The Math of Lawn Mowing

Google and Yahoo have apparently solved their lawn mowing needs by hiring a herder with 200 goats to spend a week, eating the grass and fertilizing at the same time. If you are fortunate enough to own a lawn, but cannot find any goats in the neighborhood, and local rabbits cannot handle this amount of work, you may need to take care of the lawn yourself. Probably, by means of mowing rather than eating the grass. Now, a natural question comes to mind: where to start and in what pattern should you mow to be most efficient?

Consider these three potential mowing patterns.


Which one should you pick and why? Obviously, you want to walk less. More importantly, you want to consume less gas and make fewer sharp turns, as it is rather inconvenient with a bulky mower.

Assume your lawn is 50' by 100', and the blade of your mower is 2' wide.

In the mowing pattern of vertical parallel lines (left), you will walk 25 stripes of 100' each, 2500' total. You will turn half a circle (180 degrees) 24 times.

In the second scenario, horizontal lines (center), you will walk 50 stripes of 50' each, 2500' total. You will turn half a circle 49 times, twice more than in the first case! (You should try turning 180 degrees with a heavy mower to understand how un-fun this is going to be.)

In the third case (right), you will be moving in concentric motions, and you will walk:
100' + 48' + 98' + 46' + 96' + ... + 56' + 4' + 54' + 2' + 52 '=
(100' + 98' + ... + 56' + 54' + 52') + (48' + 46' + 4' + 2') =
152' x 12.5 + 50' x 12' =
1900' + 600' =
2500'.
Same distance! But you will make 48 90-degree turns, which are much friendlier than 180-degree turns.

Overall, the concentric pattern is your best choice. It does not save you any distance, but it allows you to avoid pirouetting with your mower. Only sharp parade turns. Better yet, forget about lawn corners, smooth your mowing angles and turn concentric rectangles into elegant ovals. No sharp turns at all! Just like Google's goats.


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