Ark-Typal Miscalculations

Rhizon Schein (schein@toosies.toosies.arkcom)
Thu, 12 Feb 1998 15:20:04 -0800 (PST)

T.S. Eliot facetiously criticized those who construe the Christian
intellectual task as making arguments for or against the virgin birth, on
the basis of calculating the probabilities of human conception by
spontaneous parthenogenesis. I suppose the justifiably infamous "ark
calculations" on both sides are of a similar sort. Perhaps we should let
them languish in numerological purgatory. But I confess, the
problem-solving aspect is kind of fun, and I post the following for that
reason - not to offer a biophysical defense for the ark, and certainly not
to suggest anything terribly significant hangs on such formulaic

Glenn Morton's revised & corrected calculations for heat transfer from the
ark still contain significant errors of at least three kinds.

A. Small Point
>Heat escape through the thicker sides and bottom would be negligible.

While it is true that thicker sides & walls would decrease conductance, the
specific heat and thermal conductivity of water is substantially higher
than that of air, plus hydraulic turbulence would decrease boundary layer
resistance and move heat away from the external surface by mass movement
much more effectively than at the ark's roof. Thus it's not so clear that
heat loss from submerged sides & bottom would be negligible relative to
that from the roof.

B. Big Point
>Given the 35,000 sheepsized animals on the ark which Morris and Whitcomb say
>were there, and assuming that each sheep used energy like a human, say
>2,000,000 calories per day...2,000,000*35,000=70,000,000,000 calories

Simply not so.
1. 2,000 kCal/day "energy usage" is caloric ingestion, not metabolic rate,
since not all ingested calories get as far as metabolism, i.e., MR =
consumption - (elimination + storage). Measured mean MR for adult humans
is 70.8 kCal/hr * 24 = 1700 kCal/da.
2. Assuming a sheep-sized mammal's metabolism to be roughly equal to that
of humans is highly errant, since sheeps' mean body mass is 42.7 vs 70 kg
for humans. While MR does not scale linearly with BM, the *measured* MR
for sheep (Schmidt-Nielsen) is 1104 kCal per day -- about one half Glenn's
3. Moreover, if Glenn is going to critique Morris & Whitcomb's approach
using their estimates, then he must be fair to conduct heat calculations
within the context of their assumption that animals were not at full active
metabolisms, or even at normal basal metabolisms: M & W posit animals were
in torpor or perhaps full hibernation. [Contrary to their problems with
sedimentation, this notion does not require a "miracle" but only the
admittedly speculative though by no means "supernatural" extrapolation of
observed processes by as yet undescribed mechanisms - in precisely the same
way microevolutionary processes are posited to result in macroevolutionary
change or even biogenesis itself, by presently undescribed mechanisms.)
Even moderate torpor would cut metabolic rates to a fraction of what Glenn
has assumed, and puts heat load and requisite dissipation rates well within
achievable ranges. Without torpor, we're still down to half the heat load.

C. Serious but Complicated Point
>70,000,000,000/31,370,000 cm^2=2231 calories per cm^2/day or .025 calories
>/cm^2 /sec.
> flux = -(conductivity)*(area)*(dT/dX)
> 0.025 = -2.0E-04 * 1 * (dT/dX)
> DT/DX= 0.025/(-2.0E-4) = -125 deg C/cm

Thermal conductivity of wood is quite variable, and I don't know how we'd
confidently estimate it for the ark when there's no consensus even about
what "gopher wood" was; however the more general & serious problem with the
above approach to estimating heat exchange is that it calculates heat
transferred only by conduction to the surrounding air, and overlooks
radiative fluxes, which may be very substantial. The thermal emmisivity of
virtually all wood in the IR (earth temperature) range approaches black
body efficiency (.95 - .97); moreover, unlike the above formula, the
driving force (dT) for radiative exchange is calculated using the 4th power
of temperature. Finally, and most significantly, after dissolution of
raincloud cover, objects would be radiating to deep space @ close to 0
Kelvin - entailing a temperature differential of around 300 degrees!

Finally, there are issues of heat transfer via evaporative fluxes (the
significant role of heat of vaporization), issues of heat retention w/out
temperature increases via thermal reservoirs within the ark, issues of heat
absorption via solar irradiance, etc. I'm sure I've left out many factors
and made errors myself; to do this all correctly requires a really messy
equation for energy exchange that nobody has attempted, and hopefully
nobody will waste their time doing!

If one starts with M & W assumption of lowered metabolism, there's no
problem at all. And without that assumption, it's still not cut & dried.
Moreover, there's the "Eliot factor" - aside from the fun of it, does it
matter one way or another?