Hot Air Balloons - Calculate the Lifting Force
Calculate hot air ballon lifting force.
Hot Air Lifting Force
The lifting force from a hot air balloon depends on the density difference between balloon air and surrounding air, and the balloon volume. The lifting force can be calculated as
F l = V (ρ c - ρ h ) a g (1)
where
F l = lifting force (N, lbf )
V = balloon volume (m3, ft3 )
ρ c = density cold surrounding air (kg/m3, slugs /ft3 )
ρ h = density hot balloon air (kg/m3, slugs /ft3 )
a g = acceleration of gravity (9.81 m/s2, 32.174 ft/s2)
Example - Lifting Force created by a Hot Air Balloon
A hot air balloon with volume 10 m3 (353 ft3 ) is heated to 100 oC (212 oF) . The temperature of the surrounding air is 20 oC (68 oF). The air density at temperature 100 oC is 0.946 kg/m3 (0.00184 slugs/ft3 ) and the air density at temperature 20 oC is 1.205 kg/m3 (0.00234 slugs/ft3 ) .
The lifting force can be calculated as
F l = (10 m3 ) [(1.205 kg/m3 ) - (0.946 kg/m3 )] (9.81 m/s2)
= 25.4 N
Weight - or gravity force - can be calculated as
F g = m a g (2)
where
F g = weight - gravity force (N, lbf )
m = mass (kg, slugs )
Since lifting force of a flying air balloon equals weight (F l = F g ) - the lifted mass can be expressed by combining (1) and (2) to
m = F l / a g
= (25.4 N) / (9.81 m/s2)
= 2.6 kg
The calculation of lifting force can be done in Imperial units as
F l = (353 ft3 ) [(0.00234 slugs/ft3 ) - (0.00184 slugs/ft3 )] (32.174 ft/s2)
= 5.7 lbf
Hot Air Balloon - Specific Lifting Force
Specific lifting force (force per unit air volume) created by an hot air balloon - balloon temperature vs. surrounded air temperature - are indicated in the charts below.
SI - units
Imperial Units
Example - Specific Lifting Force from a Hot Air Balloon
If the balloon temperature is 60 oC and the surrounded temperature is -20 oC - the chart indicates a specific lifting force
3.3 N/m3
Hot Air Balloon Lifting Force Calculator
This calculator can be used to calculate the lifting force of a volume with lower density than surrounding air.
- density helium : 0.1664 kg/m3
- density hydrogen : 0.0899 kg/m3
- more gases
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