From: throopw@sheol.UUCP (Wayne Throop)
Newsgroups: talk.origins
Subject: Holden and leverage
Summary: refutation of Ted's false accusation, plus powerlifting results
Date: 28 Aug 92 02:38:56 GMT

> From: news@fedfil.UUCP (news) (Ted Holden)
> This gets back to the case which Throop first makes and then 
> claims never to have made.  

I not only *claim* never to have made it, in fact I never made it.
Ted either has me confused with someone else, or more likely, he
simply didn't understand what I was saying.

Again, I *never*, not *once* said that leverage always favors larger
creatures.  I have *always* said that leverage favors creatures with
larger ratio of joint radius to limb length.  I can support that I have
been saying this for some time, with no flip-flop as Ted claims above.
Further, I have persistently attempted to disclaim the position Ted
attributes to me.

To demonstrate this, I am appending to the end of this message
essentially every paragraph I've posted since mid 1990 with the word
"leverage" in it.  If Ted now persists in claiming I made an argument I
never made, at least others need not be taken in by Ted's error. 

> If the world were such, then the scaled lifts for Kaz would be slightly higher
> than those of the 220 lb athletes.  They're slightly lower.

But if the world were as Ted imagines it, then the scaled lifts for 220
lb athletes would be lower than those for 115 lb athletes.  This turns
out not to be the case.  Consider this table of world records for the
squat, and the Holden Numbers associated with them:

  athlete mass(kg)  lifted(kg)  HN
          ----      ------      --
           52        245.5      27.7
           56        242        26.5
           60        295        30.1
           67.5      300        28.8
           75        328        29.4
           82.5      379.5      31.7
           90        375        30.1
          100        422.5      31.5
          110        393.5      28.5
          125        413        27.9

Ted's "muscle bound" theory simply cannot explain this data.
Conventional biomechanics can explain it easily: it is a statistical
effect: middleweight athletes are picked from a larger population
than the extremes, and thus are more likely to have members far out
on the "bell curve" of performance.

For Ted's ideas to explain this, he has to come up with two completely
different causes: "muscle bound" effect for the large athletes, and some
other effect for the smaller ones.  But however Ted accounts for it, it
is very clear that scaled strength does NOT always go down with
increasing mass. 


---
Note in the following paragraphs, the consistent linking of
leverage to *thickness* and *shape* and *joint size*, and
essentially never to simple size or mass as Ted claims.

------------- "leverage" paragraphs ----------------

900603 From: throopw@sheol.UUCP (Wayne Throop)
 The general problem with Ted's arguments that I see is the tendency
 to jump to conclusions without considering all the factors, such as
 thermals in the above case, and the long-unanswered points about 
 "leverage and lifestyle" which present problems for his argument-from-
 simple-arithmetic about the impossibility of large sauropods.

900603 From: throopw@sheol.UUCP (Wayne Throop)
 ( Well, to be fair, the questions of leverage were "answered", but the
   answers showed that Ted not only hadn't any *idea* what he was talking
   about in the question of leverage, he didn't have any *suspicions*.
   The point of "lifestyle" (that he had yet to show that sauropods ever
   do "squats") has never been addressed.   )

910209 From: throopw@sheol.UUCP (Wayne Throop)
     2) Ted clearly has no idea how leverage works in animal limbs.
        In posts as long as three years ago, this was explained to him,
        but he responded that he supposed that any leverage advantage
        would be offset by an effect of his own invention, where the
        muscles would "get in each other's way" in a more leverage-efficent
        thicker limb.  Hideously pittiful.

910904 From: throopw@sheol.UUCP (Wayne Throop)
 Of course it seems clear something was overlooked here.  We're sort of
 in the right order of magnitude, but that's still much, much less muscle
 tissue than Kazmaier has available.  Isn't he trying hard enough, or
 what? Well, the most important single thing overlooked was leverage. 
 The human leg can be modeled as a class 3 lever with significant
 mechanical DISadvantage.  Taking this into consideration would result in
 calculation of a much more impressive degree of necessary pumpitude for
 Kazmaier. 

910904 From: throopw@sheol.UUCP (Wayne Throop)
 The moral, of course, is that you *must* pay close attention to details
 of exact shape in scaling, and leverage in limbs.  It is for these reasons
 that the Holden Number is largely worthless as an indicator of effort
 between dissimilarly shaped animals.

910903 From: throopw@sheol.UUCP (Wayne Throop)
    1) quadrupeds have an advantage over bipeds
    2) proportionately larger joints and similar tricks can yield
       significant leverage differences
    3) arising from a squat isn't the most efficient way to get to
       one's feet, especially if one is a quadruped

910902 From: throopw@sheol.UUCP (Wayne Throop)
 > t.o regulars have advanced the basically stupid argument that the
 > sauropods somehow got better leverage in standing than we humans do.
 This is not a "stupid argument", but a simple fact of static mechanics.
 The size of a joint is essentially an input lever arm, and the limb
 an output lever arm.  If the joint is larger in proportion to the
 limb length (as is the case in sauropods, elephants etc) there simply
 IS more leverage.  Again, there is no "argument" here, it is simply
 a fact.  See any elementary physics text.

910902 From: throopw@sheol.UUCP (Wayne Throop)
 Note further that chimps and gorillas are perhaps twice a strong as
 humans, primarily because of the increased leverage in their lower limbs. 
 Humans are "designed" for striding, not weightlifting.  (Of course,
 other primates aren't "designed" for weightlifting either, but they
 happen to be better "preadapted" for it.)

910902 From: throopw@sheol.UUCP (Wayne Throop)
 The flaw isn't in supposing muscle limits consistent with known
 vertibrates.  Ted's flaw is in neglecting biped/quadruped differences,
 limb leverage differences, and in oversimple models of physical
 activity.

910902 From: throopw@sheol.UUCP (Wayne Throop)
     - differences between biped and quadruped are overlooked
     - leverage advantages of thicker joints relative to limb length
       and differing ligament attachment points (both analogous to
       increasing the length of a lever) are overlooked
     - the weightlifting event chosen does not correspond to any
       activity that limits animal size (and other weightlifting
       acts have higher limits)

910902 From: throopw@sheol.UUCP (Wayne Throop)
 Ted's theory leading him to claim that "leverage would tend to favor the
 smaller creature beyond the size of Kaz [..Ted's example
 weightlifter..]" is not consistent with actual data from weightlifting
 records. 

910908 From: throopw@sheol.UUCP (Wayne Throop)
 The point I was making is that disadvantage "as they grow larger" is
 only true once the median of the population is reached.  The statement
 as made by Ted is, indeed, in error.  I point out this error mainly
 because Ted tends to use this erronious claim to support the notion that
 thick muscles somehow "get in each other's way" (or in this posting
 "bind against each other", and that this effect can (somehow not
 quantitatively specified) negate any advantage due to leverage. 

910908 From: throopw@sheol.UUCP (Wayne Throop)
 Further, having proportionately larger joints (or proportionately 
 shorter limbs) to improve leverage in no way implies a thicker muscle.
 Ted's position on this point is ill-founded.

910908 From: throopw@sheol.UUCP (Wayne Throop)
 This still doesn't get us to mumblesaur levels, but it falsifies the
 claim that Kazmaier is the limit, and lends real world factual 
 credibility to the calculations dealing with leverage and actual cross 
 section, instead of the oversimplified Holden Number.  Those
 calculations DO get us to mumblesaur levels of performance.

910907 From: throopw@sheol.UUCP (Wayne Throop)
 Back then, "the regular crew" didn't attempt to argue that Ted's result
 was invalid because of biped/quadruped differences.  Ted's result was
 (and is) invalid because he neglected leverage, didn't measure the
 actual muscle cross section, and still insists (falsely) that elephants
 don't know how to get to their feet in the easiest way.

910926 From: throopw@sheol.UUCP (Wayne Throop)
 ( Interestingly enough, 1500 lbs gives a Holden Number of 37.  This
   would incorporate, for example, the violations of the previous Holden
   Limit of 27 by chimps (32) and elephants (perhaps 36).  Thus Ted could
   preserve his position by raising the bar a bit, and claiming that THIS
   time there's really and TRULY a limit at 37.  Such a stance would
   still not address the issue of limb leverage, or the various evidences 
   that sauropods had to be subjected to 1G, but Ted has traditionally 
   ignored or downplayed those points anyway. )

910930 From: throopw@sheol.UUCP (Wayne Throop)
 Indeed, Ted has NOT demonstrated the required invariants.  And his
 sometimes-made assertion that leverage isn't all that important is
 clearly wrong, as Andy Wilcox shows:

910930 From: throopw@sheol.UUCP (Wayne Throop)
 Clearly, Ted's assertions that any leverage increases would be
 counteracted by "larger muscles binding together" or "getting in each
 other's way" is false.  We're talking about the same muscles, the same
 limbs, and just moving a ligament a few centimeters to
 gain 40%.  The example was for a flexor, but the same principle
 applies to extensors, by enlarging the "pulley" that the tendon
 passes over the joint upon, and moving the attachment point similarly.

910930 From: throopw@sheol.UUCP (Wayne Throop)
 It would not be at all surprising to get a 2/1 improvement over a
 human limb in the effective force applied by a limb by tinkering with
 leverage alone.

920503 From: throopw@sheol.UUCP (Wayne Throop)
      1) Biped to quadruped differences.  It is simply incorrect to claim,
         as Ted does, that square/cube scaling accounts for this difference.
      2) Limb leverage differences.  Ted claims these differences are
         negligable.  They are not.  They alone can easily account for a
         two-to-one factor of available force from a muscle.
      3) Incorrect model.  Ted claims that the powerlifting "squat" event
         models what sauropods (or any land animal) must accomplish.
         He has neither established that (say) sauropods ever were OFF
         their feet as adults, nor the accuracy of the analogy.

920426 From: throopw@sheol.UUCP (Wayne Throop)
 In fact, it is a hallmark of Holden physical arguments, from the Holden
 Number through the heat budget of venus to proposed orbits for earth
 around saturn, that when the details are investigated, Ted's "big
 picture" proves to be impossible to justify.  And, of course, since Ted
 is far too lofty an intellect to deal with mere detail work, he offers
 no explanations.  Examples of this in the above three cases are,
 respectively, effects of leverage, the inability to turn heat into
 mechanical work without an off-planet heat sink, and the problems of
 constant torque (among other things) required to stabilize his proposed
 orbits. 

920531 From: throopw@sheol.UUCP (Wayne Throop)
 Finally, even Ted's wildly overestimated 560,000 lbs corresponds to
 a Holden Number of less than 83, and I've already shown how correcting
 Ted's scaling to account for leverage and bipedal-to-quadruped differences
 can yield numbers in the low eighties.  And that's not even going into
 the question of whether the "squat" is an adequate model of a sauropod
 getting to its feet (if the larger ones ever DID get to their feet
 as adults).

920531 From: throopw@sheol.UUCP (Wayne Throop)
 Second, 40% is far, FAR from the maximum effect of such changes.  In
 fact, given human limbs, two-to-one improvements would not be
 implausible.  Human limb configuration trades off strength to gain a
 long stride and upright posture.  The human skeleton just isn't
 optimized for leverage in lifting weights, no matter how much muscle
 mass is added onto the skeleton. 

920516 From: throopw@sheol.UUCP (Wayne Throop)
 Second, Kazmaier may have bulked up to the maximum reasonable muscle
 cross section, but he did not alter his joints for increased leverage. 
 If his knee joints (note: not his muscle cross section, and not the
 outer radius of the knee, but the radius of the knee whereover the
 extensor tendons of the leg pass) were made twice as thick as they are,
 he would have another 2-times factor increase in the weight he could
 lift.  ( For those of you (and Ted) who don't follow why, the reason is
 that the radius of the joint acts as the input arm of a so-called "class
 two" lever, and thus the force applied by the limb is proportional to
 the ratio of this radius to the limb length.  ) ( Note also that Ted in
 the past has said that this wouldn't work because thicker muscles would
 "get in each other's way".  Note, no muscle change is made here, so this
 objection of Ted's is irrelevant.  ) ( Finally, if you doubt that there
 is room to increase the radius of the knee in a powerlifter, just look
 at their pictures.  Their legs are much thicker at, say, midthigh than
 at the knee joint; there is plenty of room for increase at the knee.  )

920516 From: throopw@sheol.UUCP (Wayne Throop)
 Third, I had no trouble understanding Ted's assertion.  In particular,
 his account was of measuring the circumference of the exhibit at the
 Smithsonian and then comparing the available cross section in the four
 elephant limbs with Kazmaier's thighs.  Unfortunately, he neglected to
 measure the joint size, or he would have realized that while Kazmaier's
 legs pinch in significantly at the knee, the elephant's do not.  The
 elephant has significantly more (perhaps 1.5 times more by my rough
 calculations) leverage than does Kazmaier. 

920530 From: throopw@sheol.UUCP (Wayne Throop)
 Other posters have explained why this line of reasoning is incorrect.
 Proportional scaling does not change leverage, and I never claimed it did.
 NON-proportial scaling of joints and tendon attachment points can
 change leverage.  Others have pointed out why this is so for a flexor
 muscle in a hinge joint.  I'll also explain here why this is so for
 an extensor muscle in a hinge joint.  Consider:

920530 From: throopw@sheol.UUCP (Wayne Throop)
 No matter how you do the arithmetic, Ted is a little off here.  In fact,
 just by accounting for leverage and biped/quadruped differences, which
 Ted traditionally ignores, we can see how the numbers say that the
 ultrasaur could, in principle, get to its feet directly from a squat
 under current effective acceleration.

920527 From: throopw@sheol.UUCP (Wayne Throop)
 Of course, I'm ignoring leverage, but that's only fair since Ted is
 always claiming that leverage doesn't make any significant difference... 
 I may post a more detailed treatment later, but this rough version is
 enough to show that strength isn't really a limiting factor, at least up
 to the size of known dinosaurs.  Ted denies this, but anybody can work
 the arithmetic and work out the mechanics of the situation for
 themselves.  Elephant size is simply not a limit due to muscle strength. 

920317 From: throopw@sheol.UUCP (Wayne Throop)
 Ted apparently has a private meaning of "clearly shown".  The only thing
 the Holden Number shows is that an animal very nearly the same shape as
 Bill Kazmaier, if large enough to weigh what large elephants do, would
 not be able to stand up using the technique of the squat.  If the animal
 used its forlimbs to lift, had better relative leverage in its
 joints, and used a better technique to stand up, much larger limits
 would obtain.

920405 From: throopw@sheol.UUCP (Wayne Throop)
 The problem is that Ted claims this "generalized cross section"
 nonsense, which is demonstrably not true.  His calculation of "about 27"
 as the Holden Limit is flawed, because he doesn't take account of
 quadruped vs biped differences, limb leverage differences, and the
 inaccuracy of the "squat" weightlifting events as a model. 

920719 From: throopw@sheol.UUCP (Wayne Throop)
 The observed diameters of bones go as m^(1/2.73), not m^(1/3) as Ted's
 calculation requires.  So, correcting for the additional cross section
 and leverage implied by this thickness ratio, we get this:

920719 From: throopw@sheol.UUCP (Wayne Throop)
 Solving the above formula for Kazmaier's 350 lbs of mass and 1660 total
 load, then calculating the mass of the animal just able to stand with no
 additional load in 1G gravity, we get about 600,000 lbs of mass.  This
 is well beyond any of the largest dinosaur estimated masses.  (Note: Ted
 estimates masses for breviparopus as larger, but his estimate for
 breviparopus and seismosaur are both erronious due to his confusion over
 Diplodocids and Bracihosaurids.) (Note also: earlier versions of this
 corrected formula I used corrected only for cross section, not for
 leverage...) (Note again also: I do NOT claim that this estimate is very
 accurate, only that it correctly accounts for some factors that Ted
 overlooks.  Somewhat more complicated corrections would be needed to get
 accurate results.)

920719 From: throopw@sheol.UUCP (Wayne Throop)
 ... is a non-sequitur.  I never claimed that leverage would "simply
 favor larger and heavier creatures".  Leverage "favors" creatures which
 have thicker limbs compared to length.  I am certainly not claiming that
 larger creatures are stronger pound-for-pound.  Merely that they are not
 AS much at a disadvantage as an uncorrected square-cube scale-up would
 suggest.  (Ted's frequent comment that thicker limbs have some sort of
 disadvantage that would counteract the leverage advantage has never been
 explained.)

920719 From: throopw@sheol.UUCP (Wayne Throop)
 The bottom line is, Ted's attempted demonstration of a limit simply
 doesn't work out, when real-world data about shape and leverage are
 included.  For Ted to persist shows quite clearly that he is very
 willing to abandon actual measured data and stick to a theory that
 doesn't model reality, given only that the theory gives the result
 he wishes it to. 

920802 From: throopw@sheol.UUCP (Wayne Throop)
 ( As an aside, I've pointed out several times recently that even pretty
   unequivocal evidence as the radiation problems with Ted's scenarios can't
   really logically force him to abandon his position.  He can always
   retreat to safe ground, eg: by saying that the "felt effect" of
   radiation on biological tissue was less then, or that some undiscovered
   nonlinear effect allows the dose to be less, or that it was some
   electro-gravitic form of radiation yet to be discovered with just
   the right properties.  He has already retreated in essentially just
   this way in regards to how to stabilize his orbits for earth around
   saturn, and in "muscle boundedness" effects to (according to him)
   counteract leverage advantages due to changing limb shape.

920816 From: throopw@sheol.UUCP (Wayne Throop)
      1)  biped/quadruped differences
      2)  proportional scaling differences
      3)  leverage differences

920816 From: throopw@sheol.UUCP (Wayne Throop)
 We can add a factor correcting for leverage to our formula by assuming
 that limb length scales as cube root of mass, while joint radius scales
 as 2.73 root of mass.  Working it out, we get this (note that the
 limit this time is 22):

920816 From: throopw@sheol.UUCP (Wayne Throop)
 Anyway, I think you can now see why I'd say that Ted is adding apples
 to apples... his calculations have the correct dimentionality (though
 Ted himself calls the Holden Number "dimensionless", which is, of course,
 another error on his part).  He just isn't adding up all the apples
 he has, choosing to ignore those in his "quadruped", "limb proportions"
 and "leverage" baskets.

920819 From: throopw@sheol.UUCP (Wayne Throop)
 >>      3)  leverage differences
 > This one is idiotic.  Throop is claiming here that differences in leverage
 > due to size always favor the larger creature.  If so, then larger creatures
 > should always be stronger on a lb. per lb. basic than smaller, while we
 > know the opposite to be the case.
 I have never claimed that "differences in leverage due to size always
 favor the larger creature".  Never.  Not ever.  Not once.  This is a
 figmenet of Ted's imagination, and has nothing to do with my position.

920819 From: throopw@sheol.UUCP (Wayne Throop)
 I HAVE claimed that leverage favors the thicker limb (specifically, the
 limb with a higher ratio of joint thickness to limb length).  It is
 trivial to see that this *must* be so, because joint thickness is an
 input lever arm, and limb length is an output lever arm.

920819 From: throopw@sheol.UUCP (Wayne Throop)
 Further, leverage is only one factor, so *even*if* a creature has a
 better leverage, to then say that it "should always be stronger"
 is simply a non-sequitur.  

920819 From: throopw@sheol.UUCP (Wayne Throop)
 Also note: the "mysterioso" factor Ted seems to have so much trouble
 understanding is simply accouting for the added cross section and
 leverage that the ultrasaur would have if its legs were only 20 percent
 thicker than Kazmaier's.  It doesn't matter whether this is so for most
 animals or not: the point is, it is *possible* for the ultrasaur, and
 *if* the ultrasaur had legs and pelvis only 20 percent thicker than
 Kazmaier's, it could stand up.  Not having soft tissues, we don't
 know how much thicker they actually were: I'm working on getting
 actual figures on the best preserved specimines, and see abou	t that.
--
Wayne Throop  ...!mcnc!dg-rtp!sheol!throopw