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Perpetual motion!

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Cycling Equipment
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1 February 2008
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  1. Hi All,

    Suppose a Rube Goldberg bicycle of sorts was constructed with a gizmo
    that raised some weights when the freewheel was freewheeling (down a
    hill), and allowed these weight to lower when pedaling, using this
    potential energy to assist in pedalling.

    Would this contraption be faster over a hilly course with the system
    engaged vs disengaged and just along for the ride?

    Joseph

  2. Quoted message said:

    Hi All,

    Suppose a Rube Goldberg bicycle of sorts was constructed with a gizmo
    that raised some weights when the freewheel was freewheeling (down a
    hill), and allowed these weight to lower when pedaling, using this
    potential energy to assist in pedalling.

    Would this contraption be faster over a hilly course with the system
    engaged vs disengaged and just along for the ride?

    If the contraption was ideally constructed, the elevation of the weight
    could remain constant.

    So when you went down a hill, the weight would effectively stay at the
    top of the hill, although it would be moving forwards with the bike.

    When you went uphill, the weight would drop relative to the bike, but
    remain at the same absolute elevation.

    You should then find your performance roughly equivalent to not having a
    weight at all (apart from drag in the mechanism etc.) since no
    gravitational potential energy change occurs to the weight.

    If you disengaged the mechanism, you'd just be carrying a weight around,
    so that would be worse.

    If the mechanism was only capable of limited height or power
    input/output, I would expect a performance somewhere between the two
    extremes: better than just carrying a dead weight, but not as good as
    not carrying a weight at all.

  3. Quoted message said:

    Hi All,

    Suppose a Rube Goldberg bicycle of sorts was constructed with a gizmo
    that raised some weights when the freewheel was freewheeling (down a
    hill), and allowed these weight to lower when pedaling, using this
    potential energy to assist in pedalling.

    Would this contraption be faster over a hilly course with the system
    engaged vs disengaged and just along for the ride?

    Joseph

    With an ideally efficient contraption: I'm guessing faster with it
    engaged; you'll go downhill /slower/, as you're storing energy in the
    contraption. This will decrease energy losses to air resistance, which
    are extremely large on high speed descents. Releasing the stored energy
    on uphills at low to moderate speeds would incur lower air resistance
    losses. Net result: less overall air resistance energy losses, it's
    gotta be faster... but ...

    Of course that's if the contraption /works/ and is highly efficient at
    that. My guess is such would be far from achievable in practice; and
    that's neglecting the difference between a bare bike and one with the
    contraption mounted.

    Mark J.

  4. email hidden said:

    Hi All,

    Suppose a Rube Goldberg bicycle of sorts was constructed with a gizmo
    that raised some weights when the freewheel was freewheeling (down a
    hill), and allowed these weight to lower when pedaling, using this
    potential energy to assist in pedalling.

    Would this contraption be faster over a hilly course with the system
    engaged vs disengaged and just along for the ride?

    Joseph

    It will be possible provided the following two things are true; 1) The
    device has the capacity to store at least as much energy as you can
    put into it on a descent. 2) Energy is released in such a way that
    you don't run out of it on the climb. If it winds all the way up at
    the top of the descent and winds all the way down at the very
    beginning of a climb, it's dead weight the rest of the time. Even if
    the device has real losses, they will be countered by the aerodynamic
    efficiency gain associated with making your velocity as close to
    constant as possible. That's enough to be theoretically possible, but
    practicality is an issue. Let's say you and your bike are 80 kilos
    and you're riding over 50 meter hills. Not a very taxing test case.
    For the moving weight gizmo to be practically attached to a bicycle,
    the weight will have a maximum vertical travel of about a meter. In
    order to bank a modest quarter of your potential energy coming down
    the hill, the gizmo needs to be 1000 kilos.

  5. On Fri, 1 Feb 2008 03:27:17 -0800 (PST),
    "[email hidden]" <[email hidden]> may have

    Quoted message said:

    Hi All,

    Suppose a Rube Goldberg bicycle of sorts was constructed with a gizmo
    that raised some weights when the freewheel was freewheeling (down a
    hill), and allowed these weight to lower when pedaling, using this
    potential energy to assist in pedalling.

    Would this contraption be faster over a hilly course with the system
    engaged vs disengaged and just along for the ride?

    TTBOMK, no method of energy recovery and storage is more efficient
    than the inertia of the rider and bike, and lighter riders have a
    decided advantage over heavy ones with the same force generation
    capacity on climbs, so I would have to predict that this Goldbergian
    system would fail to produce the results desired. It would also fail
    to exceed the performance of mere increased mass.

    --
    My email address is antispammed; pull WEEDS if replying via e-mail.
    Typoes are not a bug, they're a feature.
    Words processed in a facility that contains nuts.

  6. Quoted message said:

    On Feb 1, 6:27 am, "[email hidden]"

    Quoted message said:

    Hi All,

    Quoted message said:

    Suppose a Rube Goldberg bicycle of sorts was constructed with a gizmo
    that raised some weights when the freewheel was freewheeling (down a
    hill), and allowed these weight to lower when pedaling, using this
    potential energy to assist in pedalling.

    Quoted message said:

    Would this contraption be faster over a hilly course with the system
    engaged vs disengaged and just along for the ride?

    Quoted message said:

    Joseph

    It will be possible provided the following two things are true; 1) The
    device has the capacity to store at least as much energy as you can
    put into it on a descent.  2) Energy is released in such a way that
    you don't run out of it on the climb.  If it winds all the way up at
    the top of the descent and winds all the way down at the very
    beginning of a climb, it's dead weight the rest of the time.  Even if
    the device has real losses, they will be countered by the aerodynamic
    efficiency gain associated with making your velocity as close to
    constant as possible.  That's enough to be theoretically possible, but
    practicality is an issue.  Let's say you and your bike are 80 kilos
    and you're riding over 50 meter hills.  Not a very taxing test case.
    For the moving weight gizmo to be practically attached to a bicycle,
    the weight will have a maximum vertical travel of about a meter.  In
    order to bank a modest quarter of your potential energy coming down
    the hill, the gizmo needs to be 1000 kilos.

    The subject line was misleading. I don't expect the contraption to be
    able to keep going, or to require no input from the rider. So the
    amount of energy stored need not be the total from a descent, nor even
    1/4. In fact the amount doesn't really matter at all, as long as it is
    something.

    The idea is to slow down the descent a wee bit and store the energey
    used to do so, and to later release it on the up slope where it will
    give more effect in terms of saved time for the course.

    Joseph

  7. Werehatrack said:

    On Fri, 1 Feb 2008 03:27:17 -0800 (PST),
    "[email hidden]" <[email hidden]> may have

    Quoted message said:

    Hi All,

    Quoted message said:

    Suppose a Rube Goldberg bicycle of sorts was constructed with a gizmo
    that raised some weights when the freewheel was freewheeling (down a
    hill), and allowed these weight to lower when pedaling, using this
    potential energy to assist in pedalling.

    Quoted message said:

    Would this contraption be faster over a hilly course with the system
    engaged vs disengaged and just along for the ride?

    TTBOMK, no method of energy recovery and storage is more efficient
    than the inertia of the rider and bike, and lighter riders have a
    decided advantage over heavy ones with the same force generation
    capacity on climbs, so I would have to predict that this Goldbergian
    system would fail to produce the results desired.  It would also fail
    to exceed the performance of mere increased mass.

    The issue is that on a descent at high speed marginal power increases
    have little effect on lowering total time, while on ascents, marginal
    increases in power have a much more marked effect. So rather than
    "wasting" energy pushing faster through the air down a hill, some of
    the kinetic energy from the descent can be used to raise the weight to
    save some as potential energy which can be used when it has more
    effect.

    Joseph

  8. On Fri, 1 Feb 2008 09:03:09 -0800 (PST),
    "[email hidden]" <[email hidden]> may have

    Quoted message said:
    Werehatrack said:

    On Fri, 1 Feb 2008 03:27:17 -0800 (PST),
    "[email hidden]" <[email hidden]> may have

    Quoted message said:

    Hi All,

    Quoted message said:

    Suppose a Rube Goldberg bicycle of sorts was constructed with a gizmo
    that raised some weights when the freewheel was freewheeling (down a
    hill), and allowed these weight to lower when pedaling, using this
    potential energy to assist in pedalling.

    Quoted message said:

    Would this contraption be faster over a hilly course with the system
    engaged vs disengaged and just along for the ride?

    TTBOMK, no method of energy recovery and storage is more efficient
    than the inertia of the rider and bike, and lighter riders have a
    decided advantage over heavy ones with the same force generation
    capacity on climbs, so I would have to predict that this Goldbergian
    system would fail to produce the results desired.  It would also fail
    to exceed the performance of mere increased mass.

    The issue is that on a descent at high speed marginal power increases
    have little effect on lowering total time, while on ascents, marginal
    increases in power have a much more marked effect. So rather than
    "wasting" energy pushing faster through the air down a hill, some of
    the kinetic energy from the descent can be used to raise the weight to
    save some as potential energy which can be used when it has more
    effect.

    Mechanical losses and gross systemic inefficiency will always eat that
    savings. Remember, the mass you're carrying in order to perform this
    trick also increases the mass of the bike. In order to store any
    significant fraction of the energy involved, either the mass or the
    lift distance must must be relatively large, and in either case the
    effects upon the efficiency of the system as a whole will greatly
    outweigh any marginal return received. You're up against the
    fundamental regenerative/storage braking system problem here;
    real-world experience has been that you will never get back more than
    15% (typically less than 5%) of the energy theoretically available for
    capture in a descent, and the return is never matched by the
    inefficiency of the additional hardware required. (The sole exception
    to this is when dealing with an electric drive system whose
    fundamental design permits recapture via regen braking without the
    addition of any hardware at all; in that instance, a trivial amount of
    recovery becomes practical, but it's not the source of much
    operational efficiency.)

    The most efficient way to use the energy of a descent in climbing the
    next hill is to be inside a minimum-drag high-efficiency vehicle and
    don't use any braking at all. This is not always practical. No
    currently constructable regen braking system for a bicycle can come
    close.

    You nailed it when you chose the subject; as proposed, this is a
    perpetual motion project, and those, without exception, *ALWAYS* fail.

    --
    My email address is antispammed; pull WEEDS if replying via e-mail.
    Typoes are not a bug, they're a feature.
    Words processed in a facility that contains nuts.

  9. "Ben C" wrote: If the contraption was ideally constructed, the elevation
    of the weight

    Quoted message said:

    could remain constant.

    So when you went down a hill, the weight would effectively stay at the
    top of the hill, although it would be moving forwards with the bike.
    (clip)


    ^^^^^^^^^^^^^^^^^^^^^
    Your idea is that the weight would change speed with the bicycle, but not
    elevation, so it would store kinetic energy on the descents, and release it
    on the ascents. However, if you allowed the weight to go up and down with
    the bike, it would store abd release potential energy as well. How do you
    figure that potential energy is not as beneficial as kinetic energy? BTW,
    since this is only a thought experiment, I would substitute a wind-up spring
    for the weight. This would wind up on downhills, are unwind on uphills. If
    it were very light (ideally, weightless) this would be equivalent to keeping
    the weight at the elevation of the top of the tallest hill for the entire
    ride.

  10. On Fri, 01 Feb 2008 18:49:19 GMT, "Leo Lichtman"

    may have said:


    "Ben C" wrote: If the contraption was ideally constructed, the elevation
    of the weight

    Quoted message said:

    could remain constant.

    So when you went down a hill, the weight would effectively stay at the
    top of the hill, although it would be moving forwards with the bike.
    (clip)


    ^^^^^^^^^^^^^^^^^^^^^
    Your idea is that the weight would change speed with the bicycle, but not
    elevation, so it would store kinetic energy on the descents, and release it
    on the ascents. However, if you allowed the weight to go up and down with
    the bike, it would store abd release potential energy as well. How do you
    figure that potential energy is not as beneficial as kinetic energy? BTW,
    since this is only a thought experiment, I would substitute a wind-up spring
    for the weight. This would wind up on downhills, are unwind on uphills. If
    it were very light (ideally, weightless) this would be equivalent to keeping
    the weight at the elevation of the top of the tallest hill for the entire
    ride.

    While in theory a smaller mass could be lifted above the starting
    point of the descent (like the reverse of an elevator counterweight
    that uses a multiple-pulley block-and-tackle arrangement) this
    requires a structure which renders the potential gains moot. Trying
    to go the other way, using a larger mass with the mechanical advantage
    flipped, the system becomes an always-loses exercise no matter what
    else is done. Inertial storage, even into a spinning flywheel, is
    always going to come in second to reduced mass and the same power
    input level. Conversion of kinetic to chemical potential energy or
    induction storage in a superconductor coil will allow as much as 10 to
    15% recovery in ideal circumstances, but you still have to weigh that
    against the 30 to 150% (or more) increase in climbing energy required
    as a result of the increased mass of the devices and increased drag
    from other practical effects which accrued in the process of tacking
    on the machinery required to obtain that small recovery.

    Many a student hour has been used in trying to overcome these
    limitations in enginering schools around the world. Oddly enough, not
    a single one has yielded a "better mousetrap".

    --
    My email address is antispammed; pull WEEDS if replying via e-mail.
    Typoes are not a bug, they're a feature.
    Words processed in a facility that contains nuts.

  11. "Werehatrack" <[email hidden]> wrote in message
    news:[email hidden]...

    Quoted message said:


    Many a student hour has been used in trying to overcome these
    limitations in enginering schools around the world. Oddly enough, not
    a single one has yielded a "better mousetrap".

    Got that right.
    Years ago when my son was young and in the cub scouts, I remember
    the pinewood derby races. We actually had adult races to keep us out of the
    kids projects. I asked quite a few physicist and engineers on weight
    placement, of course everyone had different ideas, none on which I used.
    You would think the scouts would have this down to perfection by now after
    all these years of pinewood derby racing, but they still argue on where to
    place the weight.

    I ended up doing my own test with a sliding weight on a wedge for a curved
    sloped track, and using an electronic light source to record time in
    milliseconds. As it turned out, placing the weight above the rear wheels
    (equally divided) and slightly forward (kind of about where one sits on a
    bicycle slightly forward of the rear wheel) made for the fastest times.

    So at the race, all these fathers & mothers brought their exotic cars.
    Painted
    all shinny and decaled beautiful. All I had was a unpainted wedge, wasn't
    even sanded and looked pretty crude, but I ended up winning the Adult race.
    -tom

  12. Werehatrack said:

    On Fri, 01 Feb 2008 18:49:19 GMT, "Leo Lichtman"

    may have said:

    "Ben C"  wrote:  If the contraption was ideally constructed, the elevation
    of the weight

    Quoted message said:

    could remain constant.

    Quoted message said:
    Quoted message said:

    So when you went down a hill, the weight would effectively stay at the
    top of the hill, although it would be moving forwards with the bike.
    (clip)


    ^^^^^^^^^^^^^^^^^^^^^
    Your idea is that the weight would change speed with the bicycle, but not
    elevation, so it would store kinetic energy on the descents, and release it
    on the ascents.  However, if you allowed the weight to go up and down with
    the bike, it would store abd release potential energy as well.  How do you
    figure that potential energy is not as beneficial as kinetic energy?  BTW,
    since this is only a thought experiment, I would substitute a wind-up spring
    for the weight.  This would wind up on downhills, are unwind on uphills..  If
    it were very light (ideally, weightless) this would be equivalent to keeping
    the weight at the elevation of the top of the tallest hill for the entire
    ride.

    While in theory a smaller mass could be lifted above the starting
    point of the descent (like the reverse of an elevator counterweight
    that uses a multiple-pulley block-and-tackle arrangement) this
    requires a structure which renders the potential gains moot.  Trying
    to go the other way, using a larger mass with the mechanical advantage
    flipped, the system becomes an always-loses exercise no matter what
    else is done.  Inertial storage, even into a spinning flywheel, is
    always going to come in second to reduced mass and the same power
    input level.  Conversion of kinetic to chemical potential energy or
    induction storage in a superconductor coil will allow as much as 10 to
    15% recovery in ideal circumstances, but you still have to weigh that
    against the 30 to 150% (or more) increase in climbing energy required
    as a result of the increased mass of the devices and increased drag
    from other practical effects which accrued in the process of tacking
    on the machinery required to obtain that small recovery.

    Many a student hour has been used in trying to overcome these
    limitations in enginering schools around the world.  Oddly enough, not
    a single one has yielded a "better mousetrap".

    --
    My email address is antispammed; pull WEEDS if replying via e-mail.
    Typoes are not a bug, they're a feature.
    Words processed in a facility that contains nuts.

    There is no doubt the extra mass makes the whole thing slower than a
    regular bike without the extra mass, but the question is would the
    contraption be faster with the gizmo engaged than not.

    If the system were manual, the rider could engage the hoisting of the
    weight (in my mind a couple cinder blocks on a 2m crane on the back of
    the bike!) as speed built up down a hill, ideally at some high speed,
    and then at some point later on a climb, the rider could relese the
    weights so they fall down and since they are somehow connected to the
    drivetrain, this gives a bit of a boost to the power the rider is
    supplying.

    Lets say a 1km 5% descent followed by a 1km 5% climb. Total mass of
    110kg, 10 of which are the weights. Lets raise the weights 1m.

    How much energy is it to lift the 10kg 1m? How much does that slow the
    descent? How much faster is the 1km climb with this "additional"
    energy?

    Joseph

  13. On Fri, 1 Feb 2008 03:27:17 -0800 (PST),

    Quoted post said:

    Hi All,

    Suppose a Rube Goldberg bicycle of sorts was constructed with a gizmo
    that raised some weights when the freewheel was freewheeling (down a
    hill), and allowed these weight to lower when pedaling, using this
    potential energy to assist in pedalling.

    Would this contraption be faster over a hilly course with the system
    engaged vs disengaged and just along for the ride?

    Joseph

    Dear Joseph,

    Forget the weights--the more energy they store, the heavier they are
    and the harder it will be for you to reach the top of the hill and
    find out that they don't work.

    Just imagine storing force by winding a spring up by some brake gizmo
    on the downhill. Or charging a battery.

    Overall, you still lose.

    You can't get more energy out than you put into closed system. You
    can't even get as much energy out as you put in.

    Trying to store the energy downhill and then release the energy uphill
    just loses more energy than straightforward pedaling. Less total
    energy applied to moving the bike means lower overall speed.

    Think about how long you apply energy at rate X uphill, as opposed to
    how long you apply energy at rate Y downhill.

    Cheers,

    Carl Fogel

  14. Quoted message said:

    Suppose a Rube Goldberg bicycle of sorts was constructed with a gizmo
    that raised some weights when the freewheel was freewheeling (down a
    hill), and allowed these weight to lower when pedaling, using this
    potential energy to assist in pedalling.

    Would this contraption be faster over a hilly course with the system
    engaged vs disengaged and just along for the ride?

    Although it may be possible to store end retrieve some energy in some
    way (think of a big watchspring for example) the frictional and or heat
    losses and the mechanism's weight itself become significant to something
    as underpowered and light as a bicycle. Theoretically maybe but in
    practice probably at a cost you wouldn't want to bear, for no net gain.

    Would you go sledding walking uphill with a 50 pound backpack so you
    could descend with more mass?
    --
    Andrew Muzi
    www.yellowjersey.org
    Open every day since 1 April, 1971

  15. Two things: 1.) Lets stop arguing about whether this is practical. It was
    proposed by the OP as a thought experiment, calling for an application of
    physical principles--not an idea that he wants to implement. 2.) This is
    not a perpetual motion idea; I am pretty sure the OP used that subject
    heading TIC. This is more like the question: "Is it better to put money in
    the bank when prices are high, then take it out and spend it when prices
    are low?" The number of dollars (Euros) doesn't change, but their
    usefulness does. Similarly, a person who can draw energy from the "bank" to
    help him climb, at low speed, gets more from it than he would get by
    allowing it to be used to fight drag while coming down at high speed.

  16. A Muzi said:

    Would you go sledding walking uphill with a 50 pound backpack so you
    could descend with more mass?

    No, but it I had to carry 50 pounds for some reason, it would be nice
    to have some way of it not being entirely dead weight.

    Joseph

  17. A Muzi said:


    Would you go sledding walking uphill with a 50 pound backpack so you
    could descend with more mass?

    No, but I might use an energy-capture device on the downhill (in place
    of brakes, say, so the sled metaphor is a little weak) in order to
    assist on the uphill.

    Normally the weight bogey would more than cancel any benefits, but
    what if you needed to add the weight anyway to hoiit the UCI minimum
    for racing? Maybe that's why devices since this one have been banned
    since the 1920's, as I recall.Any historians who can documentation at
    hand?

    --rick

    PS: Hi Andy! Thanks for the sushi in 1992, which was the last time we
    met F2F.

  18. Quoted message said:
    A Muzi said:

    Would you go sledding walking uphill with a 50 pound backpack so you
    could descend with more mass?


    Oops. I meant to type "historians who have documentation," of course.
    Or maybe just asking someone to documentate, as our President would
    say.

    --rv

    Quoted message said:


    No, but I might use an energy-capture device on the downhill (in place
    of brakes, say, so the sled metaphor is a little weak) in order to
    assist on the uphill.

    Normally the weight bogey would more than cancel any benefits, but
    what if you needed to add the weight anyway to hoiit the UCI minimum
    for racing? Maybe that's why devices since this one have been banned
    since the 1920's, as I recall.Any historians who can documentation at
    hand?

    --rick

    PS: Hi Andy! Thanks for the sushi in 1992, which was the last time we
    met F2F.

  19. Quoted message said:
    A Muzi said:

    Would you go sledding walking uphill with a 50 pound backpack so you
    could descend with more mass?

    Quoted message said:

    No, but I might use an energy-capture device on the downhill (in place
    of brakes, say, so the sled metaphor is a little weak) in order to
    assist on the uphill.
    Normally the weight bogey would more than cancel any benefits, but
    what if you needed to add the weight anyway to hoiit the UCI minimum
    for racing? Maybe that's why devices since this one have been banned
    since the 1920's, as I recall.Any historians who can documentation at
    hand?
    --rick
    PS: Hi Andy! Thanks for the sushi in 1992, which was the last time we
    met F2F.

    mmmmmmm... sushi...
    --
    Andrew Muzi
    www.yellowjersey.org
    Open every day since 1 April, 1971

  20. Leo Lichtman said:


    "Ben C" wrote: If the contraption was ideally constructed, the elevation
    of the weight

    Quoted message said:

    could remain constant.

    So when you went down a hill, the weight would effectively stay at the
    top of the hill, although it would be moving forwards with the bike.
    (clip)


    ^^^^^^^^^^^^^^^^^^^^^
    Your idea is that the weight would change speed with the bicycle, but not
    elevation, so it would store kinetic energy on the descents, and release it
    on the ascents.

    That's true, although I didn't think of that.

    Quoted message said:

    However, if you allowed the weight to go up and down with
    the bike, it would store abd release potential energy as well. How do you
    figure that potential energy is not as beneficial as kinetic energy?

    Potential energy is fine, and regenerative braking is a sound idea in
    principle, especially if the descents are tricky enough that you have to
    brake anyway for safety reasons.

    But carrying extra dead-weight as we know reduces your performance
    (although the reasons why aren't totally obvious).

    So if you have a regenerative braking system you have to ask how much
    energy can you store for a given weight overhead.

    Usually when considering such things there's no straightforward physical
    relationship between the amount of energy you can store and the mass
    needed to store it in. The fact that you get so many Joules capacity
    for a kilogram of lead/acid is just a contingent fact about the way
    those batteries happen to work.

    But if you're storing energy by winching weights, the stored energy is
    closely related to the weight-- it's just a function of the weight and
    the height.

    The higher you can raise the weights, the less weight you have to carry
    for a given energy storage capability.

    You could store a lot of energy in a carbon-fibre pea weighing 5g if you
    winched it hundreds of miles into the air. That bike would probably work
    quite well (this is a thought experiment of course...). On that machine
    you'd winch the weight up at a much faster rate than that at which you
    descended.

    On the other hand if you put 100kg on the bike and only lift it up and
    down a metre or so, you're very unlikely to win.

    So I think the crossover point, between winning and losing, may be the
    point at which you lift and lower the weight by just the amount
    necessary for it to have a constant elevation throughout the ride.

    But the details need more working out to be sure about that.

    To answer the original question, you're always better to engage the
    winch than not if you have to carry this weights arrangement anyway.

    Quoted message said:

    BTW, since this is only a thought experiment, I would substitute a
    wind-up spring for the weight. This would wind up on downhills, are
    unwind on uphills. If it were very light (ideally, weightless) this
    would be equivalent to keeping the weight at the elevation of the top
    of the tallest hill for the entire ride.

    This is a slightly different question. If you have to brake anyway, then
    you will definitely win with a practically weightless spring (similar in
    principle to a high-altitude carbon fibre pea). But if you don't, then
    is there any point in regen-braking?

    I suspect that when you take air resistance into account there is. If
    you go down hills quite slowly storing up energy in your regen brakes,
    you're losing less energy to the wind, although you're going a bit
    slower. But you should be able to more than make up that lost time up
    the hills when you take the stored energy back. You will have a
    smaller deviation in your speed over the course and a higher average
    speed for the same net energy expenditure. By avoiding such high speeds
    you lose less energy in total to the wind. This is because wind
    resistance power goes roughly as the cube of speed.

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