X-Message-Number: 1983
Date: Thu, 18 Mar 93 12:59:01 CST
From: Brian Wowk <>
Subject: CRYONICS Foam Thickness
It has been pointed out by Charles Platt and Steve Bridge that
the floor space charge is too large to ignore in my foam thickness
calculations. I have therefore expanded my optimization formula to
include floor space costs. The optimum foam thickness in meters is now
given by
T = sqrt( (475 * cA) / (rkA + fP))
where as before c is the LN2 cost per liter, A is the surface area of
the room in square meters, r is the amortization rate, k is the
insulation cost per cubic meter, f is the floor space charge per square
meter per year, and P is the room perimeter in meters. Unfortunately
the optimum thickness is no longer independent of the room dimensions
(although the formula does reduce back to the old one in the limit of a
very large room, or very cheap floor space).
It has also been pointed out that I was charging too little for
LN2. A will henceforth assume 30 cents per liter.
With c=0.3 dollars per liter, and a floor space charge f=50
dollars per square meter per year ($5 per square foot), where do we
stand? Well, the optimum foam thickness for a 5m x 5m x 3m high room is
now 2.75 meters! As you can see, the new floor space factor was more
than made up for by the greater LN2 cost.
Of course when the wall thickness is this large in relation to
the room size, there is another factor that must be considered. I have
not considered that the outer area of the insulation will be greater
than the inner area (interior area of the room), and this will tend to
reduce the optimum thickness somewhat. But clearly we are still in the
2 meter range.
Steve Bridge:
> Better find a MUCH more efficient insulator.
Why? If 2 meters of foam insulation is the cheapest way to build
and operate a -130'C storage room (even when floor space is charged for),
then why not use 2 meters of foam?
Mike Darwin:
> There must be something Brian is missing if he gets optimum foam
> thicknesses in the 2-meter range! Ettinger, Harris, NASA and
> others have done these numbers too and don't come up with anything
> like 2-meters. This is possibly due to flaws in the cost assumptions
> that Brian makes. For one thing, Trymer cryogenic foam is NOT cheap.
> To do the dry ice box we have here at BPI, we paid $6.00 a cubic foot.
> Second, as Steve Bridge points out, liquid nitrogen ain't a dime a
> liter anywhere that I know of, at least NOT since the 1960's when the
> US made steel and LN2 was a by-product of oxygen production for steel.
> When you figure in transfer losses and other factors you wil probably
> pay 50 to 60 cents per liter.
Well, Ettinger, Harris, and NASA are wrong! Seriously though,
Steve Harris' June 1986 article in Cryonics magazine did not address the
question of optimization. He simply calculated the performance of a 200
square foot -135'C room with 1 foot foam insulation. No justification
for the 1 foot thickness was given.
Let's look at Steve's numbers: The room had a surface area of
1000 square feet, which at 1 foot foam thickness would require 1000
cubic feet of insulation. Even if expensive Trymer was used, this room
would only cost $6000 to insulate. Now, by Steve's own calculation
(which he admits are "best case") this room would boiloff 176 liters of
LN2 per day, or 64,000 liters per year. This is $19,000 worth of LN2
per year! Clearly your walls are not thick enough if their capital cost
is exceeded by the first 4 months of LN2 expense.
My own calculations, even considering floor space charges, and
even using Trymer at $200 per cubic meter (twice as expensive as
styrofoam) still show the optimum thickness to be 2 meters.
Furthermore, if you pay more than 30 cents per liter for LN2, then the
optimum (cost-minimizing) thickness increases even more.
--- Brian Wowk
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