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  1. #1
    Clyde on a mission!
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    Singlespeed physics. Why SS works.

    Bear with me here, my physics knowledge is old high school stuff, going from memory.

    I just had a chat with a friend about the geared vs. ss thing and like so many other non-ss'ers he had a hard time believing me when I told him that riding ss isn't that much harder than riding geared. You've all been through the same debate a million times, no doubt..

    It got me to thinking about the physics involved.

    I weight roughly 240 lbs. My geared bike and my ss both weigh roughly the same, I'm guessing around 25 lbs. That's 265 lbs for rider and bike.

    I arrive at the foot of a particular climb. It has a particular gradient. Getting 265 lbs up that particular climb in say 1 minute takes a certain amount of kilojoules. That's just plain physics, a certain weight moved up a certain gradient in a certain time equals a certain energy required.

    It doesn't matter if I sit and spin or stand and mash, if I make it up that climb in 1 minute I've put in the same amount of energy no matter what bike I ride, if it's done sitting or standing or which gear was used. Getting to the top in 1 minute = X amount of kJ's.

    On my geared bike I have the luxury of choosing a lower gear and climbing the hill in 2 minutes rather than 1. Doing so requires me to only spend half the energy to get to the top (unless I remember my physics wrong). Same task (get 265 lbs to the top) in twice the time equals half the energy required.

    On my ss I don't have many options on how to climb the hill. Too fast in and I probably won't make it to the top. Too slow and I'll grind to a halt. I have to time it just right to get to the top.

    So what it boils down to is the difference in energy needed between climbing the hill on my geared bike vs my ss is measured in how long it takes me to get to the top. I tend to climb hills slightly faster on my ss which means it's slightly harder than climbing it on my geared bike. But it's not like it's huge difference, my estimate is that I'm probably 10% faster up a hill on my ss, which means I'm spending 10% more energy compared to riding my geared bike.

    On a complete ride I ride the climbs a bit faster on my ss but I relax more on the downhill because I can't pedal fast enough anyway and on the flat bits I go a bit slower compared to on my geared. On my geared bike I climb slower and save some energy there, but tend to ride the downhill and flats a bit faster spending a bit more energy compared to my ss.

    That explains why my overall ride time are pretty close on my ss and my geared and why riding ss isn't as impossible as the geared riders seems to think it must be.

    Then again, my physics might be rusty and my formulas off, please correct me if it's the case, but I feel it kinda explains why ss'ing isn't as impossibly hard as some believes, it's just the same weight going up the same climb but delivering the same amount of energy in a slightly different way (standing and mashing rather than sitting and spinning).

    Does it make sense?

  2. #2
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    Singlespeed physics. Why SS works.

    I like toast!

  3. #3
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    No machine, in this case a bike, is 100% efficient. While a geared bike may seem to be "easier" as in less force excreted compared to a single speed, the person does more rotation, hence increasing the distance the foot goes around. Besides this, he extra contact points in the derailleur causes energy to be wasted do to more friction. The single speed may require more force, the person will spin less decreasing total distance the foot travels around the axel. Also less energy wasted from friction. Work= Force x Distance

  4. #4
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    B+H=D^2

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  5. #5
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    ? My physics is rusty too but I remember it does not matter how long it takes, 1 minute or ten minutes moving a certain weight moved up a certain gradient is the same amount of work its just how much energy you spend a second that is different.
    2011 Kona unit with some carbon.

  6. #6
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    You're 100% correct in principle. I didn't check the numbers but it doesn't really matter because the general idea is correct: moving the weight of your body and bike upwards in a certain time requires the same amount of energy. Doing it faster means you need more watts per hour. Moving up faster could be accomplished by increasing your speed or increasing the gradient. The important figure is how high you end up vertically.

    I increased the tooth count of one of my SS rides by two in the rear to make climbing easier. After attacking the first couple of hills I was stumped because the climbs were just as hard as before. The logical explanation made me feel really stupid: of course they were as hard, because I was riding just as fast as before, just spinning at a higher cadence. It's pretty clear when you think about it in terms of physics.

    What does affect the equation is that there is an optimum cadence for your power output, and the closer you are to (your) optimum, the more efficient you are. Too fast or too slow means you're wasting energy, even though the work you do is the same.

    So if you happen to climb a certain hill at a speed that puts you in optimum cadence on your SS machine, riding a geared bike up the same hill at the same speed would be harder.

  7. #7
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    Quote Originally Posted by ALBM View Post
    I like toast!
    Biscuits are better.
    Just stick it in granny and start grinding.

  8. #8
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    Work and energy are measured in joules. Watts on the other hand is the amount of work/time. And I agree biscuits are way better then toast. Maybe a little honey drizzled ovEr them.

  9. #9
    Just Ride
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    Blah, to much mathematical nonsense. I just ride to have fun. Let geared riders think they have it easier if it lets them sleep better at night. We all know SS is more fun and that's all that really matters anyway!
    SS ==> Nut up or Shut up!

  10. #10
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    Climbing the same climb with constant gradient and with no obstacles at any speed (constant) requires the same mechanical work/energy (joules/kalories). But if you climb 2 times faster your power=work/time (watts) would be 2 times greater. But when the gradient is not constant and there are some obstackles, the faster you go the easier it is because of the momentum. If you are spinning a granny gear there is no momentum to help you. Another reason may be personal preferences and has to do smth with psychology - it seems easier for me to attack the climb at max effort and to get to the top fast (what you do on SS) than spin, spin and spin to the top for a long time.

  11. #11
    Ride,Smile, Pedal Damn it
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    I ride a SS because it's fun and people think I'm some kind of a maniac w/ unlimited power. I don't buy the, "I ride a SS so i don't have to think about shifting gears". Please... if you have to think about shifting gears, and its a strain.... , you have other issues. I rarely ride my 1X9 and don't have issues about thinking about shifting. Most of us ride SS's because: it's quiet, harder and people think we are brutes, crazy, and no bleeping miss shifts.
    As for the physics, Potential energy equation doesn't change. PE = m x g x h
    So, Slow with east revolutions or faster with harder revolution requires the same energy. It's the same energy needed to get to the top. If you are a masher, go with a SS. If you are a spinner go with a geared and spin away. I prefer to get there faster, and use a big gear , this way my downhill bombing gets more pedaling than most SS. Nice post. Making the SS's think.

  12. #12
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    Climbing a hill with 32/20 gearing- Heart rate: 220. vision: blurry. brain function: minimal- basic life support functions only.

    Climbing same hill with 32/28 gear- Heart rate: chill. vision: "pretty flowers!" brain function: "I'm bored".

    I agree with the premise that momentum is your friend and that many times a quick burst of power is more economical than down shifting. Usually you have to pay for speed though and that cost is often measured in oxygen deprivation and pain, and there aint no formula that's gonna convince me otherwise.

  13. #13
    Clyde on a mission!
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    Quote Originally Posted by J.B. Weld View Post
    Climbing a hill with 32/20 gearing- Heart rate: 220. vision: blurry. brain function: minimal- basic life support functions only.

    Climbing same hill with 32/28 gear- Heart rate: chill. vision: "pretty flowers!" brain function: "I'm bored".
    That is correct assuming that you climb the hill slower with the 32/28 gear.

    If you ride the 32/28 to the top in the same time you do on the 32/20 then you're going to get just as blurry visioned, you're delivering the same amount of joules over the same amount of time, you're just spinning your legs faster to do it.

    Saul has a point though, at some rpm your body is better at delivering power, which again can mean that climbing with a 32/28 gear is better suited for your "optimum rpm" than the 32/20 gear, so even though the energy needed is the same, you'll have an easier time delivering it because the cadence suits you better.

    So try hammering up a particular hill in a tall gear while running a stopwatch, then try repeating the climb in a lower gear while aiming to set the same time as before. Same hill, same time to the top = same amount of energy needed - being geared just allows your to choose at what rpm to deliver that energy.

  14. #14
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    Screw physics - it just forces you to HTFU!

  15. #15
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    Quote Originally Posted by kjlued View Post
    Biscuits are better.
    No biscuits or toast.

    Crushing roadies on climbs with a 25 lb. large volume tire buzzing SS 29er is far more satisfying than either breakfast food

  16. #16
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    I won't try and get into much of a physics discussion- I'm a bike mechanic who's education is all focused on human performance, anatomy, and physiology, with not a lot of mathematics or high-level physics.
    What I do experience, however, is that after 12 years of riding exclusively SS off road I have a harder time climbing with gears.
    I'm expected, when the bike shop I work for has an employee demo day, to demo bikes we sell. I'll invariably have much more difficulty climbing stuff on a geared bike that I normally climb on the SS.
    Adaptation's an amazing thing.

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  17. #17
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    Quote Originally Posted by Sandrenseren View Post
    So try hammering up a particular hill in a tall gear while running a stopwatch, then try repeating the climb in a lower gear while aiming to set the same time as before. Same hill, same time to the top = same amount of energy needed - being geared just allows your to choose at what rpm to deliver that energy.
    Theoretically if I climbed the same hill at the same speed in different gear ratios the energy used might be equal but in reality this test isn't possible because if I hammer up a hill in a 32/20 there is no way I could equal that time using a 32/28.

    You can run a car up a hill in a lot of different gears but there is always one that is the sweetest, and there will come a time when the grade becomes too steep for the motor to pull in 5th gear and you'll have no choice but to downshift, stop, or bust a rod.

  18. #18
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    Quote Originally Posted by Saul Lumikko View Post
    You're 100% correct in principle... It's pretty clear when you think about it in terms of physics. What does affect the equation is that there is an optimum cadence for your power output, and the closer you are to (your) optimum, the more efficient you are...
    This ^ exactly explains how each SS rider discovers their own magic gear.

    Never been a spinner, I tend to grind away in a bigger gear than most.
    Once going SS, find I change gear combos to fit the trail, and maximize flow.
    Know that I can stand / mash my way up a hill following a geared rider spinning away, and if I pass, am able to say Hi & thanks, while often they're sucking wind. Not implying that I'm fast, or in shape, only that I'm operating within my comfort zone, which is at a very low cadence. When riding gears, sustained climbing above 90 rpm makes me implode.
    The best is the one you want to ride most often..

  19. #19
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    Quote Originally Posted by Sandrenseren View Post
    .

    I weight roughly 240 lbs. My geared bike and my ss both weigh roughly the same, I'm guessing around 25 lbs. That's 265 lbs for rider and bike.

    I arrive at the foot of a particular climb. It has a particular gradient. Getting 265 lbs up that particular climb in say 1 minute takes a certain amount of kilojoules. That's just plain physics, a certain weight moved up a certain gradient in a certain time equals a certain energy required.
    You're not taking into account Newton's Second Law of Motion- which has an effect on VO2 Max and strength fatigue.

    Here is an example:

    Grab a 35 pound dumbbell. Do the max number of curls. Let's say you do 10.

    Now fully rest back to 100%. Grab a 70 pound dumbbell and do do curls. With your logic you should be able to do 5 reps. After all, it uses the same amount of energy to move twice as much weight half as many times. But that is not true. It is doubtful that you would be able to do even 1 rep of 70 pounds if your max rep curl with half the weight is 10.

    Here is another example:

    Jump on a treadmill. Set it to 6mph. Run 2 miles. Now fully rest, set the speed to 12mph, and run for 1 mile. Piece of cake right? It's twice as fast but only half the distance. You could be able to do that just as easily as you did the 2 miles at 6mph right?

    Newton's second law says Force = Mass times Acceleration. In my example of the dumbbell It takes more Force because the Mass is twice what it was. In my example of running the Acceleration is doubled so it is going to require more Force (energy).

    Having gears lets you go slower (less Acceleration). Which ends up as less Force so your VO2 max, oxygen, muscles, etc... won't be taxed as much. This means you can exert yourself at a comfortable level for much longer than someone going 100% out on a SS- even if the SS rider is going much faster (assuming fitness levels are equal). The SS rider has to have the Acceleration to move his/her mass up the hill. This uses more Force and causes quicker Oxygen debt and muscle fatigue.

    SS riding works because it raises the training standard and makes our bodies extremely fit through interval like exertion (which has been proven in countless studies to be more effective than a constant low aerobic method of training). We have no choice but to push up hills as fast as possible or we won't make it up. That type of training environment isn't available to a geared rider because there is always the temptation of downshifting to reduce Acceleration and make the ride easier on the oxygen debt. Take that fit SS rider, throw him/her on a geared bike, and they would still outperform the average fit geared rider because of VO2 max and strength levels gained through interval training.

    The reason your SS times and geared bike times are around the same is all mental. If you're good with all your shifting, and monitored your hear rate/ oxygen levels during the ride, and set your gears to put the most efficient amount of exertion on your climbs- than the geared bike should be faster. Don't be worried though- cause I'd bet that most of the riders on this forum are faster on a SS than on the same bike with gears. SS is a simple way to raise the training levels of your ride. The bike forces you to HTFU in a way that keeps us pushing our fitness levels.

  20. #20
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    my feeling is that depending on your level of fitness, gearing and trails, there is a "sweet spot" with SSing where once conditioned, you get all the benefits of constant momentum, carrying off tech obstacles faster, cornering and climbing faster, drivetrain efficiency, and less wheel slippage with speed and gearing. I am not so sure that this would apply to all trails for all riders...the best riders will still be the ones that perform really well on all terrain. For a lot of singletrack without huge sustained climbs SSing works really well.

  21. #21
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    Quote Originally Posted by michaelscott View Post
    You're not taking into account Newton's Second Law of Motion- which has an effect on VO2 Max and strength fatigue.

    Here is an example:

    Grab a 35 pound dumbbell. Do the max number of curls. Let's say you do 10.

    Now fully rest back to 100%. Grab a 70 pound dumbbell and do do curls. With your logic you should be able to do 5 reps. After all, it uses the same amount of energy to move twice as much weight half as many times. But that is not true. It is doubtful that you would be able to do even 1 rep of 70 pounds if your max rep curl with half the weight is 10.

    Here is another example:

    Jump on a treadmill. Set it to 6mph. Run 2 miles. Now fully rest, set the speed to 12mph, and run for 1 mile. Piece of cake right? It's twice as fast but only half the distance. You could be able to do that just as easily as you did the 2 miles at 6mph right?

    Newton's second law says Force = Mass times Acceleration. In my example of the dumbbell It takes more Force because the Mass is twice what it was. In my example of running the Acceleration is doubled so it is going to require more Force (energy).

    Having gears lets you go slower (less Acceleration). Which ends up as less Force so your VO2 max, oxygen, muscles, etc... won't be taxed as much. This means you can exert yourself at a comfortable level for much longer than someone going 100% out on a SS- even if the SS rider is going much faster (assuming fitness levels are equal). The SS rider has to have the Acceleration to move his/her mass up the hill. This uses more Force and causes quicker Oxygen debt and muscle fatigue.

    SS riding works because it raises the training standard and makes our bodies extremely fit through interval like exertion (which has been proven in countless studies to be more effective than a constant low aerobic method of training). We have no choice but to push up hills as fast as possible or we won't make it up. That type of training environment isn't available to a geared rider because there is always the temptation of downshifting to reduce Acceleration and make the ride easier on the oxygen debt. Take that fit SS rider, throw him/her on a geared bike, and they would still outperform the average fit geared rider because of VO2 max and strength levels gained through interval training.

    The reason your SS times and geared bike times are around the same is all mental. If you're good with all your shifting, and monitored your hear rate/ oxygen levels during the ride, and set your gears to put the most efficient amount of exertion on your climbs- than the geared bike should be faster. Don't be worried though- cause I'd bet that most of the riders on this forum are faster on a SS than on the same bike with gears. SS is a simple way to raise the training levels of your ride. The bike forces you to HTFU in a way that keeps us pushing our fitness levels.

    Excellent points and well said, I highlighted my 2 favorites.

  22. #22
    San Miguel Beer Drinker
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    SSing allows me to drink more beer.

  23. #23
    Clyde on a mission!
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    Quote Originally Posted by J.B. Weld View Post
    Theoretically if I climbed the same hill at the same speed in different gear ratios the energy used might be equal but in reality this test isn't possible because if I hammer up a hill in a 32/20 there is no way I could equal that time using a 32/28.
    Then reverse the experiment, try getting up a hill as fast as possible using 32/28, then try to match the time on the 32/20. Apart from your body's "comfort zone cadence" it isn't really the gear that determines how hard a climb is, it's the speed.

    Quote Originally Posted by J.B. Weld View Post
    You can run a car up a hill in a lot of different gears but there is always one that is the sweetest, and there will come a time when the grade becomes too steep for the motor to pull in 5th gear and you'll have no choice but to downshift, stop, or bust a rod.
    Yes, but engines have a defined and constant power curve. If your car can deliver 78 hp at 3500 rpm, it can deliver 78 hp at 3500 rpm all day.

    The human body doesn't work the same way. If I can deliver 200 W spinning at 85 rpm I can't keep it up for long before my body overheats and my legs burn.

    There is a particular very, very steep hill on my usual route. I've climbed it at a snails pace in granny gear and I've climbed it quite a bit faster in a taller gear. Doing it faster means spending quite a bit more energy, so slow and granny should be the way to go. However at slow and granny my heart rate keeps climbing and I have a hard time getting to the top before everything gets blurry. In the taller gear I'm faster, my heart rate goes up faster, but I manage to get to the top before I explode.

    So even if climbing that hill faster means spending more energy, my body has an easier timer delivering that higher energy for a shorter time rather than delivering a lower energy for a longer time.

    Quote Originally Posted by michaelscott View Post
    Grab a 35 pound dumbbell. Do the max number of curls. Let's say you do 10.

    Now fully rest back to 100%. Grab a 70 pound dumbbell and do do curls. With your logic you should be able to do 5 reps. After all, it uses the same amount of energy to move twice as much weight half as many times. But that is not true. It is doubtful that you would be able to do even 1 rep of 70 pounds if your max rep curl with half the weight is 10.
    If I gained another 240 lbs I wouldn't be able to climb anything.

    Quote Originally Posted by michaelscott View Post
    Jump on a treadmill. Set it to 6mph. Run 2 miles. Now fully rest, set the speed to 12mph, and run for 1 mile. Piece of cake right? It's twice as fast but only half the distance. You could be able to do that just as easily as you did the 2 miles at 6mph right?
    Both your examples fail because they both put me out of what my body is capable off.

    I would probably be able to do 20 reps or more with a 17 pound dumbbell or walk 4 miles or more at 3 mph, which makes the same point, only in a direction that's physically possible for me.

    Quote Originally Posted by michaelscott View Post
    Having gears lets you go slower (less Acceleration). Which ends up as less Force so your VO2 max, oxygen, muscles, etc... won't be taxed as much. This means you can exert yourself at a comfortable level for much longer than someone going 100% out on a SS- even if the SS rider is going much faster (assuming fitness levels are equal). The SS rider has to have the Acceleration to move his/her mass up the hill. This uses more Force and causes quicker Oxygen debt and muscle fatigue.
    Agreed. Going slower uses less energy.

    Quote Originally Posted by michaelscott View Post
    SS riding works because it raises the training standard and makes our bodies extremely fit through interval like exertion (which has been proven in countless studies to be more effective than a constant low aerobic method of training).
    How does that explain that my first ride on my SS worked pretty well too? Did my body suddenly become much fitter because I left the gears at home?

    I agree that ss is a great work out and over time it makes you a stronger rider, no doubt in my mind about that.

    But ss also works for first timers, not because they suddenly become stronger, but because as long as they ride at roughly the same pace as they are used to, they use the same amount of energy. Surely they get better at climbing after a handful of rides, not because they have become much stronger, but rather because they get more and more used to delivering power by standing and mashing.

    Like sslos says, he's having a hard time riding with gears. Not because bringing gears suddenly makes him weaker, but because sitting and spinning is no longer the way his muscles is trained to deliver the energy needed to get to the top.

    I don't buy into this "ss makes you superman" stuff. I ride ss but am no superman. I don't have to be superman because there isn't much difference between the energy I need to deliver riding ss rather than geared, I just have to deliver it using my "standing and mashing muscles" rather than my "sitting and spinning muscles". The overall energy needed is roughly the same because the hills are the same, I weight the same and the speed is roughly the same.

  24. #24
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    How tall are you?

  25. #25
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    SS doesn't work any better than geared. It just forces you to ride better and more efficient, to use momentum, to brake less.

    Though rigid really works better and is much more efficient on climbs than suspension (at least on not very tachnical climbs).

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