BALLOONING

 There are three principles by which we can fly first is by being lighter than air which is used by air balloons second is by pushing the air down as done by aircraft and the third is by pushing something else downward which is used in rocket propulsion. The principle used by mankind for the flight was by being lighter 18^th century balloon flight was the first manned flight and it remained the only way to fly for over a century. Before humans duck, rooster and sheep were made to fly, they were specially chosen as none of them fly this allowed us to check whether we would be able to survive at high altitude or not and on 21 Nov 1783 first human flight was possible in which hot air balloons were used for the flight. For long time people thought that this is the only future of flight. In 19^th century to early 20^th century ballooning was used to fly when it was used to transport passengers in large airships in which instead of hot air lighter air like hydrogen and helium were used. The main advantages of the airships were highly efficient if stationary as it generates the lift for free and could go very high.  Along with this there were some serious disadvantages like because of their large volume they were slow and generate high drag force.

aerostatics

Gas law

Pv=nRT

P=ρRT/M equation of states

Principle of ballooning

Archimedes buoyancy principle
max F=mg=ρ_airVg-ρ_gasVg
(neglecting the payload)

P₁=p₂

ρ₁RT₁/M₁=ρ₂RT₂/M₂

ρ1/ρ2=T2/T1.M1/M2

F=ρ_atmVg(1-ρ_gas/ρ_atm)

F=ρ_atmVg(1-(T_atm/_Tgas).(M_gas/M_atm))

M_H2=2 g/mol

M_He=4 g/mol

M_air=28.97g/mol

Now let us compare the gas balloon with the hot air balloon

First consider the helium balloon

Since temperature inside and outside is approximately same so by using the above equation we get

F=ρ_atmVg(1-M_gas/M_atm)

F=ρ_atmVg(1-4/28)

F=ρ_atmVg.6/7

Now consider the hot air balloon

Here the molar mass remains same so from above equation we get

F=ρ_atmVg(1-_Tatm/T_gas)

To generate same amount of lift we would require the temperature of the gas inside the balloon to be 7 times the temperature of the atmosphere

i.e, T_gas=7.T_atm

if T_atm=300K

Then we would need T_gas=2100K which is the temperature of blow torch

That is why F_He>>>F_{hot air}