Axle Loads & Pavement formula solvers

Annual ESALs from a Truck Count (Truck Factor)

W18=365AADTTTFW_{18} = 365 \, \mathrm{AADTT} \cdot \mathrm{TF}

Axle Loads & PavementYearly equivalent single axle loads from a daily truck count and the ESALs an average truck delivers per pass. The truck factor is the sum of the equivalency factors of all the truck's axles, and it is a property of the LOAD that trucks carry on that road, not of the trucks themselves.

Axle Group Load Against the Legal Cap

U=PPlimU = \frac{P}{P_{\mathrm{lim}}}

Axle Loads & PavementHow close an axle, an axle group or a whole vehicle sits to the weight it is allowed, as a percentage of the cap. The caps are INPUTS, because they are jurisdiction-specific: 20,000 lb single, 34,000 lb tandem and 80,000 lb gross are the US interstate figures, and a spring load restriction can cut them to half overnight.

Cumulative ESALs with Traffic Growth

Wc=w1(1+g)Y1gW_c = w_1 \cdot \frac{(1+g)^{Y} - 1}{g}

Axle Loads & PavementTotal equivalent single axle loads accumulated over a design period when traffic grows at a compound annual rate. The growth factor is already a SUM over the whole period, which is why multiplying it by the number of years again — a mistake made constantly — inflates the answer by that many times.

Design Lane ESALs

w18=DDDLW18w_{18} = D_D \, D_L \, W_{18}

Axle Loads & PavementThe share of a highway's total equivalent single axle loads that lands in the one lane the pavement is designed for, after splitting the two-way total by direction and then by lane. Pavement is designed for the worst lane, not the average one.

Equivalent Tyre Contact Radius

a=Pπpa = \sqrt{\frac{P}{\pi \, p}}

Axle Loads & PavementThe radius of the circle that carries the same wheel load at the same contact pressure as the real footprint. Layered-elastic pavement analysis is built on circular loaded areas, so every real, roughly rectangular tyre print gets turned into this before anything can be calculated.

Federal Bridge Gross Weight Formula

W=500(LNN1+12N+36)W = 500 \left( \frac{L\,N}{N-1} + 12\,N + 36 \right)

Axle Loads & PavementThe federal limit on how much any group of consecutive axles may weigh, set by how far apart the outer axles of the group are spread. Written into 23 U.S.C. § 127(a)(2), it is the reason a five-axle semi needs 51 feet from steer to rear trailer axle before it can gross 80,000 pounds.

Kingpin and Bogie Load Split on a Semitrailer

Rkp=WLaLR_{kp} = W \, \frac{L - a}{L}

Axle Loads & PavementHow a semitrailer's weight divides between the kingpin at the tractor's fifth wheel and the trailer's own axle group, from one moment balance. No standard governs this; it is plain statics, and it is the arithmetic behind every trailer bogie slid forward or back at a weigh station.

Load Equivalency Factor (the Fourth Power Law)

LEF=(PP18)n\mathrm{LEF} = \left( \frac{P}{P_{18}} \right)^{\,n}

Axle Loads & PavementHow much pavement damage one axle does compared with the standard 18,000 lb (80 kN) single axle, as a power of the load ratio. The exponent is an INPUT here and defaults to 4, because the famous fourth power is a later curve fit and not a finding of the AASHO Road Test, whose own load exponents were 4.79 flexible and 4.62 rigid.

Structural Number of a Flexible Pavement

SN=a1D1+a2D2m2+a3D3m3SN = a_1 D_1 + a_2 D_2 m_2 + a_3 D_3 m_3

Axle Loads & PavementThe single number that stands for the whole strength of a flexible pavement: each layer's thickness multiplied by a coefficient for what it is made of, and by a drainage coefficient for the unbound layers. Layer coefficients are INPUTS — they are regionally calibrated, they live in copyrighted design guides, and no honest tool bakes them in.

Tyre Contact Area

A=PpA = \frac{P}{p}

Axle Loads & PavementThe area of the patch a loaded tyre presses onto the pavement, taken as the wheel load divided by the contact pressure. Contact pressure is NOT inflation pressure: van Vuuren measured it as much as 30% lower, and the textbook rule of adding ten per cent was found completely unacceptable.