Summary
The 132 in the smoke density formula is the part that never quite sticks.
D_s = 132 \log_{10}\!\left(\frac{100}{T}\right)
It is not a physical constant of smoke. It is three chamber dimensions divided into each other.
132 \approx \frac{18}{0.0456 \times 3}
Chamber volume, divided by specimen exposed area, divided by light path length. Remember that one line and you never have to memorize 132 again.
How do you turn smoke into a number?
Soot and fine particles in smoke absorb and scatter light, so the denser the smoke, the less light reaches the detector.
Measure how much it dropped and you have an optical measure of smoke. Two quantities come out of that.
- Transmittance T — what percentage of light got through
- Optical density D — how much attenuation that represents
They are not the same thing. One is a ratio; the other is the logarithm of that ratio.
D = \log_{10}\!\left(\frac{100}{T}\right)
| Transmittance T | Optical density D |
|---|---|
| 100% | 0 |
| 50% | about 0.301 |
| 10% | 1 |
| 1% | 2 |
Transmittance down, optical density up.
Why a logarithm at all
Light lost to smoke does not fall off in fixed steps. It falls off exponentially, because photons keep meeting more particles along the way.
That is the Lambert-Beer relation.
I = I_0\, e^{-KL}
K is the attenuation coefficient and L is the distance the light travels through smoke. To work with an exponential decay, taking a logarithm is the natural move, and rearranging gives the optical density above.
The log is there because the physics is exponential, not because it makes arithmetic tidy.
But D alone cannot compare materials
The same quantity of smoke gives different readings under different conditions.
- A small chamber concentrates it; a large chamber dilutes it
- A longer light path attenuates more at the same concentration
- A larger specimen produces more smoke to begin with
So the reading has to be normalized to the apparatus. That normalized value is the specific optical density, Ds.
D_s = \frac{V}{A \times L}\, D
V is chamber volume, A is exposed specimen area, L is light path length. That fraction is the geometric factor G.
And there is the 132
The NBS smoke density chamber used by ASTM E662 has fixed dimensions.
| Symbol | Meaning | Value |
|---|---|---|
| V | Chamber volume | 18 ft³ |
| A | Exposed specimen area | 0.0456 ft² |
| L | Light path length | 3 ft |
Substitute and divide.
G = \frac{V}{A \times L} = \frac{18}{0.0456 \times 3} = \frac{18}{0.1368} = 131.58 \approx 132
So in E662, Ds = 132D, and putting the log expression back in gives the formula everyone memorizes.
D_s = 132 \log_{10}\!\left(\frac{100}{T}\right)
The trap: 132 shows up twice
Run the numbers and 132 appears again, meaning something else entirely.
At 10 percent transmittance, D equals 1, so
D_s = 132 \times 1 = 132
The geometric factor 132 and the Ds value at 10 percent transmittance are two different quantities that happen to share a number. Do not conflate them.
For reference, 50 percent transmittance gives a Ds of roughly 39.7.
Why the chamber is 18 ft³
Not because 18 ft³ is physically optimal.
It is the size of the standard apparatus NBS built, and the purpose is repeatability and comparability between materials. Real fire compartments are far larger and far messier.
Actual smoke concentration in a building depends on ventilation, ceiling height, fire size, burning rate, oxygen concentration, smoke temperature, buoyancy, openings and airflow. A Ds from an 18 ft³ chamber is not a building smoke concentration.
The 3 ft path is the same kind of choice. Different apparatus path lengths make raw optical densities incomparable, so it was fixed — and that 3 is sitting inside the 132.
Two test modes
E662 is not simply setting a sample alight.
- Flaming mode — radiant heat plus a pilot flame, for flaming combustion
- Non-flaming mode — radiant heat only, measuring smoke from pyrolysis without flame
The two represent the main ways a product participates in a fire. The radiant exposure used is around 25 kW/m² (2.5 W/cm²), a level chosen to model early-stage fire conditions rather than post-flashover severity.
More than one Ds matters
Because smoke is tracked over time, the test reports several values.
| Value | Meaning |
|---|---|
| Ds1.5 | Specific optical density at 1.5 minutes |
| Ds4.0 | Specific optical density at 4 minutes |
| Dm | Maximum specific optical density over 20 minutes |
Early on there is almost no smoke; pyrolysis starts, smoke builds, transmittance drops, Ds climbs, and at some point it peaks at Dm. How fast the smoke arrives matters as much as how much of it there is, which is why the timed values exist.
Does a high Ds mean a dangerous material?
Not that simply.
ASTM says so explicitly. E662 results depend on specimen form, thickness and density, must not be treated as an intrinsic material property, and the test alone is not held to predict smoke levels in a real fire.
Real fire hazard also involves toxic gases, flame spread, heat release rate, oxygen concentration, ventilation, growth rate and the escape environment.
What I took away
- 132 is not a constant of smoke; it is a geometric factor from apparatus dimensions
- The chain is transmittance T → optical density D → factor G → specific optical density Ds
- The logarithm is there because attenuation is exponential (Lambert-Beer)
- The geometric factor 132 and the Ds at 10 percent transmittance are different things with the same number
- 18 ft³ and 3 ft are standardization choices, not laws of nature
- Ds1.5, Ds4.0 and Dm exist because timing matters
- A high Ds does not by itself make a material dangerous
If the 132 will not come to mind, rebuild it from one line.
132 = \frac{18}{0.0456 \times 3}
On the strength of this evidence
Values and test conditions change with revisions. Check the current edition before relying on them.
- ASTM E662, Standard Test Method for Specific Optical Density of Smoke Generated by Solid Materials : the source for chamber dimensions, test modes and the definition of Ds
- NIST, formerly NBS : where the smoke density chamber was developed
- SFPE Handbook of Fire Protection Engineering : optical properties of smoke and visibility
⚠ This is a textbook-level summary; I did not check each clause of ASTM E662 against the original. The 132 itself I did compute directly from the three values above.
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