A bicycle headlamp uses an emitter and optics to distribute light ahead of the rider. This calculator explores intensity, illuminance and distance along one direction of its beam. It does not predict road-hazard recognition or certify a safe riding speed.
Bicycle Lamp Interactive Calculator
Enter illuminance measured at a known distance, a comparison threshold and a riding speed. Explore the optical distance model and a separate, explicitly assumed stopping-distance example.
Equation Used
- Measured illuminance and test distance refer to the same direction in the beam and stable lamp output.
- The source is sufficiently distant for inverse-square behavior; the target is perpendicular to the ray.
- The threshold is user-selected, not a universal hazard-recognition threshold.
- Braking comparison assumes level motion,1.5 s reaction and constant 4 m/s² deceleration; actual conditions are not modeled.
All four inputs and numerical formulas are retained, but misleading visibility and safety labels are corrected. The animation uses a perpendicular test plane to match the inverse-square model.
What the lamp and model do
A bicycle lamp combines a light source, power supply and optics. The lens or reflector determines how intensity varies with direction. Mounting and aiming determine where those directions meet the road.
The animation shows a lamp on a bicycle and a moving measurement plane. The plane faces the light directly, matching the normal-incidence equation used by the calculator. The beam outline is illustrative and the longitudinal scale is compressed; it is not an optical ray trace or a manufacturer’s measured beam map.
Real road illumination requires the directional intensity distribution, lamp height and aim, surface geometry and incidence angle. Whether an object can be recognized also depends on contrast, reflectance, glare and the observer. A single lux value cannot establish that distance.
Using the calculator
Use this tool to understand the difference between illuminance in lux and luminous intensity in candela, or to compare measurements taken at known distances along the same beam direction. It does not compare complete lamp patterns, battery runtime, dynamo performance or regulatory compliance.
Optical distance and the separate stopping example
For normal incidence in the far field, E = I/r², so a measured Etest at rtest implies I = Etest rtest². For an entered target illuminance Etarget, the axial threshold distance is r = √(I/Etarget).
At speed v in metres per second, travel time over r is r/v. The retained stopping example is dstop = 1.5v + v²/(2 × 4), using 1.5 seconds reaction and 4 m/s² constant deceleration. The displayed distance difference is r − dstop. These assumed values do not describe every rider, surface, gradient or braking condition.
Worked example
An illustrative 100 lx measurement at 10 m gives 10,000 cd along the measured direction. With a target of 1.5 lx, the normal-incidence threshold distance is √(10,000/1.5) =81.6 m.
At 28 km/h, v =7.78 m/s. Travel time over 81.6 m is 10.5 s. The assumed stopping distance is 1.5 ×7.78 +7.78²/8 =19.2 m, giving a numerical difference of 62.4 m. This does not mean an actual road hazard will be visible 81.6 m away.
What to compare beyond one lux value
A useful lamp comparison considers beam distribution, mounting, aiming, output stability, power supply and the intended riding environment. Total luminous flux in lumens and illuminance in lux are different quantities. This one-direction model does not rank products or replace measured beam-pattern information.
Frequently asked questions
Is threshold distance the distance at which I can see a hazard?
No. It is the modeled distance at which a perpendicular detector receives the entered illuminance along one beam direction. Road lighting and object recognition require additional information.
Why does changing test distance change inferred intensity?
At the same entered illuminance, a farther measurement implies a stronger source. Measurements of the same source should approximately follow the inverse-square relation in the far field.
Does a positive distance difference prove I can stop safely?
No. It compares the optical model with a stopping calculation using fixed assumptions. Neither real visibility nor actual braking is established.
Does speed change the lamp brightness?
Not in this model. Speed affects travel time and the assumed stopping distance. Electrical behavior of a dynamo or battery lamp is not simulated.
References
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