Lesson Notes By Weeks and Term v3 - Senior Secondary 1
Scales
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Scales
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Subject: Technical Drawings
Class: Senior Secondary 1
Term: 2nd Term
Week: 4
Theme: Geometrical Constructions
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Explain the term “scale” and its uses. List type of scales Construct types of scales
2.1 Definition of Scale A scale in technical drawing is the ratio of the linear dimension of an element in a drawing to the true linear dimension of the same element of the object. It indicates how much the actual object has been reduced or enlarged to fit on the drawing paper. For instance, a drawing of a house is much smaller than the actual house, but it maintains the correct proportions, thanks to the scale. 2.2 Purpose of Scales Scales are used for: Representation: To represent large objects (e.g., buildings, landscapes) on a smaller sheet of paper in a manageable size.
Detailing: To enlarge very small objects (e.g., tiny machine parts) for clearer representation and detailing.
Accuracy: To ensure that the drawing maintains correct proportions and dimensions relative to the actual object, allowing for accurate measurement directly from the drawing.
Standardization: To conform to industry standards and facilitate communication among designers, engineers, and fabricators. 2.3 Representative Fraction (RF) The Representative Fraction (RF) is the ratio of the length of the drawing to the actual length of the object, expressed as a fraction or a ratio.
Formula: RF = (Length of the drawing) / (Actual length of the object)
Expression: Usually expressed with a numerator of 1 (e.g., 1/100 or 1:100).
Interpretation: Reducing Scale (e.g., 1:100): This means 1 unit on the drawing represents 100 units on the actual object. Used for large objects like buildings.
Full-Size Scale (1:1): 1 unit on the drawing represents 1 unit on the actual object. Used when the object fits the paper. Enlarging Scale (e.g., 2:1): 2 units on the drawing represent 1 unit on the actual object. Used for very small objects like watch parts.
Example 1: Calculating RF A drawing of a Nigerian bungalow is 50 cm long. The actual bungalow is 25 meters long. Determine the RF of the drawing.
Step 1: Convert all units to the same measurement. Actual length = 25 meters = 25 100 cm = 2500 cm Drawing length = 50 cm Step 2: Apply the RF formula. RF = (Drawing length) / (Actual length) = 50 cm / 2500 cm Step 3: Simplify the fraction. RF = 1/50 or 1:
5
0. This means 1 cm on the drawing represents 50 cm (or 0.5 meters) in reality. 2.4 Types of Scales A. Plain Scales Plain scales are used to represent two consecutive units (e.g., metres and decimetres, kilometres and hectometres, inches and tenths). They are typically used for direct measurement and showing precise lengths.
Principle of Construction: A plain scale is constructed by drawing a line, dividing it into main divisions, and then subdividing the first main division into smaller units. Construction Steps for a Plain Scale (Example): "Construct a plain scale of RF 1:100 to read metres and decimetres, long enough to measure up to 6 metres."
1. Determine the Length of Scale (LOS): RF = 1/100 Maximum length to be measured = 6 metres LOS = RF × Maximum length = (1/100) × 6 metres = (1/100) × 600 cm = 6 cm. Teacher
Note: This LOS is for the main primary divisions. Often, we add one more primary division to the left for the secondary units. So, the total length might be (6+1) primary divisions worth of length, if 6m is the total length needed for measurement. For practical drawing, we calculate LOS for the total length capacity (e.g. 6m), and then divide it. Let's assume 6m is the maximum value on the scale.
Re-evaluation for LOS: The LOS should represent the primary divisions. If the scale needs to measure UP TO 6m, and 1m is a primary division, then 6 primary divisions are needed. LOS = 6m (1/100) = 0.06m = 6cm.
Common practice:* To read metres and decimetres, we draw a line representing the maximum length (e.g., 6m at 1:100 scale = 6cm). Then, divide it into 6 main parts (each representing 1m). The first main part (from 0 to 1m) is then subdivided into 10 smaller parts (each representing 1 decimetre).
Re-evaluation for LOS: The LOS should represent the primary divisions. If the scale needs to measure UP TO 6m, and 1m is a primary division, then 6 primary divisions are needed. LOS = 6m (1/100) = 0.06m = 6cm.
Common practice: To read metres and decimetres, we draw a line representing the maximum length (e.g., 6m at 1:100 scale = 6cm). Then, divide it into 6 main parts (each representing 1m). The first main part (from 0 to 1m) is then subdivided into 10 smaller parts (each representing 1 decimetre).
Let's refine: If the scale is to measure "up to 6 metres", we need 6 primary divisions (each representing 1 metre). The total length of the scale drawn on paper will be 6m RF = 6m (1/100) = 0.06m = 6cm.
2. Draw the Scale Line: Draw a horizontal line AB of length 6 cm (LOS). Draw another line parallel to AB, say CD, about 5 mm above AB, and close the ends to form a thin rectangle. This gives the scale visual thickness.
3. Divide into Primary Divisions: Divide line AB into 6 equal parts. Each part represents 1 metre.
Method: From point A, draw a light inclined line AX. Mark 6 equal divisions on AX using a compass (or ruler). Join the 6th mark to B. Then, draw lines parallel to this last line from the other marks on AX to line A
B. These will divide AB into 6 equal parts.
Label the divisions: Start from the second mark from the left as '0', then '1', '2', '3', '4', '5' (metres). The leftmost division (from A to '0') will be for decimetres.
4. Subdivide the Leftmost Primary Division (Secondary Divisions): The leftmost primary division (from A to '0') represents 1 metre. To read decimetres, divide this section into 10 equal parts. Each small part will represent 1 decimetre (1/10 of a metre).
Method: From point A, draw another short inclined line AY. Mark 10 equal divisions on AY. Join the 10th mark to '0'. Draw lines parallel to this line from the other marks on AY to the line segment A-'0'.
Label these secondary divisions: '0', '2', '4', '6', '8', '10' (decimetres).
5. Add Readings: Write "Metres" below the primary divisions and "Decimetres" above the secondary divisions.
Write the RF (1:100) prominently below the scale. Shade alternate divisions for clarity. B. Diagonal Scales Diagonal scales are used to read three consecutive units (e.g., metres, decimetres, and centimetres; or inches, tenths, and hundredths of an inch). They are more precise than plain scales.
Principle of Diagonal Division: The principle is based on similar triangles. A diagonal line is drawn across a set of parallel lines, and the segments cut by the parallel lines on the diagonal line decrease uniformly. This allows for reading of the third unit. Construction Steps for a Diagonal Scale (Example): "Construct a diagonal scale of RF 1:50 to read metres, decimetres, and centimetres, long enough to measure up to 4 metres."
1. Determine the Length of Scale (LOS): RF = 1/50 Maximum length = 4 metres LOS = RF × Maximum length = (1/50) × 4 metres = (1/50) × 400 cm = 8 cm.
2. Draw the Scale Base Line: Draw a horizontal line AB of length 8 cm. Draw another line parallel to AB, say CD, 4-5 cm above AB. This height is for the diagonal divisions (usually 10 units for centimetres). Close the ends to form a rectangle ABCD.
3. Divide into Primary Divisions: Divide line AB into 4 equal parts. Each part represents 1 metre.
Label divisions: Start from the second mark from the left as '0', then '1', '2', '3' (metres). The leftmost division (from A to '0') is for decimetres.
4. Subdivide the Leftmost Primary Division (Secondary Divisions): The leftmost primary division (A to '0') represents 1 metre. Divide this segment into 10 equal parts. Each part represents 1 decimetre. Draw vertical lines upwards from each of these divisions to the rectangle ABCD.
3. Divide into Primary Divisions: Divide line AB into 4 equal parts. Each part represents 1 metre.
Label divisions: Start from the second mark from the left as '0', then '1', '2', '3' (metres). The leftmost division (from A to '0') is for decimetres.
4. Subdivide the Leftmost Primary Division (Secondary Divisions): The leftmost primary division (A to '0') represents 1 metre. Divide this segment into 10 equal parts. Each part represents 1 decimetre. Draw vertical lines upwards from each of these divisions to the top line CD.
5. Create Diagonal Divisions (for Centimetres): Along the vertical line AD (left end of the rectangle), mark 10 equal divisions (each representing 1 cm, if the total height AD represents 1 decimetre). Number these divisions from '0' at D to '10' at A. Draw horizontal lines from these 10 marks, parallel to AB, across the entire scale.
6. Draw Diagonal Lines: From the '0' mark of the secondary divisions (first mark to the right of A, along AB), draw a diagonal line to the 10th mark (point A) on the vertical line AD. From the '1' mark of the secondary divisions, draw a diagonal line to the 9th mark on A
D. Continue this pattern: from '2' to '8', '3' to '7', and so on, until from '9' to '1'. Teacher
Note: The common method is to draw a diagonal from the 0 of the first primary division (where primary units start) to the 10th mark of the vertical division above the
0. Then, from the 1st primary division mark (on the main line) to the 9th mark of the vertical division, and so on. Let's stick to the common method described below for clarity and less confusion: Mark 10 equal divisions on the vertical line at the extreme left (AD), starting from D (0) upwards to A (10). Similarly, mark 10 equal divisions on the vertical line at the 0-mark (the line extending from 0 on AB upwards), starting from the bottom (0) upwards to the top (10). Join the 0-mark on AD with the 10th mark on the vertical line from '0'. Join the 1st mark on AD with the 9th mark on the vertical line from '0'. Continue this pattern up to joining the 10th mark on AD with the 0-mark on the vertical line from '0'. This creates the diagonal grid.
7. Add Readings: Write "Metres" below the primary divisions. Write "Decimetres" above the secondary divisions. Write "Centimetres" along the side of the vertical diagonal divisions.
Write the RF (1:50) prominently below the scale. 2.5 Reading Scales To read a measurement on a constructed scale: Plain Scale: Locate the metre reading on the main scale, then move left to read the decimetre value on the subdivided leftmost part. * Diagonal Scale: Locate the metre reading on the main scale. Move along the corresponding vertical line to the right to find the decimetre reading. Then, follow the diagonal line from that decimetre mark until it intersects the horizontal line corresponding to the desired centimetre reading. 3.1 Teacher Activities Introduction (10 min): Begin by showing examples of scaled drawings (e.g., a map of Nigeria, a building plan, a circuit board layout). Ask students how these large/small items are represented on paper. Introduce the concept of scale as a ratio and its importance.
Explanation of Key Concepts (20 min): Define scale, purpose, and Representative Fraction (RF) using clear examples, including calculations relevant to Nigerian contexts (e.g., calculating RF for a map of their state). Explain the difference between reducing, full-size, and enlarging scales. Demonstration of Plain Scale Construction (30 min): On the whiteboard or using a projector/digital drawing tool, demonstrate step-by-step the construction of a plain scale. Ensure all calculations (LOS, divisions) are shown clearly. Use an example like "Construct a plain scale of RF 1:200 to read metres and decimetres, long enough to measure 5 metres." Emphasise neatness, accuracy, and proper use of drawing instruments. Demonstration of Diagonal Scale Construction (40 min): Follow with a step-by-step demonstration of a diagonal scale construction, explaining the diagonal principle. Use an example like "Construct a diagonal scale of RF 1:75 to read up to 3 metres, showing metres, decimetres, and centimetres." (Directly addresses the evaluation guide requirement). Highlight the differences in complexity and precision compared to plain scales.
Reading Scales (15 min): Demonstrate how to read specific measurements from both constructed plain and diagonal scales. Provide examples like "Read 2.3 metres on the plain scale" and "Read 1.75 metres on the diagonal scale." Guided Practice Introduction (10 min): Distribute relevant worksheets or direct students to specific exercises in their technical drawing notebooks. Monitor students as they begin working, providing immediate feedback and clarification. 3.2 Student Activities Active Listening and Note-Taking: Students pay attention during explanations and take comprehensive notes.
Q&A: Students ask questions for clarification during teacher explanations and demonstrations.
RF Calculations: Students practice calculating RF for various scenarios presented by the teacher.
Instrument Familiarisation: Students ensure they have all necessary drawing instruments (pencils, rulers, set squares, compasses) ready.
Plain Scale Construction: Students follow the teacher's demonstration and attempt to construct a plain scale in their drawing books.
Diagonal Scale Construction: Students attempt to construct a diagonal scale after the teacher's demonstration.
Scale Reading Practice: Students practice reading given measurements on scales drawn by the teacher or found in provided examples.
Peer Discussion: Students discuss their work and challenges with peers, under teacher guidance.
Architecture and Building Construction (e.g., Lagos, Abuja): Nigerian architects use scales to design floor plans, elevations, and sections of residential homes, commercial buildings, schools, and hospitals. These scaled drawings guide artisans, bricklayers, carpenters, and plumbers on site. For example, a drawing showing a 1:100 scale allows a builder in Ojo, Lagos, to understand that 1cm on the plan represents 1 metre on the actual building. Cartography and Land Surveying (e.g., Niger Delta, Northern farmlands): Mapping agencies and land surveyors in Nigeria extensively use scales. Maps of Nigerian states, local government areas, or even detailed site plans for resource exploration (like oil and gas pipelines in the Niger Delta) are all drawn to scale. Farmers in Kano might use scaled maps of their farmlands to plan irrigation or plot new crop allocations, with the scale indicating the ratio of distances on the map to actual distances on the ground. Mechanical and Electrical Engineering (e.g., Industrial Zones): In industrial areas like Agbara Estate or Port Harcourt, engineers design machinery components, electrical circuit diagrams, and assembly layouts using scales. For very small parts (e.g., for vehicle manufacturing or power generation equipment), enlarging scales (e.g., 5:1) are used to show intricate details that would otherwise be invisible. For large assemblies, reducing scales are employed.