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Re: Scaling problems in Hutchinson 2004



I'm sure that this could wind up a very interesting
thread. I don't have time to say too much about it,
and I'm sure HP John Hutchinson would be better
qualified to answer these challenges, if he had the
time.

With that said, there are some statements here that
just seemed off. I agree with what Jaime has already
said on the matter. With that said, I hope my response
doesn't sound too redundant.

GSP makes a variety of comments that point to the fact
that the larger one gets, the larger one's potential
absolute speed becomes. I agree with this statement up
to a point. The bigger one gets, the larger one's
stride should become (barring any strange evolutionary
"shrinking" of the limbs), but GSP forgets to mention
that as one gets larger, more and more of one's muscle
mass is devoted to holding up the body. Id est: the
larger one gets, the less muscle there is available to
do anything other than hold oneself up.

Anyone who's had to suffer through a gym class [and
let's face it, we all have. :)] probably knows that
whenever the gym teacher forces everyone to do
chin-ups, it always seems to be the small guy that can
do the most of them. Smaller bodies require less
muscle mass to hold them up. As such, a 5ft tall guy
with the same muscle mass as a 6ft tall guy, will
always wind up appearing stronger. This can also make
for some helpful trivia for any short guys out there
trying to attract girls. :)

The scaling comparisons are far greater, and more
drastic, at insect sizes (WARNING: very simplified
scaling examples are about to follow). Thanks to Honey
I Shrunk the Kids, everyone knows that an ant can lift
50 times its own weight, and thanks to Bill Nye (among
others) it's also become common knowledge that an ant
that could be grown to the size of a small cat, would
be lucky to be able to lift its head up. The bigger
one gets, the more muscle one will need to
do...anything.

GSP also repeatedly states that small creatures aren't
fast, but fails to qualify what he means in most of
his statements. I assume he means that absolute speed
increases. In the sense that one can travel a farther
distance with a longer stride, this statement holds
true. Relatively, though, smaller creatures are far
faster than larger ones. Relatively speaking, an
American cockroach is over 3 times faster than a
cheetah running at full tilt.


GSP wrote:
> The reasons it becomes easier to move at a given
> speed as size increases 
> involves many factors, including improving muscle
> efficiency due to decreasing 
> stride frequency and limb excursion arcs.

Maybe I'm just misreading this, but it sounds like 
muscle efficiency increases as size increases. Judging
from the ant example given, the fact that a flea can
jump 1000 times its body length in one leap, and
dozens of other examples from the insect world, I'd
have to say that this is patently false. 

Smaller bodies require less muscle power to them hold
up, which translates to a greater percentage of muscle
freed up to do other work. Hence why so many small
critters are so, apparently, overmuscled.


GSP wrote:

 Basically
> it is a matter of moving body 
> lengthes per unit of time. To achieve 50 km/h (30
> mph) an ant must run its 
> own body length a couple of thousand times each
> second, a chihuahua must do 50 
> body lengthes, and Tyrannosaurus about one. It is
> simply impossible for small 
> animals to move their bodies so many multiples of
> their length in so short a 
> time, for big animals it is easy. Obviously, as size
> goes up so does the length 
> of the limbs, and the increase in stride length is
> more rapid than the 
> decrease in stride frequency as shown my McMahon, so
> top speed rises (unless the big 
> animal is poorly adapted for high speed).

This paragraph came out a tad convoluted. It sounds
like larger animals find it easier to move their
entire body lengths than smaller ones. Yet, if we were
to view the cockroach example again, it would appear
not. An American cockroach, which hits about 1.5
inches at its maximum, can run 50 body lengths per
second. 

A large male cheetah, roughly 7ft long, can do 13 body
lengths per second (keep in mind that this is an
animal that is built specifically for speed). In order
for the cheetah to get up to 50 body lengths per
second, it would have to run 238 miles/hour. Geez, at
that speed, you'd think they'd be more successful at
catching stuff. >:)

I think GSP meant that as one gets larger, the
distance traveled in a single body length becomes
larger, even though body lengths/second decrease with
size. As such, overall speed increases. I mean, even
though a roach can cover its body length 3.8 times
faster than a cheetah, it's overall speed is only
about 4.2 miles/per hour. The cheetah does 15 times
that, even though its relative speed is slower.

Anyway, those were the points that were bugging me.
The moral of the story: muscle abilities/freedom
changes with size. So beware of scaling. 

I leave the rest to more knowledgable posters.
Besides, I think I'm enjoying this bodymass scaling
trivia a little too much.

For instance, if a cheetah could do 1,000 times its
body length per second, it would be traveling at Mach
6. Imagine that thing on the Serengeti. *Boom*

Okay, I'm done.

Jason

=====
"I am impressed by the fact that we know less about many modern [reptile] types 
than we do of many fossil groups." - Alfred S. Romer


                
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