Introduction:
~ Hydrogen is the lightest of the elements with an atomic weight of 1.0
~ LH2 has a density of 0.07 grams per cubic centimeter = 70 g / 1 liter
~ water has a density of 1.0 g/cc = 1kg/1 liter
~ gasoline about 0.75 g/cc = 750g / 1 liter
~ Liquid hydrogen (LH2) is a common liquid rocket fuel for rocket applications
~ LH2 is found naturally in the molecular H2 form, thus the H2 part of the name
~ H2 must be pressurised and cooled to 20.27 K (-423.19 °F/-252.88°C)
~ storing H2 as liquid LH2 takes less space than storing it as a gas at normal temperature and pressure
~ LH2 can be maintained as a liquid in pressurised and thermally insulated containers
~ LH2 can be used as a fuel in an internal combustion engine
~ hydrogen will gradually evaporate, typically 1.7 percent per day
~ resulting exhaust of LH2 engines is very clean water with traces of ozone and hydrogen peroxide

Advantages:
~ LH2 stores approximately 2.6 times the energy per unit mass as gasoline
~ LH2 burns more efficiently than gasoline, for example 1.33 times more efficiently in automobiles

Disadvantages:
~ LH2 needs about 4 times the volume for a given amount of energy

Example 1:
~ V _{Gasoline_tank} = 15 gallon (US) = 56.78 liter = V _water = 56 780 cm³ - space needed for gasoline tank
~ W _{Gasoline_tank} = 90 pounds = 40.82 kg = 56.78 l × 0.75 kg/ l - weight of gasoline
~ V_{LH2_tank} = 4 ×V _{Gasoline_tank} = 60 gallon = 227.12 liter = 227 120 cm³ - volume of corresponding LH2 tank
~ W_LH2 = 70 g × 227.12 = 15.898 kg = 35 pounds - weight of LH2 itself 227 120 cm³ = 60 gallon size
~ LH2 weighs 35 pounds i.e. less than gasoline BUT needs much bigger tank i.e.
~ four liters of LH2 are needed to match the same energy content of one liter of gasoline
~ 35 pounds = 0.11 × W_{LH2_tank} <=> 318 pounds = W_{LH2_tank} = 42 kg - the mass of H2 stored in a tank has been maximum 11 % of the mass of the tank
~ W_total = W_{LH2_tank} + W_LH2 = (318+35) = 353 pounds = 160 kg i.e. the total weight caused by LH2 is a challenge
~ V_{LH2_tank} = 227 120 cm³ i.e. the total space needed for LH2 is the challenge !
~ if LH2 burns more efficiently than gasoline, for example 1.33 times, the above calculations are pessimistic

Example 2:
~ 9.5 kg of hydrogen is equivalent to 25kg of gasoline
~ 17 kg i.e. storing 25 kg of gasoline requires a tank with a mass of 17 kg,
~ the storage of 9.5 kg of hydrogen requires 55kg
~ the volume of hydrogen fuel is about 4 times greater for the same energy content of gasoline
~ hydrogen burns 1.33 times more efficiently than gasoline in automobiles

»BMW 745H HYBRID !

M_tank = 75 kg - a BMW 745h liquid-hydrogen test vehicle with a 75 kg tank
E_tank = E_40lgasoline - the energy equivalent of 40 liters of gasoline
a fuel efficiency: 10 km per gasoline liter = 100 km per 10 liter
D_tank = 10 km/l × 40 gasoline l = 400 km - a cruising range in traffic was 400 km in one hour

Running on hydrogen, the 745h produces
~ HP_BMW745h = 184 horsepower
~ S_BMW745h = 133 mph = 214 km/h - a top speed of 133 mph
~ R_LH2 cruising range is 190 miles = 305 km

Runnign on BOTH fuels
~ 400-mile range of the normal fuel tank of 88l <=> 22l / 100 miles = 161km <=> 13.66 l/100km consumtion of benzin
~ 200-mile range of LH2 with 140-litre LH2 tank <=> 70l/100 miles <=> 43.48 l /100km consumtion of LH2
~ 600 miles between fill-ups

»Hydrogen Car 745H
~ Tanksystem:
~ V_Kryotank = 140 l - Kryotank für Flüssigwasserstoff hinter der Rücksitzlehne
~ V_Benzintank = 88 l - Benzintank aus dem Serien-7er
~ V_Totaltank = V_Benzintank + V_Kryotank = 228 l = 228 000 cm³

»Hydrogen fuel update /when running on LH2 750hL
~ 12-cylinder engine develops 204 horsepower
~ tops 100 km/h in 9.6-seconds and
~ is capable of a top speed of 226 km/h
~ 140-litre cryogenic hydrogen tank gives a range of 350 km = 40 liters/100 km !
~ runs on gasoline when needed - you won't find a hydrogen filling station on every street corner just yet

Example 4: LH2 price calculation (years old)
~ commercial hydrogen is more expensive than gasoline
~ assuming $0.05 per kwh of electricity from a nuclear power plant during low demand,
~ hydrogen would cost $0.09 per kwh
~ this is the equivalent of $0.67 per liter of gasoline
~ gasoline was calucalted to sell at the pump in the United States for about $0.30 per liter
~ estimates of the real cost of burning a liter of gasoline were caluclate to be in range from $1.06 to $1.32
~ when production, pollution, and other external costs are included
~ based on these calculations hydrogen fuel was estimated to become competitive