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Hot Air Balloons - Calculate Lifting Weights

Calculate hot air ballons lifting forces.

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Air Balloon - Hot Air 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, lb f )

V = balloon volume (m 3 , ft 3 )

ρ c = density cold surrounding air (kg/m 3 , slugs /ft 3 )

ρ h = density hot balloon air (kg/m 3 , slugs /ft 3 )

a g = acceleration of gravity (9.81 m/s 2 , 32.174 ft/s 2 )

Example - Lifting Force created by a Hot Air Balloon

A hot air balloon with volume 10 m 3 (353 ft 3 ) is heated to 100 o C (212 o F) .   The temperature of the surrounding air is 20 o C (68 o F). The air density at temperature 100 o C is 0.946 kg/m 3 (0.00184 slugs/ft 3 ) and the air density at temperature 20 o C is 1.205 kg/m 3 (0.00234 slugs/ft 3 ) .

The lifting force can be calculated as

F l = (10 m 3 ) [(1.205 kg/m 3 ) - (0.946 kg/m 3 )] (9.81 m/s 2 )

= 25.4 N

Weight - or gravity force - can be calculated as

F g = m a g (2)

where

F g = weight - gravity force (N, lb f )

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/s 2 )

= 2.6 kg

The calculation of lifting force can be done in Imperial units as

F l = (353 ft 3 ) [(0.00234 slugs/ft 3 ) - (0.00184 slugs/ft 3 )] (32.174 ft/s 2 )

= 5.7 lb f

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

Hot Air Balloon - Specific Lifting Force

Imperial Units

Hot Air Balloon - Specific Lifting Force - Imparial Units

Example - Specific Lifting Force from a Hot Air Balloon

Hot Air Balloon - Lifting Force Example

If the balloon temperature is 60 o C and the surrounded temperature is -20 o C - the chart indicates a specific lifting force

3.3 N/m 3

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.

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