Hot Air Balloons - Calculating Lifting Force

This calculator computes for the lifting force and the mass an air baloon can carry.
CalculationInputs
﻿﻿Baloon Vol
:10 m^3​
﻿
﻿﻿Desnity of air
:1.205 kg/m^3​
﻿
﻿﻿Density of hot air
:0.943 kg/^3​
﻿
﻿﻿Gravity
:9.81 m/s^2​
﻿
﻿
Output
﻿﻿Lifting Force
:25.70​
﻿
﻿
FL =V(ρc − ρh) agF_L = V (ρ_c - ρ_h) a_gFL​ =V(ρc​ − ρh​) ag​
﻿﻿Mass
:2.62​
﻿
﻿
m = FL/agm\ =\ F_L/a_gm = FL​/ag​
﻿
﻿
Parameters
ExplanationThe lifting force of a hot air balloon is primarily determined by the buoyant force of the hot air relative to the cold air surrounding it.
When the air inside the balloon is heated, it expands and becomes less dense than the surrounding cooler air. 
This difference in density causes the balloon to float upwards or in other words, it creates a lifting force.
﻿
The lifting force is calculated as:
﻿
FL =V(ρc − ρh) agF_L = V (ρ_c - ρ_h) a_gFL​ =V(ρc​ − ρh​) ag​
As the lifiting force is equal to the weight or gravity force, the equations can be combined and rearranged to calculate the mass:
﻿
m = FL/agm\ =\ F_L/a_gm = FL​/ag​
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