The Compressive Curve Becomes the Reflex
The Compressive Curve Becomes the Reflex
Ada re-derives this chapter’s own numbers step by step, at full precision
ADA · CALCULATION AUDIT
The Compressive Curve Becomes the Reflex
A light-following Braitenberg vehicle steers on an LDR whose resistance follows R = R_ref × (E / E_ref)^-γ, with R_ref = 10 kΩ at 10 lux and γ = 0.7, fed through a 3.3 V divider. The chapter warns that near a lamp this curve compresses the vehicle’s own steering signal — 900 and 1000 lux can produce nearly the same output, leaving the vehicle indecisive. This audit asks the question that compression invites: exactly how much steering voltage does each 10× jump in light still deliver once the sensor is close to the lamp?
Companion to the chapter Braitenberg Transfer Tuning — every number here comes from that chapter.
See the relationship before changing it
The figure reads from left to right. The blue card is illuminance. The middle card applies this page's rule. The green card is divider output. Walk the arrows once: set the input, apply the rule, then read the result with its unit.
The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only illuminance, so the numeric fixture does not switch without explanation.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline is 1000 lux.
- 2
Name the relationship. R = 10 kOhm x (lux / 10)^-0.7; V = 33 / (10 + R)
- 3
Substitute with units. at 1,000 lux: R = 0.3981 kOhm and V = 3.1737 V
- 4
Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.
Predict, then change illuminance
Try Predict the direction of R = 10 kOhm x (lux / 10)^-0.7; V = 33 / (10 + R). Test another illuminance, then compare divider output.
Observe The LDR power law and divider rail compress equal light ratios into smaller voltage steps. Reset illuminance to 1000 and compare divider output.
Explain The LDR power law and divider rail compress equal light ratios into smaller voltage steps.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
Evaluate the LDR model with Rref = 10 kΩ, Eref = 10 lux, gamma = 0.7 at 10, 100, and 1000 lux, then feed each resistance into the 3.3 V divider.
The divider output moves 1.6500 V → 2.7511 V → 3.1737 V; the second tenfold light increase adds only 0.423 V versus 1.101 V for the first.
The negative power law compresses resistance at high illuminance, and the divider approaches its 3.3 V rail, so equal light ratios produce progressively smaller steering-voltage changes.
Ada: This chapter makes a strong claim – that equal 10x jumps in light produce shrinking signal steps – and it is worth carrying the power law and the divider at full precision to see exactly how much the vehicle’s reflex dulls near the lamp. The LDR follows R = R_ref x (E / E_ref)^(-gamma) with R_ref = 10 kohm at 10 lux and gamma = 0.7:
- At 100 lux:
10 kohm x (100/10)^-0.7 = 10 kohm x 10^-0.7 = 10 kohm x 0.199526 = 1.9953 kohm - At 1000 lux:
10 kohm x (1000/10)^-0.7 = 10 kohm x 100^-0.7 = 10 kohm x 0.039811 = 0.3981 kohm
Each 10x brighter step multiplies resistance by the same 0.1995, but the resistance change shrinks: 10 - 1.9953 = 8.005 kohm then 1.9953 - 0.3981 = 1.597 kohm, matching the chapter’s 8 kohm and 1.6 kohm. Now feed that into the divider Vout = 3.3 V x 10 kohm / (R_ldr + 10 kohm):
- 10 lux:
3.3 x 10 / (10 + 10) = 1.6500 V - 100 lux:
3.3 x 10 / (1.9953 + 10) = 2.7511 V - 1000 lux:
3.3 x 10 / (0.3981 + 10) = 3.1737 V
The conditioned signal steps are 2.7511 - 1.6500 = 1.101 V for the first 10x and only 3.1737 - 2.7511 = 0.423 V for the second – the chapter’s 1.10 V then 0.42 V. The design-meaningful conclusion is that the vehicle’s steering authority is not a fixed gain: the same 10x change in light delivers less than half the voltage swing once the lamp is close, so the compressive sensor curve, not any line of code, is what makes the vehicle lunge in the dark and crawl in the light.
Every number above is taken from the chapter’s own material and re-derived step by step.
Technical boundaries: This ideal static LDR-divider model leaves out sensor tolerance and lag, resistor error, ADC reference and quantisation, lamp geometry, motor deadband, wheel slip, and controller saturation.