source : engineeringtoolbox.com

## Hot Air Balloon – 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

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)

Hot Air Balloon – Lifting Force – Engineering ToolBox – 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 asHot air balloons work because hot air rises. By heating the air inside the balloon with the burner, it becomes lighter than the cooler air on the outside. This causes the balloon to float upwards, as if it were in water. Obviously, if the air is allowed to cools, the balloon begins to slowly come down.With this in mind we can calculate the density of the heated air at a given temperature, using the Ideal gas law, as follows: P = ρRT Where: P is the absolute pressure of the gas, in Pa ρ is the density of the gas, in kg/m 3 R is the gas constant, in Joules/kg.K T is the absolute temperature of the gas, in Kelvins (K) Now, Normal atmospheric

What happens as the air inside a hot air balloon is heated? – Ultra Hi-Float and Super Hi-Float are liquid products designed to provide a thin layer of protection inside the balloon that helps helium balloons float 10 to 25 times longer, according to Hi-float.com. Additional ways to lengthen the life of a helium balloon include coating the outside with a silicone spray or hair spray, inflating the balloon at the same temperature as the area of itsHot air balloons float in the air because of the difference in density between cold and hot air. In this problem, you will estimate the minimum temperature the gas inside the balloon needs to be, for it to take off. To do this, use the following variables and make these assumptions:The absolute temperature of the cold air outside the balloon is and its density is.The absolute temperature of the hot air inside the balloon is (where).The balloon is open at the bottom, so that the pressure inside and outside of the balloon is the same. Assume that we can treat air as an ideal gas. Use for the magnitude of the acceleration due to gravity.

Hot Air Balloon Physics – The balloon is open at the bottom, so that the pressure inside and outside the balloon is the same. ASsume that we can treat air as an ideal gas. Use g for the magnitude of the acceleration due to gravity. For the balloon to float, what is the minimum temperature Tmin of the hot air inside it in terms of the variables given?A recreational (open) hot air balloon (i.e., Pinside is approximately Poutside) has a volume of 2267 m3 when fully inflated. The total weight of the balloon, basket, ballast and pilot is 1989.4 N (448 lbs). By how much must the density of the air in the balloon be smaller than that of the surrounding atmosphere in order to keep the balloon floating level near the ground?Hot air balloons float in the air because of the difference in density between cold and hot air. In this problem, you will estimate the minimum temperature the gas inside the balloon needs to be, for it to take off. *Assumptions* The combined weight of the pilot basket together with that of the balloon fabric and other equipment is W.