| Topic: |
Science > Physics |
| User: |
"Front Office" |
| Date: |
02 Sep 2005 09:01:07 AM |
| Object: |
The Power of a Hurricane |
I estimate - _guess_, actually - that a category
4/5 hurricane such as Katrina is somewhere between
50 terrawatts (i.e., 50-trillion watts) and 500 Tw.
For comparison, humanity's average energy use rate
is about 13 Tw (~3 Tw for the U.S. alone), with a
peak of about twice that.
(I also estimate that the instantaneous energy of a
hurricane, due to kinetic energy of the rotating air
mass plus gravitational potential energy of suspended
water and the latent heat of vapor, is on the order
of 10^18 joules [~500 megatons of TNT equivalent].)
Hurricanes are powered by sunlight - i.e., they are
solar-powered. (It's interesting to try to imagine
ways to nurture, sustain, and put in harness, a
permanent hurricane in the Gulf of Mexico. Doing
such a thing would require an engineering project
whose scale would far exceed that of Apollo or
Manhattan, but if electricity could be produced from
it, then it might be a useful project.)
What variables and assumptions should be taken into
account in calculating, or making a refined estimate
of, the power of a hurricane?
Open to suggestions . . .
b
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| User: "Richard Henry" |
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| Title: Re: The Power of a Hurricane |
02 Sep 2005 12:49:20 PM |
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"Front Office" <YoMo@erols.com> wrote in message
news:43185B23.7090702@erols.com...
I estimate - _guess_, actually - that a category
4/5 hurricane such as Katrina is somewhere between
50 terrawatts (i.e., 50-trillion watts) and 500 Tw.
For comparison, humanity's average energy use rate
is about 13 Tw (~3 Tw for the U.S. alone), with a
peak of about twice that.
(I also estimate that the instantaneous energy of a
hurricane, due to kinetic energy of the rotating air
mass plus gravitational potential energy of suspended
water and the latent heat of vapor, is on the order
of 10^18 joules [~500 megatons of TNT equivalent].)
Hurricanes are powered by sunlight - i.e., they are
solar-powered. (It's interesting to try to imagine
ways to nurture, sustain, and put in harness, a
permanent hurricane in the Gulf of Mexico. Doing
such a thing would require an engineering project
whose scale would far exceed that of Apollo or
Manhattan, but if electricity could be produced from
it, then it might be a useful project.)
What variables and assumptions should be taken into
account in calculating, or making a refined estimate
of, the power of a hurricane?
Open to suggestions . . .
Hurricanes extract energy from the ocean. The fastest-growing hurricanes
move quickly over warm water. A permanently-fixed hurricane would require a
corresponding inflow of warm water, or it would become a large refrigerator.
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| User: "Alex Terrell" |
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| Title: Re: The Power of a Hurricane |
02 Sep 2005 03:11:55 PM |
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Assume 10,000km2, and 10km high = 100,000km3 = 100E12kg of air
V = 50m/s.
E = 1/2 * 100E12 * 50^2 = 1.25E17 Joules
There are about 100,000 seconds in a day. Assume you tap the energy
evenly over 10 days, = 1E6 seconds.
Power = 1.25E11 Watts = 125 GW.
The biggest variable is the time. Something like Katrina over the ocean
does not expend too much energy. Power would be less than 125GW.
Put up a 10km high wall to stop it within 10,000 seconds, and you have
12.5TW.
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| User: "G=EMC^2 Glazier" |
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| Title: Re: The Power of a Hurricane |
02 Sep 2005 05:17:13 PM |
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Alex I'm an expert on hurricanes. Last year I was hit by three. It is
the tornadoes inside these.hurricanes that are the killers. Winds of
135 mph do lots of wide spread damage. Winds of 275mph kill. Bert
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| User: "tj Frazir" |
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| Title: Re: The Power of a Hurricane |
02 Sep 2005 06:32:58 PM |
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equal the energy it takes to undo it.
100,000 homes ..1000 roads ..5000 dead people
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| User: "Edward Green" |
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| Title: Re: The Power of a Hurricane |
03 Sep 2005 09:14:02 AM |
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Alex Terrell wrote:
Assume 10,000km2, and 10km high = 100,000km3 = 100E12kg of air
V = 50m/s.
E = 1/2 * 100E12 * 50^2 = 1.25E17 Joules
There are about 100,000 seconds in a day. Assume you tap the energy
evenly over 10 days, = 1E6 seconds.
Power = 1.25E11 Watts = 125 GW.
The biggest variable is the time. Something like Katrina over the ocean
does not expend too much energy. Power would be less than 125GW.
Put up a 10km high wall to stop it within 10,000 seconds, and you have
12.5TW.
Ok. That's a good start. Now that you've made the initial and more
difficult creative ansatz, second order critique becomes easier. :-)
You're assuming the hurricane is like a giant top that is running down.
The real hurricane is more like a lossy flywheel which is continually
being run up by the atmospheric engine and dissipating kinetic energy.
So average power over the life of the storm is greater than the
instantaneous kinetic energy divided by a lifetime.
The OP suggested 1TW. Given your answer, this seems like a reasonable
ballpark guess (what genie did he contact to pull a reasonable order of
magnitude estimate out by guesswork?).
Possibly the tail end of the storm, weakening over land, is more like
your model: removed from water, we're no longer yanking on the string,
and the top runs down.
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| User: "" |
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| Title: Re: The Power of a Hurricane |
04 Sep 2005 05:35:53 AM |
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In article <1125756842.757153.130780@g49g2000cwa.googlegroups.com>,
"Edward Green" <spamspamspam3@netzero.com> wrote:
Alex Terrell wrote:
Assume 10,000km2, and 10km high = 100,000km3 = 100E12kg of air
V = 50m/s.
E = 1/2 * 100E12 * 50^2 = 1.25E17 Joules
There are about 100,000 seconds in a day. Assume you tap the energy
evenly over 10 days, = 1E6 seconds.
Power = 1.25E11 Watts = 125 GW.
The biggest variable is the time. Something like Katrina over the ocean
does not expend too much energy. Power would be less than 125GW.
Put up a 10km high wall to stop it within 10,000 seconds, and you have
12.5TW.
Ok. That's a good start. Now that you've made the initial and more
difficult creative ansatz, second order critique becomes easier. :-)
You're assuming the hurricane is like a giant top that is running down.
The real hurricane is more like a lossy flywheel which is continually
being run up by the atmospheric engine and dissipating kinetic energy.
So average power over the life of the storm is greater than the
instantaneous kinetic energy divided by a lifetime.
The OP suggested 1TW. Given your answer, this seems like a reasonable
ballpark guess (what genie did he contact to pull a reasonable order of
magnitude estimate out by guesswork?).
Possibly the tail end of the storm, weakening over land, is more like
your model: removed from water, we're no longer yanking on the string,
and the top runs down.
I don't know if this applies, but...
What I don't understand is why this hurricane, which has meandered
for some time over the Atlantic Ocean, hadn't accumulated a lot
of energy, but after going over Florida's traffic bumps, it
managed to acquire enought to get to a Cat. 4 and 5. Was
it the "squeezing"?
/BAH
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| User: "Richard Henry" |
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| Title: Re: The Power of a Hurricane |
04 Sep 2005 08:59:15 AM |
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<jmfbahciv@aol.com> wrote in message
news:dfeim9$8nc_005@s824.apx1.sbo.ma.dialup.rcn.com...
In article <1125756842.757153.130780@g49g2000cwa.googlegroups.com>,
"Edward Green" <spamspamspam3@netzero.com> wrote:
Alex Terrell wrote:
Assume 10,000km2, and 10km high = 100,000km3 = 100E12kg of air
V = 50m/s.
E = 1/2 * 100E12 * 50^2 = 1.25E17 Joules
There are about 100,000 seconds in a day. Assume you tap the energy
evenly over 10 days, = 1E6 seconds.
Power = 1.25E11 Watts = 125 GW.
The biggest variable is the time. Something like Katrina over the ocean
does not expend too much energy. Power would be less than 125GW.
Put up a 10km high wall to stop it within 10,000 seconds, and you have
12.5TW.
Ok. That's a good start. Now that you've made the initial and more
difficult creative ansatz, second order critique becomes easier. :-)
You're assuming the hurricane is like a giant top that is running down.
The real hurricane is more like a lossy flywheel which is continually
being run up by the atmospheric engine and dissipating kinetic energy.
So average power over the life of the storm is greater than the
instantaneous kinetic energy divided by a lifetime.
The OP suggested 1TW. Given your answer, this seems like a reasonable
ballpark guess (what genie did he contact to pull a reasonable order of
magnitude estimate out by guesswork?).
Possibly the tail end of the storm, weakening over land, is more like
your model: removed from water, we're no longer yanking on the string,
and the top runs down.
I don't know if this applies, but...
What I don't understand is why this hurricane, which has meandered
for some time over the Atlantic Ocean, hadn't accumulated a lot
of energy, but after going over Florida's traffic bumps, it
managed to acquire enought to get to a Cat. 4 and 5. Was
it the "squeezing"?
It spent a couple of days in the very warm Gulf of Mexico.
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| User: "Autymn D. C." |
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| Title: Re: The Power of a Hurricane |
03 Sep 2005 06:11:04 AM |
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Hurricanes are hollow, duh.
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| User: "Tim Keating" |
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| Title: Re: The Power of a Hurricane |
03 Sep 2005 09:08:25 AM |
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On 2 Sep 2005 13:11:55 -0700, "Alex Terrell" <alexterrell@yahoo.com>
wrote:
Assume 10,000km2, and 10km high = 100,000km3 = 100E12kg of air
V = 50m/s.
E = 1/2 * 100E12 * 50^2 = 1.25E17 Joules
There are about 100,000 seconds in a day. Assume you tap the energy
evenly over 10 days, = 1E6 seconds.
Power = 1.25E11 Watts = 125 GW.
The biggest variable is the time. Something like Katrina over the ocean
does not expend too much energy. Power would be less than 125GW.
Put up a 10km high wall to stop it within 10,000 seconds, and you have
12.5TW.
way... way off... You missed the whole bit about water
evaporation/condensation cycle.
I suggest using energy input as a way to determine
Hurricane Power..
============
Here are some very rough calcs for Katrina after it got into the
Gulf of Mexico.. Based on Sea surface temp change of ocean.. which
dropped by approximate 5 degrees C..
(Based on before and after SST sat readings)
Area of temp reduction 1200 Km x 800Km ..Average depth of high
temp thermocline 5m. Temp change 5C.. 3 Days to traverse gulf.
Note: I'll use fresh water for heat capacity calcs, which close enough
to get a rough idea..
----------
Energy input..
1200E+3(X axis) meters * 800E+3(Y axis) meters * 5 (Z axis, depth
of temp change) meters * 5 degree C temp change * 1000Kg/M^3
(conversion M^3 to mass) * 2100 J/(Kg.K) (specific heat of H20) ==
5.04E+19 (joules(watt/seconds) of thermal energy consumed)
---
Time duration over gulf..
3(days) * 24(hours/day) * 60(Minutes/hour) *60(Seconds/Minutes) ==
2.592E+5..
---
Average energy input..
5.04E+19/2.592+5 == 1.94 E+14 (joules per second/watt seconds)
or...194,000 GigaWatts !!!
(Enough thermal energy consumed in each 19 hour period to equal the
US's total electrical energy generation for a whole year.)
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| User: "Edward Green" |
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| Title: Re: The Power of a Hurricane |
03 Sep 2005 11:33:49 AM |
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Alex Terrell wrote: <...>
Power = 1.25E11 Watts = 125 GW.
Tim Keating wrote: <...>
194,000 GigaWatts
Hmm. Over three order of magnitude! That is serious, even for the
back of an envelope. However, I can offhand see several factors which
would tend to reconcile these numbers.
First, we should agree whether we are calculating the total work done
by the storm, or the total energy flux. Since we are using the term
"power", and comparing the results to measures of the total useful
work consumed by the US over certain periods, I take it we want work.
As I may have already mentioned, Alex Terrel assumes all the capacity
of a storm to do work is stored up in it at one moment, like a spinning
top, which runs down over a course of days. The storm is more like a
pumped lossy top, which in continually dissipating energy and being
spun up by the weather system.
Terrel uses a 10 day lifetime for the top to run down. Suppose we
instead assumed that the instantaneous stored kinetic energy of the
storm represented one day's work input on the top: this increases his
power estimate by a an order of magnitude.
Tim Keating on the other hand bases his figures on heat transfer out of
the warm water. He is modeling the energy input to a heat engine, but
we know a heat engine is thermodynamically limited in efficiency, and
that practically the efficiency is always lower than the limit. Say
the actual overall efficiency of the process is 10%: applied to power,
this decreases his estimate by an order of magnitude.
Now we have:
Terrell (modified) ~ 1,250 GW
Keating (modified) ~ 19,000 GW
Well, still over an order of magnitude, but at least on the back of the
same envelope. ;-)
If the storm dissipates its instantaneous stored kinetic energy more
than once a day on average, or if the overall thermodynamic efficiency
is even lower, we can get closer. We have neglected both the potential
energy loss of falling rain, and sources of the potential to do work
other than temperature differences, which factors would tend to
increase the individual estimates, in that order.
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| User: "Tim Keating" |
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| Title: Re: The Power of a Hurricane |
03 Sep 2005 01:56:52 PM |
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On 3 Sep 2005 09:33:49 -0700, "Edward Green"
<spamspamspam3@netzero.com> wrote:
Alex Terrell wrote: <...>
Power = 1.25E11 Watts = 125 GW.
Tim Keating wrote: <...>
194,000 GigaWatts
Hmm. Over three order of magnitude! That is serious, even for the
back of an envelope. However, I can offhand see several factors which
would tend to reconcile these numbers.
snip...
Tim Keating on the other hand bases his figures on heat transfer out of
the warm water. He is modeling the energy input to a heat engine, but
we know a heat engine is thermodynamically limited in efficiency, and
that practically the efficiency is always lower than the limit. Say
the actual overall efficiency of the process is 10%: applied to power,
I suspect your conversion factor is off by quite a bit..
A large hurricane could achieve conversion efficiencies
substantial higher than 35%.
1st.
Consider the input Temp(33C) and pressure(900MB) verses the
temp(-150C, maybe even lower) and pressure(17 MilliBar) at outflow???
2nd.
Friction at lower altitudes (waves, cloud) get's recycled back
into back into the driving energy source. Only energy lost on the
storm fringes doesn't get recycled.
I suspect that the larger and more powerful hurricanes gain
substantial efficiency advantages as they get stronger..
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| User: "Edward Green" |
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| Title: Re: The Power of a Hurricane |
03 Sep 2005 09:34:06 PM |
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Tim Keating wrote:
On 3 Sep 2005 09:33:49 -0700, "Edward Green"
<spamspamspam3@netzero.com> wrote:
Tim Keating on the other hand bases his figures on heat transfer out of
the warm water. He is modeling the energy input to a heat engine, but
we know a heat engine is thermodynamically limited in efficiency, and
that practically the efficiency is always lower than the limit. Say
the actual overall efficiency of the process is 10%: applied to power,
I suspect your conversion factor is off by quite a bit..
A large hurricane could achieve conversion efficiencies
substantial higher than 35%.
1st.
Consider the input Temp(33C) and pressure(900MB) verses the
temp(-150C, maybe even lower) and pressure(17 MilliBar) at outflow???
I take it these figures are appropriate to the upper atmosphere, and so
you may be right about the temperature of the cold reservoir, but I
would quibble that the pressure difference is misleading: the pressure
gradient is an equilibrium pressure gradient, and doesn't help us do
work. We can run a heat engine between upper and lower atmosphere, but
not a simple turbine.
2nd.
Friction at lower altitudes (waves, cloud) get's recycled back
into back into the driving energy source. Only energy lost on the
storm fringes doesn't get recycled.
Hmm... I see your point. As if our steam engine had one of its
bearings immersed in the hot reservoir. In calculating efficiency,
that loss to frictional heating never really left the reservoir.
I suspect that the larger and more powerful hurricanes gain
substantial efficiency advantages as they get stronger..
On the other hand, they are quite irreversible!
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