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# Hot Air Balloons - Calculate the 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.

#### 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.

## Related Topics

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## Related Documents

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### Buoyancy

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### Elevators - Force and Power

Required force and power to lift an elevator.

### Force

Newton's third law - force vs. mass and acceleration.

### Lift and Drag

Lift and drag forces acting on a body like an air foil in a fluid flow.

### Mass vs. Weight

Mass vs. weight - the Gravity Force.

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