Talk:Fourth power law

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width of wheels and relation to fourth power law

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?

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]