4 ms·

I'd never heard of that fourth-power-law, fascinating. In fact I can't think of any other relationship in 'nature' scaling with the fourth power, and it seems t

by mckirk 2y ago

I'd never heard of that fourth-power-law, fascinating. In fact I can't think of any other relationship in 'nature' scaling with the fourth power, and it seems that that is indeed rare, given the fact that the Wikipedia article is literally called 'fourth power law' and only refers to this effect. (Though I sure would have liked more background info on the actual physics involved; it seems they basically just observed cars and trucks driving on roads, measured the damage to the road, and called it a Law.)

QuadmasterXLII 2y ago
Thermal radiation is the other classic
- eesmith 2y ago
  I too immediately thought of https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law . There's also radar reflection, "Observe that the received power drops with the fourth power of the range, so radar systems must cope with very large dynamic ranges in the receive signal processing." - https://www.eetimes.com/radar-basics-part-1/ https://www.eetimes.com/radar-basics-part-1/ I would also call it a classic as I learned it from this scene in Robert Heinlein's book "Rolling Stones": "The result was eight shiny right-angled corners facing among them in all possible directions —a radar reflector. ... The final result was to step up the effectiveness of radar from an inverse fourth-power law to an inverse square law — in theory, at least. In practice it would be somewhat less than perfectly efficient ...", https://archive.org/details/rollingstones0000robe_q7v9/page/128/mode/2up?q=%22fourth+power%22 https://archive.org/details/rollingstones0000robe_q7v9/page/... A quick search on Google Scholar finds there's a fourth-power law for shock waves: "A fourth-power law relating the stress jump through a steady structured shock wave and the maximum strain rate within the shock wave has received recognition as a unifying relation over a sensibly wide range of materials and shock compression amplitudes." - https://pubs.aip.org/aip/jap/article-abstract/107/1/013506/287070/Structured-shock-waves-and-the-fourth-power-law?redirectedFrom=fulltext https://pubs.aip.org/aip/jap/article-abstract/107/1/013506/2... "Observations on the fourth-power scaling of high-pressure shock waves in solids" at https://pubs.aip.org/aip/jap/article-abstract/130/24/245901/1065688/Observations-on-the-fourth-power-scaling-of-high?redirectedFrom=fulltext https://pubs.aip.org/aip/jap/article-abstract/130/24/245901/... and one with irradiance, though at the forth-power of the cosine: "The cosine-fourth-power law states that the irradiance at any point in the image formed by a photographic lens, in the absence of vignetting, is equal to E_0 cos^4 β" - https://nvlpubs.nist.gov/nistpubs/jres/39/jresv39n3p213_A1b.pdf https://nvlpubs.nist.gov/nistpubs/jres/39/jresv39n3p213_A1b.... I also found the following at https://pubs.aip.org/aip/jap/article-abstract/75/6/3075/400188/Gold-nanoparticles-ion-implanted-in-glass-with https://pubs.aip.org/aip/jap/article-abstract/75/6/3075/4001... : "The third‐order nonlinear optical susceptibility χ(3) of this glass was found to be proportional to the fourth power of the radius of the colloid particles or the fourth power of the absorption coefficient at the peak of a plasmon band when the total volume of the colloid particles was constant."
euroderf 2y ago
Doesn't the cost of heating a dwelling involve a fourth power of the difference in temperature, outside/inside ?
PaulHoule 2y ago
Flow through a pipe scales as the fourth power of the radius https://sino-inst.com/pipe-flow-vs-pressure-relationship-calculate/ https://sino-inst.com/pipe-flow-vs-pressure-relationship-cal... This came to my attention when I was teaching Physics 102 at Cornell which was an auto tutorial course for pre-meds that had an unusual focus on fluid mechanics for an intro physics course.
Aloisius 2y ago
It's more a rule of thumb than anything approaching a law. The exponent varies based on a number of factors like existing road condition, road construction standards, speed, weather conditions, etc.

by mckirk 2y ago

QuadmasterXLII 2y ago

Thermal radiation is the other classic

eesmith 2y ago
I too immediately thought of https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law . There's also radar reflection, "Observe that the received power drops with the fourth power of the range, so radar systems must cope with very large dynamic ranges in the receive signal processing." - https://www.eetimes.com/radar-basics-part-1/ https://www.eetimes.com/radar-basics-part-1/ I would also call it a classic as I learned it from this scene in Robert Heinlein's book "Rolling Stones": "The result was eight shiny right-angled corners facing among them in all possible directions —a radar reflector. ... The final result was to step up the effectiveness of radar from an inverse fourth-power law to an inverse square law — in theory, at least. In practice it would be somewhat less than perfectly efficient ...", https://archive.org/details/rollingstones0000robe_q7v9/page/128/mode/2up?q=%22fourth+power%22 https://archive.org/details/rollingstones0000robe_q7v9/page/... A quick search on Google Scholar finds there's a fourth-power law for shock waves: "A fourth-power law relating the stress jump through a steady structured shock wave and the maximum strain rate within the shock wave has received recognition as a unifying relation over a sensibly wide range of materials and shock compression amplitudes." - https://pubs.aip.org/aip/jap/article-abstract/107/1/013506/287070/Structured-shock-waves-and-the-fourth-power-law?redirectedFrom=fulltext https://pubs.aip.org/aip/jap/article-abstract/107/1/013506/2... "Observations on the fourth-power scaling of high-pressure shock waves in solids" at https://pubs.aip.org/aip/jap/article-abstract/130/24/245901/1065688/Observations-on-the-fourth-power-scaling-of-high?redirectedFrom=fulltext https://pubs.aip.org/aip/jap/article-abstract/130/24/245901/... and one with irradiance, though at the forth-power of the cosine: "The cosine-fourth-power law states that the irradiance at any point in the image formed by a photographic lens, in the absence of vignetting, is equal to E_0 cos^4 β" - https://nvlpubs.nist.gov/nistpubs/jres/39/jresv39n3p213_A1b.pdf https://nvlpubs.nist.gov/nistpubs/jres/39/jresv39n3p213_A1b.... I also found the following at https://pubs.aip.org/aip/jap/article-abstract/75/6/3075/400188/Gold-nanoparticles-ion-implanted-in-glass-with https://pubs.aip.org/aip/jap/article-abstract/75/6/3075/4001... : "The third‐order nonlinear optical susceptibility χ(3) of this glass was found to be proportional to the fourth power of the radius of the colloid particles or the fourth power of the absorption coefficient at the peak of a plasmon band when the total volume of the colloid particles was constant."

euroderf 2y ago

Doesn't the cost of heating a dwelling involve a fourth power of the difference in temperature, outside/inside ?

PaulHoule 2y ago

Flow through a pipe scales as the fourth power of the radius https://sino-inst.com/pipe-flow-vs-pressure-relationship-calculate/ https://sino-inst.com/pipe-flow-vs-pressure-relationship-cal... This came to my attention when I was teaching Physics 102 at Cornell which was an auto tutorial course for pre-meds that had an unusual focus on fluid mechanics for an intro physics course.

Aloisius 2y ago

It's more a rule of thumb than anything approaching a law. The exponent varies based on a number of factors like existing road condition, road construction standards, speed, weather conditions, etc.