# Hot Air Balloons - Calculate Lifting Weights

### 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*. The temperature of the surrounding air is

^{ o }C (212^{ o }F)*20*The

^{ o }C (68^{ o }F).*air density*at temperature

*100*is

^{ o }C*0.946 kg/m*and the air density at temperature

^{ 3 }(0.00184 slugs/ft^{ 3 })*20*is

^{ o }C*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

#### Imperial Units

#### Example - Specific Lifting Force from a Hot Air Balloon

If the balloon temperature is * 60 ^{ o } C * and the surrounded temperature is

*-20*- the chart indicates a specific lifting force

^{ o }C* 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.

- density helium :
*0.1664 kg/m*^{ 3 } - density hydrogen :
*0.0899 kg/m*^{ 3 } - more gases

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