics involved with motion, but the biomechanics that come into play in both cycling and walking get pretty complicated. In a typical situation, a bicycle is definitely the most efficient form of transportation, due to a lot of factors including, gear reduction and the ability to coast. However, there comes a point (when going up an imposibly steep hill) when the mechanics change.
    I think we are in agreement. When you no longer can push the pedals you don't have enough leverage to overcome the hill, the work needs to be reduced by slowing the bike and you run into the balance problem. Walking solves both. Even though you use more calories to stand than sit, you have to slow down and you have to balance. But, in addition to that....

    A lot of the mechanics can now change, absolutely, yes. You can lean forward using your weight to push the bike, you can now use your arms, you can use your back differently. You can use all sorts of different muscles and you can tip lever, push etc the bike in many new mechanical ways. You can squat and push up with your legs etc. Most of the changes are in you. There are all sorts of different levers and fulcrums etc.

    I think the primary and most typical mechanical change is the way you now use your legs differently and different muscles are powering the bike and you up the hill. The leverage is just plain different and the muscle groups are different. I think I am agreeing with you 100% ?

  22. #22
    cab horn
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    Less talk more biking.

  23. #23
    Super Biker Mtn Mike's Avatar
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    Quote Originally Posted by 2manybikes
    I think we are in agreement.

    I think the primary and most typical mechanical change is the way you now use your legs differently and different muscles are powering the bike and you up the hill. The leverage is just plain different and the muscle groups are different. I think I am agreeing with you 100% ?

  24. #24
    Videre non videri
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    Quote Originally Posted by Mtn Mike
    You give some conversion factors here, but I see nothing to compare the efficiency of biking to walking. The actual comparison in wattage output for both would be helpfull, if anyone knows it. However, no matter how efficient a bike might be going up hill, there comes a point when it's just imposible to ride up a hill. And in my mind, THAT is truly when walking is more "efficient". Sure the required wattage output on a bike might always be less, but how efficient are you in reality when you fall backwards on your rear, or spin your tires out?
    True, I didn't compare the two.
    I just explained how to make a bike climb a 100% hill at an easy 80 RPM.

    But given the choice between walking up and spinning up, what would you choose?

  25. #25
    Dog is my co-pilot 2manybikes's Avatar
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    Quote Originally Posted by operator
    Less talk more biking.

    Good Idea I'm going to try and improve my biomechanical systems today !! It's warm.

    Mtn Mike: Refer to above statement.

    Hope you guys can do the same.

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