Talk:Fourth power law

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width of wheels and relation to fourth power law[edit]

how much impact does the surface area of the wheel have on the calculation? do thinner wheels do more damage? 85.147.66.47 (talk) 12:53, 3 February 2023 (UTC)[reply]

Incorrect/Misleading application of fourth power law?[edit]

According to the Australian Road Research Board Internal Report "Review of the Fourth Power Law" by D.F. Kinder (AIR 000-248), in section 4.2 ("Doubling the axle load does not necessarily produce 16 times the damage"):

However, if relative total damage rather than relative unit-incremental damage is being considered, it is not always true that doubling the load produces 16 times the damage, even if the pavement follows a 4th power law. This can be demonstrated by way of an example. Suppose the performance of a pavement is such that when rutting is used as a measure of damage (D), the damage caused by N applications of load with magnitude (P) is given by eqn(6) with the exponent values m=0.8 and m/x=0.2. These values are similar to the ones obtained from an analysis of the ALF test on the pavement at Somersby, NSW (see Section 3.2). Eqn(7) demonstrated that such a pavement obeys the 4th power law. However, for the case where P = 2P_s and N = N_s, eqn(6) shows that the damage is:
[equation 12]
$D(2P_{a},N_{s})=c(2P_{s})^{m}(N_{s})^{m}/x=c2^{0}.8(P_{s})^{0}.8(N_{s})^{0}.2=1.74.D(P_{a},N_{s})$

So, N passes of an axle with twice the standard load produces only 1.74 times more damage than N passes of a standard axle. That is, for the example given, doubling the load produces not 16 times the damage, but only 118% of that amount.
Another related example is the case where P = 2P_s and N_s = 2N. In this case, apart from the rare load, freight carried is equivalent in each situation (2P_x N = P_x 2N). Under these circumstances eqn(6) shows that the damage caused by N passes of the higher load is only 1.52 times the damage caused by 2N passes of a standard axle.
It follows from these examples that it is not appropriate to use the factor (P/P_a)^4 to estimate the increase in damage to new pavements corresponding to a general increase in the distribution of loads applied to it.

As such, I think the example of a truck with 10x axle load may be misleading. I'm no expert in this topic, so it would be good if someone else could take a look. Rangerunseen (talk) 19:36, 3 February 2024 (UTC)[reply]