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I cannot imagine a cyclist imagining this to be true! Obviously aerodynamics play a part, however the cyclist's 'engine is cut' on the downhill and on big cros

I cannot imagine a cyclist imagining this to be true! Obviously aerodynamics play a part, however the cyclist's 'engine is cut' on the downhill and on big cross country roads no brakes need be used on the descents. When the 'engine' is on it goes at a certain not-quite-racing amount whether up hill or on the flat. But place a hill in the way of A to B and vastly more 'fuel' is used than A to B 'going the flat way'.

nkurz 11y ago
Consider a different visualization: what if instead of a hill, you were crossing a valley? Starting at the top of the hill, you coast down and make it most of the way up the other side. Are you certain this will take more energy than pedaling the whole way across the flat? What if you can start by coasting 90% of the distance with zero expenditure of energy? What if it was 95%? Now assume that your chain is extremely rusty (low efficiency drivetrain). Would it be possible that the energy to go the short distance up the remaining hill (after coasting downhill and halfway up the other side) might be less than overcoming the friction of pedaling the whole way? I'm not certain that they occur on a bicycle in the real world (perhaps you need a custom crafted rusty chain that has essentially constant high losses regardless of pedaling speed), but I think there are cases where the variable losses due to friction might make the hilly case more efficient than the flat. (Yes, I realize that chain friction is not the dominant factor in the real world. It's a stylized example.)
- kaybe 11y ago
  The best terrain I've ever ridden a bike on was a well-paved path of little resistance over forrested dunes. You start on top of a dune, pedal a little on the way down (not a lot of effort) and arrive on the top of the next dune with nearly zero speed. Perfect coasting and a cool breeze most of the time.
- Theodores 11y ago
  Even a rusty chain is ridiculously efficient - in the high 90%'s. An ICE and drive chain is pitiful in comparison, so let's substitute the chain for a missing rear axle nut so that, when pedalling, the wheel pulls to one side and creates tangible frictional losses. I grew up in a very hilly area plus I have done a few continental rides where hills can be graded nicely and go on for 10 - 20 miles with little change of gradient. The hope to coast up the other side of the valley never really works out as well as one might hope, with a road that goes down a big hill you are invariably pedalling on the lower reaches of the down hill part, even if you were doing a good 30+ mph at the top. This can be due to the valley heating during the day giving a prevailing headwind due to air expanding. Meanwhile, in the steep hills I grew up in, you can get a measured 40+ mph, conservative guessing (I would be boasting if I mentioned top measured speeds as they can be quite incredible but 40 mph is the town limits speed and it is cool to exceed it on a bike). Clearly this speed scrubs off with aerodynamics not being favourable. So you really do not blissfully roll up the other side, roller-coaster style. On a daily basis I go over an arched bridge that does have a hill leading in to it. So you can coast down the hill, up over the arch and on down the other side. The fun is to not pedal over the bridge, to be in 'roller-coaster' mode. This feels good, and easy, but there is a psychological factor going on here. One's brain is distracted by the 'roller coaster' (or traffic) and not really noticing how much of a slog things are. Essentially the only way things could work out anywhere near how you imagine is if there is no atmosphere. The cost of speed is aero and you just do not get the free ride up the other side of the valley, period. If it was quicker/more efficient to go up and down hills we wouldn't have land speed records be they by bicycle or rocket car set on dead-flat courses, would we? With the sibling reply regarding undulating paths, that is part 'mind trick' as it is mentally stimulating going up and down like that. It is just an illusion... However, I can in part rescue your line of thinking on this - muscle groups... I actually like hills and you can use your arms, legs and plenty of muscles in between to 'conquer' a hill. On the flat you are more likely to just spin (unless sprinting). Maybe if you factor in the baseline power your body needs for pumping blood around, maybe that could make things 'possible'. But the more I think about it - no... Look at motorways and trucks. Trucks are more efficient than cars even if they have lots of wheels and no obvious aerodynamic considerations. Lorry drivers do not choose the undulating 'A road next to the motorway when one is available. They stay on the motorway doing their most efficient speed (as that is how to make a profit). Hills that any car or lorry could go up are cut through with motorways, to make things as flat as possible.
  - TylerE 11y ago
    > If it was quicker/more efficient to go up and down hills we wouldn't have land speed records be they by bicycle or rocket car set on dead-flat courses, would we? That's a total non-sequitur. Land speed record attempts happen in flat places to keep them from turning into AIR speed record attempts.
    - Theodores 11y ago
      Nope. If your vehicle goes over a hump back bridge then maybe, but not if you go down one side of a valley and up the other side, obviously with an inverted wing shaped profile to the vehicle?
      - TylerE 11y ago
        Wing = drag.
  - nkurz 11y ago
    Did you read the linked stackoverflow discussion? I thought it made a convincing case that greater efficiency was possible across a valley given a sufficiently-aerodynamic low-rolling-resistance vehicle with an engine of non-constant efficiency. Would your intuition also say that analysis is wrong? Is it?

nkurz 11y ago

Consider a different visualization: what if instead of a hill, you were crossing a valley? Starting at the top of the hill, you coast down and make it most of the way up the other side. Are you certain this will take more energy than pedaling the whole way across the flat? What if you can start by coasting 90% of the distance with zero expenditure of energy? What if it was 95%? Now assume that your chain is extremely rusty (low efficiency drivetrain). Would it be possible that the energy to go the short distance up the remaining hill (after coasting downhill and halfway up the other side) might be less than overcoming the friction of pedaling the whole way? I'm not certain that they occur on a bicycle in the real world (perhaps you need a custom crafted rusty chain that has essentially constant high losses regardless of pedaling speed), but I think there are cases where the variable losses due to friction might make the hilly case more efficient than the flat. (Yes, I realize that chain friction is not the dominant factor in the real world. It's a stylized example.)

kaybe 11y ago
The best terrain I've ever ridden a bike on was a well-paved path of little resistance over forrested dunes. You start on top of a dune, pedal a little on the way down (not a lot of effort) and arrive on the top of the next dune with nearly zero speed. Perfect coasting and a cool breeze most of the time.
Theodores 11y ago
Even a rusty chain is ridiculously efficient - in the high 90%'s. An ICE and drive chain is pitiful in comparison, so let's substitute the chain for a missing rear axle nut so that, when pedalling, the wheel pulls to one side and creates tangible frictional losses. I grew up in a very hilly area plus I have done a few continental rides where hills can be graded nicely and go on for 10 - 20 miles with little change of gradient. The hope to coast up the other side of the valley never really works out as well as one might hope, with a road that goes down a big hill you are invariably pedalling on the lower reaches of the down hill part, even if you were doing a good 30+ mph at the top. This can be due to the valley heating during the day giving a prevailing headwind due to air expanding. Meanwhile, in the steep hills I grew up in, you can get a measured 40+ mph, conservative guessing (I would be boasting if I mentioned top measured speeds as they can be quite incredible but 40 mph is the town limits speed and it is cool to exceed it on a bike). Clearly this speed scrubs off with aerodynamics not being favourable. So you really do not blissfully roll up the other side, roller-coaster style. On a daily basis I go over an arched bridge that does have a hill leading in to it. So you can coast down the hill, up over the arch and on down the other side. The fun is to not pedal over the bridge, to be in 'roller-coaster' mode. This feels good, and easy, but there is a psychological factor going on here. One's brain is distracted by the 'roller coaster' (or traffic) and not really noticing how much of a slog things are. Essentially the only way things could work out anywhere near how you imagine is if there is no atmosphere. The cost of speed is aero and you just do not get the free ride up the other side of the valley, period. If it was quicker/more efficient to go up and down hills we wouldn't have land speed records be they by bicycle or rocket car set on dead-flat courses, would we? With the sibling reply regarding undulating paths, that is part 'mind trick' as it is mentally stimulating going up and down like that. It is just an illusion... However, I can in part rescue your line of thinking on this - muscle groups... I actually like hills and you can use your arms, legs and plenty of muscles in between to 'conquer' a hill. On the flat you are more likely to just spin (unless sprinting). Maybe if you factor in the baseline power your body needs for pumping blood around, maybe that could make things 'possible'. But the more I think about it - no... Look at motorways and trucks. Trucks are more efficient than cars even if they have lots of wheels and no obvious aerodynamic considerations. Lorry drivers do not choose the undulating 'A road next to the motorway when one is available. They stay on the motorway doing their most efficient speed (as that is how to make a profit). Hills that any car or lorry could go up are cut through with motorways, to make things as flat as possible.
- TylerE 11y ago
  > If it was quicker/more efficient to go up and down hills we wouldn't have land speed records be they by bicycle or rocket car set on dead-flat courses, would we? That's a total non-sequitur. Land speed record attempts happen in flat places to keep them from turning into AIR speed record attempts.
  - Theodores 11y ago
    Nope. If your vehicle goes over a hump back bridge then maybe, but not if you go down one side of a valley and up the other side, obviously with an inverted wing shaped profile to the vehicle?
    - TylerE 11y ago
      Wing = drag.
- nkurz 11y ago
  Did you read the linked stackoverflow discussion? I thought it made a convincing case that greater efficiency was possible across a valley given a sufficiently-aerodynamic low-rolling-resistance vehicle with an engine of non-constant efficiency. Would your intuition also say that analysis is wrong? Is it?