Labels, alarms and the senses

Letter height — viewing distance, the acuity you are designing for (6/6, 6/12, 6/18 …) and a reserve. Standard acuity reads a letter subtending 5 arcminutes, so the threshold letter height is h ≈ d × 5 × 0.000291 ≈ d × 0.00145. Multiply by the acuity ratio (×2 for 6/12, ×3 for 6/18) and by a reserve of two to three for comfortable reading. Enter an existing letter height to see the angle it subtends, how far it can be read, and how it compares. The book’s worked example is a button: a 3 mm label read 4 m away needs 5.8 mm at the 6/6 threshold, 11.6 mm for 6/12, and about 23–35 mm with reserve.

Eye optics — P = 1 / f, the far point of a myope, and the extra plus power needed to read at a given distance from the accommodation left at a given age (the book’s ~10 D at 20, ~4–6 D at 40 and ~1 D by 60; between those ages the tool interpolates and shows a range). A 60-year-old reading at 40 cm needs 2.5 D, has about 1 D, and so needs about +1.5 D. Then find your blind spot: the angle is arctan(8 / D) for a dot 8 cm from the cross, against the ~15° in the text.

Alarm audibility — a level measured at one distance, the number of equal sources (+3 dB for two), and the listener’s distance (−6 dB per doubling in open space), compared with the room’s level. The book’s click — 50 dB(A) at 0.5 m — is about 32 dB(A) at 4 m, below a 45–55 dB(A) classroom. Enter a tone frequency to be warned that 3–4 kHz alarms may be missed by older listeners. Below that, the 85 dB(A), 3-dB exchange rule: 8 h at 85, 4 at 88 … about 15 minutes at 100.

Ear mechanics — the ear canal as a quarter-wave resonator, f = c / 4L ≈ 343 / (4 × 0.025) ≈ 3.4 kHz, and the middle ear’s pressure gain, area ratio ≈ 17 × lever ≈ 1.3 ≈ 22, or 20·log₁₀ 22 ≈ 27 dB.

Touch — marker spacing against the two-point discrimination threshold at the fingertip, palm, forearm or back. Two dots 3 mm apart on a palm grip are one dot; on a fingertip they are two.

Image check — open a photo of a label or a screenshot (or use the sample). It is shown as people with protan, deutan and tritan colour-vision deficiency would roughly see it, in greyscale (monochrome printing), and blurred for a viewing distance and acuity, given the real width the photo shows. The image is processed in your browser and never uploaded. This is a simulation only.

Visual angle, the 0.00145 rule, the threshold table, the 2–3× reserve, dioptres, reading add, accommodation by age, the blind spot, the decibel rules, the exposure table, ear-canal resonance, middle-ear gain, and the worked example (label and click at 4 m): chapter 8 and its questions 7 and 12; the same figures are collected in appendix C. Labels for a group at 1–2 m (6–9 mm at 1 m for 6/12 with reserve): chapter 12.

Two-point discrimination thresholds and the share of people with colour-vision deficiency: chapter 7.

Colour-vision simulation: the severity-1.0 matrices from G. M. Machado, M. M. Oliveira and

Exposure: the 85 dB(A), 3-dB exchange criterion is the NIOSH recommended exposure limit (NIOSH publication 98-126, 1998).

Blur: three box blurs approximating a Gaussian, with its full width at half maximum set to the smallest detail the chosen acuity resolves (the acuity ratio × 1 arcmin at that distance).

Not a clinical acuity test, and not a hearing test. Acuity thresholds are for high-contrast letters under test conditions; real labels need more in poor light, at low contrast, or for users who are moving, stressed or older.

The sound calculation is free-field. Indoors, reflections make the fall-off with distance smaller, background noise varies, and whether a cue is noticed depends on its frequency, pattern and the listener. Phone sound-level apps are uncalibrated: use their readings as relative, not absolute.

The exposure table is a criterion for planning hearing protection, not a statement that any level is harmless. Other criteria exist (OSHA uses 90 dB(A) and a 5-dB exchange).

Reading adds are arithmetic from the book’s round figures, not a prescription. The tool covers ages 20–90 and holds accommodation at ~1 D after 60, where the book’s figure stops.

Two-point thresholds are typical orientation values; they vary with method, age and the person.

The colour-vision views model complete (dichromatic) deficiency; milder forms are more common and show smaller shifts. The blur is an illustration of lost detail, not an optical model of the eye.

A cue that works is a cue that works at a stated distance, level and lighting, for a stated user. Test it in the real room, with someone who did not make it.