A weather station reports a daily solar radiation dose of $480.0 \text{ Langleys per day}$. What is the average solar irradiance over this 24-hour period in Watts per square meter ($\text{W/m}^2$)? (Note: $1 \text{ Langley} = 1 \text{ cal/cm}^2$, $1 \text{ cal} = 4.184 \text{ J}$, and $1 \text{ day} = 86,400 \text{ s}$)