## Estimating the total root length in an average lawn

##### 29 November 2014

I read a seemingly unbelievable “fact”, that the average lawn has enough roots to equal 15 round trips between the sun and earth.

Healthy turfgrass will have a well-developed and fibrous root system, but 15 round trips, really? I’m taking that “fact” to mean that the length of all the roots in an average lawn will equal 30 times the average distance between the sun and the earth.

This is something that is pretty simple to estimate.

The average distance between the sun and the earth is 1 astronomical unit, which is about 150,000,000 km. And the average lawn is one-fith of an acre.

```
# 1 astronomical unit expressed in km
earth_sun_distance_km <- 149597870700 / 1000
# 15 round trips
earth_sun_15_round_trip_km <- earth_sun_distance_km * 15 * 2
# one acre in square meters
one_acre_m2 <- 4047
# average lawn size, 1/5 acre
average_lawn <- one_acre_m2 * 0.2
```

Now how many roots may there be in an `average_lawn`

? I’ve used root length density (RLD) data from Schlossberg and Karnok (2001) and from Jordan et al. (2003) to get an estimate of the length of roots in a given soil volume for creeping bentgrass. Based on those data, I’m using in these calculations a RLD of 24 cm of roots per 1 cm^{3} of soil.

I’ll assume that in this `average_lawn`

, the roots go to a depth of 40 cm, and have a RLD of 24 cm cm^{-3}. The total root length in the `average_lawn`

will then be the RLD times the soil volume.

```
# RLD of 24 cm/cm3
root_length_density <- 24
# volume of lawn rootzone in cm3, to depth of 40 cm
average_lawn_soil_volume_cm3 <- average_lawn * 100 * 100 * 40
# avg lawn root length in cm
total_root_length_cm <- root_length_density * average_lawn_soil_volume_cm3
# avg lawn root length in km
total_root_length_km <- total_root_length_cm * 10^-5
```

The distance of 15 round trips between the sun and the earth is 4.487936110^{9} km. And in the `average_lawn`

described above, the total root length is 7.7702410^{4} km. That’s not close at all. The distance of 15 round trips between the sun and earth is 5.775801210^{4} times more than the total root length of the `average_lawn`

.

The roots do make an impressive length however.

```
# circumference of the earth
earth_circumference_km <- 40075
# distance from the earth to the moon
earth_moon_distance_km <- 384400
```

The roots in an `average_lawn`

with RLD of 24 and root depth of 40 cm have a total length 1.9389245 times the circumference of the earth and 0.2021394 of the distance from the earth to the moon. Pretty impressive, but not even close to a single trip to the sun, let alone 15 round trips.