Re: [Phys-l] A golf dome (thermal) physics problem

[John Denker <jsd@av8n.com>]

On 03/15/2008 11:04 AM, Steve Highland wrote:
> Last night on our local news it was announced that our golf dome is coming
> down soon because it just cost too much to heat the thing.  The dome is one
> of those large inflated tent-like gizmos that is sorely needed needed if you
> want to do any sort of golf practice in the winter in Duluth.  (I¹m no
> golfer ‹ I¹m a bowler and this thing is next door the the bowling alley, so
> I couldn¹t help but notice it...)
>
> This sounds like a great opportunity for physics and engineering to come to
> the rescue.  Does anyone know of neat tricks that would make the heat loss
> more manageable?  Or is Duluth, MN just the wrong place for one of these
> domes?

That's an interesting problem.  As is characteristic of
real-world problems, there are many many angles that need
to be looked at.

Here's how I would start the analysis:

The dome serves three main purposes
 a) Cuts down the wind.
 b) Keeps the snow off the ground.
 c) Retains heat over some timescale.

If they just turn off the heaters, the dome will continue to
serve purposes (a) and (b).  

You might think that an unheated dome would work just fine.
It is possible to play golf in moderate cold, if there's no
snow and no wind-chill factor.

The main gotcha, I'll bet, is that the structure behaves, in 
effect, as an anti-greenhouse.  That is, the dome is opaque 
or (worse) reflective, so that no sunlight gets in.  That 
deprives them of many hundreds of watts per square meter of 
free heat.  Therefore without expensive internal heat sources, 
the insides will get quite cold.

Designing an inflatable dome to serve as a greenhouse is
tricky.  Most transparent plastics are quickly destroyed
by UV.  The invention of black UV-resistant plastic was
a hugely profitable invention.  But black doesn't work
so well for greenhouse windows.  If you're clever it is 
possible to design around this:
  http://newmars.com/wiki/index.php?title=Structure_of_the_greenhouse

There appears to be "some" market for things in this general
category:
  http://www.sundancesupply.com/
  http://www.hoophouse.com/greenhouse-glazing-options.html
but this market seems very small compared to what I would
have expected.

So presumably there's something I'm overlooking.  Maybe the
longevity of the transparent stuff is not sufficient for serious 
large-scale projects.  Sheerfill has longevity, but is only 20% 
transparent:
 http://www.fff.saint-gobain.com/Data/Element/Node/ProductLine/Product_line_edit.asp?ele_ch_id=L0000000000000001940

===================

Here's another part of the design exercise:  What do they do
with the thing in the summer?  Deflate it?  Keep it inflated
but otherwise ignore it?  Use it to keep rain off?

These are important questions because summer revenue and
summer costs count toward the overall budget.  Money is
fungible;  that's why money was invented.

A structure that serves as a greenhouse in winter might be
ultra-unbearable in the summer.

======================

Greenhouse (i.e. solar heating) is not the only possible design.

We know that any sort of office space generates more heat than
it needs, even in a Minnesota winter.  There is a nice scaling
argument for that.
  http://www.av8n.com/physics/scaling.htm#sec-scalable
The catch is that the heat budget of the golf dome doesn't
scale the same way;  it does not have a *volume* filled with
sources of free (i.e. byproduct) heat.

On the third hand, if you could colocate the golf range with
some enterprise that throws off excess heat, all you would
need to pay for is heat exchange (rather than heat generation).
The key here is that all we need is low-grade heat;  we're
not trying to run a steam engine with the heat, just trying
to warm up the space.  Using high-grade heat (e.g. natural
gas) is a waste of G even if it uses the same E.

  Here G is the Gibbs potential, the Gibbs Free Enthalpy.
  E is the plain old energy.  Keeping track of the E does
  not suffice, because not all E has the same price.

====================

Anyway, it's an interesting problem.  Lots of angles.