Engineering & Technology · Sketches, Models & Technical Communication
Sketches, orthographic views and spatial reasoning
A workshop wants a small stepped block to hold a sample at two heights. A photograph makes the step easy to recognise, but the far edge is hidden. A front sketch shows the step clearly, yet says little about how far the block extends away from us. The useful question is which views, taken together, remove the ambiguity.
Use units and simple arithmetic from Measurement, Units & Engineering Evidence. This chapter introduces its own coordinates, projections and model vocabulary; multiplication and division are enough for the worked cases. The geometry, system, data and results are original teaching constructions. They are not observed experiments, build specifications or operating instructions. No conformance to a drafting, piping or NASA standard is claimed.
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Use several labelled views of the same object to recover its three-dimensional shape without mistaking one silhouette for the whole object.
Keep the object still and change the viewing direction
Our original teaching block has width 60 mm, depth 40 mm and maximum height 30 mm. Its base is 10 mm high everywhere. Across the leftmost 20 mm of its width, an upper portion reaches the full 30 mm height, along the entire depth. There are no holes, curves or internal cavities. Picture two rectangular solids joined together.
A freehand sketch records an idea without requiring instruments. A pictorial sketch shows several faces at once and helps a reader recognise shape. Its apparent sloping lines need not represent sloping surfaces. In a perspective picture, distance also changes apparent size. Before measuring anything, establish what kind of representation you are reading.
Read each view as a separate question
An orthographic view looks along a fixed direction using parallel projection lines perpendicular to the viewing plane. Our front view looks along the depth direction: width runs horizontally and height vertically. The depth is collapsed. The top view keeps width and depth but collapses height. The right-side view keeps depth and height but collapses width.
In the figure, the front view has a step-shaped outline. The top view is a rectangle with an edge at the change in height. The right-side outline is a full rectangle: the tall portion behind the low portion still reaches the full depth. The horizontal line 10 mm above its bottom separates visible faces at different distances. Trace the same upper portion through all three views.
Use the views together
A rectangle in one view does not prove the object is a rectangular block. A cylinder, a plate and our stepped block can each have rectangular projections from some directions. Match shared extents: front and top share width; front and side share height; top and side share depth. A mismatch is a clue that a view, label or assumption needs checking.
Drawings may use dashed hidden edges, centre lines, section views and formal projection arrangements. Each has a defined purpose in its drawing convention. Here every panel is explicitly named and all relevant exterior edges are visible in at least one view. The illustration teaches projections; it is not a manufacturing drawing checked against a drafting standard. Always read the stated projection convention on a professional drawing instead of guessing from page position.
Reconstruct the block from two views, then test the third
From the front, identify a 60 mm-wide base 10 mm high and a 20 mm-wide portion rising to 30 mm. This alone leaves the depth undetermined: the shape could extend 5 mm or 40 mm away from us.
The top view supplies the 40 mm depth and shows the change in height at the same 20 mm width position across that depth. Combining those facts gives the two joined rectangular portions described above.
Predict the right-side view before looking: its overall size must be 40 mm deep by 30 mm high. Its outline is rectangular, with a horizontal edge at 10 mm. If your side sketch has a step-shaped outer edge, you have probably carried the front silhouette into the wrong viewing direction.
Try the reasoning
Which two views share the block’s 60 mm width?
Show the answer and reasoning
The front and top views. Width is collapsed in the right-side view, which shows depth and height instead.
The right-side outline is rectangular. Does that contradict the front view’s step?
Show the answer and reasoning
No. The tall left portion extends through the full depth and remains visible from the right above the low portion. Different projections can have different outlines.
Can you recover every possible interior feature from these three exterior views?
Show the answer and reasoning
No. The stated absence of cavities is part of this teaching case. A real object may need hidden-edge information, sections or additional views to describe its interior.
What to carry forward
A view preserves two directions and collapses the third. Reconstruct shape by matching information across labelled views.
References
Teaching resources and research supporting this lesson’s explanations and examples.