Pavement Number: questions to ask before applying the method

The suspiciously thin base course

A factor-of-ten error does not announce itself with a red flashing cell.

South African pavement design methods sit within a broader design framework; TRH4 is one original reference for that context. (CSRA, 1996)

Make the centimetres agree with the millimetres

Governing relationship: 0.15 m × 1000 = 150 mm.

Conversion factor = 1,000 mm per metre. h = 0.15 m.

The incorrect transcription is 15 mm; the correct value is 150 mm.

The film first plots thickness (mm), then follows the calculation and plots ratio (dimensionless). The wrong value is one tenth of the correct thickness: relative error = −90%. Conversion precedes method-specific calculation.

Dimensional experiment

Unit consistency before method selection

Unit conversion is computed; pavement-number coefficients are not invented.

Download example data (CSV)

Model, calculations and transcriptEquations, worked steps, source notes and a timed reading guide

Understand the model

A valid-looking numerical input can still have the wrong unit. Validate the source conversion before evaluating a method-specific parameter.

Work through the inputs and equations below, then compare the calculated output with the film. All numerical inputs in this study are synthetic.

Inputs and symbol key

hm; hmm

The same thickness expressed in metres and millimetres.

hwrong; hcorrect

Incorrect and corrected thickness expressed in one common unit.

εrel

Relative input error (dimensionless; multiply by 100 for percent).

Values used in this film

• Conversion factor = 1,000 mm per metre. h = 0.15 m.
• The incorrect transcription is 15 mm; the correct value is 150 mm.

The mathematical relationships

1. Equation 1

   Source and scope
   $$h_{mm}=1000h_m$$

   One metre contains 1000 millimetres, so 0.15 m is 150 mm.

2. Equation 2

   Source and scope
   $$\epsilon_{rel}=\frac{h_{wrong}-h_{correct}}{h_{correct}}$$

   Subtract the correct thickness from the incorrect one and divide by the correct value. This is the input error, not an inferred error in Pavement Number.

Work through the example

Use the relationships above with consistent units. These substitutions are our worked example, not values quoted from the source.

1. Source thickness

   15 cm × 10 = 150 mm

   mm

2. Incorrect entry

   15 mm / 150 mm = 0.1

   dimensionless ratio

3. Relative error

   (15 − 150) / 150 = −0.9

   −90%

4. Independent stack

   40 + 150 + 200 = 390; wrong stack = 255

   mm total thickness

Read the output

The wrong value is one tenth of the correct thickness: relative error = −90%. Conversion precedes method-specific calculation.

Check your understanding

Round-trip source units through the canonical representation and compare against the original value. Validate each layer separately, preserve source units, and withhold a derived-method result when the source equation or applicability remains unresolved.

Assumptions and limits

Unit conversion is computed; pavement-number coefficients are not invented.

Return to the full references and method notes to check the cited edition and its applicability.

Timestamped film transcript 24 short entries · select a time to revisit the film

1. 0:00

   Unit consistency before method selection. A 0.15 m input has been incorrectly transcribed as 15 mm.

2. 0:01

   MATHEMATICS · define the relationship and the meaning of each symbol before calculating.

3. 0:07

   Conversion factor = 1,000 mm per metre. h = 0.15 m. The incorrect transcription is 15 mm; the correct value is 150 mm.

4. 0:14

   INPUT · two values in a common unit · read the axis units and the numerical values.

5. 0:23

   A 0.15 m input has been incorrectly transcribed as 15 mm.

6. 0:34

   150 mm / 15 mm = 10. Correct the input before applying any method-specific coefficient.

7. 0:43

   OUTPUT · relative magnitude · read the axis units and the numerical values.

8. 0:52

   The wrong value is one tenth of the correct thickness: relative error = −90%. Conversion precedes method-specific calculation.

9. 0:59

   CALCULATION · substitute the defined inputs; keep units through each intermediate step.

10. 1:05

    Source thickness: 15 cm × 10 = 150 mm mm

11. 1:08

    Incorrect entry: 15 mm / 150 mm = 0.1 dimensionless ratio

12. 1:11

    Relative error: (15 − 150) / 150 = −0.9 −90%

13. 1:14

    Independent stack: 40 + 150 + 200 = 390; wrong stack = 255 mm total thickness

14. 1:17

    SENSITIVITY · change one declared input · read the axis units and the numerical values.

15. 1:26

    Base 15 mm: 255 mm total stack. Surfacing 40 mm plus base 15 mm plus subbase 200 mm.

16. 1:29

    Base 150 mm: 390 mm total stack. Correctly converted base; other layers unchanged.

17. 1:33

    Base 165 mm: 405 mm total stack. A separate +10% base-thickness sensitivity case.

18. 1:36

    Check: Round-trip source units through the canonical representation and compare against the original value. Validate each layer separately, preserve source units, and withhold a derived-method result when the source equation or applicability remains unresolved.

19. 1:42

    ONE ROW · A factor-of-ten error does not announce itself with a red flashing cell.

20. 1:55

    PARAMETER MAP · 6060 evaluated cells. The colour limits stay fixed across every row.

21. 2:05

    Most rows convert centimetres to millimetres correctly. Every tenth row deliberately leaves the number unchanged. The regular low bands are planted defects in an import test, not a

22. 2:15

    material trend. Compare equal reported thicknesses across batches: the unit conversion should be invariant to delivery date or file name.

23. 2:22

    INTERPRETATION · These are discrete states. Read the map cell by cell; a smooth surface would invent intermediate categories.

24. 2:31

    Unit conversion is computed; pavement-number coefficients are not invented.

Download the timed captions (VTT)

The transcript records the on-screen wording. Formula provenance and interpretation are explained in the source note above.

Audit the method record

Before evaluating a Pavement Number result, request the exact method/source edition, required inputs, layer-combination rules, material applicability and calculation version. Keep original layer records available alongside any combined representation.

A useful pre-calculation check

Create a synthetic inventory with layer names, thickness units and source observations. Flag a thickness entered in centimetres where millimetres are expected. Resolve that inconsistency before discussing the derived parameter.

Confirm the method identity

No Pavement Number equation is implemented in this explainer. Source equations, constants and reference benchmarks need independent checking before a numerical calculator is released.

A method identity card

An original method identity card should name the parameter, source, edition, input units, material assumptions and calculation version. Attach an independently checked reference example before relying on a software result.

For instance, a synthetic thickness entered as 15 may mean 15 cm or 15 mm. Converting 15 cm to 150 mm resolves the unit difference; it does not establish that the layer properties or the method are appropriate.

TRH4 is cited here for design context, not as evidence for an unspecified Pavement Number equation. Before publishing a detailed calculator, the exact method equations and benchmarks must be sourced and reviewed. That distinction keeps this article useful without inventing a universal formula.

Treat the units as part of the input, not as a footnote

A source sheet contains a base thickness of “15 cm”, but an import field expects millimetres. Entering 15 directly supplies 15 mm instead of 150 mm. The converted value is ten times the incorrect input; the input error is 135 mm, or 90% below the intended thickness.

Case review

Stop the unit error before the method starts

Is the base course 15 mm thick or 15 cm thick?

Misread input · 15 Thickness (mm)

The discriminating check

Confirm the source unit, convert explicitly and verify the method edition and required layer inputs.

Evidence supports the comparison

With units and method identity established, compare against a trusted reference calculation.

Evidence is missing or incompatible

With an unspecified unit or unverified method, resolve that gap before producing a numerical method result.

What you can conclude. This case validates a thickness input. It does not supply Pavement Number coefficients or a capacity equation.

Original worked case. Read the source editions and method notes.

That is a serious data difference even before any derived parameter is calculated. Yet a numerical output may still look plausible if the software accepts the value. Range checks can prompt review, but they do not replace the source unit and conversion record.

Step	Value	Interpretation
Source observation	15 cm	Preserve as received
Unit conversion	15 × 10	Convert centimetres to millimetres
Normalised input	150 mm	Supply to the selected method
Method result	Not calculated here	Requires the actual method and inputs

The phrase Pavement Number does not by itself identify an equation, source edition or material applicability. Ask for those explicitly. TRH4 is cited for the broader design framework; it is not used here to authenticate an unspecified Pavement Number formula. (CSRA, 1996)

A reproducible calculation needs an independently checked reference case, a declared implementation version and traceable inputs. When an engineer reviews a result, the first question should not be whether the number looks reasonable. It should be whether the number was produced by the intended method from the intended data. Only then can its engineering interpretation be assessed.

Calculation laboratory

How can a unit error survive an apparently plausible result?

Calculation step	Substitution or result	Units and interpretation
Source thickness	15 cm × 10 = 150 mm	mm
Incorrect entry	15 mm / 150 mm = 0.1	dimensionless ratio
Relative error	(15 − 150) / 150 = −0.9	−90%
Independent stack	40 + 150 + 200 = 390; wrong stack = 255	mm total thickness

Dimensional validation and method validation answer different questions. A layer thickness can be dimensionally valid in millimetres while being wrong by a factor of ten. A complete stack can also look credible because the other layers dilute the relative error: the base is 90% too thin, but the total stack changes from 390 mm to 255 mm, a 34.62% reduction. Checking only total depth may therefore miss a serious layer-specific problem.

For a derived result F(h), first-order propagation is δF approximately F′(h)δh. The relative sensitivity is hF′(h)/F(h), which depends on the actual selected equation. It is not defensible to say a 90% thickness error creates a 90% Pavement Number error without that equation. For large errors the linear approximation may fail anyway, requiring direct recomputation with corrected inputs.

This article intentionally exposes the calculation boundary. TRH4 supplies design context; an executable Pavement Number method needs its own verified equation, coefficients, applicability and reference case. The film calculates unit conversion and layer-stack geometry only. A method identity record should therefore distinguish a verified input transformation from an unimplemented derived parameter, rather than presenting a provisional coefficient as established engineering practice. (CSRA, 1996)

Controlled sensitivity experiment

Controlled case	Calculated output	What changes
Base 15 mm	255.000000 mm total stack	Surfacing 40 mm plus base 15 mm plus subbase 200 mm.
Base 150 mm	390.000000 mm total stack	Correctly converted base; other layers unchanged.
Base 165 mm	405.000000 mm total stack	A separate +10% base-thickness sensitivity case.

CALCULATION LABORATORY

How can a unit error survive an apparently plausible result?

Compare the cases on a fixed scale. Select a case to inspect its input change and calculated output.

Sensitivity case1. Base 15 mm2. Base 150 mm3. Base 165 mm

Base 15 mm: 255 mm total stack. Surfacing 40 mm plus base 15 mm plus subbase 200 mm.

Reproduce and challenge the result

Round-trip source units through the canonical representation and compare against the original value. Validate each layer separately, preserve source units, and withhold a derived-method result when the source equation or applicability remains unresolved.

These are original synthetic calculations. The sensitivity cases vary the stated input while retaining the other assumptions; they are not field observations or treatment thresholds. The film’s calculation and sensitivity chapters use the same numerical cases as this table.

Spot the conversion error across batches

Most rows convert centimetres to millimetres correctly. Every tenth row deliberately leaves the number unchanged. The regular low bands are planted defects in an import test, not a material trend. Compare equal reported thicknesses across batches: the unit conversion should be invariant to delivery date or file name.

Reproduce the experiment. h_mm = 10h_cm; every tenth synthetic batch deliberately omits ×10. The downloadable table contains 6,060 evaluated cells, with the two input coordinates and output value retained on every row. These are parameter combinations, not that many independent field observations. The equation extends the worked example above; it is original teaching arithmetic, not a new standard or calibrated prediction.

Computed parameter atlas · 6,060 cells

The suspiciously thin base course

A factor-of-ten error does not announce itself with a red flashing cell.

Download every calculated cell (CSV) · Open full-size explorer · Equation source and tests (ZIP)

This tests input validation only. No Pavement Number formula, layer coefficient or structural capacity is inferred from thickness.

References and method notes

1. CSRA (1996). TRH4: Structural Design of Flexible Pavements for Interurban and Rural Roads. 1996 edition. Original source (Accessed: 5 September 2026).Design framework; confirm project applicability

Use the source edition and project requirements that apply to your work. Educational examples are not site-specific design advice.