A Low-Vision Designer and Three Rings That Do Not Close
Anita, 17, has low vision (6/60 in the better eye), works with a 4x magnifier and needs high contrast and large print. She is designing a wall hanging for the school exhibition: a 300 mm x 300 mm plywood board, an outer ring of bottle caps, an inner ring of caps, and a coconut-shell disc of 80 mm diameter at the centre. Caps measured 30 mm across the crown, so she calculated the number of caps from 30 mm and drew the rings with an HB pencil on white paper, writing dimensions in small handwriting. Her drawing shows 24 caps on an outer ring of 120 mm radius and 12 caps on an inner ring of 70 mm radius, with one dimension chain missing. When she laid caps on the board, adjacent caps overlapped by about 3 mm at the skirt and the last cap had no place to sit. Ten of the twelve units she has to make are now on hold, the exhibition is nine days away, and workshop time is 45 minutes a day.
1. Explain the cause of the overlap and the missing last place, and give corrected dimensions for the outer ring.
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Cause: the wrong diameter and the wrong spacing rule.
- Measured at the wrong place. The cap is 30 mm at the crown but about 32.5 mm at the skirt, which is the part that touches its neighbour when caps lie side by side on a board. Her pitch of 30 mm was therefore 2.5 mm too small before any gap was allowed.
- Gap not allowed. A working gap of 1.0-1.5 mm is needed for paint thickness, glue squeeze-out and hand placement error. Required pitch = 32.5 + 1.5 = 34.0 mm.
- Arc length used instead of chord. Caps sit on a circle, so the distance between neighbouring centres is the chord, not the arc. The formula is pitch = 2 x r x sin(180 degrees / N), so r = pitch / (2 x sin(180/N)).
Recalculating the outer ring
- With N = 24: sin(7.5 degrees) = 0.1305, so r = 34 / (2 x 0.1305) = 130.2 mm.
- Overall diameter = 2 x 130.2 + 32.5 = 292.9 mm on a 300 mm board. That leaves 3.5 mm border, which is not enough to survive sawing and handling.
- With N = 22: sin(8.18 degrees) = 0.1423, so r = 34 / (2 x 0.1423) = 119.5 mm; overall diameter 271.5 mm, giving a 14 mm border.
Decision: change the outer ring to 22 caps at r = 119.5 mm. The inner ring of 12 caps at r = 70 mm gives a pitch of 2 x 70 x sin(15 degrees) = 36.2 mm, which is more than 34 mm, so it is safe as drawn. Reducing the cap count is the correct answer, not squeezing the last cap in.
2. List what you will change in the drawing and working documents so Anita can work from them independently.
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Drawing changes
- Redraw at 1:1 on the 300 x 300 board, because full size removes the need to convert scale mentally.
- Line weight and contrast: 0.7 mm black felt-tip for outlines on white card, no pencil, no blue or light colours; ring centrelines as dashed black.
- Dimensioning: one continuous baseline dimension chain from the left edge, in millimetres, numerals at least 7 mm high, arrows outside the drawing where space is tight; never stack dimensions inside a crowded ring.
- Labelling: number every cap position 1 to 22 with the start point marked 'START' and an arrow for direction, so a missed cap is obvious.
- Centre marks: crosshair on the board centre, plus a cardboard template with the two ring circles cut out, so she can place it and feel the line rather than read it.
Working documents
- Cutting list: board 300 x 300 x 6 mm, 34 caps at 32.5 mm skirt, one coconut disc 80 mm, hanging loop 120 mm.
- Tolerance block on the drawing: cap centre position plus or minus 1.5 mm, ring centre plus or minus 1 mm, gap 1.0-2.0 mm, no cap overhanging the board edge.
- Operations checklist in large print, one line per step with a box to tick: mark, drill, paint, glue, check gap, cure.
- A tactile sample board of five glued caps at correct pitch, so she can compare by touch as well as by sight.
- Verbal backup: read the checklist aloud once at the start of each session and keep it at eye level, not flat on the bench.
3. Plan the nine days of 45-minute sessions for 12 units and state what you will change if the plan does not fit.
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Plan
- Day 1: finish the corrected drawing, make the two ring templates and the cap jig (a plywood nest holding one cap for drilling).
- Day 2: cut and sand 12 boards, mark centres with the template.
- Day 3: drill and clean 34 caps for the prototype plus 34 for unit 2; caps are the slowest step, so start early.
- Day 4: glue the prototype rings, check gaps with a card gauge, correct the jig if pitch drifts.
- Days 5-7: batch by operation, not by unit: all drilling, then all painting, then all gluing; 4 units a day is realistic at 45 minutes once the jigs exist.
- Day 8: cure, fit hanging loops, quality check against the tolerance block.
- Day 9: pack, label, and prepare the display card that explains the waste material used.
Numbers check: 45 minutes x 9 days = 6.75 hours. At roughly 30 minutes per unit after jigs, 12 units need 6 hours, leaving almost nothing for drying and correction. That is too tight.
If it does not fit, change in this order
- Reduce to 8 units and display the prototype with a process chart; an exhibition shows method as much as quantity.
- Simplify to one ring plus centre disc, keeping the same skills.
- Ask for one extra afternoon session rather than shortening the glue cure time, because a wet joint will fail in handling and cost more than it saves.