# Grading

## Expressing slope

### Slope gradient

Slope gradients are are common form of expression for steeply sloped areas like the sides of swales. Expressed as Y:X where Y is a single unit of rise and X is the corresponding run. It can be calculated by dividing the rise by the run: e.g.\[\frac{rise}{run}=\frac{4\ m}{12\ m}=\frac{1}{3};we\ say\ the\ slope\ =1:3\ or\ 1\ in\ 3\]

### Slope percentage

Slope percentage is calculated similarly by dividing rise by run, but then multiplying by 100 to get a percentage:
e.g.\[slope=\left (\frac{rise}{run}\right )\times 100=\left(\frac{4\ m}{12\ m}\right)\times 100= 33\%\]
**But** for many calculations the *rise/run* isn't multiplied by 100, and instead is left as a decimal. e.g. 0.33 in the example above.

### Slope in degrees

Expressing a slope in degrees requires using the *tangent* trigonometric function.
e.g.\[\tan \theta =\left ( \frac{4\ m}{12\ m} \right ); \theta =\tan^{-1}\left ( 0.33 \right )=18.3^{\circ}\]

## Normal range of slopes

The Accessibility for Ontarians with Disabilities Act^{[1]} provides a bare minimum to which public spaces must be designed. e.g. cross slope not to exceed 2 %.

Consider designing landscapes to universal design principals instead^{[2]}^{[3]}.

Use | Extreme range (%) | Desirable range (%) |
---|---|---|

Public Streets | 0.5 - 10 | 1 - 8 |

Private streets | 0.5 - 20 | 1 - 12 |

Service lanes | 0.5 - 15 | 1 - 10 |

Parking areas | 0.5 - 8 | 1 - 5 |

Parking ramps | up to 20 | up to 15 |

Collector walks | 0.5 - 12 | 1 - 8 |

Entrance walks | 0.5 - 8 | 1 - 4 |

Pedestrian ramps | up to 12 | up to 8 |

Stairs | 25 - 50 | 33 - 50 |

Game courts | 0.5 - 2 | 0.5 - 1.5 |

Paved gutters | 0.25 - 100 | 1 - 50 |

Grassed swales | 0.5 - 15 | 2 - 10 |

Terraces and sitting areas | 0.5 - 3 | 1 - 2 |

Grassed banks | up to 50 | up to 33 |

Planted banks | up to 100 | up to 50 |

## Freeboard

- In swales conveying flowing water a freeboard of 300 mm is generally accepted as a good starting point.
- In bioretention the freeboard is the difference between the invert elevation of the overflow structure and the inlet. 150 mm will suffice, so long as the inlet will not become inundated during design storm conditions.
- In above grade stormwater planters, the equivalent dimension would be the difference between the invert elevation of the overflow structure and the lip of the planter (150 mm minimum)

## Additional Resources

- File:Huang 2012.pdf
- File:Matusik 2004.pdf
- File:Tiner 2014.pdf
- http://www.slopemeter.com/images/Slope_Conversion_Tables.xls - external resource

- ↑ Ontario. O. Reg. 191/11: INTEGRATED ACCESSIBILITY STANDARDS, 2011. https://www.ontario.ca/laws/regulation/r11191.
- ↑ Universal Design.com. 2018. “The Leading Source for News and Information on Universal Design - The Leading Source for News and Information on Universal Design.” 2018. http://www.universaldesign.com/.
- ↑ Institute for Human Centered Design. 2018. “Principles.” 2018. https://www.humancentereddesign.org/inclusive-design/principles.
- ↑ Strom, S., Nathan, K., Woland, J. Site Engineering for Landscape Architects (6th Ed.) 2013, Wiley and Sons