paving the way

When I was growing up, the pavements in Penrith’s main streets were constructed using thin rectangular slabs of the local stone—Penrith sandstone—known as ‘flagstones’. Sadly, these were all ripped up in the 1960s and replaced by either concrete or tarmac. However, in the last couple of decades, amorphous concrete has been replaced by parallel courses of precast concrete blocks, which are certainly more interesting than featureless concrete.

I don’t think I’d have noticed any of this had my attention not previously been attracted by the brick pavements in Fanling and the incredible range of patterns to be seen there. There are no deliberate colour variations in the pavements of Penrith, although the basic hue of the blocks does vary from location to location. However, when walking over them, I couldn’t help but wonder what criteria were used by the paviour to determine which block to lay next.

This is a typical example of block paving:

The blocks have been arranged in parallel courses running transverse to the direction of travel of most of the foot traffic hereabouts. This is the standard arrangement. The first thing I noticed was that there appears to be an absolute prohibition against having the corners of four blocks meet at a single point, what I will refer to subsequently as a ‘crossroads’.

The next thing I noticed was that the blocks are not of arbitrary sizes. In the example above, there are three distinct and consistent sizes, examples of which I’ve labelled L, M and S. Closer inspection shows that the mathematical relationship between the lengths of the blocks is S+M=L (I’ve defined length in terms of the orientation of the course, which in the case of the S block means that it’s wider than it is long). The other point to note is the frequency: it makes sense to use an L block wherever possible, and, conversely, S blocks are relatively uncommon.

However, in the next example, M blocks have been used most frequently—the total is significantly more than the combined totals of the frequencies of the two other blocks. And there is no obvious mathematical relationship between the lengths of the blocks although it may be that 2S=L:

I had thought that more than two contiguous blocks was a rare occurrence—check out the first photo, where even two blocks of the same size touching is a relatively infrequent occurrence. However, there are examples of six in a row in this photo, and in the area where the photo was taken, I’ve noted several such sequences that are significantly longer! In this location, the courses are up to 6–7 metres long, and there are benches to sit on, so I can imagine a game for bored children: who can find the longest sequence of blocks that are all the same size?

It seems to me that the easiest way to decide which size of block to lay next is to make alternate courses identical, as in this example of a narrow pavement:

The next photo shows something similar, although in this case, the relevant section is part of a larger area of paving with courses running in different directions. The thing to note here is that the mathematical relationship between the block sizes is 3M=L+2S. Also, while there is only one way to arrange three contiguous blocks that are the same size, an L and two S blocks can be arranged in three different ways, none of which result in a crossroads. However, none of the alternatives has been used here.

Note too the single narrow course near the bottom of the photo. This feature can be seen in a number of locations, although where it does occur, the number of standard-width courses between each narrow course is arbitrary.

The next photo shows an added complication. With a narrow section of parallel courses like this, it’s probably going to be necessary to cut blocks to fit. The blocks that have been cut are marked:

I had begun to think that every block-paved area consisted of three sizes of block, but I eventually discovered a location where four sizes have been used:

In this photo, there are alternating wider and narrower courses. Four blocks have been used for the wider course, indicated by the numbers 1–4 in ascending size order. Only three blocks (1–3) have been used for the narrower course. Notice that while the smallest and largest blocks in each course are the same length, the intermediate lengths are different.

Unbelievably, I found a location where only two sizes have been used, although as usual I’m defining size as the dimension parallel to the orientation of the course. This is another example of alternating narrower/wider courses, but the lengths are the same in both courses:

I mentioned above the requirement that there should be no ‘crossroads’ in the gaps between blocks, but of course I did find an example:

You might think that I’m being picky here, because there is a slight offset, but I regard this as a mistake anyway, because the next two junctions to the right have an only slightly larger offset.

However, I do not consider the next example a mistake. I think it was deliberate:

Look again! The crossroads here is right in the middle of the pavement and would thus be noticeable by anyone looking down as they passed. It stands out. At least, it does for me. And it could have been avoided merely by exchanging the two blocks marked X!

And there’s a lot more to block paving than you think.

update
Sod’s Law in action! When I posted this analysis yesterday, I did so because I thought that I’d covered all the significant features of block paving. However, this morning I was walking through a yard that I rarely pass through, because there is a parallel yard a few metres to the north with an excellent example of English bond brickwork. I took the following photograph:

This is the only example I’ve found of a repeating sequence of blocks—in this case SSSSL—in each course. And there are only two block sizes. There is also a narrow course following each run of five wide courses.

I took the photo because the repeating sequence of four S blocks seemed obvious, but when I examined the photo, I noticed that there is a run of five S blocks in the foreground. And it doesn’t seem necessary.