Traffic growth and E80s: show the assumptions behind design traffic

A small percentage acquires a long shadow

Three percent feels modest until the planning horizon gives it thirty opportunities to compound.

TRH4 includes traffic in its pavement design framework. The project method determines how traffic observations and design assumptions are used. (CSRA, 1996)

Let the growth rate compound

Governing relationship: Qn = Q0(1 + g)ⁿ; C = Σ Qn, n = 1…5.

Q0 = 1,000 annual units; g is an annual growth fraction, not a percentage numeral.

Future-year sum excludes year 0. No E80 equivalency factor is assumed.

The film first plots annual growth (%), then follows the calculation and plots cumulative units. At 3%, year 5 is 1,159.27 units, while the five-year sum is 5,468.41. Annual and cumulative quantities are different outputs.

Growth scenario

Annual and cumulative traffic

Annual quantities are scenario inputs; E80 factors require an applicable method.

Download example data (CSV)

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

Understand the model

An annual quantity compounds from a base year. Adding the future-year quantities produces a cumulative total with a different meaning.

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

Q₀; Qn

Base-year and year-n annual quantities (annual units).

g; n

Annual growth fraction (3% = 0.03); years from the base year.

C₅

Total quantity in future years 1 through 5; excludes year 0.

Values used in this film

• Q0 = 1,000 annual units; g is an annual growth fraction, not a percentage numeral.
• Future-year sum excludes year 0. No E80 equivalency factor is assumed.

The mathematical relationships

1. Equation 1

   Source and scope
   $$Q_n=Q_0(1+g)^n$$

   Raise the annual growth multiplier to the number of years elapsed. Enter 3% as 0.03.

2. Equation 2

   Source and scope
   $$C_5=\sum_{n=1}^{5}Q_n$$

   Sum years 1 through 5. Year 0 is excluded, and the annual base quantity is already annualised.

Work through the example

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

1. Year one

   1000 × 1.03 = 1030

   annual units

2. Year five

   1000 × 1.03⁵ = 1159.274074

   annual units

3. Geometric sum

   1000 × 1.03 × (1.03⁵ − 1) / 0.03 = 5468.409884

   five-year units

4. Zero-growth limit

   5 × 1000 = 5000

   five-year units

Read the output

At 3%, year 5 is 1,159.27 units, while the five-year sum is 5,468.41. Annual and cumulative quantities are different outputs.

Check your understanding

Compare the loop and geometric expression, test g = 0, and check the year-one term. Preserve whether the starting input is daily or annual; apply a daily-to-annual conversion only once and document the selected calendar convention.

Assumptions and limits

Annual quantities are scenario inputs; E80 factors require an applicable method.

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

Timestamped film transcript 27 short entries · select a time to revisit the film

1. 0:00

   Annual and cumulative traffic. Q0 = 1,000 annual units; g = 0%, 3% and 5%.

2. 0:01

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

3. 0:07

   Q0 = 1,000 annual units; g is an annual growth fraction, not a percentage numeral. Future-year sum excludes year 0. No E80 equivalency factor is assumed.

4. 0:14

   INPUT · growth scenarios · read the axis units and the numerical values.

5. 0:23

   Q0 = 1,000 annual units; g = 0%, 3% and 5%.

6. 0:27

   g = 0%: year 5 = 1,000.00; sum of years 1–5 = 5,000.00 units.

7. 0:33

   g = 3%: year 5 = 1,159.27; sum of years 1–5 = 5,468.41 units.

8. 0:40

   g = 5%: year 5 = 1,276.28; sum of years 1–5 = 5,801.91 units.

9. 0:43

   OUTPUT · five future years · read the axis units and the numerical values.

10. 0:52

    At 3%, year 5 is 1,159.27 units, while the five-year sum is 5,468.41. Annual and cumulative quantities are different outputs.

11. 0:59

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

12. 1:05

    Year one: 1000 × 1.03 = 1030 annual units

13. 1:08

    Year five: 1000 × 1.03⁵ = 1159.274074 annual units

14. 1:11

    Geometric sum: 1000 × 1.03 × (1.03⁵ − 1) / 0.03 = 5468.409884 five-year units

15. 1:14

    Zero-growth limit: 5 × 1000 = 5000 five-year units

16. 1:17

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

17. 1:26

    Growth 0%: 5000 cumulative units. Five future years; year zero excluded; starting annual quantity 1000.

18. 1:29

    Growth 3%: 5468.41 cumulative units. Five future years; year zero excluded; starting annual quantity 1000.

19. 1:33

    Growth 5%: 5801.91 cumulative units. Five future years; year zero excluded; starting annual quantity 1000.

20. 1:36

    Check: Compare the loop and geometric expression, test g = 0, and check the year-one term. Preserve whether the starting input is daily or annual; apply a daily-to-annual conversion only once and document the selected calendar convention.

21. 1:42

    ONE ROW · Three percent feels modest until the planning horizon gives it thirty opportunities to compound.

22. 2:00

    PARAMETER MAP · 7381 evaluated cells. The colour limits stay fixed across every row.

23. 2:10

    Trace one growth-rate row through time before comparing rates. The same base quantity of 1,000 units/year anchors every scenario. The upper rows pull away increasingly with time

24. 2:20

    because each increase compounds on the previous quantity. Fractional times draw the mathematical curve; annual reporting uses integer years.

25. 2:27

    VALUE LANDSCAPE · Height and colour encode Annual quantity (units/year). This is a graph over the two input axes, not automatically a physical pavement shape.

26. 2:39

    Prescribed constant growth scenarios, not a forecast. No daily-to-annual conversion, vehicle classification, directional allocation or E80 factor has been silently added.

27. 2:47

    Annual quantities are scenario inputs; E80 factors require an applicable method.

Download the timed captions (VTT)

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

Keep the scenario readable

State the base year, traffic measure, direction/lane allocation, growth assumption and analysis period. Distinguish an observed vehicle count from equivalent standard axle loading. Do not label ordinary vehicle growth as an E80 calculation.

A transparent growth example

For a synthetic annual quantity of 1,000 units with constant 3% annual growth, year five is 1,000 × 1.03^5 = 1,159.27 units. The interactive model demonstrates compound growth only. It does not convert vehicles to E80s.

Keep loading assumptions visible

A constant growth assumption is a scenario, not a forecast guarantee. Axle equivalency and lane allocation require their own justified inputs.

Annual quantity and cumulative quantity differ

The value at year five is a point in the scenario. The total across several years is a sum of the annual quantities. State whether the first term is the base year or the first future year; otherwise, two seemingly identical spreadsheets may include different periods.

At 0% growth, the illustrative annual quantity stays at 1,000 units. Five equal annual terms sum to 5,000 units. At 3%, the year-five quantity rises to approximately 1,159.27 units, but that single number is not the five-year total.

Equivalent standard axle loading introduces additional assumptions beyond this growth example. Preserve the traffic measure and conversion basis rather than relabelling the graph “E80s”. The film and controlled cases show annual growth and cumulative quantities separately.

Sum the declared years, not the last point on the chart

The annual scenario starts at 1,000 units and grows by 3% per year. Year five is 1,000 × 1.03⁵ = 1,159.27 units/year. That is the annual quantity in year five, not the accumulated quantity through year five.

Case review

Do not add an annual quantity to a cumulative total

Which loading quantity does the design-period question actually require?

Base year · 1000 Annual units/year

The discriminating check

Keep the base year, annualisation, growth period, directional allocation and any axle-equivalency assumptions explicit.

Evidence supports the comparison

When those assumptions are supported, calculate annual and cumulative quantities separately and test scenarios.

Evidence is missing or incompatible

When vehicle classes or equivalency factors are missing, report the observed traffic quantity without relabelling it E80.

What you can conclude. The compounding surface explores assumptions. It is not a forecast or a vehicle-to-E80 conversion.

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

If the analysis includes future years one through five, sum 1,030 + 1,060.90 + 1,092.727 + 1,125.50881 + 1,159.2740743 = 5,468.41 units, rounded at the end. Including the base year instead would change the period represented. An index beginning at zero is a calculation convention with a real consequence.

Reporting choice	Meaning
Base year	The quantity from which growth starts
Year-five value	One annual quantity
Years one through five	Five future annual quantities summed
Growth assumption	A scenario input, not guaranteed demand

Traffic used for pavement design requires more than this annual-growth calculation. Direction, lane allocation, the traffic measure and axle-equivalency assumptions need their own justified basis under the selected method. Ordinary vehicle counts are not automatically equivalent standard axle loading. TRH4 provides the cited design context. (CSRA, 1996)

A useful review presents a small set of explicit scenarios rather than a single unexplained total. At zero growth, five annual quantities of 1,000 sum to 5,000. At 3%, the stated future-year convention yields 5,468.41. The comparison makes the influence of the assumption visible while keeping axle conversion outside this example.

Calculation laboratory

How do year numbering and growth affect cumulative demand?

Calculation step	Substitution or result	Units and interpretation
Year one	1000 × 1.03 = 1030	annual units
Year five	1000 × 1.03⁵ = 1159.274074	annual units
Geometric sum	1000 × 1.03 × (1.03⁵ − 1) / 0.03 = 5468.409884	five-year units
Zero-growth limit	5 × 1000 = 5000	five-year units

The first payment-like traffic term here is year one, already increased by one growth factor. Summing years zero through four instead produces 5309.135810 units at 3%. Neither convention is inherently an arithmetic error, but they describe different periods. State the opening date, base year and first included year before comparing demand totals.

The closed form follows from multiplying a finite geometric sum by its common ratio and subtracting the original sum. At zero growth its written fraction becomes 0/0, so the implementation must use the limit nQ0 or a numerically stable equivalent. A simple loop is also transparent for a short horizon and readily extends to year-specific growth factors.

Vehicle counts and E80 demand are different quantities. A possible accounting structure sums annual vehicle-class quantities multiplied by justified class equivalency factors and direction/lane allocation factors. Those factors need their own source data and applicability; this example does not supply them. Assuming a fixed fleet mix while applying a single growth rate can hide a change in heavy-vehicle loading even when total vehicle growth is known. Present demand scenarios as assumptions to test within the design framework, not as measured future traffic. (CSRA, 1996)

Controlled sensitivity experiment

Controlled case	Calculated output	What changes
Growth 0%	5,000.000000 cumulative units	Five future years; year zero excluded; starting annual quantity 1000.
Growth 3%	5,468.409884 cumulative units	Five future years; year zero excluded; starting annual quantity 1000.
Growth 5%	5,801.912813 cumulative units	Five future years; year zero excluded; starting annual quantity 1000.

CALCULATION LABORATORY

How do year numbering and growth affect cumulative demand?

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

Sensitivity case1. Growth 0%2. Growth 3%3. Growth 5%

Growth 0%: 5,000 cumulative units. Five future years; year zero excluded; starting annual quantity 1000.

Reproduce and challenge the result

Compare the loop and geometric expression, test g = 0, and check the year-one term. Preserve whether the starting input is daily or annual; apply a daily-to-annual conversion only once and document the selected calendar convention.

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.

Thirty years of compounding, side by side

Trace one growth-rate row through time before comparing rates. The same base quantity of 1,000 units/year anchors every scenario. The upper rows pull away increasingly with time because each increase compounds on the previous quantity. Fractional times draw the mathematical curve; annual reporting uses integer years.

Reproduce the experiment. Q(t,g) = 1000(1+g)^t. The downloadable table contains 7,381 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 · 7,381 cells

A small percentage acquires a long shadow

Three percent feels modest until the planning horizon gives it thirty opportunities to compound.

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

Prescribed constant growth scenarios, not a forecast. No daily-to-annual conversion, vehicle classification, directional allocation or E80 factor has been silently added.

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.