Unit 3: Reading Measuring Tools and Using Scales

Learning Objectives and Fundamental Skills

• The primary goal of Unit 3 is to provide a comprehensive understanding of reading measuring tools and utilizing various scales effectively.

• Students are expected to master reading both customary (English) rules and tapes alongside metric rules.

• Critical skill development includes the ability to convert between customary and metric units using precise mathematical factors.

• Understanding drawing scales is essential, specifically identifying the scale indicated on a technical print and accurately reading dimensions from it.

• Mastery of physically making measurements is required for two specialized tools:     - The architect’s scale.     - The engineer’s scale.

• A fundamental conversion constant provided for all calculations is: $1\,\text{inch} = 25.4\,\text{millimeters}$.

Technical Terminology and Definitions

• Architect’s Scale: A specialized ruler used by architects and builders to convert scaled drawings into actual dimensions, typically involving fractions of an inch representing feet.

• Centimeter (cm): A metric unit of length equal to one-hundredth of a meter ($10^{-2}\,\text{m}$).

• Engineer’s Scale: A ruler used primarily for civil engineering and site plans where increments are based on decimals and whole numbers (e.g., $1\,\text{inch} = 10\,\text{feet}$).

• Fractional Rule: A measuring tool, such as a standard ruler or tape measure, divided into fractions of an inch (halves, quarters, eighths, sixteenths).

• Full-divided Scale: A scale where the entire length of the tool is divided into the smallest units of measurement.

• Meter (m): The basic unit of length in the metric system.

• Metric Rule: A measuring tool graduated in millimeters and centimeters.

• Metric Scale: A tool used to create or measure drawings using metric units.

• Millimeter (mm): A metric unit of length equal to one-thousandth of a meter ($10^{-3}\,\text{m}$).

• Open-divided Scale: A scale where only the main divisions are marked along the length, while the end units are subdivided into smaller fractions.

• Scale: The ratio of the size of an object in a drawing to the actual size of the object in reality.

Types of Measuring Tools and Scales

• General measuring tools include:     - Tape measure.     - Fractional rule (customary units).     - Metric rule (metric units).

• Specialized scaling tools for professionals:     - Architect’s scale: Available in three-sided (triangular) forms and flat forms.     - Engineer’s scale: Used for large-scale projects like site plans.

The Fractional Rule (English/Customary System)

• The fractional rule utilizes major divisions categorized by:     - Feet.     - Inches.     - Fractions of an inch.

• Standard major divisions of an inch on a fractional rule include:     - $1/2$: Providing $2$ divisions per inch.     - $1/4$: Providing $4$ divisions per inch.     - $1/8$: Providing $8$ divisions per inch.     - $1/16$: Providing $16$ divisions per inch, which is typically the smallest division necessary for standard construction and drafting.

• Examples of measurements read from a fractional rule:     - $3\,7/16''$     - $11\,7/8''$     - $1'-5\,3/16''$     - $1'-7\,3/4''$     - $2'-9\,1/16''$     - $2'-10\,15/16''$

The Metric Rule

• The metric rule uses the meter ($m$) as the foundational unit.

• Precise readings often include units in millimeters ($mm$).

• Examples of metric rule measurements:     - $6\,mm$     - $34\,mm$     - $897\,mm$     - $1017\,mm$     - $1653\,mm$     - $2005\,mm$     - $2369\,mm$     - $2922\,mm$

Unit Conversion Standards

• Precise conversion from English (customary) to Metric units is achieved using the following values:     - $1\,\text{inch} = 25.4\,mm$     - $12\,\text{inches} = 304.8\,mm$     - $1\,\text{yard}\;(36\,\text{inches}) = 914.4\,mm$     - $39.37\,\text{inches} = 1000\,mm = 1\,m$

Understanding and Identifying Drawing Scales

• Construction drawings are almost always created at a reduced scale to allow large structures to fit on manageable paper sizes.

• Architect’s Scale Relationships:     - $1/4'' = 1'-0''$: Every $1/4''$ on the drawing represents $1\,\text{foot}$ of actual physical length.     - $1/8'' = 1'-0''$: Every $1/8''$ on the drawing represents $1\,\text{foot}$ of actual physical length.

• Engineer’s Scale Relationships:     - A "10 scale" indicates that $1''$ on the drawing represents $10\,\text{feet}$ in reality.     - This scale contains $10$ tic marks between each inch on the physical tool.     - For a 10 scale, each individual tic represents $1\,\text{foot}$.     - For a 20 scale, each individual tic represents $2\,\text{feet}$.

• Common Engineer Scales include:     - $1'' = 10'$\n - $1'' = 20'$\n - $1'' = 30'$\n - $1'' = 40'$\n - $1'' = 50'$\n - $1'' = 60'$\n - Note: These can work in multiples of 10, such as $100'$ or $1000'$

Using the Architect’s Scale

• This tool is specifically commonly used for making drawings for buildings.

• Reading Procedure:     1. Locate the specific scale marked on the edge (e.g., the $1/4$ mark).     2. Feet: Starting at the zero ($0$) mark, the scaled measurements of feet are numbered in one direction (e.g., to the left), following increments like $2, 4, 6, 8$, etc.     3. Inches: Inches are located in the small subdivided section to the opposite side of the zero (e.g., to the right).     4. Method for Layout: To measure a distance such as $6'-3''$, align the line indicating $6'$ with the starting point, move to the zero mark, and then continue further into the inch subdivisions to reach the $3''$ mark.     5. Measurement Example: $11'-8''$: Start at the line indicating $11'$ and extend past the zero to the $8''$ graduation.     6. Adjustment Logic: When reading, line up the closest foot mark that still allows the object/line to extend into the fractional foot (inch) area.

• Example: At a scale of $1\,1/2'' = 1'$, a measurement might be identified as $2'-10''$.

Using the Engineer’s Scale

• This tool is typically reserved for civil drawings, site plans, maps, and any project elements outside the building envelope.

• Measurements are referred to in whole numbers.

• Example: A "20 scale" is noted as $1'' = 20'$.

• High-level examples include identifying site details like handicapped parking signs, curbing (Concrete Curb Section at Scale: $1/4'' = 1'-0''$), or asphalt details.

• On a Site Plan (SP-1), symbols like North arrows and specific lot boundary details (e.g., Lot 6, R=360) are used in conjunction with the scale (e.g., $1'' = 30'$).

Practice and Skill Acquisition

• Comfort with reading scales requires consistent practice.

• Recommended learning strategy:     - Pair with an experienced user to verify readings on scaled drawings.     - Measure lines that already have printed dimensions to self-verify.     - Draw lines on graph paper at specific scales and measure them for drills.

Knowledge Assessment and Activity Solutions

Test Your Knowledge Answer Key

• Question 1: $B.\;635\,mm$

• Question 2: $D.\;3.73\,m$

• Question 3: $A.\;1\,1/2''$

• Question 4: $A.\;57'-1\,7/8''$

• Question 5: True

• Question 6: $A.\;64.2\,m$

• Question 7: $C.\;4'-8''$

• Question 8: $E.\;\text{None of these answers is reasonable.}$

• Question 9: True

• Question 10: True

• Question 11: $C.\;1/4'' = 1'-0''$

• Question 12: $D.\;\text{Construction standards using the metric system have not been established}$

• Question 13: False

• Question 14: False

• Question 15: False

• Question 16: True

• Question 17: $A.\;1''$, $B.\;1''$, $C.\;1/4''$, $D.\;1/4''$

• Question 18: $D.\;1'' = 20'$

• Question 19: $3450\,mm$

• Question 20: $1100\,mm$

Activity 3-3: Reading a Scale

• Measurements identified: $7''$, $4\,1/4''$, $6\,1/2''$, $10\,3/4''$, $1/2''$, $6''$, $13'-9''$, $2'-7\,3/4''$, $3'-4''$.

Activity 3-4: Identifying Missing Dimensions

• Dimensions retrieved: $15'-0''$, $12'-10''$, $2'-2''$, $3'-0''$, $14'-6''$, $2'-10''$, $1'-8''$, $8'-2''$, $10'-6''$, $3'-11''$, $4'-0''$.

Activity 3-5: Scaling I (Architectural)

• Scale $1/4'' = 1'-0''$: $17'-6''$

• Scale $1/8'' = 1'-0''$: $35'-0''$

• Scale $3/4'' = 1'-0''$: $3'-4''$

• Scale $1\,1/2'' = 1'-0''$: $4'-4''$

• Scale $3/8'' = 1'-0''$: $10'-8''$

• Scale $3/16'' = 1'-0''$: $26'-0''$

• Scale $3'' = 1'-0''$: $2'-0\,3/4''$

• Scale $1/2'' = 1'-0''$: $13'-9''$

• Scale $1'' = 1'-0''$: $5'-8\,1/4''$

• Scale $3/32'' = 1'-0''$: $64'-0''$

Activity 3-5: Scaling II (Engineering)

• Scale $1'' = 10'$: $44'$

• Scale $1'' = 20'$: $88'$

• Scale $1'' = 60'$: $150'$

• Scale $1'' = 100'$: $650'$

• Scale $1'' = 40'$: $160'$

• Scale $1'' = 50'$: $244'$

• Scale $1'' = 30'$: $188'$

• Scale $1'' = 20'$: $137'$

• Scale $1'' = 10'$: $57'$

• Scale $1'' = 60'$: $358'$

Activity 3-5: Dimensioning I (Actual Fractions)

• Lengths determined: $3\,1/6''$, $2\,15/16''$, $5\,7/8''$, $5\,11/16''$, $4\,15/16''$, $6\,3/16''$, $6\,7/16''$, $3\,61/96''$, $5\,5/12''$, $5\,5/8''$.

Activity 3-5: Dimensioning II (Decimal Equivalents)

• Lengths determined: $5.55''$, $5.25''$, $3.74''$, $6.60''$, $0.83''$, $5.53''$, $0.89''$, $5.55''$, $1.73''$, $6.03''$.