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# Hot Air Balloons - Calculate Lifting Weights

## Calculate hot air ballons lifting forces.

### 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

Fl = V (ρc - ρh) ag                         (1)

where

Fl = lifting force (N, lbf)

V = balloon volume (m3, ft3)

ρc = density cold surrounding air (kg/m3, slugs/ft3)

ρh = density hot balloon air (kg/m3, slugs/ft3)

ag = 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

Fl = (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

Fg = m ag                       (2)

where

Fg = weight - gravity force (N, lbf)

m = mass (kg, slugs)

Since lifting force of a flying air balloon equals weight (Fl = Fg) - the lifted mass can be expressed by combining (1) and (2) to

m = Fl / ag

= (25.4 N) / (9.81 m/s2)

= 2.6 kg

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

Fl = (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.

balloon volume (m3)

balloon volume density (kg/m3)

surrounding air density (kg/m3)

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## Citation

• The Engineering ToolBox (2003). Hot Air Balloons - Calculate Lifting Weights. [online] Available at: https://www.engineeringtoolbox.com/hot-air-balloon-lifting-force-d_562.html [Accessed Day Month Year].

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9.19.12