A3 Isometric of a Stepped Die Block: Scale, Ellipse and Set-Out
In a trade practical test an ITI candidate must produce an isometric view of a die block on an A3 sheet (420 × 297 mm, 20 mm border all round, title block 180 × 60 mm in the bottom right corner) within 40 minutes. The block is 60 mm long, 40 mm wide and 30 mm high, with a step 20 mm deep cut across the full width at one end, and a Ø20 mm hole drilled vertically through the remaining top face. The candidate has read that isometric lengths are 0.816 times true length, so scales every dimension by 0.816, and then draws the hole on the top face as an ellipse whose major axis is 20 mm and which is placed with that major axis vertical. The marking scheme awards separate marks for overall size, correct ellipse and correct orientation of the step.
1. Decide whether 0.816 should be applied, verify by calculation that the finished view fits the drawing area, and state the consequence for marking if the candidate is inconsistent.
Read the worked answer
What 0.816 means. 0.816 ≈ √(2/3) is the factor that converts a true length into its isometric projection. An isometric projection uses it; an isometric drawing (the normal workshop practice) sets all three axes out at full scale along lines at 30° to the horizontal. Either is acceptable, but the whole drawing must use one convention only.
Fit check for full scale (L = 60, W = 40, H = 30)
- Overall isometric width = (L + W) cos 30° = 100 × 0.866 = 86.6 mm
- Overall isometric height = H + (L + W) sin 30° = 30 + 100 × 0.5 = 80 mm
- Available drawing area ≈ (420 − 40) × (297 − 40) = 380 × 257 mm, minus the title block at the bottom right.
86.6 × 80 mm fits with ample margin, so full scale is the simpler and preferred choice; applying 0.816 gives only 70.7 × 65.3 mm and buys nothing.
Marking consequence: scaling everything by 0.816 is not an error in itself, but mixing scales - for example plotting axis-parallel edges at full size and then multiplying a feature by 0.816 - produces a distorted block and loses the overall-size and orientation marks. Consistency, not the factor, is what is being tested.
2. Correct the hole representation: give the ellipse dimensions and the correct orientation, and explain where the figures come from.
Read the worked answer
Correct ellipse for a Ø20 circle in isometric
- Major axis = 1.22 d = 1.22 × 20 ≈ 24.5 mm
- Minor axis = 0.71 d = 0.71 × 20 ≈ 14.1 mm
- Orientation: the major axis is horizontal, i.e. at right angles to the vertical isometric axis.
Reasoning. A circle in isometric becomes an ellipse because the face containing it is foreshortened. The circle's diameter survives as the major axis of the ellipse (it is the chord that lies parallel to the picture plane after the face is tilted), which is why the major axis is longer than the true diameter. The minor axis is the foreshortened diameter, hence 0.71 d. The rule to remember is that the major axis is always perpendicular to the axis normal to the face: the top face's normal is the vertical axis, so the major axis lies horizontal.
Construction. Enclose the circle in a 20 × 20 square, draw that square as a 20 mm rhombus in isometric, and inscribe the ellipse by the four-centre method; the points of tangency must fall at the mid-points of the rhombus sides.
The candidate's drawing is wrong twice: a 20 mm major axis is too short by 4.5 mm, and setting the major axis vertical rotates the ellipse 90°, so the hole reads as if it were in a vertical face.
3. Explain how the trainee should set out the 20 mm step and any edge that is not parallel to an isometric axis, and state what should be done about hidden detail of the hole.
Read the worked answer
Axis-parallel edges (most of this block). The step faces the full width, so its edges are parallel to the three isometric axes: vertical edges stay vertical, and the two horizontal directions are drawn at 30° to the horizontal. These can be measured directly at scale along the axes - no 0.816 for an isometric drawing.
Non-isometric lines. Any edge not parallel to an axis - a chamfer, a diagonal, a taper - must not be scaled along its own direction, because its isometric length is not a simple multiple of the true length. Instead:
- Locate both end points by measuring along the three axes from a known corner (offsets in L, W, H).
- Join the located points; the resulting line is an isometric line and is automatically correct. This is the commonest mistake in trade tests: measuring a sloped edge directly and finding the block will not close.
Set-out order. Box in the full 60 × 40 × 30 prism first, then mark the 20 mm step on the top face along the length axis, drop the vertical face, and finally locate the hole centre from the two nearest edges (not from the block centre) and draw the ellipse.
Hidden detail. For a through hole in a solid block, omit hidden lines in an isometric unless the examiner asks for them; show the top ellipse and, if the hole is visible through the step face, only the visible portion. Dashed lines in isometric are hard to read and are normally dispensed with.