# 4: Calculations

The previous section on gravity and the following sections on calculations are used to size the necessary components of built (i.e. active) rainwater harvesting systems like the ones this book covers. These components can often be calculated with rules of thumb, but the more in-depth calculations will engender a deeper understanding and the ability to adapt to more customized systems. Laboring through the calculations builds your toolbox and ability to apply knowledge between different types of rainwater systems or even between entirely different systems such as rainwater and greywater.

• 4.1: Usage
Rainwater harvesting systems are typically sized based upon supply or demand. In either case, it is important to calculate, and maybe even conserve, demand. Many sources of demand can exist for a system with varying methods to determine their relative demands. Sinks, showers, garden hoses, and various household leaks, among other items, are determined by their volumetric flow and time used.
• 4.2: Catchment Area
Rain falls. In rainwater catchment, our job is to catch that rain and use it with purpose. The catchment area is the area which intercepts the rain. Knowing the catchment area is the first step in calculating the volume of water that can be caught from rainfall. A flat roof is a great example of a catchment area. Another example is an open barrel sitting alone out in the rain, in which the catchment area would just be the circular open top of the barrel
• 4.3: Gutter and Downspout Sizing
Once the rain falls on the roof, gutters (i.e., conveyance) are usually needed to direct the rainfall to any treatment, storage, and/or end use. Pipes that are too small will restrict water from flowing through the system fast enough, resulting in overflow or overloading. Pipes that are too large will convey the water easily but could prove cost-restrictive or unsightly. More slope will help evacuate the pipes faster but may be harder to build and less attractive.
• 4.4: First-Flush Sizing
There is no single true method to determine the first-flush volume. This lack of assuredness is due to the great environmental variability of systems, including the level of pollution present, the ease of washing away pollution from roofing material, the time between rains, the strength of the rain, etc. As a rule of thumb, contamination is halved for each mm of rainfall flushed away. Area-based and exponential decay-based are the two ways to determine the appropriate size of a first-flush.
• 4.5: Catchment Volume
The catchment volume is calculated from the precipitation falling on the collection area with some loss due to the efficiency of the collection materials (and leaks). In addition, conversion factors are used to yield the desired units of volume. Typically, monthly catchment values are calculated based on monthly average precipitation data.
• 4.6: Usage Versus Catchment and Storage
Many locations can collect sufficient water to meet needs. Often the limiting factor ends up being storage volume. Calculating monthly collection capacities minus monthly demand shows how much storage is needed. The spreadsheet in Figure 4-4 shows the monthly rainfall, collection, usage, and storage calculated for a house in Columbia, Missouri with a footprint of 541 ft2, a roof efficiency of 0.8, and a storage tank of 800 gallons.