## How To Calculate Equivalent Single Wheel Load(ESWL)

**Mathematical Problem**: Example

The loaded weight on the rear dual wheels of a track is 5500 Kg. The centre-to-centre spacing and clear space in dual wheels are 30 cm and 10 cm respectively. Calculate the equivalent single wheel load or ESWL for pavement thickness 20 cm, 40 cm, and 70 cm.

**Solution:**

Formula for ESWL calculation is

[latex] \log_{10}ESWL = \log_{10}P + \frac{0.301\log_{10}(\frac{Z}{d/2})}{\log_{10}(\frac{2S}{d/2})} [/latex]

Where,

- P is the wheel load (single wheel load) = 5500/2 = 2750 Kg.
- S is the centre to centre distance between the two wheels = 30 cm.
- d is the clear distance between two wheels = 10 cm
- Z is the thickness of the pavement.

**1. For Z = 20 cm**

[latex] \log_{10}ESWL = \log_{10}2750 + \frac{0.301\log_{10}(\frac{20}{10/2})}{\log_{10}(\frac{2 \times 30}{10/2})} [/latex]

[latex] \log_{10}ESWL = \log_{10}2750 + \frac{0.301\log_{10}(\frac{20}{5})}{\log_{10}(\frac{60}{5})} [/latex]

[latex] \log_{10}ESWL = \log_{10}2750 + \frac{0.301\log_{10}4}{\log_{10}12}[/latex]

[latex] \log_{10}ESWL = 3.43933 + 0.16792 [/latex]

[latex] \log_{10}ESWL = 3.60725 [/latex]

[latex] ESWL = 10^{3.60725} [/latex]

ESWL = 4048 Kg

**2. For Z = 40 cm**

[latex] \log_{10}ESWL = \log_{10}2750 + \frac{0.301\log_{10}(\frac{40}{5})}{\log_{10}(\frac{60}{5})} [/latex]

[latex] ESWL = 10^{3.69123} [/latex]

ESWL = 4912 Kg

**3. For Z = 70 cm**

[latex] \log_{10}ESWL = \log_{10}2750 + \frac{0.301\log_{10}(\frac{70}{5})}{\log_{10}(\frac{60}{5})} [/latex]

[latex] ESWL = 10^{3.7590} [/latex]

ESWL = 5741 Kg

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