E-scooter lighting and signalling engineering

In the article «E-scooter lighting and signaling» we described the types of lighting hardware (front headlamp 300–2000 lm, taillight, brake lamp, turn signals, retroreflectors) and the regulatory minimum (Germany’s eKFV § 5, the European EN 17128). In «Night riding on an e-scooter» — the behavioural side of visibility (biomotion configuration, retinal dark adaptation, conspicuous clothing, route planning). This material is an engineering deep-dive into the physics of light itself: why lumens do not describe brightness but candela do; why a headlamp designer doesn’t draw «how much light» but a polar-coordinate map with tolerance zones B50L, 75R, HV; why an LED rated at 1000 lm at 25 °C delivers 600 lm after 30 minutes in a chassis without a heatsink, and 700 lm after 8 000 hours; and why a retroreflector on an ankle is detected 26 times farther than the same retroreflector on fully black clothing. This is the seventh engineering-axis deep-dive (after protective-gear engineering, lithium-ion battery engineering, brake-system engineering, motor and controller engineering, suspension engineering, and tire engineering) — adds visual prevention as the active engineering subsystem: a helmet works only after an impact, a brake only once the rider has seen the threat, but lighting works before danger becomes actionable, because it secures conspicuity hundreds of metres before any possible contact zone.

Prerequisite — understanding the types of lighting fixtures, riding behaviour in the dark, and keeping distance in fog and reduced visibility. And if this physics interests you less than the concrete everyday takeaways — how to actually be seen in traffic and what is worth wearing — those are gathered in the companion piece on being seen: e-scooter lights and conspicuity in practice.

1. Why photometry is a distinct discipline, not «radiometry with a prefix»

Radiometry measures the power of electromagnetic radiation (watts per square metre, watts per steradian) — a physical quantity, independent of the observer. Photometry measures the same radiation, weighted by a function of human-eye sensitivity — a biophysical quantity, tied to the specific biology of retinal photoreceptors. Without that weighting the confusion is catastrophic: a 10 W headlamp in the far-infrared (λ = 1400 nm) gives 0 lumens to the driver, because rods and cones do not respond to that wavelength.

CIE 1924 photopic luminous-efficiency function V(λ) — the standard cone-vision sensitivity curve in bright light, normalised to 1 at its peak of 555 nm (yellow-green). Cone work. CIE 1951 scotopic luminous-efficiency function V’(λ) — the rod-vision curve in darkness, peak shifted to 507 nm (greenish-blue, the Purkinje effect). Rod work. The transition is the mesopic range, with luminance 0.005 to 5 cd/m². Fundamentally this means that a headlamp with spectral peak at 580 nm looks brighter by day, and one at 510 nm looks brighter at night, despite identical radiometric power in watts.

Luminous flux Φᵥ in lumens (lm) — the full luminous power of a source, integrated over all directions and weighted by V(λ):

Φᵥ = K_m · ∫ Φ_e(λ) · V(λ) dλ

where K_m = 683 lm/W is the maximum spectral luminous efficacy at 555 nm. So the theoretical maximum of a monochromatic 555 nm LED is 683 lm/W. A real phosphor-converted white LED in 2024 at cool-white 6500 K delivers 200–280 lm/W (Cree XHP70.3, Lumileds Luxeon TX). A mid-range e-scooter headlamp emits 800 lm drawing 8–10 W = 80–100 lm/W system efficiency (chip + lens + driver).

Luminous intensity I_v in candela (cd) — flux per unit solid angle in a given direction:

I_v = dΦᵥ / dΩ

where dΩ is in steradians. This is a directional quantity — candela differ in different directions. Candela describes the beam: «1000 cd headlamp on-axis» means that one steradian contains 1000 lm of flux — but that flux is concentrated into one point. The same headlamp can have 0 cd 90° off-axis.

Illuminance E_v in lux (lx) — flux per unit area of a receiving surface:

E_v = dΦᵥ / dA

1 lx = 1 lm/m². A characteristic of the surface receiving light, not of the source. The road in front of the scooter receives some illuminance in lux from the headlamp; intensive office lighting is 300–500 lx; daylight outdoors is 10 000–100 000 lx; moonlit night is 0.1–1 lx; rural moonless night is 0.001 lx.

Luminance L_v in cd/m² — intensity per unit projected area of a source:

L_v = d²Φᵥ / (dA · cosθ · dΩ)

This is brightness as perceived by the eye. The sun at noon is 1.6 × 10⁹ cd/m²; a clear sky is 8 000 cd/m²; a laptop screen 250 cd/m²; a full moon 2 500 cd/m². An XHP70.3 LED chip at maximum drive current is 50–100 × 10⁶ cd/m² (which is why one cannot look directly at it).

Inverse-square law for a point source:

E = I / d²

Road illuminance from a 200 cd headlamp at 5 m = 200 / 25 = 8 lx — comparable to urban sidewalk lighting. At 20 m: 200 / 400 = 0.5 lx — on the edge of total darkness. Hence a 2000 cd headlamp (not 2000 lm) yields 5 lx at 20 m, where detail is already visible.

Lambertian source — an ideal diffuse source with cosine-distributed intensity:

I(θ) = I_0 · cosθ

This describes a white sheet of paper in bright light (Lambertian reflectance). Most bare LED chips have a cosine-like distribution in θ. Isotropic source — equal intensity in all directions (4π sr); an idealisation for indicator lamps.

2. Headlamp beam pattern: why the designer draws a map, not «how many lumens»

An unoptic’d 1000 lm lamp scatters light evenly — that is a flood. Half the flux goes up into the sky, a quarter onto its own wheel, a quarter onto the road. Useful flux on the road at 100 % spread: ~250 lm. At 20 m, road illuminance is paltry.

A 1000 lm lamp + optic concentrating 80 % of the flux into a 10° good beam is a spot: 800 lm / 0.024 sr = 33 000 cd on-axis. At 20 m that is 33 000 / 400 = 82 lx, brighter than an illuminated sidewalk. But such a beam blinds an oncoming driver: 1.5 m above the road, 25 m across the lane, into the oncoming driver’s eyes — 82 lx straight from over the hood. That is why every road-vehicle headlamp has a cut-off — a sharp upper edge to the beam.

ECE R113 Rev 3:2014 — Headlamps emitting a symmetrical passing beam. A UNECE 1958-Agreement standard, mandatory in Europe for two-wheelers (mopeds, motorcycles) and transitively for PLEV class M3 in the EU. Test procedure:

• Headlamp mounted 25 m before a test screen at standard height h (typically 1.2 m for two-wheelers).
• Photometric zones are marked on the screen.
• A photometer with a 65 mm aperture traverses the grid.

Point	Description	Intensity requirement
B50L	50 m ahead, 0.57° left	max 0.4 lx (minimum glare to oncoming)
75R	75 m ahead, 1.09° right, 0.57° down	min 12 lx (road illumination in the comfortable-visibility zone)
HV	Horizontal-vertical intersection	min 0.7 cd + max 0.7 cd above cut-off
50V	50 m ahead, on vertical axis, 0.86° down	min 6 lx
25L1+25L2	25 m, ±0.52° left	min 1.5 lx (lateral visibility)
25R1+25R2	25 m, ±0.52° right	min 1.5 lx

Cut-off line — the sharp horizontal boundary between lit and unlit zones. Its quality is measured by gradient G:

G = log₁₀(E_above / E_below)

ECE R113 requires G ≥ 0.13 in the test 0.25° above/below cut-off. That means in a 0.5° span, illuminance drops by a factor of at least 1.34. A good cut-off line has G > 0.3 (3× drop). A poor one G < 0.1, i.e. a smeared beam that blinds the oncoming driver.

Asymmetric-beam geometry. A European passing beam (low beam) opens asymmetrically — in right-hand-traffic countries the beam extends further on the right (illuminating the shoulder and signage), and is trimmed lower on the left (so as not to blind oncoming traffic). In left-hand-traffic countries (UK, Japan) — mirrored. ECE R113 has two versions: «right-hand traffic» and «left-hand traffic».

What this means for a scooter. Budget LED headlamps 200–500 lm without optics are flood. Premium ones (Apollo Phantom V2 «automotive-grade», NAMI Burn-E 2 with a projector-style lens) attempt to approximate cut-off, but are not formally R113-certified (there is no such requirement for PLEV). Technically, however: a cut-off headlamp delivers 75R = 12 lx at 75 m at 25–30 km/h, which corresponds to a 9-second reaction window from detection to contact. A flood lamp of the same lumen rating gives an even 1–2 lx at 75 m — insufficient to discriminate an obstacle.

3. LED chip thermal physics: why paper 1000 lm is 600 lm after 30 minutes

An LED chip converts electrical energy into light with 30–55 % efficiency (high-power white LEDs in 2024). The remainder is heat, dissipated through the package. This is a fundamental engineering problem: the higher the current through the diode, the higher the optical power, and the higher the thermal power. Without adequate heat removal the junction temperature Tj rises — the LED loses luminous flux (lumen droop), shifts colour (chromaticity shift Duv), and degrades faster.

Thermal model as an equivalent electrical circuit. As in Ohm’s I = V / R, in thermal:

ΔT = P_th · R_θ

where P_th is thermal power in watts, R_θ is thermal resistance in K/W. The total resistance from crystal to ambient air is the sum:

R_θja = R_θjc + R_θcb + R_θba

Layer	Typical R_θ	Determined by
R_θjc (junction-to-case)	5–15 K/W	Chip architecture: silicon substrate, ceramic submount, internal die-attach
R_θcb (case-to-board)	1–5 K/W	Solder paste, PCB material (MCPCB > FR4 by 30–50× in thermal conductivity)
R_θba (board-to-ambient)	10–30 K/W	Heatsink area and design, natural vs forced convection

For a 10 W high-power LED without a heatsink (FR4 only, no metal sink): P_th = 10 × 0.6 = 6 W thermal; R_θja ≈ 50–80 K/W; ΔT = 6 × 60 = 360 °C. Clearly such a chip would burn out in minutes. With MCPCB and a passively cooled 50 cm² aluminium heatsink: R_θja ≈ 8–12 K/W; ΔT = 6 × 10 = 60 °C; Tj = 25 + 60 = 85 °C — well within the safe range (typical Tj_max = 125–150 °C for a high-power LED).

Lumen droop. LED luminous output falls with temperature approximately as:

Φᵥ(Tj) = Φᵥ(Tj_ref) · [1 − α · (Tj − Tj_ref)]

where α is the temperature coefficient (1/K), typically 0.002–0.004 for a white phosphor LED (i.e. 0.2–0.4 % loss per degree). Heating from 25 to 85 °C: Δ60 °C × 0.3 %/K = 18 % loss of lumens. So paper 1000 lm at 25 °C becomes 820 lm hot. Without a heatsink (Tj 130 °C): 1000 × (1 − 0.003 × 105) = 685 lm.

Chromaticity shift Duv. A phosphor-converted white LED creates «white» from a blue chip + a yellow phosphor (Y₃Al₅O₁₂:Ce³⁺ — YAG:Ce). The phosphor absorbs blue (450 nm) and re-emits broadband yellow (550–650 nm); the combination yields white. At high Tj > 105 °C the phosphor degrades (unevenly, because YAG:Ce has a temperature-dependent quantum yield), and the light shifts toward blue (Duv > 0 negative-direction from the Planckian locus). Visible to the naked eye as a «cooler» tint. ECE R113 + R148 set chromaticity limits per the CIE 1931 xy chromaticity diagram — white must lie in a box 0.310 < x < 0.500 and 0.300 < y < 0.440 (warm white) or 0.260 < x < 0.360 (cool white).

IES TM-21-19 + TM-28-22 — lumen-maintenance lifetime. Roughly: an LED’s life is not «burns out at once» but a gradual fall in luminous flux. Life is characterised by L70, L80, L90 — hours at which flux falls to 70 / 80 / 90 % of initial.

LM-80-08 is the IES standard for testing LEDs at 6 000 hours at several Tj (typically 55 °C, 85 °C, 105 °C). TM-21-19 is the extrapolation method from LM-80 results via an exponential law:

Φᵥ(t) = B · exp(−α · t)

where α depends on Tj through the Arrhenius equation:

α(Tj) = A · exp(−E_a / kT)

E_a is the activation energy of degradation (eV, typically 0.4–0.9 for YAG phosphor); k is the Boltzmann constant 8.617 × 10⁻⁵ eV/K; T is Tj in Kelvin. TM-21 caps extrapolation at 6× test time (so 36 000 hours from a 6 000-hour test) — further than that the forecast is unreliable.

Typical L70 for a high-power LED:

Tj	L70
55 °C	60 000+ hours (TM-21 limit 36 000)
85 °C	30 000–50 000 hours
105 °C	15 000–25 000 hours
125 °C	5 000–10 000 hours

For a scooter ridden 1 hour per day, 30 000 hours = 82 years — irrelevant. But if the headlamp is cooled only by airflow on the move, at standstill Tj can reach 110 °C, then L70 = 20 000 hours = 55 years, but L80 = 8 000–12 000 hours = 22–33 years. So a 5-year scooter is 1 800 hours — the headlamp should retain ≥ 90 % luminous output. If not, this is not a «burned-out lamp» but a poorly designed chassis thermal path.

4. Optical design: reflector, projector, TIR — three fundamental architectures

An LED chip by itself has cosine intensity distribution (Lambertian). Turning it into a useful beam requires optics.

Reflector (parabolic). The chip sits at the focus of a parabolic mirror; all light from the focus reflects parallel to the axis (formally — for a point source). A real LED chip is not a point — typically 1 × 1 mm or 1 × 3 mm. This creates finite source size, which smears the parallel beam. The beam divergence α ≈ d_chip / f (where f is parabola focal length). For f = 30 mm and d = 1 mm: α ≈ 1.9°. Enough for a headlight; not enough for a laser pointer.

A reflector is the cheapest and most efficient option (95–98 % optical efficiency for metallised aluminium), but the cut-off line is smeared. So it is used in budget headlamps and auxiliary lights.

Projector (lens with cut-off shield). A three-part architecture:

1. LED + primary optic (concentrating).
2. Cut-off shield — a physical metal blade in the focal plane of the lens, blocking the upper half of the beam.
3. Aspherical lens — focuses the beam onto the road.

The cut-off shield creates a sharp boundary — like the edge of a flashlight spot through a slit. This is the fundamental principle of «sharp light/dark transition» in automotive headlamps after the move to projector-style optics in the 1990s (BMW 7 Series 1986 — first mass-market). Optical efficiency 70–85 % (losses to shield + lens absorption + lens surfaces). Expensive, heavy, but delivers gradient G > 0.4 and clear 75R / B50L compliance.

TIR (Total Internal Reflection) lens. Architecture of a polymer lens with full internal reflection at the side surfaces. The LED is «hidden» in a small cavity; light exits through two surfaces — direct refraction through centre (a normal lens) and TIR reflection off the annular side surface. This is capturing all 180° from the chip into one collimated beam without mirror losses.

TIR lenses are usually polycarbonate (n = 1.586 at 588 nm), because PC has better thermal stability (HDT 130–140 °C) and is cheaper than PMMA. PMMA (n = 1.491) gives better optical clarity, but HDT 80–95 °C; works poorly near a hot LED.

Critical angle for TIR at the polycarbonate/air interface: sin θ_c = 1/n = 1/1.586 = 0.631 → θ_c = 39.1°. Whatever strikes the side surface at an angle > 39.1° to the normal is totally reflected. This is laid out geometrically in CAD.

Optical efficiency of a complete optical path:

η_o = Φ_out / Φ_chip

Optic type	η_o
Parabolic reflector, alum	0.90–0.95
TIR lens, polycarbonate	0.80–0.90
Projector with shield	0.70–0.85
Flood (no optic)	0.40–0.60

UV photodegradation of polycarbonate. Polycarbonate (bisphenol-A polycarbonate) contains ester linkages (carbonate groups −O−CO−O−) that undergo photolysis under UV radiation with λ < 320 nm:

E_UV = hc / λ = (6.626 × 10⁻³⁴ J·s × 3 × 10⁸ m/s) / (300 × 10⁻⁹ m) = 6.6 × 10⁻¹⁹ J = 4.1 eV

That energy exceeds the C−O ester-linkage bond energy (~3.4 eV). The result is gradual yellowing and clouding. Under direct sunlight without a UV stabiliser (Tinuvin or Cyasorb) — 5–7 years to noticeable yellowing. With UV stabiliser + acrylic-siloxane hardcoat — 15–20 years.

The transparency of a scooter headlamp after 3–5 years of use is an indicator of lens-material quality. Economy polycarbonate without stabiliser or hardcoat yellows in 2–3 years. In cheap scooters this manifests as «dimming» of the headlamp — actually the lens has become a blue-filtering attenuator (Rayleigh-like wavelength-dependent attenuation).

5. Retroreflectivity: the physics that makes passive markers 26× more effective

A diffuse reflector (white paper) reflects incident light into a hemisphere — approximately by Lambert’s law. From 1 lx of incident light only ~0.3 lx/sr returns toward the source (because power is divided across π sr). At 50 m from a driver whose headlight delivers 50 cd: illuminance on the clothing = 50 / 50² = 0.02 lx. Returned toward the headlamp = 0.02 / π = 0.006 cd/m². The driver’s eye does not see this.

A retroreflector works differently — it directs light back exactly toward the source, regardless of incidence angle (within limits). That gives a gigantic gain in the source direction at the cost of complete absence of light in other directions.

Two mechanisms of retroreflection:

(a) Glass-bead retroreflector. A glass sphere (n = 1.9–2.1 for barium titanate glass) — two refraction surfaces + one internal reflection. Light enters the front surface, focuses on the back (waves converge at a focus by paraxial optics — focal length f = R · n/(2(n−1)) = R · 0.90 for n = 2.0, approximately at the rear pole of the sphere). A mirror coat on the back reflects; on exit refraction again reverses the direction. A grid of millions of such beads (typical diameter 30–80 µm) on fabric or film is 3M Scotchlite Glass Bead (1939, 3M Corporation).

Efficiency ~30–50 % at 0° observation angle; falls sharply above 5° (because focus shifts off the back focal point). Cheap, flexible, washable.

(b) Micro-prismatic retroreflector. A trigonal pyramid (corner cube) with total internal reflection on three orthogonal faces. Incident light is reflected sequentially off three faces and exits exactly back (the law of triple reflection from three orthogonal mirrors). This is 3M Diamond Grade, Avery Dennison T-Series.

Theoretically 100 % efficiency. Works across a wider range of entrance angles (up to ±30°). More expensive, harder (polycarbonate or acrylic), washes less easily (dirt collects in micro-grooves). Road signs are micro-prismatic; high-visibility clothing — mostly glass-bead on the larger surface + prismatic patches on the highest-conspicuity zones.

Coefficient of retroreflection R_A in cd/(lx·m²) is the fundamental characteristic. Definition (CIE 54.2-2001):

R_A = I_r / (E_n · A)

where I_r is the intensity of retroreflected light; E_n is the illuminance on the surface; A is the area. Test geometry:

• Observation angle α — between source direction and observer direction (i.e. driver and his headlamp). Typical test values: 0.2°, 0.33°, 1°.
• Entrance angle β — between incidence and surface normal. Test values: ±5°, ±30°.

Material	R_A (cd/(lx·m²)) at α = 0.2°, β = 5°
White paper (diffuse)	0.01–0.1
White plastic	0.1–0.5
Glass-bead Scotchlite (EN 471 class 1)	100–300
Glass-bead Scotchlite (EN 471 class 2)	330
Glass-bead Scotchlite (EN 471 class 3)	500
Micro-prismatic 3M Diamond Grade	800–1000
Road signs (high-intensity prismatic)	1000–2500

ASTM E810-22 is the standard for measuring R_A with a portable retroreflectometer (3M, Delta, Zehntner). ASTM E811 — hand-held instruments. EN 471:2003 + EN ISO 20471:2013 is the high-visibility apparel standard, with three classes:

• Class 1 — minimum (background fabric ≥ 0.14 m², retro-material ≥ 0.1 m²).
• Class 2 — standard for workers (0.5 m² + 0.13 m²).
• Class 3 — maximum (0.8 m² + 0.2 m²).

Biomotion effect. Wood et al. (Queensland University of Technology, 2010s series) showed: the same area of retro-material on ankles, knees, wrists (where limbs move) yields 3× longer detection distance than the same area on the torso (vest). Versus fully black clothing — 26× longer. This is not optics, it’s psychophysics of recognition: moving points in the lower visual field trigger «this is a person walking/riding» in the driver’s brain, whereas static horizontal stripes on the torso read as «road sign» and are filtered out. One of the most useful conclusions for night scooter safety: not «vest» but retro-strips on ankles and knees + palms.

6. Photometric specifications for signal lamps: stop, turn, position

Stop lamp, turn signal, and position (parking) lamp are detectable devices. Their job is not to illuminate the road, but to be visible across a wide angle from a driver behind or to the side. Hence different criteria: a wide pattern (60–90° total angle), high contrast ratio, precisely specified colour.

SAE J586 — Stop Lamps for Use on Motor Vehicles Less Than 2032 mm in Overall Width. SAE is a voluntary US standard, de facto mandatory via reference in FMVSS 108 49 CFR § 571.108. Requirements:

Parameter	Value
Min central intensity	80 cd
Max central intensity	300 cd
Visibility angle	≥ 20° H × 10° V up / 5° V down
Colour	red (CIE 1931 dominant wavelength 610–660 nm)
Ramp-up time	< 100 ms

SAE J588 — Turn Signal Lamps for Use on Motor Vehicles Less Than 2032 mm in Overall Width. Front vs rear turn signals have different requirements because of different background:

Parameter	Front	Rear
Min on-axis	80 cd	50 cd
Max on-axis	700 cd	350 cd
Colour	amber (590 nm)	red or amber
Flash rate	60–120/min	60–120/min
Duty cycle	30–75 % on	30–75 % on

Front turn signals are brighter, because they compete with front headlights and daytime sun background. Rear ones — on a dark/black rear surface, so contrast is already high.

ECE R6 — Direction Indicators for Power-Driven Vehicles and Their Trailers. European analog to J588 with categories 1, 1a, 1b (front 175–700 cd), 2 (rear 50–500 cd), 2a (offset 0.3–28.5 cd). Polar-angle variation: ECE allows a wider vertical sector (15° H × 15° V).

ECE R7 — Position, Stop, End-Outline Lamps. Combined standard for parking, stop and end-outline lamps. Position lamp colour — red rear, white front (for cars), red rear (for two-wheelers — bicycle, motorcycle). Stop — red, 60 cd min on-axis, 18 cd at ±45°. End-outline — 4 cd min.

IEC 60809:2015 — Lamps for Road Vehicles. Technical standard for the lamps themselves (not for full lighting systems). Defines electrical characteristics, geometric tolerances, fail-safe requirements for filament + LED retrofit. The 60–120/min ±5 % flash rate originates here.

What this means for a scooter. Most scooters are not certified to SAE / ECE — even the premium ones (Apollo Phantom, NAMI). This does not mean «bad signalling», it means engineering is left to in-house judgement. The result is wide spread: NAMI Burn-E 2 stop lamp — 80–120 cd (meeting J586 minimum), Xiaomi M365 stop lamp — < 30 cd (failing any standard, though visually noticeable at close range). Budget turn signals are often < 50 cd and invisible by day. This is an engineering defect, not a «no-brand» feature.

7. Audible signaling: dB(A), frequency spectrum, EN 17128 § 5.6

The audible signal (horn, bell) is a different signalling axis but is regulated in the same document (EN 17128 § 5.6 for PLEV). Engineering physics:

Sound pressure level Lp in dB(A). A logarithmic scale with a reference:

Lp = 20 · log₁₀(p / p_ref)

where p_ref = 20 µPa (threshold of human hearing at 1 kHz). A sound wave of amplitude 0.2 Pa = 80 dB (a standard car horn). 6.3 Pa = 110 dB (police siren up close). Higher means more audible, but above 120 dB is the pain threshold.

A-weighting curve. A correction that maps physical SPL to human-ear perception. Logarithmically attenuates low (< 500 Hz) and high (> 5 kHz) frequencies. Based on equal-loudness contours from Fletcher-Munson 1933, updated by Robinson-Dadson 1956, finalised in ISO 226:2023 Acoustics — Normal equal-loudness-level contours.

Fundamentally: 100 dB at 50 Hz and 100 dB at 2 kHz sound completely different in loudness. A-weighting normalises, turning physical level into a «subjective» one that correlates well with loudness up to ~80 dB.

EN 17128:2020 § 5.6 — Audible warning device. Requirement for PLEV:

Parameter	Value
Min level	70 dB(A) @ 2 m
Spectral peak	1–4 kHz (zone of peak human-ear sensitivity)
Press duration to full sound	≥ 1 s
Activation	mechanical (button/lever), not voice control

70 dB is approximately a loud vacuum cleaner or mid-range hairdryer. Enough to warn a pedestrian at 5–10 m, but not enough for a deaf passenger with headphones.

Piezo speaker — the commonest architecture of an e-scooter’s electronic horn. Built from a ceramic disc (PZT — lead zirconate titanate, or lead-free analogue BaTiO₃) on a metal disc. Under AC voltage the disc bends, generating a sound wave.

Resonant frequency f_r of a piezo speaker — the frequency where the element gives maximum acoustic output for minimum electrical input. Described by an RLC equivalent circuit with resonance:

f_r = 1 / (2π · √(L·C))

where L is equivalent inductance (mechanical mass), C is equivalent capacitance (mechanical piezo-electric compliance). For a typical 20 mm piezo buzzer — f_r = 2.5–4 kHz. This is a favourable range: matches the A-weighting peak and the peak sensitivity of the human ear (~2–4 kHz).

Mechanical bell vs electronic horn. A classical bicycle bell (Knog Oi, Spurcycle) — a cast-steel resonator that emits 80–95 dB on impact. Spectrum — broadband (200 Hz to 5 kHz) with several peaks. Advantage — passive (no battery), failure mode — resonator corrosion. Electronic — active (needs charge), failure mode — electronic fault. Both are acceptable for PLEV if they hit 70 dB.

8. Pain on the road: engineering ↔ symptom matrix

Engineering theory is verified at the point where the rider notices something is wrong. The most frequent symptoms and their engineering causes:

Symptom	Engineering cause	Subsystem
Headlamp dims after 30 min of use	Tj > 100 °C from a weak heatsink → lumen droop	LED thermal
Headlamp colour shifts white → blue	Phosphor degradation at Tj > 105 °C → Duv shift	LED thermal
Beam has a «smeared» upper boundary	Low-quality optics, no cut-off shield	Optics
Headlamp yellows in 2–3 years	Polycarbonate UV degradation without stabiliser/hardcoat	Lens material
Turn signal nearly invisible by day	Intensity < 80 cd (below SAE J588 minimum)	Photometric design
Stop lamp doesn’t «pop» (slow ramp)	Driver electronic delay > 100 ms	LED driver
Retroreflector «dead» — no light return	Soiling / UV-damaged / mechanical damage	Retroreflector cleanliness
Horn quieter than background	Piezo speaker resonance detuned or < 70 dB design	Audio acoustics
Turn signal flashes at wrong rate	Flash rate outside 60–120/min window	Controller logic
Cut-off line «blinds oncoming»	B50L > 0.4 lx — headlamp not R113-certified	Beam shaping
Headlamp dims in cold (winter)	Battery cold-temperature voltage drop → driver under-volts	Power supply chain

Each of these symptoms has a concrete engineering remedy; none is solved by «buy a more expensive flashlight».

9. Standards: full comparison matrix across 14 documents

Lighting and signalling are among the most regulated areas of road transport, with parallel USA / ECE / EU / national systems. PLEV (Personal Light Electric Vehicles) is a recent category, partially covered by adapting existing standards.

Standard	Jurisdiction	Scope	Key requirements for a scooter
IEC 60809:2015 + amendments	Global (IEC)	Lamps for road vehicles	Electrical specs, geometric tolerances, fail-safe, flash rate 60–120/min ±5 %
SAE J583	USA	Front Fog Lamp	Wide-beam side lamp, max intensity 12 000 cd
SAE J586	USA	Stop Lamps	80 cd min on-axis / 300 cd max, ramp < 100 ms
SAE J588	USA	Turn Signal Lamps	Front 80–700 cd / rear 50–350 cd, 60–120/min flash, 30–75 % duty
ECE R113 Rev 3:2014	UNECE 1958 (≈ 60 countries)	Symmetrical passing beam	Photometric zones B50L 0.4 lx max / 75R 12 lx min / HV 0.7 cd / gradient G ≥ 0.13
ECE R148:2023	UNECE 1958	Consolidated signal lamps	Unifies R6 + R7 + R23 + R38 + R50 + R77 + R87 + R91 in one document
ECE R149:2023	UNECE 1958	Consolidated road illumination	Unifies R8 + R19 + R20 + R31 + R37 + R98 + R99 + R112 + R113 + R123
ECE R6	UNECE 1958	Direction Indicators	Front 175–700 cd, rear 50–500 cd, 60–120/min
ECE R7	UNECE 1958	Position+Stop+End-Outline	Stop 60 cd center, 18 cd at ±45°
EN 17128:2020 § 5.5 + § 5.6	EU (CEN)	PLEV — Personal Light Electric Vehicles	§ 5.5 reflectors front+side+rear mandatory, § 5.6 audible 70 dB(A) @ 2 m
FMVSS 108 49 CFR § 571.108	USA Federal	Lamps, Reflective Devices, and Associated Equipment	References SAE J586/J588/J583; reflectors per SAE J594
StVZO § 67	Germany (BMV)	Road Traffic Licensing Regulations	Mandatory front white headlamp + rear red taillight + reflector for bicycles + PLEV
eKFV § 5	Germany	Elektrokleinstfahrzeuge	E-scooter specific — § 5 Abs. 1 lights, § 5 Abs. 2 bell, integrated taillight + reflector allowed
CIE 54.2-2001	Global (CIE)	Retroreflection — Definition and Specification	R_A coefficient in cd/(lx·m²), observation angles α = 0.2°/0.33°/1°, entrance β = ±5°/±30°

What this means for a buyer. No mass-market scooter has full compliance with all standards at once. Apollo Phantom, NAMI, Dualtron Storm have evidence of EN 17128 § 5.5 + 5.6 conformity (reflectors + bell), often without formal R113 (cut-off line). Budget Xiaomi, NIU, Segway — mainly only eKFV § 5 minimum (headlamp + taillight). Cheap no-name models — without any formal documentation. A serious quality indicator is the presence of an e-Mark on the headlamp housing (evidence of R113 / R148 compliance) or DOT (for FMVSS 108). This is not marketing — it is a jurisdictional gateway.

10. Synthesis: lighting as active prevention, not a passive accessory

Seven engineering subsystems have now been covered in the series of deep-dives: protective gear (helmet — passive impact absorber after contact), battery (energy source), brake (reactive dissipation of kinetic energy after the rider sees the danger), motor (conversion of electrical to kinetic), suspension (vibration isolation), tire (road contact), and now lighting (preventive signalling system before contact).

A helmet is effective within a 0.1-second window after impact. A brake is effective within a 1–3-second window after a threat is detected. Lighting is effective in a window before danger becomes actionable — by virtue of another road user noticing the rider 200–300 metres ahead and having time to adjust trajectory or speed. That is a fundamental difference in action horizon: helmet — reactive; brake — reactive; lighting — proactive.

The engineering quality of lighting reduces to five parameters worth checking when choosing a vehicle and interpreting correctly from a spec sheet:

1. Headlamp lumens are total power, not brightness. The buyer should ask the manufacturer for on-axis candela (a good ratio is 30–50 cd per 1 lm for a headlight with proper optics — a spot of 200 cd per 1000 lm is low).
2. Cut-off line quality is not written on the spec sheet, but an e-Mark or DOT stamp signals R113 / FMVSS 108 compliance.
3. LED lifetime (L70) is rarely on the spec sheet; the criterion is the presence of MCPCB + a visible heatsink and the headlamp not being buried in a dust-collecting chassis cavity (where Tj rises).
4. Retroreflector class on the scooter — formally EN 17128 § 5.5 requires a reflector of minimum R_A, but without explicit class.
5. Audible level is rarely on the spec sheet (typical wording: «horn / bell»); test subjectively — at 2 m it must be «unambiguously audible».

This is the complete cycle of engineering axes of the subsystems — the scooter as an integrated system of prevention (lighting), control (motor + brake + suspension + tires), protection (helmet), and energy (battery). It works as a chain; the weakest link sets the overall reliability.

8-point recap

1. Photometry is radiometry weighted by CIE 1924 V(λ) photopic and 1951 V’(λ) scotopic functions with K_m = 683 lm/W peak sensitivity at 555 nm; inverse-square E = I / d² for a point source; Lambertian I = I_0 · cosθ for a diffuse one.
2. Lumens vs candela vs lux vs cd/m² — total power vs directional intensity vs surface illuminance vs perceived brightness; a 1000 lm flashlight without optics delivers a meagre 1–2 lx at 20 m.
3. ECE R113 photometric zones — B50L 0.4 lx max (oncoming glare), 75R 12 lx min (road visibility), HV 0.7 cd, cut-off gradient G ≥ 0.13 by G = log₁₀(E_above / E_below).
4. LED thermal physics: Tj = Ta + P_th · R_θja with R_θjc 5–15 K/W + R_θcb 1–5 + R_θba 10–30; lumen droop 0.2–0.4 %/K → 18 % loss at ΔT 60 °C; IES TM-21 L70 lifetime via Arrhenius exp(−E_a/kT) — typical L70 = 30 000–50 000 hours at Tj 85 °C.
5. Optical efficiency η_o: parabolic reflector 90–95 % > polycarbonate TIR 80–90 % > projector with shield 70–85 % > flood 40–60 %; polycarbonate UV photodegradation via E_UV = 4.1 eV at 300 nm > C−O ester bond 3.4 eV → 5–7 years to yellowing.
6. Retroreflectivity: R_A coefficient in cd/(lx·m²) per CIE 54.2-2001 with α (observation) and β (entrance) geometry; glass-bead 100–500 vs micro-prismatic 800–1000+; the biomotion effect (Wood et al.) — retro-strips on ankle/knee/wrist are 3× more effective than a vest.
7. Signal lamps: SAE J586 stop 80–300 cd / J588 turn 80–700 cd front, 50–350 cd rear / ECE R6 direction 175–700 cd front, 50–500 cd rear / IEC 60809 flash rate 60–120/min; audible EN 17128 § 5.6 ≥ 70 dB(A) @ 2 m spectral peak 1–4 kHz.
8. Standards: IEC 60809 / SAE J583+J586+J588 / ECE R113+R148+R149+R6+R7 / EN 17128 § 5.5+5.6 / FMVSS 108 / StVZO § 67 / eKFV § 5 / CIE 54.2 / EN 471+EN ISO 20471 / EN 13356 — a complete matrix of 14 documents; e-Mark and DOT stamps on the housing are the quickest indicator of compliance.

A lamp on a scooter is not an accessory; it is active prevention, working in the window before contact and defined not by marketing «lm» but by concrete engineering parameters of cd-distribution, chip thermals, and optics quality.

Related topics

• Lights and signalling on an e-scooter (device-type overview and regulatory minimum) — prerequisite to this deep-dive: device types (300–2000 lm headlamp, taillight, brake light, turn signals, reflectors), eKFV § 5 and EN 17128 §5.5 baseline; this article is the physics behind those specifications.
• Night riding on an e-scooter: visibility, dark adaptation, biomotion — behavioural side of visibility (20–30 min retinal adaptation, biomotion configuration on ankles/knees/wrists, conspicuous clothing); ties to §5 here (R_A and glass-bead vs micro-prismatic) and §1 (V(λ) vs V’(λ) — why a 555 nm headlamp is brighter by day and 507 nm at night).
• Fog and reduced visibility: distance keeping and speed choice — fog attenuation as the reverse problem to §2 photometric zones: when the B50L 0,4 lx oncoming-glare cap is no longer relevant because the fog itself is a diffuse scatterer.
• Helmet and protective-gear engineering (impact attenuation) — pair with §10 here («helmet 0,1 s after impact vs lighting in the window before contact»); reciprocal axis in the chain prevention → control → protection.
• Lithium-ion battery engineering + BMS + thermal runaway — energy source for the LED driver; §8 cold-temperature voltage drop in the diagnostic matrix here directly triggers «headlamp dims in the cold».
• Brake-system engineering + eABS + DOT 5.1 — pair with §6 photometric specs (stop-lamp ramp-up < 100 ms): brake actuation triggers the driver, which must hit the SAE J586 timing budget.
• Motor and controller engineering + BLDC/PMSM + FOC — the controller emits PWM, which couples EMI shoot-through into the LED-driver branch; §3 LED thermals here parallels §4 thermal management in the motor deep-dive.
• Tire engineering + Crr + Pacejka + grip standards — pair with §10 synthesis here: tyre as contact, lighting as prevention; both are pre-failure axes in the crash-causation chain.
• Suspension engineering + sprung/unsprung mass + damper — another pre-failure axis (ride quality + control); §10 synthesis here lists this deep-dive as the 5th engineering axis completing the chain.
• Ingress-protection engineering (IEC 60529 + IPX5/IPX7) — headlamp/taillight on a scooter is always wet: §4 optical design here (cut-off shield seal, lens gasket) is directly an IPX4-IPX5 challenge in the sister article §6 spray-test geometry; UV-yellowing in §4 also accelerates under IPX5 wash-down cycles.
• Thermal-management engineering (heat-dissipation axis) — §3 LED thermal physics here (Rθjc + Rθcb + Rθba ladder, MCPCB vs FR4 30–50× delta) is a specific application case for the general heat-flow framework in the sister article §1–§3.
• EMC/EMI engineering (electromagnetic compatibility) — the LED-driver SMPS radiates broadband up to 30 MHz; §6 driver electronic delay in the diagnostic matrix here has its prerequisite in the EMC engineering §5–§6 (CE-mark + CISPR 25 conducted/radiated limits).
• NVH engineering (noise, vibration, harshness) — pair with §7 audible signalling here: piezo-speaker resonance at 2,5–4 kHz and A-weighting intersect NVH §5 (cabin/rider acoustic environment) and §9 (psycho-acoustic Fletcher-Munson contours, ISO 226:2023).
• Connector and wiring-harness engineering — pre-stage of the LED driver; §8 diagnostic matrix here («headlamp dims in the cold») often originates in contact-resistance growth at the XT60/JST connector, which is covered in the sister article §4 (contact wipe + retention force).
• Environmental-robustness engineering (operating envelope) — UV photodegradation of polycarbonate in §4 here is a specific instance of the general environmental-stress framework in the sister article §6 (UV exposure → polymer aging).
• Defensive riding in mixed motor traffic — lane positioning + conflict avoidance — §10 synthesis here («proactive signalling system before contact») reciprocally ties to the sister article §4–§5 (right-hook / left-cross conflict zones), where lighting + conspicuity set the detection horizon at 200–300 m.

Sources

§1. Photometry as a discipline (V(λ), V’(λ), lumen/candela/lux/cd/m², Lambertian)

• CIE (Commission Internationale de l’Éclairage). CIE 018:2019 The Basis of Physical Photometry, 3rd ed. Vienna: CIE, 2019. ISBN 978-3-902842-21-5 — formal definition of photopic V(λ) (CIE 1924, revised CIE 1988) and scotopic V’(λ) (CIE 1951), K_m = 683 lm/W maximum luminous efficacy at 555 nm.
• CIE. CIE 015:2018 Colorimetry, 4th ed. Vienna: CIE, 2018. ISBN 978-3-902842-13-0 — CIE 1931 xy chromaticity diagram for the white-region boundaries cited in §3 (warm/cool white).
• IES (Illuminating Engineering Society). The Lighting Handbook, 10th ed. ed. D. DiLaura, K. Houser, R. Mistrick, G. Steffy. New York: IES, 2011. ISBN 978-0-87995-241-9 — comprehensive treatment of photometric quantities.
• Wikipedia contributors. “Luminous efficiency function,” “Lumen (unit),” “Candela,” “Lux (unit),” “Luminance,” “Lambert’s cosine law,” “Inverse-square law.” Wikipedia — open-licence reference snapshots.

§2. Headlamp beam pattern (ECE R113, cut-off, gradient)

• UNECE. Regulation No. 113 — Uniform provisions concerning the approval of headlamps for power-driven vehicles emitting a symmetrical passing beam or a driving beam or both and equipped with filament, gas-discharge light sources or LED modules. Rev. 3, 2014 + amendments. UNECE — primary source for B50L 0,4 lx max, 75R 12 lx min, HV 0,7 cd, gradient G ≥ 0,13 requirements.
• UNECE. Regulation No. 148 — Uniform provisions concerning the approval of signalling devices. 2023 consolidated edition — supersedes R6+R7+R23+R38+R50+R77+R87+R91.
• UNECE. Regulation No. 149 — Uniform provisions concerning the approval of road illumination devices. 2023 consolidated edition — supersedes R8+R19+R20+R31+R37+R98+R99+R112+R113+R123.
• Wördenweber, B., Wallaschek, J., Boyce, P., Hoffman, D.D. Automotive Lighting and Human Vision. Berlin: Springer, 2007. ISBN 978-3-540-36696-6 — engineering reference for asymmetric passing-beam geometry and projector-vs-reflector cut-off design.
• Wikipedia contributors. “Headlamp,” “Adaptive front-lighting system.” Wikipedia.

§3. LED chip thermal physics (Rθ ladder, Tj, lumen droop, IES TM-21 / TM-28, Arrhenius)

• IES. IES TM-21-19 Projecting Long-Term Luminous, Photon, and Radiant Flux Maintenance of LED Light Sources. New York: IES, 2019 — exponential extrapolation method α(T_j) = A·exp(−E_a/kT) capped at 6× test duration.
• IES. IES TM-28-22 Projecting Long-Term Luminous Flux Maintenance of LED Lamps and Luminaires. New York: IES, 2022 — luminaire-level extension of TM-21.
• IES. IES LM-80-08 Approved Method: Measuring Lumen Maintenance of LED Light Sources. New York: IES, 2008 — primary 6 000-hour test data at 55/85/105 °C feeding TM-21.
• Arrhenius, S. “Über die Reaktionsgeschwindigkeit bei der Inversion von Rohrzucker durch Säuren.” Zeitschrift für physikalische Chemie 4 (1889): 226–248 — original kinetics rate equation k = A·exp(−E_a/RT) used for LED phosphor degradation modelling. (German-language original.)
• Schubert, E.F. Light-Emitting Diodes, 3rd ed. Cambridge: Cambridge University Press, 2018. ISBN 978-1-107-17556-0 — comprehensive treatment of LED junction thermal management, droop physics, phosphor chromaticity shift.
• DOE (U.S. Department of Energy). LED Lighting Facts: Lumen Maintenance and Life. Solid-State Lighting Program — engineering primer on L70/L80/L90 metrics.
• Wikipedia contributors. “Light-emitting diode,” “Thermal resistance,” “Phosphor,” “Junction temperature.” Wikipedia.

§4. Optical design (reflector, projector, TIR, polycarbonate UV degradation)

• Wikipedia contributors. “Reflector (photography),” “Projector lens (automotive),” “Total internal reflection,” “Polycarbonate,” “Poly(methyl methacrylate).” Wikipedia.
• Smith, W.J. Modern Optical Engineering, 4th ed. New York: McGraw-Hill, 2007. ISBN 978-0-07-147687-4 — reference for parabolic-reflector aperture-vs-source-size analysis and aspheric projector design.
• Falicoff, W., Miñano, J.C. Nonimaging Optics. Burlington: Academic Press / Elsevier, 2005. ISBN 978-0-12-088479-9 — TIR-lens design fundamentals (critical-angle geometry, edge-ray principle).
• BMW Group press archive. “BMW 7 Series (E32) — first production projector-style headlamps, 1986.” BMW Group — historical reference cited in §4.
• Pickett, J.E. “Calculation of the efficiency of UV absorbers in polymers containing UV stabilizers.” Polymer Degradation and Stability 96(12) (2011): 2253–2265. DOI 10.1016/j.polymdegradstab.2011.09.011 — polycarbonate UV-degradation kinetics with/without HALS (Tinuvin) stabilizer.
• Diepens, M., Gijsman, P. “Photodegradation of bisphenol A polycarbonate.” Polymer Degradation and Stability 92(3) (2007): 397–406. DOI 10.1016/j.polymdegradstab.2006.11.018 — ester-linkage cleavage mechanism, yellowing index correlation with UV-A dose.

§5. Retroreflectivity (R_A, glass-bead vs micro-prismatic, biomotion)

• CIE. CIE 54.2-2001 Retroreflection — Definition and Measurement, 2nd ed. Vienna: CIE, 2001. ISBN 978-3-901906-09-3 — primary source for R_A coefficient definition in cd/(lx·m²), observation angle α (0,2°/0,33°/1°), entrance angle β (±5°/±30°).
• ASTM International. ASTM E810-22 Standard Test Method for Coefficient of Retroreflection of Retroreflective Sheeting Utilizing the Coplanar Geometry. West Conshohocken: ASTM, 2022.
• ASTM International. ASTM E811-20 Standard Practice for Measuring Colorimetric Characteristics of Retroreflectors Under Nighttime Conditions. West Conshohocken: ASTM, 2020.
• CEN. EN ISO 20471:2013 High-visibility clothing — Test methods and requirements. Brussels: CEN, 2013 (supersedes EN 471:2003) — three classes of retroreflective area requirements cited in §5 table.
• CEN. EN 13356:2001 Visibility accessories for non-professional use — Test methods and requirements. Brussels: CEN, 2001 — accessory retroreflectors (ankle bands, belt clips) for non-occupational use.
• Tyrrell, R.A., Wood, J.M., Owens, D.A., Whetsel Borzendowski, S., Stafford Sewall, A. “The conspicuity of pedestrians at night: a review.” Clinical and Experimental Optometry 99(5) (2016): 425–434. DOI 10.1111/cxo.12447 — biomotion-vest superiority over reflective-vest at equal retro-area.
• Wood, J.M., Tyrrell, R.A., Carberry, T.P. “Limitations in drivers’ ability to recognize pedestrians at night.” Human Factors 47(3) (2005): 644–653. DOI 10.1518/001872005774860019 — Queensland University of Technology series on biomotion-marking detection-distance gain (3× over vest, 26× over dark clothing) cited in §5.
• Balk, S.A., Tyrrell, R.A., Brooks, J.O., Carpenter, T.L. “Highlighting human form and motion information enhances the conspicuity of pedestrians at night.” Perception 37(8) (2008): 1276–1284. DOI 10.1068/p6017 — biomotion mechanism explanation (limb motion triggers pedestrian recognition, static torso markings read as signage).
• 3M Company. “Scotchlite Reflective Material — product history and technical data.” 3M Personal Safety Division. Glass-bead retroreflective sheeting invented 1939.
• Avery Dennison. T-Series Conformable Reflective Sheeting — Technical Data Sheet. Avery Dennison — micro-prismatic high-intensity-prismatic class data.

§6. Photometric signal lamps (SAE J586/J588, ECE R6/R7, IEC 60809)

• SAE International. SAE J586_201706 — Stop Lamps for Use on Motor Vehicles Less Than 2032 mm in Overall Width. Warrendale: SAE, 2017 — 80 cd min / 300 cd max centre intensity, < 100 ms ramp.
• SAE International. SAE J588_201306 — Turn Signal Lamps for Use on Motor Vehicles Less Than 2032 mm in Overall Width. Warrendale: SAE, 2013 — front 80–700 cd / rear 50–350 cd, 60–120/min, 30–75 % duty.
• SAE International. SAE J583_201801 — Front Fog Lamp. Warrendale: SAE, 2018.
• SAE International. SAE J594 — Reflex Reflectors. Warrendale: SAE, 2017.
• IEC. IEC 60809:2014+AMD1:2015 Lamps for road vehicles — Dimensional, electrical and luminous requirements. Geneva: IEC, 2015.
• UNECE. Regulation No. 6 — Uniform provisions concerning the approval of direction indicators. Geneva: UNECE — front 175–700 cd, rear 50–500 cd. Now consolidated into R148.
• UNECE. Regulation No. 7 — Uniform provisions concerning the approval of position, stop, end-outline lamps. Geneva: UNECE. Now consolidated into R148.

§7. Audible signalling (dB(A), A-weighting, equal-loudness, piezo)

• ISO. ISO 226:2023 Acoustics — Normal equal-loudness-level contours. 3rd ed., Geneva: ISO, 2023 — current authoritative equal-loudness contours superseding Robinson-Dadson 1956 and Fletcher-Munson 1933.
• Fletcher, H., Munson, W.A. “Loudness, its definition, measurement and calculation.” Journal of the Acoustical Society of America 5(2) (1933): 82–108. DOI 10.1121/1.1915637 — seminal equal-loudness contours referenced in §7.
• Robinson, D.W., Dadson, R.S. “A re-determination of the equal-loudness relations for pure tones.” British Journal of Applied Physics 7(5) (1956): 166–181. DOI 10.1088/0508-3443/7/5/302 — revised contours folded into ISO 226:1987 and subsequent revisions.
• IEC. IEC 61672-1:2013 Electroacoustics — Sound level meters — Part 1: Specifications. Geneva: IEC, 2013 — current authoritative definition of the A-weighting filter.
• ANSI. ANSI S1.4-2014 Specifications for Sound Level Meters. Washington: ANSI, 2014 — A-weighting specification (US harmonization).
• CEN. EN 17128:2020 Light motorized vehicles for the transportation of persons and goods and related facilities and not subject to type-approval for on-road use — Personal light electric vehicles (PLEV) — Requirements and test methods. Brussels: CEN, 2020 — §5.5 reflectors, §5.6 audible warning device ≥ 70 dB(A) @ 2 m, spectral peak 1–4 kHz.
• APC International. Piezoelectric Ceramics: Principles and Applications, 2nd ed. Mackeyville: APC International, 2011 — PZT and lead-free BaTiO₃ piezo-disc resonance modelling, RLC equivalent-circuit derivation.
• Wikipedia contributors. “A-weighting,” “Equal-loudness contour,” “Piezoelectric speaker,” “Sound pressure level.” Wikipedia.

§8. Diagnostic matrix (cross-axis failure modes)

• All entries above feed §8 — no separate primary sources required; the matrix integrates symptom→cause→subsystem mappings from §1–§7.
• IEEE. IEEE Std 1789-2015 Recommended Practices for Modulating Current in High-Brightness LEDs for Mitigating Health Risks to Viewers. New York: IEEE, 2015 — referenced for driver electronic-delay and PWM-flicker mitigation thresholds touched in §8 «stop-lamp slow ramp».

§9. Standards comparison matrix (14 documents)

• All UNECE / SAE / IEC / CEN / FMVSS / StVZO / CIE / EN ISO documents above; no new entries — the §9 matrix reorganizes the same primary sources by jurisdiction.
• U.S. National Highway Traffic Safety Administration. FMVSS 108 — Lamps, Reflective Devices, and Associated Equipment. 49 CFR § 571.108. NHTSA.
• German Federal Ministry of Transport. StVZO § 67 Lichttechnische Einrichtungen an Fahrrädern und einsitzigen Roll- und Krankenfahrstühlen mit Hilfsmotor. Bundesgesetzblatt — German Road Traffic Licensing Regulations, bicycle + PLEV lighting requirements.
• German Federal Ministry of Transport. Elektrokleinstfahrzeuge-Verordnung (eKFV) § 5. Bundesgesetzblatt — e-scooter–specific § 5 para. 1 (lights) + § 5 para. 2 (bell).

§10. Synthesis — prevention vs reaction time-window

• Olson, P.L., Sivak, M. “Perception-response time to unexpected roadway hazards.” Human Factors 28(1) (1986): 91–96. DOI 10.1177/001872088602800110 — empirical baseline for driver perception-reaction time used in §10 «brake reactive 1–3 s» argument.
• Green, M. “‘How long does it take to stop?’ Methodological analysis of driver perception-brake times.” Transportation Human Factors 2(3) (2000): 195–216. DOI 10.1207/STHF0203_1 — secondary review supporting §10 reactive-vs-proactive horizon argument.
• NHTSA. Crash Causation Survey (NMVCCS) DOT HS 811 059. Washington: NHTSA, 2008 — empirical pedestrian-conspicuity crash data underpinning §10 «proactive» framing.