When it comes to the question of how to most efficiently mow the lawn, arguments inevitably come down to two main approaches: You either mow in rows, or spirals. With the help of a famous puzzle maker, a few lawn-mowing experts and some simple mathematical calculations, we answer the question once and for all, which one is the better technique?
The first factor to consider is distance, and this one is easily ruled out by the first law of mowing a lawn: Don't go over the same patch twice. This given knocks out many well-meaning, but clearly inefficient routes on an unimpeded patch of lawn. (Note: For argument's sake, we compared techniques on an empty square plot—fancy garden mazes, orchards or sheds are surely part of the picture for most mowing, but in order to answer such a broad, important question as rows or spirals, we must make like the great philosophers and lay our argument down on a theoretically perfect plane.)
Now that we're down to a fixed square footage—and distance—of lawn to mow, we can focus on turns. If you have a push or zero-turn mower, you can skip straight to the next paragraph, but if you're using a riding mower, stick with us here and tackle the problem of turning distance. If you look at your every day, run-of-the-mill John Deere riding mower, you have anywhere from 15 to 22 inches of travel before you can make a 180-degree turn. Assuming the same number of turns, the way that this play will affect the outcome of your efficiency will depend on how tight your turns need to be. If your turn is as tight as the tractor is long, minus 15 to 22 inches, you're going to be left with patches—uncut grass that will force you to break the first rule of lawn mowing. In the battle between spirals and rows, this is only a hindrance for a spiral that is not perfectly plotted. For the careful mower, then, rows and spirals remain tied so far on any type of mower.
Now, onto the big question: Which technique requires more turns? As it turns out, neither. The following illustrations by master puzzler Scott Kim shows that on a square 16-foot by 16-foot lawn, both the spiral and row techniques take a total of 30 turns; 14 left and 16 right for the rows, and 30 right turns for the spiral. One could argue that to mow in rows, there are half as many turns—when you get to the end of a row you make two 90-degree turns, which you could also count as a single 180-degree turn. Still, the total number of angular degrees you turn is in either case the same.
(Please, try these yourself, take pictures and send them to email@example.com)
Left turns 14, right turns 16 = 30 total turns.
The most common pattern has about the same number of left and right turns, for a total of 30 right angle turns. There's no pattern with fewer turns that mows every square. (All illustrations and accompanying text by Scott Kim)
Left turns 0, right turns 30 = 30 total turns.
The other common mowing pattern is a spiral. The total number of turns is also 30, the same as the grid. But this time all turns are in the same direction.
The nature of the turns with these two techniques varies. To turn to only one side for the course of a mow has two possible disadvantages—mechanical and horticultural. First, the mechanics of turning one way: According to Mark Waldvogel, product manager and spokesperson for John Deere, there is "no data to indicate constant turning in the same direction would cause any long term wear on a machine." This makes sense. Like all well-engineered vehicles, a quality lawnmower is going to be capable of handling more turns than you'll ever be able to throw its way. But while Mitchell says that there is no data to indicate it would wear on the mower, he points out that "most lawn mowers discharge to the right, so the user is normally making left-hand turns on a regular basis." And this, he says, may wear on your lawn. Granted, there is no hard data out there to indicate whether the spiral will actually wear on your lawn. But if your mower discharges to the right and all your turns are to the left, you will not have an evenly mulched lawn. Our suggestion to those who choose the spiral then is this: bag it and spread it.
The Bottom Line: If you plot your turns well and are willing and able to spread bagged clippings, the battle between rows and spirals ends with a fizzle: It looks like it's a tie, folks.
Of course, the battle between spirals and rows is one for the most efficient route. These are techniques for those who have better things to do and just want to get through the mow to work on real projects—like the Ducati in the garage, or that shed that's not building itself.
What if you want to make mowing your lawn into a project in itself? To find out how to make your mow the envy of the neighborhood, we went to puzzler Scott Kim to devise 7 brilliant, mathematically pleasing ways to mow lawns. We hope that you'll try one out (and when you do, take pictures and send them to firstname.lastname@example.org). But be warned, these turn-intensive designs are not for the faint of mowing.
Left turns 16, right turns 15 = 31 total turns.
To avoid leaving your mower stranded in the middle of the lawn, try the double spiral. First spiral into the middle, leaving every other row unmowed. In the middle, turn around in an S pattern. Then spiral out, cutting all the remaining rows. This sinuous pattern takes just one more turn than a row or spiral approach. (All illustrations and accompanying text by Scott Kim)
Left turns 32 right turns 30 = 62 total turns.
Bored and looking for something to occupy your mind on a long mow? Try to chain together four spirals to make this pleasing pattern. The tighter spirals take twice as many turns: 62.
Zig Zag Grid
Left turns 120, right turns 120 = 240 total turns.
There is a two way tie for the most number of turns. Here is the first way to make a pretty headache out of your bi-weekly chore. You can't quite turn on every square, but you can come close. This path makes 240 turns, 15 shy of the theoretical maximum of 255.
Zig Zag Spiral
Left turns 114, right turns 126 = 240 total turns.
You can also zig zag in a spiral pattern for 240 turns.
Left turns 20, right turns 18 = 38 total turns.
This classical labyrinth pattern is thousands of years old. Versions of it carved in rock have been found all over the world. The path takes you almost to the center, then back out and back in, repeatedly.
Left turns 33, right turns 35 = 68 total turns.
Here's a more complex labyrinth pattern, straight from the Chartres cathedral. Walking the labyrinth is considered a metaphor for spiritual a journey, so perhaps mowing this pattern could be an interesting experience.
Left turns 101, right turns 102 = 203 total turns.
Finally we come to the Peano curve, named after Italian mathematician Giuseppe Peano. This mathematically pleasing curve has almost as many twists and turns as the zig zag patterns, but it has a very different structure: each quadrant is a smaller simpler copy of the whole curve. And each of those quadrants can be divided further into four even simpler Peano curves. And so on. This self-similar structure has tickled the fancy of mathematicians ever since Peano first discovered it 1890. Just recently scientists have discovered that the DNA molecule folds in a similar fractal manner, in order to avoid getting tangled.