PART 3: The dishtowel and the sardines

In the last episode, from the comfort of our kitchens, we looked at how a round object like an orange, on a hard, flat surface like a table, suffered from a lousy pressure distribution. This is because, on the hard surface, there was a bad fit between the shape of the orange, and the shape of the table. In fact, they only contacted at one point. This meant that the whole weight of the orange was acting on one very small area, leading to a very high pressure at that point. We looked at how softening the table (by covering it with sponge) improved the situation for the poor orange, by improving the fit, and increasing the area of contact.

By this point, you may be asking yourself: “But what does an orange have to do with the human body? My physique bears little resemblance to this particular fruit.” I’m very glad to hear it, but I’m afraid I am going to ask for your further indulgence. Let’s look at another object, with different properties again: a box of sardines.

 

 

 

The box, you will note, has a flat base, and sharp corners. If we put this box on the same hard table-top which made the orange so uncomfortable, something interesting happens. Despite the fact that the table is hard (and indeed the base of the box is hard), they fit perfectly together. So much so, that all of the base area of the box is used in supporting its weight. This means that the pressure is reduced to pretty much the minimum possible.

A pressure map would look like this.

 

So, for the box of sardines, hard does not mean bad. A hard, flat, surface is its ideal bed, if we are going to support its weight just using reaction forces (pushing back against its weight.)

Life should be that simple. However, that is not the only way beds support your weight. Another part of the bed’s toolkit for supporting you is the ‘hammock’ effect.

Consider now that the box of sardines is not sitting on the table-top, but is being supported on a dish-towel, stretched tight by the four corners. It is now making no contact with the table underneath, but its weight is still supported.

 

What is holding it up?

 

 

 

This is the view underneath the dish-towel. We still have the weight of the box of sardines, acting straight downwards. What holds it up is tension in the towel fabric, which is angled slightly upwards from the cornersof the box. This gives the tenson enough ‘upwards’ lift to take the weight.

But look where the lines of tension start from. The corners of the box. This means that all the weight of the box is now taken on the corners, which, being pointy, have very small areas. So the pressure on these corners is now very large.

A pressure map looks like this:

 

So, althought the box of sardines was very comfortable on the table-top, the tea-towel was bad news for it.

At this point, let’s revisit our long-suffering orange. How does the orange do on the tea-towel?

 

Again, we apply tension to the corners of the tea-towel, to lift the orange completely off the table, hammock-style.

 

Looking underneath the towel, again the weight of the orange is taken by tension in the towel, angled upwards enough to lift the weight of the orange.

 

However, this time there is no corner. This time, the tension does not suddenly change direction as it goes round the corner of the box, giving up all its lifting force to that point. This time, it creeps smoothly round the curve of the orange, giving an equal amount of lift all round.  The pressure map looks like this:

 

To summarise so far:

The box of sardines likes the table-top, but doesn’t like the tea-towel.

The orange likes the tea-towel, but doesn’t like the table-top (although a sponge on the table-top can help).

In the next instalment, we’ll look at two questions:

  • What do oranges and sardines have to do with my body?
  • What do tables, towels, and sponges have to do with beds?