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Game of Thrones Physics
Valyrian steel, wildfire, and gods
Dr. Jay Maron


Valyrian steel

"Ice" is the sword with the red handle

Valyrian steel is a fictional substance from "Game of Thrones" that is stronger, lighter, and harder than steel. The only elements that qualify are beryllium, titanium, and vanadium, none of which were known in Earth history until the 18th century. Valyrian steel could be of these elements, an alloy, or a magical substance. According to George Martin, magic is involved.

The fact that it is less dense than steel means that it can't be a fancy form of steel such as Damascus steel or Wootz steel. Also, fancy steel loses its special properties if melted and hence cannot be reforged, whereas Valyrian steel swords can be reforged.

In Earth history, the first metal discovered since iron was cobalt in 1735. This launched a frenzy to smelt all known minerals and most of the smeltable metals were discovered by 1800. Then the battery and electrochemstry were discovered in 1800 and these were used to obtain the unsmeltable metals, which are lithium, beryllium, magnesium, aluminum, titanium, vanadium, niobium, and Uranium. Almost all of the strong alloys use these metals, and so the Valyrians must have used either electrochemistry or magic to make Valyrian steel.


Candidates for Valyrian steel

The following metals and alloys are both stronger and lighter than steel and could hypothetically be Valyrian steel.

                Yield     Density  Strength/Density
                strength  (g/cm3)   (GJoule/kg)
                (GPascal)
Beryllium            .34     1.85     .186
Aluminum + Be        .41     2.27     .181
LiMgAlScTi          1.97     2.67     .738
Titanium             .22     4.51     .050
Titanium + AlVCrMo  1.20     4.6      .261
Vanadium             .53     6.0      .076
AlCrFeCoNiTi        2.26     6.5      .377
AlCrFeCoNiMo        2.76     7.1      .394
Steel                .25     7.9      .032     Iron plus carbon
Copper               .12     9.0      .013
"Yield strength" is the maximum pressure a material can sustain before deforming. "Strength/Density" is the strength-to-weight ratio. Steel is stronger and lighter than copper.
Lore

Petyr Baelish: Nothing holds an edge like Valyrian steel.

Tyrion Lannister: Valyrian steel blades were scarce and costly, yet thousands remained in the world, perhaps two hundred in the Seven Kingdoms alone.

George Martin: Valyrian steel is a fantasy metal. Which means it has magical characteristics, and magic plays a role in its forging.

George Martin: Valyrian steel was always costly, but it became considerably more so when there was no more Valyria, and the secret of its making were lost.

Ned Stark's stord "Ice" is melted down and reforged into two smaller swords, "Oathkeeper" and "Widow's Wail". This rules out Valyrian steel being Wootz steel because Wootz steel loses its special properties when reforged.

Appearances of Valyrian steel in Game of Thrones:

        Name          Owner

Sword   Longclaw      Jon Snow
Sword   Heartsbane    Samwell Tarly
Dagger                Petyr Baelish
Sword   Ice           Eddard Stark         Reforged into Oathkeeper and Widow's Wail
Sword   Oathkeeper    Brienne of Tarth
Sword   Widow's Wail  The Crown
Sword   Lady Forlorn  Ser Lyn Corbray
Sword   Nightfall     Ser Harras Harlow
Sword   Red Rain      Lord Dunstan Drumm
Arakh                 Caggo
Armor                 Euron Greyjoy
Horn    Dragonbinder  The Citadel of The Maesters
Some Maesters carry links of Valyrian steel, a symbol of mastery of the highest arts.
Wildire

Copper

The burn rate of gasoline is limited by the supply of oxygen.

C8H18 + 12.5 O2  →  8 CO2 + 9 H2O
Gunpowder has oxygen in the mixture in the form of KNO3 which makes it burn faster.
3 C + S + 2 KNO3  →  K2S + N2 + 3 CO2
We know that wildfire contains an oxidizer otherwise it wouldn't be able to explode as it did on the show. Wildfire is made from manure, which contains KNO3.

Copper burns with a green flame. Adding copper powder to the explosive adds energy to the blast.

Three types of incendiaries are:

Gasoline:          Flame spreads slowly. Needs oxygen from the air.
Gunpowder:         Contains oxygen. Buns faster than gasoline. Subsonic pressure wave.
Plastic explosive: Pressure wave spreads supersonically as a shock.

Explosives

Medieval-style black powder
Modern smokeless powder

               MJoules  Rocket  Shock  Density  Boil
                 /kg     km/s   km/s   g/cm3  Kelvin 

Beryllium+ O2     23.2   5.3
Aluminum + O2     15.5
Magnesium+ O2     14.8
Hydrogen + O2     13.2   4.56             .07    20
Kerosene + O3     12.9
Octanitrocubane   11.2          10.6     1.95
Methane  + O2     11.1   3.80             .42   112
Octane   + O2     10.4                    .70   399
Kerosene + O2     10.3   3.52             .80   410
Dinitrodiazeno.   9.2          10.0     1.98
C6H6N12O12        9.1                   1.96        China Lake compound
Kerosene + H2O2   8.1   3.2
Kerosene + N2O4   8.0   2.62
HMX (Octogen)     8.0   3.05    9.1     1.86
RDX (Hexagen)     7.5   2.5     8.7     1.78
Al + NH4NO3       6.9
Nitroglycerine    7.2           8.1     1.59        Unstable
PLX               6.5                   1.14        95% CH3NO2 + 5% C2H4(NH2)2
Composition 4     6.3           8.04    1.59        91% RDX. "Plastic explosive"
Kerosene + N2O    6.18
Dynamite          5.9           7.2     1.48        75% Nitroglycerine + stabilizer
PETN              5.8           8.35    1.77
Smokeless powder  5.2           6.4     1.4         Used after 1884. Nitrocellulose
TNT               4.7           6.9     1.65        Trinitrotoluene
Al + Fe2O3        4.0                               Thermite
H2O2              2.7   3.1             1.45   423  Hydrogen peroxide
Black powder      2.6   3.08     .6     1.65        Used before 1884
Al + NH4ClO4            2.6
NH4ClO4                 2.5
N2O               1.86  1.76
N2H4              1.6   2.2             1.02   387  Hydrazine
NH4NO3            1.4   2.0     2.55    1.12        Ammonium nitrate
Bombardier beetle  .4                               Hydroquinone + H2O2 + protein catalyst
N2O4               .10                  1.45   294

Rocket: Rocket exhaust speed
Shock:  Shock speed
H2O
Li2O
BeO
B2O3
CO2
N2O
O2
OF2
Nitrocellulose
TNT
RDX
HMX
PETN
Octanitrocubane

Nitrocellulose
TNT
RDX
HMX
PETN
Octanitrocubane

Dinitrodiazenofuroxan
Nitromethane


High explosives

High explosives have a large shock velocity.


                MJoules   Shock  Density
                  /kg     km/s    g/cm3

Octanitrocubane    11.2   10.6     1.95
Dinitrodiazeno.     9.2   10.0     1.98
C6H6N12O12          9.1            1.96    China Lake compound
HMX (Octogen)       8.0    9.1     1.86
RDX (Hexagen)       7.5    8.7     1.78
PLX                 6.5            1.14    95% CH3NO2 + 5% C2H4(NH2)2
Composition 4       6.3    8.04    1.59    91% RDX. "Plastic explosive"
Dynamite            5.9    7.2     1.48    75% Nitroglycerine + stabilizer
PETN                5.8    8.35    1.77

Fuel and liquid O2
       O2 rocket   Fuel+oxidizer density
         km/s         g/cm3

H2 + Be   5.30       .24          ½H2 + ½Be
H2        4.46       .32
C2H4      3.64       .89
CH4       3.62       .83
C2H6      3.58       .9
C12H26    3.51      1.03
N2H4      3.46      1.07

Oxidizer
    Energy/Mass       Energy/Mass        Rocket           Rocket         Boil    Density
   with keroseene  as monopropellant  with kerosene  as monopropellant  Kelvin   g/cm3
     MJoule/kg         MJoule/kg          km/s             km/s

O3      12.9           2.97                                              161
O2      10.3           0                  3.52             0             110     1.14
H2O2     8.1           2.7                3.2              1.6           423     1.45
N2O4     8.00           .10               2.62                           294     1.44
N2O      6.18          1.86                                1.76          185
N2H4     -             1.58                                2.2           387     1.02

Solid rocket fuel
               MJoules  Rocket   Density
                 /kg     km/s    g/cm3

C6H6N12O12        9.1             1.96        China Lake compound
HMX (Octogen)     8.0   3.05      1.86
RDX (Hexagen)     7.5   2.5       1.78
Al + NH4NO3       6.9
Al + NH4ClO4            2.6
NH4ClO4                 2.5
NH4NO3            1.4   2.0       1.12        Ammonium nitrate

History
~808  Qing Xuzi publishes a formula resembling gunpower, consisting of
      6 parts sulfur, 6 parts saltpeter, and 1 part birthwort herb (for carbon).
~850  Incendiary property of gunpower discovered
1132  "Fire lances" used in the siege of De'an, China
1220  al-Rammah of Syria publishes "Military Horsemanship and Ingenious War
        Devices", describes the purification of potassium nitrate by
        adding potassium carbonate with boiling water, to precipitate out
        magnesium carbonate and calcium carbonate.
1241  Mongols use firearms at the Battle of Mohi, Hungary
1338  Battle of Arnemuiden.  First naval battle involving cannons.
1346  Cannons used in the Siege of Calais and the Battle of Crecy
1540  Biringuccio publishes "De la pirotechnia", giving recipes for gunpowder
1610  First flintlock rifle
1661  Boyle publishes "The Sceptical Chymist", a treatise on the
      distinction between chemistry and alchemy.  It contains some of the
      earliest modern ideas of atoms, molecules, and chemical reaction,
      and marks the beginning of the history of modern chemistry.
1669  Phosphorus discovered
1774  Lavoisier appointed to develop the French gunpowder program.  By 1788
         French gunpowder was the best in the world.
1832  Braconnot synthesizes the first nitrocellulose (guncotton)
1846  Nitrocellulose published
1847  Sobrero discovers nitroglycerine
1862  LeConte publishes simple recipes for producing potassium nitrate.
1865  Abel develops a safe synthesis of nitrocellulose
1867  Nobel develops dynamite, the first explosive more powerful than black powder
      It uses diatomaceous earth to stabilize nitroglycerine
1884  Vieille invents smokeless gunpowder (nitrocellulose), which is 3 times
         more powerful than black powder and less of a nuisance on the battlefield.
1902  TNT first used in the military.  TNT is much safer than dynamite
1930  RDX appears in military applications
1942  Napalm developed
1949  Discovery that HMX can be synthesized from RDX
1956  C-4 explosive developed (based on RDX)
1999  Eaton and Zhang synthesize octanitrocubane and heptanitrocubane

Above 550 Celsius, potassium nitrate decomposes. 2 KNO3 ↔ 2 KNO2 + O2.

Black powder           =  .75 KNO3  +  .19 Carbon  +  .06 Sulfur
1 kg TNT equivalent    =   4.184   MJ
Fission bomb           =   9.20e13 J     =  22000 tons of TNT equivalent
Fission bomb           =   420     kg
Fission bomb           =   2.19e11 J/kg
Fusion bomb maximum    =   2.51e13 J/kg   (Maximum theoretical efficiency)
Fusion bomb practical  =   1.0 e13 J/kg   (Practical efficiency achieved in real bombs)

Cryogenics
            Boil   Density
           Kelvin   g/cm3

Hydrogen     20      .07
Oxygen       90     1.14
Methane     112      .42
NO          121
Ozone       161
Ethane      185      .54
N2O         185
Propane     231      .60
Butane      274      .60
N2O4        294     1.44
Pentane     309      .63
Hexane      342      .65
Heptane     372      .68
N2H4        387     1.02
Octane      399      .70
H2O2        423     1.45
Dodecain    489      .75
Hexadecane  560      .77

Black powder

Sulfur
Sulfur
Saltpeter
Saltpeter

Charcoal
Icing sugar and KNO3
Mortar and pestle
Mortar and pestle

Potassium nitrate  KNO3     75%       (Saltpeter)
Charcoal           C7H4O    15%
Sulfur             S        10%

Oversimplified equation:  2 KNO3 + 3 C + S  →  K2S + N2 + 3 CO2

Realistic equation:       6 KNO3 + C7H4O + 2 S  →  KCO3 + K2SO4 + K2S + 4 CO2 + 2 CO + 2 H2O + 3 N2
Nitrite (NO3) is the oxidizer and sulfur lowers the ignition temperature.
Fuel air explosives
                   MJoules
                     /kg

Hydrogen + Oxygen     13.16
Gasoline + Oxygen     10.4


        Mass   Energy    Energy/Mass
         kg      MJ         MJ/kg

MOAB    9800   46000        4.7               8500 kg of fuel

Phosphorus
White phosphorus
White, red, violet, and black phosphorus
Red phosphorus

Violet phosphorus
Black phosphorus
Black phosphorus

Form      Ignition    Density
          (Celsius)

White        30        1.83
Red         240        1.88
Violet      300        2.36
Black                  2.69
Red phosphorus is formed by heating white phosphorus to 250 Celsius or by exposing it to sunlight. Violet phosphorus is formed by heating red phosphorus to 550 Celsius. Black phosphorus is formed by heating white phosphorus at a pressure of 12000 atmospheres. Black phosphorus is least reactive form and it is stable below 550 Celsius.
Matches

Striking surface
P4S3

The safety match was invented in 1844 by Pasch. The match head cannot ignite by itself. Ignitition is achieved by striking it on a rough surface that contains red phosphorus. When the match is struck, potassium chlorate in the match head mixes with red phosphorus in the abrasive to produce a mixture that is easily ignited by friction. Antimony trisulfide is added to increase the burn rate.

Match head                 Fraction             Striking surface   Fraction

Potassium chlorate    KClO3  .50                Red phosphorus      .5
Silicon filler        Si     .4                 Abrasive            .25
Sulfur                S      small              Binder              .16
Antimony3 trisulfide  Sb2S3  small              Neutralizer         .05
Neutralizer                  small              Carbon              .04
Glue                         small
A "strike anywhere" match has phosphorus in the match head in the form of phosphorus sesquisulfide (P4S3) and doesn't need red phosphorus in the striking surface. P4S3 has an ignition temperature of 100 Celsius.
Flint

Before the invention of iron, fires were started by striking flint (quartz) with pyrite to generate sparks. Flintlock rifles work by striking flint with iron. With the discovery of cerium, ferrocerium replaced iron and modern butane lighters use ferrocerium, which is still referred to as "flint".

Cerium        .38      Ignition temperature of 165 Celsius
Lanthanum     .22
Iron          .19
Neodymium2    .04
Praseodymium  .04
Magnesium     .04

Nitrous oxide engine

Nitrous oxide is stored as a cryogenic liquid and injected along with gaoline into the combustion chamber. Upon heating to 300 Celsius the nitrous oxide decomposes into nitrogen and oxygen gas and releases energy. The oxygen fraction in this gas is higher than that in air (1/3 vs. .21) and the higher faction allows for more fuel to be consumed per cylinder firing.

Air density                  =  .00122 g/cm3
Nitrous oxide gas density    =  .00198 g/cm3
Diesel density               =  .832   g/cm3
Gasoline density             =  .745   g/cm3
Diesel energy/mass           =  43.1   MJoules/kg
Gasoline energy/mass         =  43.2   MJoules/kg
Nitrous oxide boiling point  = -88.5   Celsius
Air oxygen fraction          =  .21
Nitrous oxide oxygen fraction=  .33
Nitrous oxide decompose temp =  300    Celsius
Nitrous oxide liquid pressure=   52.4  Bars     Pressure required to liquefy N2O at room temperature

Bombardier beetle

Hydroquinone
P-quinone

Hydroquinone and peroxide are stored in 2 separate compartments are pumped into the reaction chamber where they explode with the help of protein catalysts. The explosion vaporizes 1/5 of the liquid and expels the rest as a boiling drop of water, and the p-quinone in the liquid damages the foe's eyes. The energy of expulsion pumps new material into the reaction chamber and the process repeats at a rate of 500 pulses per second and a total of 70 pulses. The beetle has enough ammunition for 20 barrages.

2 H2O2  →  2 H2O +  O2           (with protein catalyst)
C6H4(OH)2  →  C6H4O2 + H2        (with protein catalyst)
O2 + 2 H2  →  2 H2O

Firing rate                     = 500 pulses/second
Number of pulses in one barrage =  70
Firing time                     = .14 seconds
Number of barrages              =  20

Flame speed

A turbojet engine compresses air before burning it to increase the flame speed and make it burn explosively. A ramjet engine moving supersonically doesn't need a turbine to achieve compression.

Turbojet
Ramjet

Airbus A350 compression ratio  =  52
Air density at sea level       = 1    bar
Air density at 15 km altitude  =  .25 bar
Air density in A350 engine     =  13  bar
From the thermal flame theory of Mallard and Le Chatelier,
Temperature of burnt material    =  Tb
Temperature of unburnt material  =  Tu
Temperature of ignition          =  Ti
Fuel density                     =  Dfuel
Oxygen density                   =  Doxygen
Reaction coefficient             =  C
Reaction rate                    =  R  =  C Dfuel Doxygen
Thermal diffusivity              =  Q  = 1.9⋅10-5 m2/s
Flame speed                      =  V

V2  =  Q C Dfuel Doxygen (Tb - Ti) / (Ti - Tu)

Shocks

Spherical implosion
Mach < 1,    Mach = 1,     Mach > 1

If the pressure front moves supersonically then the front forms a discontinuous shock, where the pressure makes a sudden jump as the shock passes.


Energy boost

Metal powder is often included with explosives.

        Energy/mass    Energy/mass
        not including  including
        oxygen         oxygen
        (MJoule/kg)    (MJoule/kg)

Hydrogen    113.4      12.7
Gasoline     46.0      10.2
Beryllium    64.3      23.2
Aluminum     29.3      15.5                                      
Magnesium    24.5      14.8                                      
Carbon       12.0       3.3
Lithium       6.9       3.2
Iron          6.6       4.6                                      
Copper        2.0       1.6

Fireworks

Li
B
Na
Mg
K
Ca
Fe

Cu
Zn
As
Sr
Sb
Rb
Pb

BaCl (green), CuCl (blue), SrCl (red)
Zero gravity
Bunsen burner, O2 increases rightward
Methane


Oxygen candle

Sodium chlorate

An oxygen candle is a mixture of sodium chlorate and iron powder, which when ignited smolders at 600 Celsius and produces oxygen at a rate of 6.5 man-hours of oxygen per kilogram of mixture. Thermal decomposition releases the oxygen and the burning iron provides the heat. The products of the reaction are NaCl and iron oxide.


Metallurgy

Stone age
Copper age
Bronze age
Iron age
Carbon age

      Discovery   Yield    Density
       (year)    Strength  (g/cm3)
                (GPascals)

Gold     Ancient   .20     19.3
Silver   Ancient   .10     10.5
Copper   -5000     .12      9.0
Bronze   -3200     .20      9      Copper + Tin.   Stronger than copper
Brass    -2000     .20      9      Copper + Zinc.  Stronger than copper
Iron     -1200     .25      7.9    Stronger than bronze and brass
Carbon    1987    1.4       1.75
The "yield strength" is the maximum stress a material can sustain before breaking.
The carbon age began in 1987 when Jimmy Connors switched from a steel to a carbon racquet.

Discovery of elements

The ancient metals such as iron, copper, tin, and zinc are obtained by carbon smelting minerals. Cobalt was the first metal discovered since iron and it's discovery inspired people to smelt every known mineral in the hope of yielding a new metal. By 1800 nearly all of the carbon smeltable metals had been discovered.

Some elements can't be carbon smelted and require electrolysis to isolate. Electrochemistry began in 1800 with the invention of the battery and most of the remaining metals were discovered soon after. Sodium and potassium were isolated by electrolysis in 1807 and these were used to smelt metals that couldn't be smelted with carbon.

         Discovery   Method of
          (year)     discovery

Carbon     Ancient   Naturally occuring     Coal, diamond
Gold       Ancient   Naturally occuring
Silver     Ancient   Naturally occuring
Sulfur     Ancient   Naturally occuring
Lead         -6500   Smelt with carbon
Copper       -5000   Smelt with carbon
Bronze (As)  -4200                          Copper + Arsenic
Bronze (Sn)  -3200                          Copper + Tin
Tin          -3200   Smelt with carbon
Brass        -2000                          Copper + Zinc
Mercury      -2000   Heat the oxide
Iron         -1200   Smelt with carbon      In the form of steel
Zinc          1300   Smelt with carbon      Date first produced in pure form
Antimony      1540   Smelt with iron
Arsenic       1649   Heat the oxide
Phosphorus    1669   Heat the oxide
Cobalt        1735   Smelt with carbon      First metal discovered since iron
Platinum      1735   Naturally occuring
Nickel        1751   Smelt with carbon
Hydrogen      1766   Hot iron + steam
Oxygen        1771   Heat HgO
Nitrogen      1772   From air
Manganese     1774   Smelt with carbon
Molybdenum    1781   Smelt with carbon
Tungsten      1783   Smelt with carbon
Chromium      1797   Smelt with carbon
Palladium     1802   Chemistry
Osmium        1803
Iridium       1803
Rhodium       1804   Smelt with zinc        Smelt Na3RhCl6 with zinc
Sodium        1807   Electrolysis
Potassium     1807   Electrolysis
Magnesium     1808   Electrolysis
Cadmium       1817   Smelt with carbon
Lithium       1821   Electrolysis
Zirconium     1824   Smelt with potassium
Aluminum      1827   Smelt with potassium
Silicon       1823   Smelt with potassium
Beryllium     1828   Smelt with potassium
Thorium       1929   Smelt with potassium
Vanadium      1831
Uranium       1841   Smelt with potassium
Ruthenium     1844   Smelt with carbon
Tantalum      1864   Smelt with hydrogen
Niobium       1864   Smelt with hydrogen
Fluorine      1886   Electrolysis
Helium        1895   From uranium ore
Titanium      1910   Smelt with sodium
Hafnium       1924
Rhenium       1928   From molybdenite
Scandium      1937

Gold was the densest element known until the discovery of platinun in 1735. It was useful as an uncounterfeitable currency until the discovery of tungsten in 1783, which has the same density as gold.

Wood fires are 200 Celsius short of the copper smelting temperature. Coal has to be used.

Titanium can't be smelted with carbon because it produces titanium carbide (TiC).


Discovery of the strong metals

The usefulness of a metal as a sword depends on its strength/density ratio. The table below shows all the metals with a ratio of at least 5 MJoules/kg. For these metals, strength tends to be proportional to density and the strength/density ratio has a characteristic value of 10 MJoules/kg. Beryllium is the sole outlier with a superlatively large value of 71 MJoules/kg.

The low density metals are ones up to vanadium on the periodic table. None are carbon smeltable and all require electrochemistry to isolate. The first low density metal to be produced was magnesium in 1808.

        Protons  Strength  Density  Strength/Density   Carbon    Discovery
                  (GPa)    (g/cm3)   (MJoule/kg)      smeltable    year

Beryllium    4      132      1.85      71.4          no      1828
Magnesium   12       17      1.74       9.8          no      1808
Aluminum    13       26      2.70       9.6          no      1827
Scandium    21       29      3.0        9.7          no      1937
Titanium    22       44      4.5        9.8          no      1910
Vanadium    23       47      6.0        7.8          no      1831
Chromium    24      115      7.2       16.0          yes     1797
Manganese   25       75      7.2       10.4          yes     1774
Iron        26       82      7.9       10.4          yes    -1200
Cobalt      27       75      8.9        8.4          yes     1735
Nickel      28       76      8.9        8.5          yes     1751
Copper      29       48      9.0        5.3          yes    -5000
Zinc        30       43      7.1        6.0          yes     1746
Molybdenum  42      120     10.3       11.7          yes     1781
Ruthenium   44      173     12.4       14.0          yes     1844
Rhodium     45      150     12.4       12.1          yes     1804
Tungsten    74      161     19.2        8.4          yes     1783
Rhenium     75      178     21.0        8.5          yes     1928
Osmium      76      222     22.6        9.8          yes     1803
Iridium     77      210     22.6        9.3          yes     1803
Uranium     92      111     19.1        5.8          no      1841

Strength:          Shear modulus            (GPascals)
Density:           Density                  (grams/cm3)
Strength/Density:  Shear modulus / Density  (MJoules/kg)

Metals known since antiquity

For a metal, the stiffness is characterized by the "shear strength" and the sword worthiness is characterized by the shear strength over the density (the "strength to weight ratio"). For example for iron,

Shear modulus    =  S         =   82 GJoules/meter3
Density          =  D         = 7900 kg/meter3
Sword worthiness =  Q  = S/D  = 10.4 MJoules/kg

Metals

This plot includes all metals with a strength/density at least as large as lead, plus mercury. Beryllium is beyond the top of the plot.


Wootz steel

-600  Wootz steel developed in India and is renowned as the finest steel in the world.
1700  The technique for making Wootz steel is lost.
1790  Wootz steel begins to be studied by the British Royal Society.
1838  Anosov replicates Wootz steel.
Wootz steel is a mix of two phases: martensite (crystalline iron with .5% carbon), and cementite (iron carbide, Fe, 6.7% carbon).

Iron meteorites

In prehistoric times iron meteorites were the only source of metallic iron. They consist of 90% iron and 10% nickel.


Alloys

Copper
Orichalcum (gold + copper)
Gold

Alloy of gold, silver, and copper


Superstrong amorphous alloys

Crystal, polycrystal, amorphous

New alloys have been discovered that are stronger and ligher than diamond. These alloys have an amorphous structure rather than the crystalline structure of conventional alloys. A crystaline alloy tends to be weak at the boundaries between crystals and this limits its strength. Amorphous alloys don't have these weaknesses and can be stronger.

Pure metals and alloys consisting of 2 or 3 different metals tend to be crystaline while alloys with 5 or more metals tend to be amorphous. The new superalloys are mixes of at least 5 different metals.

A material's strength is characterized by the "yield strength" and the quality is the ratio of the yield strength to the density. This is often referred to as the "strength to weight ratio".

Yield strength  =  Y            (Pascals)
Density         =  D            (kg/meter3)
Quality         =  Q  =  Y/D    (Joules/kg)
The strongest allyos are:
       Yield strength   Density   Quality
       (GPa)        (g/cm3)    (MJoule/kg)

Magnesium + Lithium             .14        1.43        98
Magnesium + Y2O3                .31        1.76       177
Aluminum  + Beryllium           .41        2.27       181
Amorphous LiMgAlScTi           1.97        2.67       738
Diamond                        1.6         3.5        457
Titanium  + AlVCrMo            1.20        4.6        261
Amorphous AlCrFeCoNiTi         2.26        6.5        377
Steel     + Cobalt, Nickel     2.07        8.6        241
Amorphous VNbMoTaW             1.22       12.3         99
Molybdenum+ Tungsten, Hafnium  1.8        14.3        126
The strongest pure metals are weaker than the strongest alloys.
       Yield strength   Density   Quality
       (GPa)        (g/cm3)    (MJoule/kg)

Magnesium                        .10       1.74        57
Beryllium                        .34       1.85       184
Aluminum                         .02       2.70         7
Titanium                         .22       4.51        49
Chromium                         .14       7.15        20
Iron                             .10       7.87        13
Cobalt                           .48       8.90        54
Molybdenum                       .25      10.28        24
Tungsten                         .95      19.25        49

Alloy types
Beryllium + Li           →  Doesn't exist. The atoms don't mix
Beryllium + Al           →  Improves strength
Magnesium + Li           →  Weaker and lighter than pure Mg. Lightest existing alloy
Magnesium + Be           →  Only tiny amounts of beryllium can be added to magnesium
Magnesium + Carbon tubes →  Improves strength, with an optimal tube fraction of 1%
Aluminum  + Li,Mg,Be,Sc  →  Stronger and lighter than aluminum
Titanium  + Li,Mg,Sc     →  Stronger and lighter than titanium
Steel     + Cr,Mo        →  Stronger and more uncorrodable than steel. "Chromoly"
Copper    + Be           →  Stronger than beryllium and is unsparkable

High-temperature metals (refractory metals)
          Melting point (Celsius)

Tungsten    3422
Rhenium     3186
Osmium      3033
Tantalum    3017
Molybdenum  2623
Niobium     2477
Iridium     2446
Ruthenium   2334
Hafnium     2233
Technetium  2157
Rhodium     1964
Vanadium    1910
Chromium    1907

High-temperature superalloys

Most alloys weaken with increasing temperature except for a small subset called "superalloys" that strengthen with temperature, such as Ni3Al and Co3Al. This is called the "yield strength anomaly".

Nickel alloys in jet engines have a surface temperature of 1150 Celsius and a bulk temperature of 980 Celsius. This is the limiting element for jet engine performance. Half the mass of a jet engine is superalloy.

Current engines use Nickel superalloys and Cobalt superalloys are under development that will perform even better.

Yield strength in GPa as a function of Celsius temperature.

                   20   600   800  900  1000  1100 1200  1400  1600 1800  1900  Celsius

VNbMoTaW          1.22         .84        .82       .75  .66   .48   .4
AlMohNbTahTiZr    2.0   1.87  1.60  1.2   .74  .7   .25
Nickel superalloy 1.05        1.20   .90  .60  .38  .15
Tungsten           .95   .42   .39        .34  .31  .28  .25   .10   .08  .04
Below 1100 Celsius AlMohNbTahTiZr has the best strength-to-mass ratio and above this VNbMoTaW has the best ratio. Both alloys supercede nickel superalloy and both outperform tungsten, the metal with the highest melting point. Data:   
Entropy, nickel superalloy
Copper alloys
                  Yield strength (GPa)

Copper                  .27
Brass                   .41     30% zinc
Bronze                  .30     5% tin
Phosphor bronze         .69     10% tin, .25% phosphorus
Copper + beryllium     1.2      2% beryllium, .3% cobalt
Copper + nickel + zinc  .48     18% nickel, 17% zinc
Copper + nickel         .40     10% nickel, 1.25% iron, .4% manganese
Copper + aluminum       .17     8% aluminum

Bells and cymbals

Bells and cymbals are made from bell bronze, 4 parts copper and 1 part tin.


Metal smelting

Prehistoric-style smelter

Most metals are in oxidized form. The only metals that can be found in pure form are gold, silver, copper, platinum, palladium, osmium, and iridium.

Smelting is a process for removing the oxygen to produce pure metal. The ore is heated in a coal furnace and the carbon seizes the oxygen from the metal. For copper,

Cu2O + C  →  2 Cu + CO
At low temperature copper stays in the form of Cu2O and at high temperature it gives the oxygen to carbon and becomes pure copper.

For iron, the oxidation state is reduced in 3 stages until the pure iron is left behind.

3 Fe2O3 + C  →  2 Fe3O4 + CO
Fe3O4   + C  →  3 FeO   + CO
FeO     + C  →    Fe   + CO
Oxidation state  =  Number of electrons each iron atom gives to oxygen

       Oxidation state
CuO          2
Cu2O         1
Cu           0
Fe2O3        3
Fe3O4       8/3
FeO          2
Fe           0

Smelting temperature

The following table gives the temperature required to smelt each element with carbon.

        Smelt  Method  Year  Abundance
         (C)                   (ppm)

Gold        <0   *   Ancient      .0031
Silver      <0   *   Ancient      .08
Platinum    <0   *    1735        .0037
Mercury     <0  heat -2000        .067
Palladium   <0  chem  1802        .0063
Copper      80   C   -5000      68
Sulfur     200   *   Ancient   420
Lead       350   C   -6500      10
Nickel     500   C    1751      90
Cadmium    500   C    1817        .15
Cobalt     525   ?    1735      30
Tin        725   C   -3200       2.2
Iron       750   C   -1000   63000
Phosphorus 750  heat  1669   10000
Tungsten   850   C    1783    1100
Potassium  850   e-   1807   15000
Zinc       975   C    1746      79
Sodium    1000   e-   1807   23000
Chromium  1250   C    1797     140
Niobium   1300   H    1864      17
Manganese 1450   C    1774    1120
Vanadium  1550   ?    1831     190
Silicon   1575   K    1823  270000
Titanium  1650   Na   1910   66000
Magnesium 1875   e-   1808   29000
Lithium   1900   e-   1821      17
Aluminum  2000   K    1827   82000
Uranium   2000   K    1841       1.8
Beryllium 2350   K    1828       1.9

Smelt:      Temperature required to smelt with carbon
Method:     Method used to purify the metal when it was first discovered
            *:  The element occurs in its pure form naturally
            C:  Smelt with carbon
            K:  Smelt with potassium
            Na: Smelt with sodium
            H:  Smelt with hydrogen
            e-: Electrolysis
            heat:  Heat causes the oxide to decompose into pure metal. No carbon required.
            chem:  Chemical separation
Discovery:  Year the element was first obtained in pure form
Abundance:  Abundance in the Earth's crust in parts per million
Elements with a low carbon smelting temperature were discovered in ancient times unless the element was rare. Cobalt was discovered in 1735, the first new metal since antiquity, and this inspired scientists to smelt every known mineral in the hope that it would yield a new metal. By 1800 all the rare elements that were carbon smeltable were discovered.

The farther to the right on the periodic table, the lower the smelting temperature, a consequence of "electronegativity".

The battery was invented in 1800, launching the field of electrochemistry and enabling the the isolation of non-carbon-smeltable elements. Davy used electrolysis in 1807 to isolate sodium and potassium and then he used these metals to smelt other metals. To smelt beryllium with potassium, BeO + 2 K ↔ Be + K2O.

Titanium can't be carbon smelted because it forms the carbide Ti3C.

Data


Thermite

Thermite is smelting with aluminum. For example, to smelt iron with aluminum,

Fe2O3 + 2 Al  →  2 Fe + Al2O3

Smelting reactions

The following table shows reactions that change the oxidation state of a metal. "M" stands for an arbitrary metal and the magnitudes are scaled to one mole of O2. The last two columns give the oxidation state of the metal on the left and right side of the reaction. An oxidation state of "0" is the pure metal and "M2O" has an oxidation state of "1".

                            Oxidation state   Oxidation state
                                at left          at right
 2  M2O   ↔  4  M     + O2        1                0
 4  MO    ↔  2  M2O   + O2        2                1
 2  M3O4  ↔  6  MO    + O2       8/3               2
 6  M2O3  ↔  4  M3O4  + O2        3               8/3
 2  M2O3  ↔  4  MO    + O2        3                2
 2  MO    ↔  2  M     + O2        2                0
2/3 M2O3  ↔ 4/3 M     + O2        3                0
 1  MO2   ↔  1  M     + O2        4                0
 2  MO2   ↔  2  MO    + O2        4                2

Gibbs energy

Let MO be a metal oxide for which the Gibbs energy of CO is larger than MO and the oxygen binds to the metal preferentially over carbon.

The entropies of most metal oxides are similar and so changing the temperature has little effect on their relative Gibbs energies. CO is special because it is a gas and hence has a larger entropy than the solid metal oxides. As temperature increases the Gibbs energy of CO decreases faster than that of MO and at the critical smelting temperature they are equal. Above this temperature the oxygen unbinds to the metal and binds to carbon.

For the smelting of cobalt,

Standard temperature                 =  T0  =  298 Kelvin  =  25 Celsius
Smelting temperature                 =  Tsmelt
Temperature change                   =  t   =  Tsmelt - T0
Gibbs energy at standard temperature =  G
Entropy at standard temperature      =  S
Gibbs energy at temperature Tsmelt    =  g   =  G - t S
CoO Gibbs energy per mole O2         =  GCoO =  -428.4   kJoule/mole
CO  Gibbs energy per mole O2         =  GCO  =  -274.4   kJoule/mole
CoO entropy per mole O2              =  SCoO =      .12  kJoule/mole
CO  entropy per mole O2              =  SCO  =      .396 kJoule/mole
At the smelting temperature, the Gibbs energies of CoO and CO are equal and the reaction is in equilibrium. Below this temperature oxygen binds to cobalt and above this temperature it binds to carbon. The calculation is approximate because it assumes entropy is a constant as a function of temperature. To calculate the smelting temperature,
    gCoO      =      gCO
GCoO - t SCoO  =  GCO - t SCO

t  =  (GCoO - GCO) / (SCoO - SCO)
   =  558 Celsius

Tsmelt  =  583 Celsius  =  t + 25 Celsius      (The actual smelting temperature is 525 Celsius)

Smelting thermodynamics
       Gibbs       Gibbs            Entropy       Entropy
    kJoule/mole  kJoule/mole(O2)  kJoule/mole  kJoule/mole(O2)

Li2O     -561.9    -1123.8
Na2O     -377       -754
K2O      -322.2     -644.4
Cu2O     -146.0     -292.0
Ag2O      -11.2      -22.4

BeO      -579.1    -1158.2
CO       -137.2     -274.4     .198      .396
MgO      -596.3    -1192.6     .0269     .0538
CaO      -533.0    -1066.0     .0398     .0769
VO       -404.2     -808.4
MnO      -362.9     -725.8     .0597     .1194
CoO      -214.2     -428.4
NiO      -211.7     -423.4
CuO      -129.7     -259.4     .0426     .0852
ZnO      -318.2     -636.4
CdO      -228.4     -456.8
HgO       -58.5     -117.0

Fe3O4   -1014       -507       .0146     .0073
Co3O4    -795.0     -397.5

B2O3    -1184       -789
Al2O3   -1582.3    -1054.9     .0509     .0339
Ti2O3   -1448       -965.3
V2O3    -1139.3     -759.5
Cr2O3   -1053.1     -702.1     .0812     .0541
Fe2O3    -741.0     -494.0     .0874     .0583

CO2      -394.4     -394.4     .214      .214
SO2                            .2481     .2481
SiO2     -856.4     -856.4     .0418     .0418
TiO2     -852.7     -852.7
MnO2     -465.2     -465.2     .0530     .0530
MoO2     -533.0     -533.0
WO2      -533.9     -533.9
PbO2     -219.0     -219.0

MoO3     -668.0     -445.3
WO3      -764.1     -509.4

V2O4    -1318.4     -659.2

Cu          0
C (gas)   672.8

Minerals

Spodumene: LiAl(SiO3)2
Beryl: Be3Al2(SiO3)6
Periclase: MgO
Magnesite: MgCO3
Dolomite: CaMg(CO3)2
Bauxite: Al(OH)3 and AlO(OH)

Quartz: SiO2
Rutile: TiO2
Vanadinite: Pb5(VO4)3Cl
Chromite: FeCr2O4
Pyrolusite: MnO2
Hematite: Fe2O3

Hematite: Fe2O3
Pyrite: FeS2
Iron meteorite
Cobaltite: CoAsS
Millerite: NiS
Chalcocite: Cu2S

Chalcopyrite: CuFeS2
Sphalerite: ZnS
Germanite: Cu26Fe4Ge4S32
Zircon: ZrSiO4
Molybdenite: MoS2
Acanthite: Ag2S
Cassiterite: SnO2
Wolframite: FeWO4
Cinnabar: HgS
Platinum nugget
Gold nugget
Galena: PbS

Fluorite: CaF2
Volcanic sulfur
Alumstone: KAl3(SO4)2(OH)6
Malachite: Cu2CO3(OH)l2
Azurite: Cu3(CO3)2(OH)2
Muscovite mica: KAl2(AlSi3O10)(F,OH)2 or KF2(Al2O3)3(SiO2)6(H2O)

       grams/cm3

Osmium      22.6
Gold        19.3
Tungsten    19.2
Silver      10.5
Sperrylite  10.6   PtAs2
Thorianite  10     ThO2
Copper       8.9
Calaverite   9.2   AuTe2
Petzite      8.7   Ag3AuTe2
Minium       8.2   Pb34
Altaite      8.1   PbTe
Cinnabar     8.1   HgS
Iron         7.9
Epsomite     1.67  MgSO4(H2O)7
Carnallite   1.6   KMgCl3(H2O)6

Aliens

Timeline of the universe

An alien planet could conceivably have formed as early as 1 billion years after the big bang, meaning that there are likely aliens with a head start on us by billions of years.

An alien civilization could easily build a fission or fusion rocket that travels at 1/10 the speed of light, which would take 1 million years to cross the galaxy. The aliens have plenty of time to get here.

                Millions of years ago

Big bang             13700
First planets formed 13000
Earth formed          4500
Photosynthesis        3000
Oxygen atmosphere      600
Multicellular life     600
Vertebrates            480
Tetrapod vertebrates   400       Mammals, birds, and reptiles are all tetrapods
Mammals                170
Dinosaur extinction     66
Cats                    25
Cheetahs                 6       Fastest land animal
Tigers                   1.8
Humans                   1
Lions                     .9
Agriculture               .01
Civilization              .005
Calculus                  .0004
Smartphones               .00001

Starship

We presently possess the technology to build a fission and fusion rocket, each of which can reach a speed of .1 times the speed of light, and such a rocket can cross the Milky Way galaxy in a time that is a small fraction of the age of the universe. If aliens had built such a rocket they could easily have already colonized the galaxy.

Speed of light                       =  C
Speed of a fission or fusion rocket  =  V  =  .1 C
Diameter of the Milky Way            =  X           =     .1 million light years
Time to cross the galaxy             =  T  =  X/V   =      1 million years
Age of the universe                                 =  13800 million light years

Divinity

The divinity hypothesis becomes persuasive if there is a physical mechanism allowing it to happen, a mechanism that obeys the known laws of physics. Such a mechanism exists. An advanced alien civilization is equivalent to a diety.


Largest churches

Saint Peter's Basilica
Saint Joseph's Oratory
Seville Cathedral

Cathedral of Saint John the Divine
Liverpool Cathedral
Milan Cathedral

Basilica of Saint Paul Outside the Walls
Saint Paul's Cathedral
Lincoln Cathedral
Washington National Cathedral

                               Volume    Area   Nave  Tower  Year
                               (k m3)   (k m2)  (m)   (m)

Saint Peter's Basilica            5000   15.2   46    136.6  1626   Vatican
Seville Cathedral                  500   11.5   42    105    1528   Spain    Seville
Cathedral of St. John the Divine   480   11.2   39     70.7  1941   USA      Manhattan
Milan Cathedral                    440   10.2   45    108.5  1965   Italy    Milan
Abbey of Santa Giustina                   9.7          75    1606   Italy    Padua
Liverpool Cathedral                450    9.7         101.0  1978   UK       Liverpool
Basilica St. Paul Outside th Walls        8.5   30     73    1823   Italy    Rome
Florence Cathedral                        8.3   45    114.5  1436   Italy    Florence
Ulm Minster                        190    8.3   41   *161.5  1890   Germany  Ulm
Basilica Cat. Lady of the Pillar          8.3                1872   Spain    Zaragoza
Hagia Sophia                       256    8.0                 537   Turkey   Istanbul
Cathedral of Our Lady                     8.0                1521   Belgium  Antwerp
Cologne Cathedral                  407    7.9   43   *157.4  1880   Germany  Cologne
San Petrino Basilica               270    7.9   45           1479   Italy    Bologna
Saint Paul's Cathedral                    7.9   38    111.3  1708   UK       London
Washington National Cathedral             7.7   31     92    1990   USA      DC
Amiens Cathedral                   200    7.7   42    112.7  1270   France   Amiens
Basilica of the National Shrine           7.1                1961   USA      DC
Palma Cathedral                    160    6.7                1346   Spain    Palma
Reims Cathedral                           6.7                1275   France   Reims
Strasbourg Cathedral                      6.0        *142.0  1439   France   Strasbourg
Bourges Cathedral                         5.9                1230   France   Bourges
Notre Dame de Paris                       5.5                1345   France   Paris
Chartres Cathedral                        5.2                1220   France   Chartres
Winchester Cathedral                      5.0                1525   UK       Winchester
Saint Mary's Church                190    5.0                1502   Poland   Gdansk
Westminster Abbey                         3.0                1018   UK       London
Basilica of Saint John Lateran                               1735   Italy    Rome
Oliwa Cathedral                                              1350   Poland   Gdansk
Cluny III                                                    1130   France   Cluny
Canterbury Cathedral                                         1077   UK       Canterbury
York Minster                                                 1472   UK       York
Lincoln Cathedral                                            1311   UK       Lincoln
Peterborough Cathedral                                       1237   UK       Peterborough
Rouen Cathedral                                              1202   France   Rouen

*:  Held the status of world's tallest building.
All churches larger than 7000 meters2 are listed, plus the largest churches constructed before 1500 CE. The appendix contains an expanded list of churches.

Among these types of buildings the cathedral is probably the best known, to the extent that the word "cathedral" is often mistakenly applied as a generic term for any large and imposing church. In fact, A cathedral doesn't have to be large or imposing, though many are. The cathedral takes its name from the word "cathedra", or "bishop's throne".


Church towers
Ulm Minster
Cologne Cathedral
Lincoln Cathedral
                       Height (m)  Year

Ulm Minster                161.5   1890 *
Lincoln Cathedral          159.7   1311 * Collapsed in 1549
Our Lady of Peace Basilica 158.0   1989
Cologne Cathedral          157.4   1880 *
Beauvais Cathedral         153.0   1569   Collapsed in 1573
Saint Mary's Church        151.0   1478 * Collapsed in 1647
Rouen Cathedral            151.0   1876 *
Old St. Paul's Cathedral   150.0   1240 * Collapsed in 1561
Saint Nikolai, Hamburg     147.3   1874 *
Strasbourg Cathedral       142.0   1439 *
Basilica Lady of Lichen    141.5   2000
Saint Peter's Basilica     136.6   1626
Saint Stephen's Cathedral  136.4   1433
New Cathedral, Linz        134.8   1924
Notre Dame et St. Lambert  134.5   1433   Destroyed in 1794
Saint Peter's Church       132.2   1878
Saint Michaelis Church     132.1   1786
Malmesbury Abbey           131.3   1180   Collapsed around the year 1500
*: Held the status of world's tallest building.
Saint Peter's Basilica

Saint Peter's Basilica was designed principally by Bramante, Michelangelo, Maderno, and Bernini. It is the most renowned work of Renaissance architecture and is the largest stone church in the world.


Arch


Catenary

Sir Robert Hooke
Blue: catenary      Red: parabola
Sir Christopher Wren

The catenary arch was discovered by Sir Robert Hooke.

Hooke: As hangs a flexible cable so, inverted, stand the touching pieces of an arch.


Parabola

A suspension bridge under zero load hangs as a catenary and under infinite load it hangs as a parabola.


Nave

Lincoln Cathedral
Saint Paul's Cathedral
Salisbury Cathedral

Bristol Cathedral
Salisbury Cathedral
Laon Cathedral


Flying buttress

A flying buttress delivers the compression force from the arch to the ground.


Organs

Sydney Town Hall
LDS Conference Center


Organ frequency
Pipe length    =  L              =  8.5 meters
Wavelength     =  W  =  2L       = 17.0 meters
Sound speed    =  V              =  340 meters/second
Pipe frequency =  F  =  ½ V / L  =   20 Hertz    (Lower limit of human sensitivity)

Marble

Marble is metamorphic limestone (CaCO3).

Marble Canyon, Colorado River

Masonic Temple, Washington DC
George Washington
Marble Arch, London

Tomb of the Unknown Soldier
Vietnam War Memorial, Illinois


Stained glass

NaO2       Colorless
FeO        Green                  Beer bottles
S          Amber
S + B2O3   Blue
S + Ca     Yellow
MnO2       Purple
Co         Blue
CuO        Turquoise
Ni         Blue or violet or black
Cr         Dark green or black
Au         Red
Cu         Dark red
Se         Pink
AgNO3      Orange
Cd         Yellow
U          Yellow
SnO        White


Tallest structure in the world
                     Height   Year
                      (m)
Gobekli Tepe, Turkey   15   -11500
Pyramid of Djoser      62    -2650
Meidum Pyramid         93.5  -2610
Bent Pyramid          101.1  -2605
Red Pyramid           105    -2600
Great Pyramid of Giza 146    -2560
Lincoln Cathedral     160     1311-1549   Collapsed
St. Mary's Church     151     1549-1647   Collapsed
Strasbourg Cathedral  142     1647-1874
St. Nikolai           147     1874-1876
Rouen Cathedral       151     1876-1880
Cologne Cathedral     157     1880-1884
Washington Monument   169     1884-1889
Eiffel Tower          300     1889-1930
Chrysler Building     319     1930-1931
Empire State Building 381     1931-1967
During the years 1311-1884 the tallest structure in the world was always a church.
Obelisks

San Jacinto Monument
Washington Monument
Lincoln Tomb

Bunker Hill Monument
Perry's Memorial
Wellington Monument

                        Height  Base   Year

San Jacinto Monument    172.92  15     1939   Texas. Topped by a 220 ton star
Washington Monument     169.05  16.80  1884   Washington DC
Perry's Memorial        107            1915   Perry's Vicry and Int. Peace Memorial
Jefferson Davis Mon.    107.0          1924   Kentucky
Capas National Shrine    70            2003   Philippines
High Point Monument      67            1930   New Jersey
Bunker Hill Monument     67            1843   Massachusetts
Wellington Monument      62            1861   Dublin
Wellington Monument      53.34  24     1854   Somerset
Nelson's Column          51.6          1843   London
Lateran Obelisk          45.7         -1500   Rome
Vendome Column           42            1810   Paris
Flaminio Obelisk         36.5         -1300   Rome
Lincoln Tomb             36            1874   Illinois
Trajan's Column          35.1    3.7    113   Rome
Obelisk of Montecitorio  34.0          -592   Rome
Solare Obelisk           33.97         -592   Rome
Veteran's Memorial       33.5          1876   Pennsylvania
Vatican Obelisk          25.5           -29   Rome
Pompey's Pillar          20.46   2.71   297   Egypt
Nelson's column
Lateran Obelisk
Trajan's Column
Montecitorio Obelisk

Trinity nuclear test site
Pompei's Column
Raising the obelisk


Wind

For a solid granite obelisk with a square cross section, we estimate the wind force required to topple the obelisk.

Height            =  H
Base side length  =  L
Pillar density    =  D     =  2650  kg/meter3  (Granite)
Air density       =  d     =  1.22  kg/meter3
Pillar mass       =  M     =  D H L2
Wind speed        =  V     =    80  meters/second   (Extreme hurricane)
Gravity consant   =  g     =   9.8  meters/second2
Gravity force     =  Fgrav  =  M g
Wind force        =  Fwind  =  ½ d L H V2
Gravity torque    =  Τgrav  =  ½ L Fgrav
Wind torque       =  Τgrav  =  ½ H Fwind

Gravity torque  =  Wind torque
  ½ D H L3 g    =  ¼ L H2 d V2

H  =  2 g L2 D / (d V2)
L2 =  ½ H V2 d / (D g)
If H = 169 meters (Washington Monument), then L = 25.4 meters.
Density
               grams/cm3    Tensile    Compression
                            strength    strength
                             (MPa)       (MPa)
Air               .00122
Water            1.0
Brick, light                    .28         7
Brick, hard                    2.8         80
Sediment         2.0  ± .3
Sandstone        2.3  ± .3     2.1         60
Slate                          3.5         95
Shale            2.35 ± .35
Limestone        2.65 ± .15    2.1         60
Granite          2.65 ± .15    4.8        130
Metamorphic      2.8  ± .2
Basalt           2.9  ± .2
Portland cement  3.15          3.5         21
Portland concrete              2.8         14

Beryllium        1.85          448
Magnesium        1.74          232
Silicon          2.33
Aluminum         2.70           50
Titanium         4.51          370
Zinc             7.14
Chromium         7.15          282
Tin              7.26          200
Iron             7.86          350
Cobalt           8.90          760
Nickel           8.91          195
Copper           8.96          210
Molybdenum      10.28          324
Silver          10.49          170
Lead            11.34           12
Tungsten        19.25         1510
Gold            19.3           127
Platinum        21.45          165
Iridium         22.56         2000
Osmium          22.59         1000

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