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Low Impact Development and Bioretention Maintenance. Module 2: Math. Contributors. The Low Impact Development Center, Inc. John Shorb Landscaping, Inc. Logo. Groundwork Anacostia River, D.C. Logo. Overview.

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Presentation Transcript
contributors
Contributors

The Low Impact Development Center, Inc.

John Shorb Landscaping, Inc.

Logo

Groundwork Anacostia River, D.C.

Logo

overview
Overview
  • Some basic math skills are needed to perform bioretention maintenance activities
  • Calculate quantities, lengths, and volumes of materials needed
  • Estimate material and labor costs
overview1
Overview
  • Basic math skills
  • Conversions
  • Geometry
  • Calculating the area of landscaped features
  • Calculating volumes for soil modification and topdressing
  • Estimating water use
slide5

2 hours

  • Reading: Mathematics for the Green Industry
  • Chapters 1-4, pp.174-190, 191-194, 211-221
expected outcomes
Expected Outcomes
  • Be able to estimate installation, maintenance, and repair costs
  • Be able to calculate area and volume of landscape features
basic math operations
Basic math operations
  • Purpose: to be able to set up and perform calculations correctly
  • Estimates are no good if you get the wrong answer!
order of operations
Order of Operations

PEMDAS

  • Parentheses
  • Exponents
  • Multiplication and Division (left to right)
  • Addition and Subtraction (left to right)
2 exponents
2. Exponents
  • Powers and square roots
3 multiplication and division
3. Multiplication and Division
  • Proceed from Left to Right

CORRECT

4 addition and subtraction
4. Addition and Subtraction
  • Proceed left to right

CORRECT

INCORRECT

put it all together
Put it all together

1. Parenthesis

2. Exponents

3. Multiplication and Division L -> R

4. Addition and Subtraction L->R

solving for x
Solving for x
  • An unknown value in an equation is represented by a letter, usually x
  • Determining which value x represents is done by isolating x on one side of the equation
  • This is done by manipulating the equation to isolate x on one side of the equals sign
  • X is isolated by making the same change to both sides of the equation
solving for x1
Solving for x

Subtract 2 from both sides

solving for x2
Solving for x

Divide both sides by 4

solving for x3
Solving for x

Multiply both sides by 4

Add 5 to both sides

ratios and proportions
Ratios and proportions

Ratio – the relative size of two quantities expressed as one divided by the other

Written as

or

proportion
Proportion
  • A proportion is a statement that two ratios are equal
  • Examples
cross multiplication
Cross multiplication

If , then

For example,

solving problems
Solving problems

Use cross-multiplication to solve for x:

Divide both sides by 2

calculating quantities
Calculating quantities

A recommended soil amendment ratio is 1 part compost to 2 parts topsoil. How much compost do you need to add to 4 cubic yards of topsoil?

You’ll need 2 cubic yards of compost

conversions
Conversions

Proportions can be used to convert values from one number system to another

Example: convert 0.25 acres to sqft

geometry
Geometry
  • How to calculate the area of different shapes
  • Used to calculate the size of an area to be maintained
  • Estimate plant quantities
  • Estimate water needs
  • Estimate materials (e.g. mulch)
area of a rectangle
Area of a rectangle

Width (w)

Length (l)

area of a parallelogram
Area of a parallelogram

Height (h)

Base (b)

area of a trapezoid
Area of a trapezoid

Base2 (b2)

Height (h)

Base1 (b1)

area of a triangle
Area of a triangle

Height (h)

Base (b)

area of a circle
Area of a circle

Where

d = diameter

d

area of an ellipse
Area of an ellipse

rminor

rmajor

area of irregular shapes
Area of irregular shapes
  • Geometric method
  • Offset method
  • Modified offset method
geometric method
Geometric method
  • Used to calculate the area of spaces that are composed of simple geometric shapes
offset method
Offset method
  • Step 1: establish a line along the longest axis
offset method1
Offset method
  • Step 2: establish equally spaced offset lines perpendicular to the first line
offset method2
Offset method
  • Step 3: measure each line from end to end

24 ft

24 ft

24 ft

22 ft

20 ft

23 ft

21 ft

20 ft

20 ft

10 ft

100 ft

offset method3
Offset method
  • Step 4: Sum the lengths of all the offset lines

24 ft

24 ft

24 ft

22 ft

20 ft

23 ft

21 ft

20 ft

20 ft

10 ft

100 ft

offset method4
Offset method
  • Step 5: Multiply the sum by the distance between the offset lines

24 ft

24 ft

24 ft

22 ft

20 ft

23 ft

21 ft

20 ft

20 ft

10 ft

100 ft

offset method5
Offset method
  • Formula:
  • Where
  • , and
modified offset method
Modified offset method
  • Used when areas cannot easily be traversed to measure the offset lines
modified offset method1
Modified offset method
  • Step 1: create a rectangle around the area to be measured

l

B

A

w

C

D

modified offset method2
Modified offset method
  • Step 2: establish equally spaced offset lines perpendicular to lines AB and CD

J1

F1

E1

G1

H1

I1

B

A

10 ft

C

D

J2

F2

E2

G2

H2

I2

modified offset method3
Modified offset method
  • Step 3a: measure the lengths of each of the offset line segments

J1

F1

E1

G1

H1

I1

B

A

C

D

J2

F2

E2

G2

H2

I2

modified offset method4
Modified offset method
  • Step 3b: Add up each pair of offset measurements
modified offset method5
Modified offset method
  • Step 4: For each of the line segments, subtract each of the sums from the width of the rectangle. Each of the results = the actual width of the figure at the offset location
modified offset method6
Modified offset method
  • Step 5: Sum the widths of the figure calculated in Step 4
modified offset method7
Modified offset method
  • Step 6: Multiply the summed value from Step 5 by the distance between offsets
calculating volume
Calculating volume
  • Used to estimate volumes of media, gravel, soil amendments, and topdressing
soil modification
Soil modification
  • Calculate the volume of an amendment to be incorporated into the soil in an area
soil modification1
Soil modification
  • Step 1: determine the surface area that needs to be modified using one of the methods discussed earlier
    • Geometric method
    • Offset method
    • Modified offset method
    • Simpson’s method
soil modification2
Soil modification
  • Step 2: convert depth of soil to be modified to feet
soil modification3
Soil modification
  • Step 3: multiply area by depth to determine volume of soil to be modified
soil modification4
Soil modification
  • Step 4: determine the volume of each soil component that is needed
  • Example: 65% sand, 20% topsoil, 15% compost
soil modification5
Soil modification
  • Step 5: convert volumes from cubic feet to cubic yards
topdressing
topdressing
  • Calculate the volume of an amendment to be placed ontop of existing soil surface (e.g. mulch)
topdressing1
Topdressing
  • Step 1: determine the surface area that needs to be modified using one of the methods discussed earlier
    • Geometric method
    • Offset method
    • Modified offset method
    • Simpson’s method
topdressing2
Topdressing
  • Step 2: convert depth of topdressing to feet
soil modification6
Soil modification
  • Step 3: multiply area by depth to determine volume of topdressing needed
soil modification7
Soil modification
  • Step 4: convert volume from cubic feet to cubic yards
water use
Water use
  • Irrigation water is measured in acre-feet
  • One acre-foot is the amount of water needed to cover one acre with water one foot deep
calculating water use
Calculating water use
  • How much water is needed to apply 1-inch of water to ½ acre?
  • Step 1: convert to ac-ft
calculating water use1
Calculating water use
  • Step 2: convert ac-ft to gallons
calculating slope
Calculating slope
  • Expressed as a ratio or a percentage
  • E.g. 1:20 or

rise

run