Natural Science Forum / Biology / Biology / July 2004

Hello physicists and biologists: (I've
included sci.skeptic since untested
claims about mattresses abound.)

I am wondering about the mechanics and
ergonomics of mattresses, and it appears
to be a harder problem than I can solve
myself.

Let's start with foam mattresses and
cover other kinds of mattresses later.
Foam mattresses are complicated enough.

The most general question here is, "What
makes a good mattress?"  There are many
foam mattresses available: latex foam,
viscoelastic foam, polyurethane foam.
They come in different sizes and
thicknesses.  They can be made from a
single chunk of foam, or layers of
different types of foam.  A given type
of foam usually comes in a variety of
"firmness levels" (a.k.a. spring
constant, or "identation load deflection
(ILD)" as it's called in the foam biz).

Mattress preference is dominated by
personal taste, but can we analyze the
situation and understand the differences
between mattresses?  Can we find any
principles that guide us toward better
mattresses?

For that matter, can we explain simple
subjective experiences?  Consider this:
most people would agree that a "too
firm" mattress feels uncomfortable on
the "pressure points", while a softer
mattress feels more comfortable.  Can we
explain this in terms of physics?

I think there is a simple physical
explanation of this general observation,
if we assume that foam mattress are
equivalent to arrays of completely
linear springs.  A hard mattress (high
k) will concentrate the pressure around
the "low points" (the parts of the body
that depress the springs the most) and a
soft mattress (low k) will distribute it
more.  This is because the difference
in force between the low points and the
high points is simply kd, where d is the
difference in height.  

But wait!  What makes a mattress hard,
subjectively hard?  Is it simply the way
it distributes the pressure, or does it
have a dynamic aspect, i.e. the way that
it responds to body movement?

Consider for a moment my theory that
people, even people lying still, are
always making tiny movements: breathing
and the whole-body response to that, and
subtle adjustments of limbs and torso.
A hard surface is unyielding to
movements.  I think that perhaps one of
the ways you know that a chair is hard,
for example, is that it doesn't respond
if you push your butt into it.  It just
pushes back without moving a detectable
amount.

If foam mattresses are just springs,
then the amount a spring yields to force
is given by Hooke's law, and again we
find confirmation of the subjective
experience: a soft mattress will yield
more to the small forces generated by
small movements. d = F/k, or yield_distance
= force / k

But there are some more subjective
observations, and I wonder how they can
be explained physically.

- Layering different firmnesses of foam
 can produce an improved subjective
 experience.  For example, putting a
 layer of very soft foam over a layer
 of firm "support" foam can make a
 mattress that feels soft, without
 letting you sink too far into it.

I don't think we explain this with foam
as linear springs.  Doesn't a stack of
two springs just act like a single
spring with a different k?  I think this
may have to do with the nonlinear
behavior of the foam.  "Bottoming out,"
for example, the region where the foam
becomes very compressed and very much
firmer.  It might have to do with shear
forces in the foam, or a "hammocking
effect" (when the tensile forces that
originate the same way as they do in a
hammock are influencing the picture).
But I'd be interested in hearing
explanations.

- Why do some people prefer the
 sensation of viscoelastic foam, and
 some latex foam?  (These two foams are
 considered among the best for making
 mattresses and mattress toppers.)  How
 do these foams behave differently than
 polyurethane foam?  Are they more
 linear?  Less linear?  (ignoring for
 the moment the dynamic properties of
 viscoelastic foam) How do they respond
 to shear forces?  Would this have any
 effect on the subjective feel?

- Let's ignore for a moment the
 time-dependant properties of memory
 foam (viscoelastic foam).  You lie on
 it and it comes to a steady state.
 How is this steady state different
 from normal foam, if at all?  How is
 this related to subjective feel?

And finally, I have an observation about
memory foam mattresses.  They are a fad
right now, but I tried one today in a
store, lying still on it for twenty
minutes, and although it felt great at
first, it eventually felt very
uncomfortable.  I noticed that it had a
"dead" feel, as though it were unwilling
to respond to my breathing and subtle
movements.  This fits the idea that it
has slow-release behavior.

Well, I'd appreciate any thoughts on the
physics of foam and how it relates to
subjective experience.

-Mike