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Hello
in my free time i was trying to find a formula for each one of these natural phenomenon to give a good approximation of the AP linked to them, and i wanna know if they are reliable/usable for estimating the power;
Volcano
the method was already accepted in this calculation
"A third way is to consider how much the pressure in the magma chamber is reduced times the reduction in volume, E=ΔP⋅VE=ΔP⋅V. A pressure drop of 5 MPa is apparently typical, and the volume reduction is proportional to the ejected volume (with some scaling factor from packed rock to ejecta)" (here)
the ejecta volume can be calculated with this formula : 10^(4+i) = volume in cubic meter with i the VEI
(a VEI of 3 will give us 0.01 km^3 [10000000 m^3] which correlates with wikipedia)
we just need to put in the typical pressure change, 10000000 * 5*10^6 = 5e+13 joules, or Town level
when we put a VEI of 8 (Highest VEI), we get
10^(4+8) * 5 * 10^6 = 5e+18 Joules, which is fairly close to maximum energy possible for a volcano (if i did not misunderstand it)
"Thus, the largest eruptions release elastic energy of the same order of magnitude as the largest earthquakes, suggesting that 10^19 J may be close to the maximum elastic energy that is available for driving earthquakes and volcanic eruptions."
The final formula is 10^(4+i) * 5*10^6 = energy in joule
so can this be possibly added to the Calculation page ? as a reference for volcano based feat (the same page we have but for earthquake)
Tsunami
from what i understood, the speed of a tsunami depends primarly on the distance it is from the sea floor, because the water particules of the tsunamis moves underwaters circularly, if the sea floor is deeper, it create less friction and slow it down less, the formula can be written as ;
sqrt(d * g), d : sea floor depth and g is gravity. (this is also used on this calculation, but i dont think it got accepted, or at least not added)
if the tsunami is supernatural, i guess we can calculate the speed direcly with basic measurements using pixels
if the wave lenght and period is known, the speed can be calculated this way :
λ * T
λ is wavelenght (in meter)
T is the period between two same points of two adjacent waves (in hertz, or 1/second)
the mass can be calculated as 1000 * h * w * d
or maybe 1000 * (h+depth of sea) * width * thickness
energy would be ;
depth of sea^2 * gravity * 500 * width * thickness
lets say the depth of sea is 4000 meter, the width of the tsunami is 10km, and its thickness is 20 meter
4000 ^2 * 9.81 * 500 * 10000* 20 = 1.5696e+16 joules, small city
i also found this one wikipedia (https://en.wikipedia.org/wiki/Wind_wave#Physics_of_waves) ;
sqrt((g * λ)/(2 * pi) * tanh((2 * pi * d)/λ)
where :
λ is wave lenght
d is ocean floor depthg is gravity
lets test it with our exemple, the depth of sea d is 4000, lets say the wavelenght is 100km
sqrt((pi* 100000)/(2 * pi) * tanh((2 * pi * 4000)/100000) = 196.016317574 m/s, which is close to the average tsunami speed in deep water
final formula would be :
(ρ * (d+h)/2 * th * w)/2 * (sqrt((g * λ)/(2 * pi) * tanh((2 * pi * d)/λ))^2
ρ is density
d is depth of sea
th is thickness of wave
w is width of wave, generally the biggest number for natural tsunamis
λ is wavelenght, 200km in average
g is gravity, or 9.801 m/s^2 on earth surface/
h is height of tsunami
can this be used ?
in my free time i was trying to find a formula for each one of these natural phenomenon to give a good approximation of the AP linked to them, and i wanna know if they are reliable/usable for estimating the power;
Volcano
the method was already accepted in this calculation
"A third way is to consider how much the pressure in the magma chamber is reduced times the reduction in volume, E=ΔP⋅VE=ΔP⋅V. A pressure drop of 5 MPa is apparently typical, and the volume reduction is proportional to the ejected volume (with some scaling factor from packed rock to ejecta)" (here)
the ejecta volume can be calculated with this formula : 10^(4+i) = volume in cubic meter with i the VEI
(a VEI of 3 will give us 0.01 km^3 [10000000 m^3] which correlates with wikipedia)
we just need to put in the typical pressure change, 10000000 * 5*10^6 = 5e+13 joules, or Town level
when we put a VEI of 8 (Highest VEI), we get
10^(4+8) * 5 * 10^6 = 5e+18 Joules, which is fairly close to maximum energy possible for a volcano (if i did not misunderstand it)
"Thus, the largest eruptions release elastic energy of the same order of magnitude as the largest earthquakes, suggesting that 10^19 J may be close to the maximum elastic energy that is available for driving earthquakes and volcanic eruptions."
The final formula is 10^(4+i) * 5*10^6 = energy in joule
so can this be possibly added to the Calculation page ? as a reference for volcano based feat (the same page we have but for earthquake)
Tsunami
from what i understood, the speed of a tsunami depends primarly on the distance it is from the sea floor, because the water particules of the tsunamis moves underwaters circularly, if the sea floor is deeper, it create less friction and slow it down less, the formula can be written as ;
sqrt(d * g), d : sea floor depth and g is gravity. (this is also used on this calculation, but i dont think it got accepted, or at least not added)
if the tsunami is supernatural, i guess we can calculate the speed direcly with basic measurements using pixels
if the wave lenght and period is known, the speed can be calculated this way :
λ * T
λ is wavelenght (in meter)
T is the period between two same points of two adjacent waves (in hertz, or 1/second)
the mass can be calculated as 1000 * h * w * d
or maybe 1000 * (h+depth of sea) * width * thickness
energy would be ;
depth of sea^2 * gravity * 500 * width * thickness
lets say the depth of sea is 4000 meter, the width of the tsunami is 10km, and its thickness is 20 meter
4000 ^2 * 9.81 * 500 * 10000* 20 = 1.5696e+16 joules, small city
i also found this one wikipedia (https://en.wikipedia.org/wiki/Wind_wave#Physics_of_waves) ;
sqrt((g * λ)/(2 * pi) * tanh((2 * pi * d)/λ)
where :
λ is wave lenght
d is ocean floor depthg is gravity
lets test it with our exemple, the depth of sea d is 4000, lets say the wavelenght is 100km
sqrt((pi* 100000)/(2 * pi) * tanh((2 * pi * 4000)/100000) = 196.016317574 m/s, which is close to the average tsunami speed in deep water
final formula would be :
(ρ * (d+h)/2 * th * w)/2 * (sqrt((g * λ)/(2 * pi) * tanh((2 * pi * d)/λ))^2
ρ is density
d is depth of sea
th is thickness of wave
w is width of wave, generally the biggest number for natural tsunamis
λ is wavelenght, 200km in average
g is gravity, or 9.801 m/s^2 on earth surface/
h is height of tsunami
can this be used ?
