By Chris Juden
Tuesday, 9 September 2014Watts, Lumens, Candles and Lux
The marketing of bike lights bamboozles us with watts, lumens, candela and lux, but doesn’t explain what they mean. Even when you do know, it doesn’t help much because they each measure different things. But it helps a bit, and with some simple maths, comparisons are possible.
Watts
Watts are how much electrical power the lamp consumes. If all lights were equally efficient that might be useful to know, but they aren’t, so it isn’t. What matters is how much visible light is produced, and that’s measured in lumens. I said it isn’t useful to know the watts. I lied. It is useful to know if a dynamo lamp is compatible with a generator and slightly interesting to know how much electricity a battery lamp consumes.
Lumens
You could measure light energy also in watts and express the efficiency of a lamp as a simple percentage, but the human eye isn’t equally sensitive to all wavelengths, i.e. colours of light. As an animal active in daylight, we’ve evolved to do best with what the sun produces most of. The SI unit lumen (lm) takes account of that with a kind of points system: awarding a maximum of 683 lumens per watt, for light in the middle of the rainbow (i.e. green) and lower values for colours either side, tapering off to zero for the infra-red and ultra-violet light we cannot see at all. Read more about that here: Carbon Lighthouse - Portfolio Income for CRE.
Efficacy
For light to appear neutral, we need to mix some of the less effective blue and red light in with top-value green, so the best that a white light can possibly be… err, well that kind of depends on how truly white you want it! Expert opinions differ, but the LED industry is aiming for 250 lm/w, with 300 or so the likely theoretical limit.
The current state of the art is 150 lm/w, ten times better than 15 lm/w we got from a halogen bulb. The lamp as a whole is never quite as good as that however, because an LED needs some additional electronic circuitry to drive it, which also takes some power, making the best LED perhaps eight times brighter for the same power input.
Of course that’s only the best LED. There are a lot of lesser LEDs on the market, some perhaps not much better than a halogen bulb. Buyer beware. See my blog on the legality of bike lights for more detail.
A dark-adjusted eye
Having said the human eye is most sensitive to green, that’s only true in good light. When things get dark, more sensitive rods take over from cones. But we have only have one type of rod cell, so these cannot differentiate between colours. Rods are nevertheless more sensitive to some wavelengths than others and peak (at the equivalent of 1700 lm/W) in the blue-green part of the spectrum. I guess rod cells evolved that way because moonlight is also biased towards blue, but now I really am guessing! Anyway: blue light gives more bang for your lighting buck in generally dark conditions, so modern headlights, for bikes as well as cars, often have a blue tinge.
Ideally we should use a different ‘scotopic’ definition of the lumen for low-level lighting, that gives more ‘points’ for blue and even less for red, so as to give these light due credit for their greater actual efficacy. If the light is bright enough however, there should be large parts of the scene that are sufficiently illuminated to get the cones working too. So conventional photopic lumens will do.
The reason a red light nevertheless looks red in the dark is that it’s putting out light of sufficient intensity to fire up a few of the observer’s red cones, and the contrast with the generally monochrome rod-powered scene makes it really stand out.
You may be wondering what happens to those super-efficient rods in daylight. The reason everything doesn’t look blue then, is that daylight is too much for the rod cells. They saturate. In daylight every single rod in the retina is sending the same maximum level of signal to the brain, which can’t make any sense of that and sensibly ignores it, concentrating instead upon the more interesting differences between different cones.
How much brighter really?
Here’s another curious thing about human perception: an eight times brighter thing does not look eight times brighter. Experts disagree (again) as to whether it’s a cube or a square-root relationship, so all we can say is that an eight times brighter thing will actually appear between two and three times brighter. But two or three times brighter is still a lot. It follows that when we do eventually get a 300 lm/w LED, although twice as bright it’ll only look about 30% brighter than the present state or the art. So wait if you like, but now is not a bad time to buy a new light.
There are two sides to the levelling effect of human perception. On the one hand it takes a huge increase in power or efficiency to make a small improvement in apparent brightness. But on the other hand, you can turn a lamp down to half power and experience only a 25 percent-ish reduction!
Be aware of this when buying lights and don’t be too impressed by big numbers. The ‘inferior’ lamp isn’t really all that different. But if it’s half the price, it will actually cost only half as much money!
Another reason not to be impressed by numbers of lumens is they’re only a manufacturer’s claim, and those claims are hard to test. Sometimes the number quoted comes straight from the LED supplier’s datasheet. There is no guarantee that the lamp in question drives this LED optimally. If it runs hot it’ll not only fail prematurely, but also yield less light. Or perhaps to avoid failure, a manufacturer might under-run the LED, which also results in below-specification output.
Let us give this lamp the benefit of the doubt and assume the LED does yield all those lumens. They are still no use until they escape the lamp; and quite a lot will be reflected and absorbed by the enclosure or in passing through the lens, so it’s anyone’s guess how many come out of the front. It’s only fair to say however, that LEDs lose less by internal reflection than sources which emit light in all directions, such as bulbs and HID (gas discharge) lamps, e.g. 20% versus 40% losses. But lamps vary. A glass lens for example, absorbs less and transmits more than even the best optical plastic.
Candles
Although we don’t really know how many of those lumens emerge from the lamp, it’s nevertheless interesting to know how they relate to the other ways of measuring emitted light. The traditional way of describing the apparent brightness of a lamp is by comparison with a candle. That’s been standardised in the SI unit of light intensity: Candela (cd). One candela is defined as an intensity of one lumen per steradian .
Q: But what the heck is a steradian!? A: It’s a stereo radian, a way of measuring angles in three dimensions. Whereas your regular two-dimensional angle
measures the spread between two lines, starting from a point, a solid angle measures the wideness of a funnel. One steradian is a funnel so wide that the area of its mouth (measured in a spherically curved way) equals the funnel side squared. A more usual way of measuring funnels, or the cone of light produced by a lamp, is the simple angle between opposite sides. It’s hard maths to translate between the two, but I can tell you that one steradian is a 66° funnel, and for anything narrower than this the solid angle is near enough equal to degrees squared, divided by 4200 .
The surface area of a whole sphere is 4πr2. So the biggest solid angle you can possibly have is 4π = 12.6 steradians. And since a candle emits light in all directions, it follows that the standard candle, emitting light of 1 cd intensity, that is 1 lumen per steradian, emits a total of 12.6 lumens .
But we don’t want our bike lamp to emit light in all directions, we want to gather and focus those lumens and send them in a specific direction. Assuming none are absorbed (unlikely) in the mirrors and lenses required to focus light into a one steradian, i.e. 66° cone, the intensity equals the number of available lumens and our standard candle thus produces 12.6cd. Focus that light in a narrower cone and it becomes more intense. In a 32° cone it’ll be four times as bright (50cd) and if concentrated into only 6.5° each lumen makes 100 candela (i.e. 1,260cd from our standard candle).
Approximately, for small angles: candela = lumens × 4200/(cone-angle squared) . For an exact formula and a longer explanation see Candela, Lumen, Lux: the equations.
Lux and distance
Everyone knows that if you want to see things further away, you need a more powerful torch. That’s because light (except laser light) spreads out according to an ‘inverse-square law’. That sounds technical but is really quite obvious, that in twice the distance the same amount of light has to cover four times the area, so the illumination is one quarter as good. Illumination of a surface is measured in lumens per square metre, or lux for short. Perhaps you’re beginning to see why candela intensity is measured in lumens per steradian, a solid angle which relates area to distance, since that makes all the other sums much easier. Thus illumination in lux equals the intensity of light in candela, divided by the distance squared from the source of that light. Put simply: Lux = Candela divided by metres squared .
To know how brightly a lamp illuminates something, in lux, you must also know how far away that something is. So it seems nonsensical to speak of a 50lux lamp. At what distance? You will nevertheless find bicycle headlamps, usually dynamo headlamps, described in those terms. That’s because the same firms make headlamps for motor vehicles, which are tested in lux against a screen at a defined distance of 25m from the vehicle. Everyone in the business knows that, so nobody mentions the 25 metres. So 1 lux equals 625cd right? Wrong. Actually, it is right for car headlamps, but bicycle headlamps, as everyone in the business knows… are conventionally tested against a screen only 10m away. So 1 lux for a bike lamp equals only 100cd.
To remove that confusion and facilitate comparisons, you can always convert lux into candela: multiply by 100 for bike lamps, or 625 for motor vehicle lamps .
Light distribution
To put some rough and ready numbers on all of that: a dynamo headlamp is 2.4W, so given a state-of-the-art LED (150 lm/W) we might get 360 lumens. Knock off a third for electrical and optical losses and that’s 240lm emitted. Focussed in a 20° cone, that amount of light has an intensity of 2500 candela, which at 10m provides 25lux illumination.
A simple, diffuse cone of light, of about 20 degrees, is exactly what you get from some bike lamps, many of which are little better than a torch with added bike mount. There’s worse things: a diffuse light may be just what you want for nocturnal exploration of the local woods by mountain-bike, but not so good when you want to go faster on unknown unlit roads. Remember that inverse square law? In order to see far into the distance you need light of great intensity, but if you shine the same intensity of light on nearby surfaces they’ll be illuminated so much more brightly that your eye will adjust to that and be disabled from seeing far ahead.
To see distant and closer surfaces equally well, you want to illuminate them similarly, with about the same number of lumens per square metre, i.e. lux. To do that you must send much more intense light into the far distance and much less intense light onto nearby surfaces, with a smooth graduation between these extremes. And the intense central spot must be flattened and spread into an oval that tapers off to the sides also. Above the beam centre the light can cut right down. Any lamp capable of lighting the road ahead will always scatter enough random light from the front of its lens to show other road users where you are, without even trying. Opposite is an example of a well graduated beam for road use, artificially coloured to denote intensity, against a 5º grid.
Secção 67 do StVZO, parte do Código da Estrada Alemão relativo à iluminação em bicicletas.
Partilho, porque há muitas luzes e dínamos, que mesmo vendidos noutros países, é tida em conta a norma alemã quando são produzidos.
E aqui vai uma tradução à Google do conteúdo:
Mais info:
Penso que a Portaria n.º 311-B/2005 https://dre.pt/dre/detalhe/portaria/311-b-2005-383016 será a legislação mais actual sobre iluminação de velocípedes. Abaixo transcrevo-a.
Portaria n.º 311-B/2005
Publicação: Diário da República n.º 59/2005, 2º Suplemento, Série I-B de 2005-03-24, páginas 9 - 10
Emissor: Ministério da Administração Interna
Data de Publicação: 2005-03-24
ELI: https://data.dre.pt/eli/port/311-b/2005/3/24/p/dre/pt/html
Versão pdf: Descarregar
SUMÁRIO
Define os sistemas de sinalização luminosa, bem como os reflectores dos velocípedes, quando circulem na via pública, com excepção da circulação no âmbito de provas desportivas devidamente autorizadas
TEXTO
Portaria n.º 311-B/2005
de 24 de Março
O n.º 3 do artigo 93.º do Código da Estrada, aprovado pelo Decreto-Lei n.º 114/94, de 3 de Maio, na redacção conferida pelo Decreto-Lei n.º 44/2005, de 23 de Fevereiro, prevê que a circulação de velocípedes esteja condicionada à utilização dos dispositivos de sinalização luminosa, a fixar em regulamento, sempre que seja obrigatório o uso de dispositivos de iluminação nos restantes veículos.
Considerando a necessidade de promover a segurança rodoviária dos utilizadores destes veículos, medida considerada prioritária no Plano Nacional de Prevenção Rodoviária, define-se, no presente diploma, os sistemas de sinalização luminosa bem como os reflectores cujo uso é obrigatório nos velocípedes destinados a circular na via pública.
Assim:
Manda o Governo, pelo Ministro de Estado e da Administração Interna, nos termos conjugados da alínea b) do n.º 2 do artigo 4.º do Decreto-Lei n.º 44/2005, de 23 de Fevereiro, e do n.º 3 do artigo 93.º do Código da Estrada, aprovado pelo Decreto-Lei n.º 114/94, de 23 de Maio, na última redacção conferida, o seguinte:
1.º O presente diploma aplica-se aos dispositivos de sinalização luminosa e reflectores dos velocípedes, quando circulem na via pública, com excepção da circulação no âmbito de provas desportivas devidamente autorizadas.
2.º Os velocípedes referidos no número anterior, quando circulem na via pública nas condições a que refere o n.º 3 do artigo 93.º do Código da Estrada, devem dispor, à frente e à retaguarda, de luzes de presença que obedeçam às características fixadas no presente regulamento.
3.º Sem prejuízo do disposto no número anterior, com a finalidade de assinalarem a sua presença, todos os velocípedes devem dispor de reflectores, à frente e à retaguarda, que respeitem as características fixadas neste regulamento.
4.º O uso dos dispositivos referidos no n.º 2.º é obrigatório, desde o anoitecer até ao amanhecer e sempre que as condições meteorológicas ou ambientais tornem a visibilidade insuficiente.
5.º A luz de presença da frente deve ter as seguintes características:
a) Número: uma;
b) Cor: branca;
c) Posicionamento:
i) Em largura: deve estar situada no plano longitudinal médio do veículo;
ii) Em comprimento: deve estar colocada na zona frontal do veículo;
iii) Em altura: deve estar colocada a uma altura do solo compreendida entre 350 mm e 1500 mm;
d) Intensidade: feixe luminoso contínuo tal que a luz seja visível de noite e por tempo claro a uma distância mínima de 100 m;
e) Orientação: para a frente.
6.º A luz de presença da retaguarda deve ter as seguintes características:
a) Número: uma;
b) Cor: vermelha;
c) Posicionamento:
i) Em largura: deve estar situada no plano longitudinal médio do veículo;
ii) Em cumprimento: deve estar colocada à retaguarda do veículo;
iii) Em altura: deve estar colocada a uma altura do solo compreendida entre 350 mm e 1200 mm;
d) Intensidade: feixe luminoso tal que a luz seja visível de noite e por tempo claro a uma distância mínima de 100 m;
e) Orientação: para a retaguarda.
7.º A luz referida no número anterior pode ser emitida continuamente ou apresentar emissão intermitente com frequência regular.
8.º O reflector da frente dos velocípedes deve ter as seguintes características:
a) Número: um, sem prejuízo do disposto no n.º 5.º;
b) Cor: branca;
c) Posicionamento:
i) Em largura: deve estar situado no plano longitudinal médio do veículo;
ii) Em comprimento: deve estar colocado na zona frontal do veículo;
iii) Em altura: deve estar colocado a uma altura do solo compreendida entre 350 mm e 1500 mm;
d) Orientação: para a frente.
9.º Para além do reflector referido no número anterior, os velocípedes devem possuir à retaguarda, no mínimo, um reflector com as seguintes características:
a) Cor: vermelha;
b) Posicionamento:
i) Em largura: deve estar situado no plano longitudinal médio do veículo;
ii) Em comprimento: deve estar colocado à retaguarda do veículo;
iii) Em altura: deve estar colocado a uma altura do solo compreendida entre 350 mm e 1200 mm;
c) Orientação: para a retaguarda.
10.º Em complemento do reflector referido no número anterior, é autorizada a instalação de um reflector adicional, colocado do lado esquerdo, delimitando a largura máxima do veículo.
11.º Os veículos devem ainda possuir, nas rodas, reflectores com as seguintes características:
a) Número mínimo em cada roda: dois se forem circulares ou segmentos de coroa circular ou apenas um se for um cabo reflector em circunferência completa;
b) Cor: âmbar, excepto se for um cabo reflector, caso em que pode ser branca;
c) Posicionamento: colocados na jante simetricamente em relação ao eixo da roda, excepto se for um cabo reflector, devendo então ser colocado entre os raios da jante, circunferencialmente, com o maior diâmetro possível;
d) Orientação: para o exterior, com a superfície reflectora paralela ao plano longitudinal médio do veículo.
12.º Os velocípedes de três ou quatro rodas com largura superior a 1200 mm devem dispor, à frente e à retaguarda, de reflectores que obedeçam às características e se encontrem colocados de acordo com o estabelecido nos n.os 8.º e 9.º do presente diploma, salvo no que se refere à colocação em largura, em que os reflectores devem estar colocados o mais próximo possível das extremidades do veículo.
13.º Podem ser utilizados dispositivos de sinalização luminosa ou reflectores que correspondam a modelo aprovado num Estado membro da União Europeia, desde que apresentem a correspondente marca de aprovação.
14.º Sempre que as disposições relativas à instalação dos dispostivos de sinalização luminosa ou dos reflectores se mostrem incompatíveis com as características dos veículos, a Direcção-Geral de Viação pode aprovar soluções causuísticas que se mostrem adequadas.
15.º O presente diploma entra em vigor 90 dias após a publicação.
O Ministro de Estado e da Administração Interna, António Luís Santos Costa, em 21 de Março de 2005.
Versão print-friendly duas colunas PDF: https://files.dre.pt/1s/2005/03/059b02/00090010.pdf