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Understanding the densities of different gases is key when discussing buoyant force and airship lift. Density is defined as mass per unit volume and is often expressed in units of kilograms per cubic meter (kg/m³). In the context of gases, their density dictates how they will behave in relation to the surrounding air.
At standard conditions of temperature and pressure:

• The density of air is approximately 1.20 kg/m³.
• Helium's density is around 0.166 kg/m³.
• Hydrogen is lighter still, with a density of about 0.0899 kg/m³.

These values indicate that helium and hydrogen are both less dense than air, meaning they will rise when released into the atmosphere. This property is vital for creating buoyancy forces that lift airships. Calculating the difference in density between a gas inside an airship and the surrounding air is the first step in determining the buoyant force.

Choosing between helium and hydrogen for airships involves considering both physical properties and safety concerns. Hydrogen provides the greatest lift due to its lower density, 0.0899 kg/m³ compared to helium's 0.166 kg/m³. This means a hydrogen airship can displace a larger volume of air for the same weight of gas, generating more buoyancy.
However, hydrogen is also highly flammable, which can lead to dangerous situations if leaks occur. Historic incidences like the Hindenburg disaster highlight the risks associated with hydrogen's flammability.
Helium, on the other hand, is inert and non-flammable, providing a safer alternative for airship programs. While helium provides slightly less lift, at approximately 113 kN compared to hydrogen's 120 kN for the scenario described, the safety benefits outweigh the reduction in lift capacity. That's why heliums' non-combustible nature makes it the preferred choice for modern airships.

The concept of lift in airships is directly connected to buoyancy principles and the properties of the gases used. An airship rises because the buoyant force, created by the denser air outside, exceeds the weight of the gas inside the airship. The lift force can be calculated using the formula:
\[ F_{\text{lift}} = (\rho_{\text{air}} - \rho_{\text{gas}}) \times V \times g \]
Where:

• \( \rho_{\text{air}} \) is the density of the surrounding air.
• \( \rho_{\text{gas}} \) is the density of the gas inside the airship (hydrogen or helium).
• \( V \) is the volume of air displaced by the airship.
• \( g \) is the acceleration due to gravity (approximately 9.81 m/s²).

By rearranging this formula, we can determine the volume of gas required to achieve a specific lift. For instance, for a required lift of 120 kN using hydrogen, one must calculate the required volume to displace enough air to create this lift force. Moreover, understanding this equation helps in comparing different gases' effectiveness in providing lift, as seen with helium versus hydrogen.