[ start of this post is the same as previous, but then lots more details
below -- way too much and way too technical. ]
In the midst of the "pedaling tricks" thread it hit me that pulling up has
an advantage over pushing down. So now I'm wondering "Which parts of
that idea are correct?" and "How much is it worth?" . . . so
I'll start with this claim:
Using the leg's own muscles to pull up the weight of the leg during the
upstroke transmits a higher percentage of its power (measured in Watts) to
the pedal and wheel -- a higher percentage than pushing down in the
downstroke (during seated pedaling in most situations).
I'm not saying that pulling up on the _pedal_ is good idea. I'm convinced
that for me trying to pull up on the _pedal_ is generally a bad idea which
will tend to reduce my net total power to the pedals. Trying to use the
leg's own muscles (hip-flexion and knee-flexion) to pull up against some
portion the leg's own weight (and against some resistance from the leg's
own down-push muscles) is less radical and somewhat different from trying to
pull up on the pedal.
Upward-pull work has greater mechanical efficiency because its force and
work is applied directly to the pedal and crank (by cancelling a portion
of negative forces on the pedal) -- while Down-push work must first be
transmitted through the ankle-joint (some also thru the knee-joint) in
order to reach the pedal and crank.
There are four kinds of power losses with down-push power:
(A) transmission loss of both knee-extension + hip-extension power thru
ankle joint.
(B) transmission loss of hip-extension power thru knee joint.
(C) problem with complicated contraints on high-power performance due to
limit on quasi-static torque thru ankle joint.
(D) problem with complicated contraints on high-power performance due to
dynamic force / speed / range-of-motion limits of knee joint.
(details further below.)
A + B are fairly straightforward to understand, but C + D are kind of
tricky, so
*** I'm wondering if I've understood these losses correctly.
How much? I'm guessing that the simple transmission losses are around one
half percent per functional muscle group per transmission joint -- thus (A)
1% for the ankle joint; (B) 0.5% for knee joint. And I'll guess that the
other two more complicated losses cost: (C) 0.5% for ankle; (D) 0.25% for
knee. So the additional mechanical inefficiency losses for push-down power
are around 2.25%.
*** I'd love to get some clues for better estimates for each part of those
power losses. (The reason I'm giving these guesses is to prod somebody to
try to offer something more accurate.)
Suppose a cyclist in a 40km time trial at 90rpm produces 350 Watts all in
down-push muscles, of which 8 Watts is lost related to downstroke knee and
ankle joints by A + B + C + D, and say 60 Watts is lost in negative work by
down-push muscles during the upstroke, so the power to the pedals is 282
Watts. It the cyclist instead shunts some of the oxygen to upward-pull
muscles, then perhaps the Down-push muscles produce 290 Watts, Upward-pull
muscles 60 Watts, the A + B + C + D losses are reduced to 6.5 Watts, the
resistance during upstroke reduced to 50 Watts, but now there is some
additional resistance by upward-pull muscles during the downstroke of say 10
Watts. So out of the 350 Watts produced by the muscles, the power delivered
to the pedals would now be 283.5 Watts -- for a gain of 0.5%
Implications:
* In high-power performance, slightly greater power to the pedals and wheel
should be achieved if oxygen is shunted somewhat disproprortionately to the
upward-push muscles. (It's possible that some experienced cyclists do this
unconsciously.) But I'd be surprised if the gain in total power from
improved mechanical efficiency is larger then 1%. And I doubt many skilled
riders use _no_ upward-pull work in a time-trial performance, so lots of us
have already received a significant portion of the mechanical efficiency
gain that's available. (Even apart from efficiency, the upward-pull muscle
fibers are attached to the leg anyway, so it makes sense to use them for
pedaling.)
* Training strategy: Disproportionately larger adaptation of upward-pull
muscles over the long term should result in higher total power to the wheel
than adaptation proportional to current power distribution between
upward-pull and down-push muscles. (There are reports that some pro racers
are pursuing this strategy)
The magnitude of the mechanical efficiency gain from shifting training
proportions is not likely to be substantial for a well-trained cyclist.
Suppose a racer currently can produce 290 Watts in 40km time trial
performance from down-push muscles and 60 Watts from upward-pull muscles,
out of which 283.5 Watts are delivered to the pedals. Then suppose this
racer can achieve a 5% increase in muscular power sustainable for a 40km TT.
If this increase is distributed proportionally according to current muscle
capacities, then the power to the pedals rises to 297.5 Watts. If the
increase were made _completely_ thru adaptation of upward-pull muscles, with
no adaptation of down-push (a very unlikely occurrence), the power to the
pedals rises to 280 Watts, due to reducing A + B + C + D losses by 0.5 Watt.
That's a difference of less than 0.2%.
So either the down-push power losses are much larger than I guesses, or
there would need to be some other special benefit to get me to put a major
focus on training upward-pull muscles. (The radical truly long-term strategy
would be to first allow all my leg muscles atrophy, then completely rebuild
them to a different proportion of muscles skewed toward upward-pull. Not
for me.)
Ken
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Data from a scientific study:
The often-cited Kautz Coyle 1991 study of pedaling technique showed that
elite racers used much more upward-pull work when pedaling at a high
workload (around 90% of VO2max power) than for pedaling at low workload
(under 70% of VO2max power) -- which fits with C + D being more significant
for high-power performances -- and fits with a strategy of (unconsciously?)
"sparing" the upward-pull muscles during lower-power periods so they'll more
available for any possible high-power (or high-force) requirement which
might arise later.
Details on sources of inefficiency
(A) + (B) transmission loss of power thru ankle + knee joints.
"Translational" forces are transmitted from bones above the joint, thru the
joint, to the bones below. As force load comes onto the joint, the soft
stuff in the joint compresses. Then as the load comes off the joint, the
stuff expands. Although the starting and finishing configuration are the
same, there's friction and turbulence during the change, which result in
some of the work being lost as heat. I think this effect is well-known to
engineers + physicists for power transmission in this kind of situation --
the main question for me about it is:
*** How much power is lost?
"Rotational" torques are transmitted thru the tendons + muscles associated
with the "extension" articulation of each joint. The knee-extension muscles
contract to apply the force and relax and extend to prepare for the next
force -- but there's some stiffness and resistance in the "extend" phase,
and the resistance is a little higher if the force and/or speed of
contraction are higher -- which are negative drags on work. Ankle-extension
muscles have somewhat different power losses. The knee and ankle tendons
stretch a little as the torque load is applied, and the "snap back" a little
when the torque load is released. Although the starting and finishing length
of the tendon are the same, there's strain and vibration during the change,
which result in some of the work being lost as heat. I think these effects
are well-known to engineers + physicists for power transmission in this kind
of situation -- the main question for me about it is:
*** How much power is lost?
Seems to me that the loss of Work in A + B has a component that's roughly
the same for each sequence move pair of loading and unloading the joints and
tendons and muscles, and another component that is higher or lower depending
on whether the magnitude of the force + torque load is higher or lower. But
I don't know whether the fixed or variable part is larger. There have been
studies which tried to measure the internal muscular losses in pedaling, but
there are several kinds of losses, so it's hard to know what portion is due
to A + B. I'd guess at least one other kind of internal muscular loss is
larger.
______________________________
C + D overview:
These other two kinds of power loss are tricky, so first a "big picture" of
what's going on, then some detail on the assumptions, then detail on each
kind of loss.
basic idea:
When you're trying to operate a mechanical system with two or more
real-world active power sources and a "linkage" with two rotational
joints -- trying to achieve its maximum sustainable power -- you're up
against several constraints at once. If you succeed in modifying one or more
of the power sources to deliver a little more power, this higher power level
in the system pushes the contraints tighter, so you have less freedom in how
to satisfy all of them. Less freedom to optimize will not usually lead to
as high a power delivery as more freedom. Thus even if the increase in
down-push muscle power is 1 Watt, usually somewhat less than that gets
delivered to the pedals and wheel. A key reason is that a normal way to deal
with these contraints is to increase cadence frequency a little, but this
results in a higher rate of loss inside each muscle in its pair of
contracting / extending moves once in each stroke-cycle (as in the Neptune
Herzog 1999 article). On the other hand, an improvement in Upward-pull
power
capacity does not have to satisfy any complicated contraints, so there is
full freedom to transmit it directly and fully to the pedal.
*** Warning *** : The following more detailed explanation gets truly gory in
the details of mechanics. Unless you're techy beyond hard-core, just stop
reading here (if not earlier)
Because C + D are about "high power output" performance, each transmission
joint has been pushed to some sort of limit. Adding 1 Watt of power to the
output of the upward-pull muscles makes no change for these joints near
their limit, because it goes directly to the pedal. But trying to add 1
power to the output of the down-push muscles puts more force + torque load
thru the ankle + knee joints in the downstroke. Since each joint it near
some limit, it cannot simply accept that additional load, but must change
its configuration. For the ankle joint, such a change to its configuration
results in less Work per stroke-cycle -- so the only way to attain the
desired 1 Watt increase in Power rate is to increase the _cadence_ frequency
of pedaling (more stroke-cycles per minute). For the knee joint, the change
in configuration moves it to a different point on its maximum Force / Speed
/ Angle-range function, which requires a higher Speed, which means a higher
_cadence_ frequency of pedaling.
Cadence is significant because there are losses of Work (measured in Joules)
in the contracting and extending of the pushing muscles which are known to
be higher at higher cadence. The leg muscles do not fully relax immediately
after making a strong contraction to push or pull. Instead the muscle is
"stiff" for a while, so it resists getting extended back to stretched out
long enough to be ready to make its next contraction, and it requires real
work from some other muscle to overcome this resistance. The Neptune Herzog
1999 study found that the level of these Work losses rises non-linearly with
cadence above 90rpm. That work could have been used to drive the pedal, but
instead it's cancelled against stiffness + resistance. The more times per
minute this sequence of contracting and extending occurs, the more Work is
lost per minute -- so the higher the cadence, the larger the difference
between the Power generated by the muscles and the Power delivered to the
pedals and the wheel. (Likely it's easier to demonstrate this result with a
well-designed realistic computer simulation of the muscles + limbs + joints
+ pedals + cranks, but we don't have that, so first we're trying to
demostrate the result conceptually, or at least try to "motivate" belief in
the likelihood of the result.)
R. R. Neptune + W. Herzog, "The association between negative muscular work
and pedaling rate." Journal of Biomechanics 32 (1999) 1021-1026.
Assumptions shared for C + D:
Scenario: The situation is that the cyclist is trying to maximize Power to
the pedals and wheel sustained for a specific Time period, say like 45
minutes. We assume that this hypothetical cyclist's control system has found
the optimal pedaling technique to deliver the maximum sustainable power rate
given the current capabilities of the leg muscles. We then improve the
capacity of either the down-push or the upward-pull muscles to be able to
produce 1 Watt more of power, then the hypothetical cyclist's control system
finds a new modified optimal pedaling technique, and we find how much higher
its power to the pedals is than before.
We assume that the resistance on the wheel and pedals can be "fine-tuned" to
match the power transmitted from the muscles (i.e. as by slightly changing
the effective grade of the hill by a "tacking" strategy, or slightly
changing the gear ratio), so that the pedal speed and cadence can remain
unchanged even though the Power transmitted from the muscles has increased.
(This assumption just means that fewer other things must be re-calculated to
adjust for an incremental increase in power capacity of one muscle. It
should be easy to relax this assumption if we had a sophisticated computer
model simulation.)
(D) ankle in downstroke -- problem with complicated contraints on high-power
performance due to limit on quasi-static torque thru ankle joint.
The ankle joint in the downstroke operates in quasi-static or
quasi-isometric mode -- its angle is not fixed, and the ankle-extension
muscles have no positive-work motion, only some slight negative-work motion.
The maximum down-push with the ankle muscles and tendon can transmit
sustainably for that period Time depends on the configuration of the ankle
relative to the pedal axis (which corresponds roughly to the "pedal angle"😉.
Basically, if the ankle has an overall higher relative position thru the
down-push, then it can handle a higher push force from the upper leg muscles
without suddenly "collapsing" in the midst of the push. If the
ankle-relative-to-pedal position is overall lower, then the amount of push
force that can be sustainably transmitted is lower -- because the effective
radius of the force to the pedal is larger, so the torque on the ankle joint
and its tendons and muscles is larger -- and there is a limit to how much
torque the ankle joint can sustain repeatably thru the whole performance
Time. The assumption is that the ankle position is the lowest which can
handle the overall Force and Work level required to deliver the Power from
the muscles at the desired cadence.
If (according the Assumptions shared Scenario above) we increase Upward-pull
muscular power capacity by 1 Watt without changing cadence, then there is no
change to the conditions on the downstroke Ankle joint, so there is no loss
of any portion of this increase to the downstroke ankle joint.
If (according the Assumptions shared Scenario above) we try to increase
Down-push muscular power without changing cadence, then the down-push Force
must increase. To transmit this force without collapsing, the ankle position
must be lower relative to the pedal. If the knee position is roughly
unchanged, then the pedal must start the down-push lower. Therefore the
Distance is smaller than before, so the increase in Work per cycle is lower
then expected, so the full additional Power is not utilized. We could try to
get the full additional power by increasing cadence -- but this would result
in higher power losses as discussed further above and in the Neptune Herzog
1999 article.
If we try to avoid this problem by keeping the starting pedal position
unchanged, then we must start with a higher ankle position relative to crank
center and seat, which also requires a higher knee position. But a higher
knee position is a different "range of motion" segment -- a starting
position associated with a lower sustainable Force (knee starting closer
to chest is more strenuous) -- but that it against our idea of adding 1
Watt to down-push power capacity. The compensating change is to
significantly increase cadence -- but this would result in higher power
losses as discussed further above and in the Neptune Herzog 1999 article.
Therefore there's no way to increase Down-push power by increasing Force
only while holding cadence unchanged. Some increase in Cadence is required,
but this increases power losses -- not a problem for increasing Upward-push
power with respect to the Ankle joint. Therefore with respect to the
constraint of force / torque transmission thru the downstroke ankle,
increasing Upward-push power is more efficient mechanically.
(D) knee in downstroke -- problem with complicated contraints on high-power
performance due to dynamic force / speed / range-of-motion limits of knee
joint.
The knee joint in the downstroke operates in active movement mode -- its
angle changes rapidly, and it does a substantial amount of positive work.
For a given performance Time period and the specific functional muscle
group's "aerobic capacity" level, the pushing capabilities it can sustain
depend on: (a) the average Force / Torque magnitude thru its main push; (b)
the Speed of its push; (c) the Range of Motion starting angle; and (d)
finishing angle. The Power the knee-extension muscles can generate is (a)
multiplied by (b), but only certain combinations of values of {(a), (b),
(c), (d)} are permitted. (The set of permitted combinations forms a region
in a 4-dimensional space, and the subset of likely candidate combinations
for maximum power forms a 3-dimensional "surface" of this region in
4-space). Once the cyclist's control system (or our computer simulation) has
found the permitted combination which produces the optimal maximum power,
any change to one of the four input parameters must result in a decrease in
Power.
A key trade-off in this constraint function is between Force versus Speed.
The highest sustainable Force is at a muscle speed of zero: isometric
contraction -- but no additional power is delivered with this Force, so this
isometric mode is only for transmitting power from other muscles. There is a
maximum speed above which the muscle cannot sustainably deliver Force (this
is a critical constraint for human _running_ on flat terrain). Somewhere in
between these two extremes is a Force / Speed combination which has maximum
Power.
If (according the Assumptions shared Scenario above) we increase Upward-pull
muscular power capacity by 1 Watt without changing cadence, then there is no
change to the conditions on the downstroke Knee joint, so there is no loss
of any portion of this increase to the downstroke ankle joint.
If (according the Assumptions shared Scenario above) we try to increase
Down-push muscular power without changing cadence, then the down-push Force
must increase. In seated pedaling, the leg's linkage of hip + knee + ankle
joints is fixed above to the seat position, and constrained below by
connection thru the pedal to the crank circle. Because of this geometrical
constraint, some of the increased force must be coming from increased Hip
joint torque -- because for much of the downstroke range, the torque thru
the Knee is "aimed" mostly radially away from the crank center, rather than
tangent along the crank circle, more aligned with the direction of the pedal
motion. The "aiming" of the hip-extension motion tends to "track" the
direction of the pedal velocity thru a larger portion of the downstroke.
The problem is that all of the increased active torque through the Hip joint
must be transmitted thru the Knee joint, because the Knee joint is between
the hip and the pedal. But the knee joint received only a portion of the
increase in power capacity of this "Assumptions shared Scenario". Therefore
in order to handle the higher total torque / force, its Speed must be a
little lower than before the attempted increase in power capacity -- lower
than expected for this capacity increase -- so the full increase is not
utilized.
So the only remaining way to try to draw the full additional power is by
increasing cadence -- but this would result in higher power losses as
discussed further above and in the Neptune Herzog 1999 article. Which is not
a problem for increasing Upward-push power with respect to the Knee joint.
Therefore with respect to the constraint of Force versus Speed trade-off in
the downstroke Knee, increasing Upward-push power is more efficient
mechanically.
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