Introduction
In high school math class I learned about rise over run. Like every high school kid I thought I’d never need this again in life.
Well, concreting is mostly about this mathematical concept. It is used almost every day when you’re concreting.
Jargon
I learned this concept named “rise over run” but there are other names used to describe the same thing. Here’s a few of them and the type of trade work that might use them:
- Slope (general language, a non-level line between 2 points)
- Grade or gradient (earthworks/concreting, describes how much rise or fall will be on works that are being built)
- Pitch (roofing, roofs are usually described as having a “pitch” which is the angle the roof is on)
- Rise or fall (plumbing/concreting, used to describe how much a slab or pipe is tilted relative to level to make water travel where we want it to)
- Batter (earthworks/landscaping, the slope of an embankment)
- Ratio (general construction/on plans, describes how much rise or fall occurs over an amount of run distance. For example: “1 in 20” or “1:20”)
- Hypotenuse (general/math, from trigonometry – Pythagoras’ Theorem. The hypotenuse is the result of rise over run strictly when working with right-angle triangles)
Explained
Rise
What is rise (or fall)?
Rise is: the difference in height between 2 points in 3D space.
To construct a slope, grade, rise or fall, we need to know two numbers:
- How much rise (or fall)?
- Over how much distance of run?
This is where the ratio mentioned earlier is useful. Plans often indicate rise or fall as a ratio like: 1 in 20
The ratio is saying: there is 1 unit of rise (or fall) in every 20 units of run.
The units in Australia are almost always in millimetres.
Run
What is run?
Run is: the distance over which the rise or fall occurs.
Where do we get the run value from?
Either from the plan that gives us the fall ratio, or if we are doing works without plans, we measure the run distance in the real world with our tape measures.
Run Examples
A carport slab might be “7 metres from the existing building” from the back to the front of the carport. This means the run is 7 metres, or 7000mm.
Council footpaths often have “2%” or 1 in 50 fall across them, and they are 1.5m (1500mm) wide. The run is the width of the footpath, because the fall is across the footpath (not ‘along’ the length of the footpath).
Exercise
We are doing a driveway that is 13 metres long and 6m wide that goes from the house’s existing garage to the property boundary. The driveway has no crossfall. The first half of the driveway starting from the garage needs to have 1 in 10 fall. From halfway down the driveway to the boundary should have 1 in 20 fall.
Click to see answer explained
From the garage to the boundary is 13.0m. Half way to the boundary is 6.5m. The run is 6.5m
The desired fall from the garage to halfway down the driveway is 1 in 20.
This means: for every 20mm of run, there is 1mm of fall.
Important! Ensure we are working in a single unit of measure: convert 6.5m into mm. 6.5m = 6500mm. Therefore, our run value is now 6500.
Remember! Our unit of measure is mm
Do the math:
Divide the run value (6500) by the run value in the desired fall ratio (1 in 10). (Remember: “1 in 10” means “1mm of fall, in every 10mm of run” – so the run value in the ratio is: 20)
6500 / 20
= 325
The fall along the driveway from the garage to halfway down is 325mm or 0.325m
Click to see answer explained
From the garage to the boundary is 13.0m. Half way to the boundary is 6.5m. The run is 6.5m
The desired fall from the garage to halfway down the driveway is 1 in 10.
This means: for every 10mm of run, there is 1mm of fall.
Important! Ensure we are working in a single unit of measure: convert 6.5m into mm. 6.5m = 6500mm. Therefore, our run value is now 6500.
Remember! Our unit of measure is mm
Do the math:
Divide the run value (6500) by the run value in the desired fall ratio (1 in 10). (Remember: “1 in 10” means “1mm of fall, in every 10mm of run” – so the run value in the ratio is: 10)
6500 / 10
= 650
The fall along the driveway from the garage to halfway down is 650mm or 0.65m
Click to see answer explained
Knowing the falls from the previous two questions, we can simply add those fall values together to get the total fall from the garage to the boundary.
Do the math:
650 + 325
= 975
The fall along the driveway from the garage to the boundary is 975mm or 0.975m
Click to see answer explained
The original instructions said that the driveway had “no crossfall”.
Crossfall is the amount of fall on the slab that is adjacent to the traffic’s general direction of travel.
This means that the driveway will be level from one side to the other, and all water control is handled by the change in height in the direction of travel.
All the fall is from the garage (the highest point) to the boundary (the lowest point) along the length of the driveway. Across the width of the driveway, there’s no fall. So the answer is: 0, none or zero.