# Lecture 3: Scientific Notation, Energy and Power Units, Some Energy and Power Examples, The R/P Ratio

Don't Panic

Sections

Caption: "Lightning over the outskirts of Oradea, Romania, during the August 17, 2005 thunderstorm which went on to cause major flash floods over southern Romania."

Electrical potential energy of charge separation in the atmosphere is converted into the energy of electromagnetic radiation, heat, and sound.

Credit: Mircea Madau, User:Lucas.

Permission: Public domain at least in USA.

# Scientific Notation

Scientific notation is a way of expressing very large and very small numbers.

It's vital in a world where quantities that must be understood and used in calculations come in vastly different sizes.

We have already used it a bit and many people may already know it well.

And it is really simple.

One expresses a number as a coefficient times a power of ten:

```
a*10**b  in my old fortran way.

a*10b in better format.

a is the coefficient which is between 1 and 10 in normalized Scientific notation.

Coefficient seems most obvious term to use, but
older works used the terms
significand
or
mantissa.

b is the exponent.

10 is ten.

Examples of
scientific notation
with some example
International System of Units (SI) prefixes and SI units.

---------------------------------------------------------------------------------

Number                              SI prefix

-----------------------------
SI energy unit   SI power unit
(power is
energy per
unit time)

---------------------------------------------------------------------------------

1  =  1*10**0  = 10**0              (nada)          joule (J)         watt (W) (joule/s)

(One can omit
the coefficient
if its 1.)

10 =  10**1                         deka (da)

100 = 10**2                         hecto (h)

1000 = 10**3                        kilo (k)        kilojoule (kJ)   kilowatt (kW)

1 000 000 = 10**6                   mega (M)        megajoule (MJ)   megawatt (MW)

(The number of digits of ordinary notation
after the lead one is the exponent
of standard scientific notation number.)

1 000 000 000 = 10**9               giga (G)        gigajoule (GJ)   gigawatt (GW)

1 000 000 000 000 = 10**12          tera (T)        terajoule (TJ)   terawatt (TW)

10**15                              peta (P)        petajoule (PJ)   petawatt (PW)

10**18                              exa (E)         exajoule (EJ)    exawatt (EW)

10**21                              zeta (Z)        zetajoule (ZJ)   zetawatt (ZW)

10**24                              yota (Y)        yotajoule (YJ)   yotawatt (YW)

(Not Yoda.)

1 day = 86400 s = 8.64*10**4 s

1 Julian year = 365.25 days
= 3.15576*10**7 s
= approx pi*10**7 s

Age of the universe = 14 Gyr

= 4.4*10**17 s

-----------------------------
SI length       Example scale

1 = 10**0                (nada)            meter (m)       human

0.1 = 10**(-1)           deci              decimeter (dm)  guinea pig

```
```

0.01 = 10**(-2)          centi             centimeter (cm) Etruscan shrew

0.001 = 10**(-3)         milli             millimeter (mm) fine marks on a meter stick

10**(-6)                 micro             micron (mu-m)   microbe

```
```
10**(-9)                 nano              nanometer (nm)  nanotechnology
This is really
sub-micron (i.e., hundreds
nanometers) technology
I think, but that doesn't
sound sexy to research funders.

10**(-10)                                  Angstrom (A)    atom

10**(-12)                pico              picometer (pm)

10**(-15)                femto             femtometer (fm) atomic nucleus
(fermi to
physicists)

---------------------------------------------------------------------------------
```
How does one multiply and divide using scientific notation?

One multiplies and divides the coefficients and adds and subtracts the components.

```
In general for multiplication:   a*10**b * c*10**d = (a*c)*10**(b+d)

Examples:

3*10**3  *  3*10**3  =  9*10**6

7*10**4  *  5*10**6  =  35*10**10 = 3.5*10**11

In general for division:   (a*10**b)/(c*10**d) = (a/c)*10**(b-d)

Examples:

( 9*10**48 )/( 3*10**(-24) ) = 3*10**(48-(-24)) = 3*10**72

( 4*10**12 )/( 8*10**24 ) = 0.5*10**(-12) = 5*10**(-13)

```
``And that's all folks for scientific notation."---as Bugs Bunny used to say.

Caption: "Still frame from the animated cartoon "Falling Hare" (1943).

A classic Bugs Bunny cartoon.

Bugs was clearly interested in energy and power.

The copyright was not Public domain. renewed and thus the cartoon has fallen into the public domain. This restored shot is taken from the version found on the Looney Tunes Golden Collection DVD set. The unrestored version can be seen at the Internet Archive, while the restored version can be seen on YouTube. Bugs is lying on his back, propped up on his left elbow, reading a book titled Victory Thru Hare Power. This title refers to the propaganda book (and Walt Disney's film of the same name) Victory Through Air Power (1943)."

Credit: Looney Tunes

Linked source: Wikipedia image "http://en.wikipedia.org/wiki/File:Falling_hare_bugs.jpg.

Public domain at least in USA.

# Weird Energy Units

It's understandable---though lamentable---that people like to stick with traditional units where they have a concrete sense of the size of the unit:

But energy is such an abstract quantity in the first place, why not use standard units for energy in all cases?

Why not use SI (Systeme International) (AKA Metric System) energy units?

Of course, it's really just us, the Burmese, and the Liberians who don't.

"Map of the world where red represents countries which do not use the metric system"

Linked source: Wikipedia image http://en.wikipedia.org/wiki/Image:Metric_s ystem.png.

Author: User Donovaly.

Public domain.

With the right prefix, there is almost always a unit of a convenient size for most contexts---except in astronomy, of course.

By always using SI energy units, people we get a good sense of the relationships between different quantities of energies in different contexts.

But no---there is a plethora of weird energy units for different contexts for which the conversion factors are NOT obvious and are tricky.

Even people writing articles on energy often merrily trip between relatively incomparable units without apology---and without shame.

So let's put some of these weird energy units in relation to SI energy units so that we know what people are talking about.

The instructor feels a bit peevish/cranky on this subject.

We are NOT going to be exhaustive.

See Conversion of Units (Wikipedia) for that.

```
-----------------------------------------------------------------
Unit Conversions
-----------------------------------------------------------------
Weird unit            In convenient    Comment
SI units
-----------------------------------------------------------------

1 food calorie        4.1868 kJ        Typical human food needs are
in the range 2000--3000 food calories.
1000 food calories    4.1868 MJ        per day.  That turns into 8--12 MJ.
So the megajoule is a perfectly
convenient unit for food energy.
It's better than food calories.

1 calorie             4.1868 J         A food calorie is really a kilocalorie.
The real calorie is the amount of
energy needed to raise the temperature
of one gram of water by 1 degree Celsius.
Various versions exist because the
amount of energy needed varies
with conditions.  The shown one
is the International Steam calorie
(See Wikipedia:  Calorie).

1 kilowatt-hour       3.6 MJ           The kilowatt-hour is hybrid unit
that is (kilojoule/second)*hour.
The MJ is good-sized replacement.

1 Btu                 1.0545 kJ        British thermal units of slightly
different size still linger around.
Kilojoules can obviously replace them.

1 kg of gasoline      44--45 MJ        About 5.5 times daily human
food needs.  You could live
on a about 0.2 kg of gasoline per day.

1 kg of oil           41.868 MJ        This is standard definition
since the chemical energy content
of oil varies.  It looks like the
calorie digits.

tonne oil equivalent  41.868 GJ        See Ton of oil equivalent.
(toe)                                  A tonne is a metric ton (1000 kilograms).
It really ought to be called a
megagram (Mg).

barrel (bl) of oil    6.12 GJ          This is approximate.  The oil
equivalent                             industry insists are reporting
oil in barrels---though no one
has put oil in barrels in a
jillion years (to be precise).
Why not just report oil quantities
in energy equivalent since energy
content is the key issue.

1 Mbl of oil          6.12 PJ          World daily consumption is often
given in mbls.

1 Gbl of oil          6.12 EJ          World yearly consumption is often
given in Gbls.

tonne coal equivalent 29.3076 GJ       This must be a standard definition
since the chemical energy content
of coal varies.  You can see one
the reasons why people prefer oil
to coal.  Oil has a higher energy
density typically.  (See tonne oil
equivalent just above.)

-----------------------------------------------------------------

```
Question: A imperial pint (= 20 fluid ounces = 568.26125 mL) of Guinness contains 198 food calories.

Recall every 1000 food calories equals about 4 MJ.

So about how much is 198 food calories in megajoules?

1. 0.8 MJ.
2. 8000 MJ.
3. 0.0008 MJ.
4. All of the above.

Answer 1---but it's hard to figure out isn't it?

The trick is to use factors of unity and algebra.

4.1868 MJ = 1000 food calories.

Therefore

```
4.1868  MJ
1 =  ------------------
1000 food calories

You can always multiply anything by 1 without changing
its size.

Thus

198 food calories = 198 food calories * 1

4.1868 MJ
= 198 food calories *  ------------------
1000 food calories

= approx 0.8 MJ  .

```
So 10 pints of Guinness provides you with all the energy you need in a day.

But man does not live by energy alone.

In any case, alcohol is slightly toxic and has psychoative effects.

Remember friends don't let friends drive drunk.

The weirdness of energy units does NOT seem to have carried over to power.

Caption: "Ratcliffe Power Plant, Nottinghamshire" (2006mar20).

The mist is probably smoke, but some could be just water vapor from the cooling towers.

It looks like some hypertrophied Satanic mill from the Industrion Revolution.

I thought this was a nuclear power station, but it's actually a coal-fired power station.

Credit: Alan Zomerfeld.

Linked source: Wikipedia image .

Licensed under the Creative Commons Attribution ShareAlike 2.5.

It seems most everyone is now on the SI team for power---which is energy transferred or transformed per unit time.

Power is almost always quoted in watts or some standard multiple:

kilowatts, megawatts, gigawatts, terawatts.

Watts we need for light-bulbs. Actually, only about 5 % of the power of an incandescent light bulb passes through the state of visible light (Wikipedia: Incandescent light bulb).

Kilowatts we need for hours evidently.

For 2005, worldwide commercial energy consumption rate of the humankind has been calculated to be 16 terawatts (= 16 x 10**12 W) ( Wikipedia: World energy resources and consumption).

The one non-SI power unit with some staying power is the horsepower (hp). There are several modern definitions, but perhaps the most common one is the
```
electrical horsepower = 746 W = 0.746 kW exactly.

```
James Watt (1736--1819) (who developed the much improved steam engine) invented horsepower to help market his invention (See Wikipedia: History of the term "horsepower").

"Chantrey's statue of James Watt, the Scottish inventor" (1986): Linked source: Wikipedia.

Caption: "Shire horses at Avon Valley Country Park, Bristol, England. Named Misty and Molly, they are six years old." (2007aug)

Linked source: Wikipedia image http://en.wikipedia.org/wiki/Image:Shire_horses_arp.jpg.

Public domain.

Horsepower has stuck around as a legacy in certain backward industries---notably---the automobile industry.

Caption: "Vehicles per thousand people." (2008apr01):

```                  ----------------------------------------------------------------
Color                 Cars per thousand persons
----------------------------------------------------------------
black                  600+
darkest green          501--600
darker green           301--500
dark green             151--300
green                  101--150
light green             61--100
lighter green           41--60
lightest green          21--40
still lighter green     11--20
almost not green at all  0--10
grey                     nearly none I guess
----------------------------------------------------------------
```
In the US every person owns at least 60 % of a car.

Author: User: TastyCakes.

Linked source: Wikipedia image http://en.wikipedia.org/wiki/Image:World_vehicles_per_capita.svg.

Public domain.

But the car folks could use kilowatts or megawatts just as easily as horsepower.

Here's another question for the class.

# Energy from the Sun

Most of the energy we deal with on
Earth comes from the Sun---and it does a lot for us:

The Sun is pretty complex, but I'd guess it's still less complex than a single living cell.

Caption: "This diagram shows a cross-section of a solar-type star." (2006oct).

In the center the Sun is of order 15 MK (i.e., 15 million kelvins) in temperature.

This is where nuclear fusion generates the power output of the Sun that emerges as electromagnetic radiation.

There are several fusion reaction chains.

The net effect of the most important one for the Sun is:

```
4*11H (4 hydrogen nuclei)

---->  24He (1 He nuclei) + 2*positrons + 2*neutrinos + 2*gamma rays

```
The heat energy output for this chain is is about 0.272 W/m**3 in the Sun's core---which is pretty small---but there is a lot of volume in the Sun's core.

The total power output of the Sun in electromagnetic radiation is 3.846*10**26 W which in astro-jargon we call the Sun's luminosity.

The energy is transported from the core to the surface by radiative transfer and near the surface by convection predominantly.

Convection is a macroscopic turbulent means of energy transport.

The tops of the convective cells make the solar granules: these are the grainy patches on the visible surface of the Sun.

Convection happens in boiling pans of water.

It's goes extensively in the Earth's atmosphere, but not often noticed since air is invisible usually.

At the Sun's suface, the Sun's energy streams away as electromagnetic radiation.

Why does the energy flow from the core to space?

Thermal energy spontaneously flows from hot to cold.

This is a basic process that can be seen as a consequence of the 2nd law of thermodynamics which we discuss in Lecture Thermodynamics.

The Sun's core is hot (15 MK) and space is cold.

The temperature of the main component of energy in space is, in fact, 2.725 K (or 2.725 kelvins above absolute zero).

This is the temperature of the cosmic microwave background radiation (CMB) that permeates all space and is a relic of the Big Bang.

Author: Project leader: Dr. Jim Lochner; Curator: Meredith Gibb; Responsible NASA Official:Phil Newman.

Linked source: Wikipedia image http://en.wikipedia.org/wiki/Image:Sun_parts_big.jpg.

Public domain.

1. The solar heating keeps the surface of the Earth warm.

2. Solar heating is the main driver of the persistant atmospheric and ocean flows. (Lunar and solar tidal effects play a role too.)

3. Solar heating is pretty much the cause of weather. (Lunar and solar tidal effects play a role too depending on what one is counting as weather.)

4. Almost all biota ultimately receive their food energy from photosynthesis powered by solar light.

5. Biota (except for deep sea and subterranean biota) mostly see (if they have vision) by solar light or solar light reflected by the Moon.

6. Fossil fuels (or such is the standard theory---of which there is little doubt) are the transformed remains of organic life and their energy content ultimately derived from the Sun.

How much energy do we actually get from Sun?

This is usually specified by giving the solar constant.

Solar constant is the solar electromagnetic radiation (light) power per unit area (perpendicular to the Earth-Sun line) at the top of the Earth's atmosphere.

The solar constant 1978--1999.

The solar constant is the power per unit area (perpendicular to the Earth-Sun line) at the top of the Earth's atmosphere. The mean value is about 1366.5 W/m**2.

In other words, a bit less than 2 horsepower per square meter.

During a full sunspot solar cycle the value varies by only by 0.1 percent from maximum and minimum. The near constancy of the solar constant is good for life on Earth.

Actually the annual variation do to the variation in the Earth-Sun distance has been removed from this plot.

This is the plot that one would get at the mean Earth-Sun distance.

The solar constant varies over about 6.9% during a year from a low of 1321 W/mē in early July when Earth is farthest from the Sun to 1412 W/mē in early January when Earth is closest to the Sun (Wikipedia Solar Constant).

Credit: NASA.

Most of the solar electromagnetic radiation is visible light.

The solar spectrum log-log plot.

Here we have a black-body radiation fit to the solar spectrum (dashed line), the solar spectrum above the atmosphere (dark blue), and the relative solar spectrum at the Earth's surface in cloud-free conditions (light blue). The wavelength range extends from far UV to far IR.

Black-body radiation is the spectrum emitted by a body that had a single temeperature: i.e., was in thermodynamic equilibrium.

Because of the small scale, absorption lines in the spectrum have been mostly smoothed out. A larger scale would show many them.

Note that the Sun spectrum peaks in the visible.

Note also that the Earth's atmosphere is opaque in the UV and in many broad bands in the IR, but the visible is pretty transparent.

The transparent bands are sometimes called WINDOWS in astro jargon.

Credit: US Naval Research Laboratory, Judith Lean; download site NASA.

A good site for the solar spectrum is NOAA's The Solar Spectrum and Terrestrial Effects site.

The solar power per unit area that actually reaches the ground averaged over the whole Earth's surface (which includes the night side) is only 170 W/m**2 (Smil 2006, p. 27). This the average power is called the average insolation, but note that Wikipedia gives it as 250 W/m**2. We will accept Smil's (2006, p. 27) value for now.

The solar constant energy is captured by the circular cross section of the Earth which has area pi*R**2, where R is the Earth's radius.

```       So the capture cross section of the Earth is pi*R**4.

But this must be spread over the whole surface area which is 4*pi*R**4.

So the fraction of the solar constant to spread over the Earth is

pi*R**4
-----------  = 1/4
4*pi*R**4
```
So the top of the Earth's atmosphere gets on average about 340 W/m**2.

But only about half of this reaches the ground. The rest is reflected above the ground.

Thus we arrive at 170 W/m**2 (Smil 2006, p. 27).

Of course, we actually can't capture 170 W/m**2.

Photovoltaics can't capture 100 % of insolation.

Currently, 10% or so is commercially feasible, but much higher efficiencies are possible.

Experimental high efficiency solar cells have reached 43 % for a current record.

So tens of W/m**2 of solar energy is possible.

On the other hand, biomass from dryland typically yields only about 0.5 W/m**2 and tops out about 1 W/m**2 (Smil 2003, p. 264).

Biofuels, as we'll discuss in lecture World Energy Resources and Consumption, are NOT going to be a dominant fuel of the future.

If one goes from power per unit area (the insolation) to total solar power reaching the Earth's surface (by multipling insolation by surface area), one find it is 89 PW = 89000 TW (World Energy Resources and Consumption: Solar Energy).

This is vastly more than the 16 TW of commercial power that humankind currently uses.

Question: By what factor is the total solar power at the Earth's surface larger than the commercial power consumption of humankind?

Don't reach for your calculators.

1. 10.
2. 100.
3. 5500.
4. All of the above.

The total solar power is about 5500 times the total commercial power consumption of humankind.

Behold:

```
(89000 TW)/(16 TW) = approximately (90/16)*10**3 = 5500.

```
This is another one of those mesmerizing numbers.

For all kinds of obvious reasons, we can only ever harvest a tiny fraction of this as commercial power.

But even a tiny fraction would be all the commercial power we can currently imagine needing.

Many people think that is feasible and the dominant source of commercial power in the future will be solar power from photovoltaics or solar-powered heat engines.

Caption: "On 140 acres of unused land on Nellis Air Force Base, Nev., 70,000 solar panels are part of a solar photovoltaic array that will generate 15 megawatts of solar power for the base." (2007dec)

``Nellis'' reminds me of Nellis St., Woodstock, Ontario where my mother's family used to live.

Author: U.S. Air Force photo/Airman 1st Class Nadine Y. Barclay.

Linked source: Wikipedia image http://en.wikipedia.org/wiki/Image:Giant_photovoltaic_array.jpg.

Public domain.

But that future may be far---100 years---more---less?

A more immediate question is what fraction of commercial power will be solar power 40 years hence---or maybe what fraction ought to be solar power 40 years hence?

A Solar Power Grand Plan (Zweibel et al. 2008, Scientific American, January, p. 64) has been proposed which would make solar power the dominant power in the US by 2050.

# Human Body Energy Use

The
human body transforms energy.

Caption: "The Burghers of Calais by Auguste Rodin, Taken April 2006 by AndyZ at Hirshhorn Sculpture Garden" (2006apr)

According to legend (with maybe some history) The Burghers of Calais (the six burghers of Calais) were volunteers for subjection to the revenge Edward III of England wished to visit on city of Calais in 1347. His wife Philippa of Hainault pleaded successfully for their lives.

Author: User: AndyZ.

Linked source: Wikipedia image http://en.wikipedia.org/wiki/Image:Burghers_of_Calais_Hirshhorn.jpg.

Public domain.

These transformations are an essential and analyzable part of living.

We intake food which carries chemical energy and our bodies overall transform this energy to kinetic energy, body heat, and infrared light.

All of these energy outputs usually end up as waste heat too in the environment (i.e., the body surroundings).

The infrared light is radiated by the body. This is not reflected light, it's light that comes at the expense of the body's heat energy.

We can be seen in the dark by it---like this poor mouse.

We will not an exhaustive presentation---which would mean describing all of life.

Actually, an anti-exhaustive presentation.

A couple of definitions can lead us off:

1. Basal Metabolic Rate (BMR): The rate of energy expended (i.e., power expended) by an animal in a state of complete rest, several hours after the last feeding (about 12 hours for humans) and in a comfortable temperature setting.

Basal in this context means base or reference.

2. Metabolic Scope: The ratio between short-term maximum power expenditure (for some defined time) and BMR (Smil 2006, p. 45).

The values of BMR for humans vary by up to 20 % between individuals who are much alike otherwise and there is significant variation among populations (Smil 2006, p. 59). Here are a few typical relevant numbers.
```
BMR women  55--80 W.

BMR men  60--90 W.

Low/high food energy rate for a sedendary/very active human

=  2000 / 4000 food calories/day

=  8.4  / 16.8 MJ/day

=  97   / 194 W

The low food energy rate for humans is only a bit above
the BMR.

So for sedentary people, most of food energy goes
into existing.

Thinking doesn't take much energy.

A typical healthy adult has a sustained metabolic scope of above 10
for some time (hours?) for example when running or swimming.

This is a power of order 800 W = 0.8 kW and is more than
1 horsepower = 0.746 kW.

But note that most of this power is going into moving the
human body and not in moving other stuff which is what we expect
of horses.

Elite athletes and traditional-society hunters can probably
sustain 1.75 kW for hours??? or a metabolic scope of 20 or more
(Smil 2006, p. 61).

This is actually very high among animals.

Only canids have a higher sustained metabolic scope for hours???
of activity:  i.e., above 30
(Smil 2006, p. 61).

Dogs love to run, you know.

```
Just a bit more on food energy:
```
----------------------------------------------------------------------------

Metabolizable (?) energy content of common foods

food              MJ/hg        The hectogram = 100 g = approximately 0.2 lb
and is of order a serving for many foods.

-----------------------------------------------------------------------------

butter            3.0

ethanol           2.93         This is just drinking alcohol in
everyday speech---we drink car fuel.

cereal grains     1.45--1.55

lean meats        0.5--1.00

fish              0.3--0.9

potatoes          0.3--0.5

fruits            0.15--0.40

vegetables        0.06--0.18

```
Lots of things go into making a healthy diet---chocolate, corn dogs, etc.

But one can see why meat and grain have been big sources of food energy.

A pint of Guinness.

Butter in large amounts is too much of a good thing. But energetically you could live on 3 hg per day---if you could metabolize all that energy content which probably you cannot.

The same could be said for ethanol which is in fact slightly toxic.

Credit: Jon Sullivan of PD Photo.org. The author has released the image into the public domain.

Download site: Wikipedia: Image:Ireland 37 bg 061402.jpg.

# Reserve/Production (R/P) Ratio

In the energy industry, there is a widely used parameter: the
reserves-to-production ratio or R/P ratio (Smil 2003, p. 181).

For future lectures, we will need to know the R/P ratio---well maybe not often, but its good to know anyway.

```
Say you have a reserve R of a quantity at t=0.

The quantity could be oil for example.

You use it at a production (consumption) rate of P which is constant.

At any time t, your reserve is R_t < R  and is given by

R_t = R - P*t   .

```
Question: What is t for R_t=0 (i.e., when will your whole reserve is exhausted)?

1. R/P
2. P/R
3. P*R
4. All of the above.

Solution by algebra:

```
0 = R - P*t

leads to t = R/P.
```
As an example, there are 1300 Gbl (gigabarrels) of recoverable oil reserves in the world as now estimated ( DOE: Energy Information Administration (2008), but this based on the Oil & Gas Journal 2008jan01) and includes some tar sands oil.

World oil production (which is also pretty much consumption) is

```
79 Mbl/day = 79 Mbl/day * 1 * 1
= 79 Mbl/day * (1 Gbl/1000 Mbl) * (365.25 days/1 year)
= 79 *0.365.25 Gbl/year
= 29 Gbl/year

```
as estimated in 2005 (Wikipedia: World oil production). See also Energy Resources and Consumption: Oil. Actually world oil production has been on a plateau since about 2005 (e.g., World Oil Production Forecast - Update May 2009 by Tony Erikson).

By the by, the US consumes 7.1 Gbl/year in 2008 ( Energy Information Administration (US Gov. Agency))---which is about 1/4 of the world energy prodcution.

For the world, we find

```
R/P= 1300 Gbl / 30 Gbl/year  = 43 years.

So in about year 2050 ...

```

As we indicated above, world production and consumption are about equal in the energy game.

The Arguello Inc. Harvest Oil Platform off the coast of California.

``The Arguello Inc. Harvest Oil Platform (figure 1) is located about 10 km off the coast of central California near Point Conception. An impressive structure, the platform is attached to the sea floor and sits in about 200 m of water near the western entrance to the Santa Barbara Channel. Conditions at Harvest are typical of the open ocean and the seas can be quite heavy. Ocean swell and wind waves average about 2 m, though waves over 7 m have been experienced during powerful winter storms. Prevailing winds are from the northwest and average about 6 m/s (15 mph). The platform is served by helicopters from the Santa Maria, California, airport, and is regularly visited by supply boats. Operational since 1991, Harvest has produced over 44 million barrels of oil (as of July, 1997).''

---quoted from Haines, B. et al. (2007).

In 6 years, the Harvest Oil Platform produced 44 Mbl = 0.044 Gbl of oil.

This is about half a day of world production/consumption of 29 Gbl/year circa year circa 2005 (Wikipedia: World oil production). See also Energy Resources and Consumption: Oil.

```
0.044 Gbl          365.25 days
------        *    -------------  = approx 0.5 days .
29 Gbl/year        1 year

```
If I recall correctly, James Bond, in Diamonds are Forever visits an ocean platform off California---but that was long ago in 1971.

Credit: An employee of NASA. As a work of the U.S. federal government, the image is in the public domain.

Download site: NASA-JPL: Ocean Surface Topography from Space.

Time zero for an R/P ratio is usually NOW.

So R/P is the time from now to exhaustion of the reserve---if the assmptions hold.

In fact, if the assumptions were valid, the current R/P would always give the same date for exhaustion: e.g., 2050 for oil.
```
Proof:

Let t be the current time measured from a reference time zero.

R_0 be the reserve at the reference time zero.

P be the constant production rate

R be the current reserve.

Note that R = R_0 - Pt

Now the time of exhaustion as measured from the
reference time is

t_exhaustion = t + R/P

= t + (R_0-Pt)/P

= t + R_0 - t

= R_0

which is a constant.

```

In reality, the reserve R for many non-renewable resources can only be estimated.

This is because we don't have NATURE'S complete inventory.

And also what is considered a reserve (or recoverable reserve or proved recoverable reserve) changes with technology and price.

And, of course, P is usually far from constant.

As a resource tends toward exhaustion, the production (consumption) rate tends to fall which delays the the exhaustion.

So the R/P ratio at best is an estimate of time to reserve exhaustion.

And at worst, it is wildly inaccurate.

For example, say the world decided to produce and consume only 3 Gbl/year (which is about what is needed to make plastics???)

In that case, the R/P ratio would be

```             t = R/P = 1300/3 = 430 years
```
We shouldn't be burning our plastics raw material.

For another example, I think I've read, but cannot now find, that the oil R/P ratio has been about 40 years for about 40 years---this may be just an incredible factoid.

If the predicted exhaustion 40 years had been an valid forecast, we would have no oil today.

But, in fact, the oil R/P ratio is still 40 years.

Used with caution, the R/P ratio it is a meaningful parameter:

Caption: "Ignorance and Want, woodcut from A Christmas Carol by Charles Dickens (1812 - 1870)" (2008feb).

Author: John Leech (1809 - 1870).

Public domain.