Mowing your lawn using Math
In the school and college years, we all must have applied math in solving different problems. But, now we will apply math in solving the lawn mowing problems. There are two types of lawn; one is simple lawns, and the other is weird type lawns.
Some people mow their lawn like they go to the end and make a 180-degree turn and come back to the other way and again repeat this mowing pattern. This pattern takes more time and effort because by adopting this way people are moving very slowly and it is like maneuvering the mower around.
Another way of mowing is in a spiral pattern rather than back and forth movement. In this pattern, you move to the end, make a right turn, go to the other end again, then go back to the end, and repeat until you finish mowing your lawn. This pattern is less time consuming because every time you take full iteration around, you will be one mower width less wide.
Now we will explain the theories behind this quick mowing pattern:-
- Each rotation takes one less width similar to the mower's width.
- Each turn will take less time as compared to the previous turn.
To graph these theories you will need graph paper, and draw a couple of lots on it. Let's assume that the lot that you are mowing is 10m×10m, and each square is 1m. So, you need to draw a vertical line on the graph by counting to 10 boxes, and a horizontal line by counting to 10 boxes. Then make a square by joining these lines altogether. Now suppose that your mower deck is 1m×1m square.
We will assume that math and geometry for this lawn mowing are the same regardless of any dimensions as long as we are dealing with the squares, and we cover every strip at 1m per second.
Mower deck = 1 2
Mow velocity = 1m/second
We will compare the number of turns to the number of turns with the amount of time each turn takes in the 180 degrees type pattern of mowing. We will assume this number as 6.
180° = 4 seconds
90° = 2 seconds
These assumptions will hold up for figuring out what we are doing. So, let's calculate how long it takes for a normal average homeowner to mow a lawn area of 10m×10m with a one-meter mower.