ρh = density hot balloon air (kg/m3, slugs/ft3)
ag = acceleration of gravity (9.81 m/s2, 32.174 ft/s2)
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)
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
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.
If the balloon temperature is 60 oC and the surrounded temperature is -20 oC - the chart indicates a specific lifting force
This calculator can be used to calculate the lifting force of a volume with lower density than surrounding air.
Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.
Thermal properties of air at different temperatures - density, viscosity, critical temperature and pressure, triple point, enthalpi and entropi, thermal conductivity and diffusivity and more.
Buoyancy is the resultant force acting on a submerged body.
Required force and power to lift an elevator.
Newton's third law - force vs. mass and acceleration.
Lift and drag forces acting on a body like an air foil in a fluid flow.
Mass vs. weight - the Gravity Force.
Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!
We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.
Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don't save this data.