Looking for an equation related to lifting force of air

In summary, the conversation discusses the process of determining the size of a hot air balloon in order to lift the basket, balloon, and passengers. The speaker asks if there is an equation for calculating the lifting force based on the amount of air and temperature. Another person shares a helpful document and explains the basic model using two forces, buoyancy and weight. The conversation concludes with confirmation that the equation is similar to what someone else has derived.
  • #1
Paranemertes
3
0
Hello,

I've been wondering for a while now how hot air balloonists figured out how big their balloons needed to be to lift themselves, the basket,the balloon itself, ect. Is there an equation that would tell me how much lifting force I could get out of x amount of air at x temperature, what volume that would take up, and maybe the pressure?

Thanks!
 
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  • #3
I didn't read the document, but you can construct a basic model just by knowing two forces: the bouyancy force and the weight force.

(mass_basket+mass_balloon+mass_air_in_balloon)*g = Volume_balloon*g*density_surrounding_air

This equation would be for if the balloon were not accelerating up or down.
 
  • #4
Yep, that is very similar to what this fine gentleman derived. Thanks!
 
  • #5


Hi there,

Thank you for your question. The equation that you are looking for is called the ideal gas law, which relates the pressure, volume, and temperature of a gas. It is expressed as PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the universal gas constant, and T is the temperature in Kelvin.

To determine the lifting force of air, you would need to consider the weight of the air in the balloon (including the basket and any other objects inside), the weight of the balloon itself, and the weight of the gas inside the balloon. By manipulating the ideal gas law equation, you can calculate the volume of gas needed to achieve a certain lifting force, given the temperature and pressure.

However, it's important to note that this equation is only applicable to ideal gases, and air is not an ideal gas. Therefore, there are other factors that need to be taken into consideration, such as humidity, altitude, and the composition of the air. In addition, the shape and material of the balloon can also affect the lifting force.

I hope this helps answer your question. Happy experimenting!

Best,
 

1. What is the equation for calculating the lifting force of air on an object?

The equation for calculating the lifting force of air on an object is: L = 1/2 * ρ * V2 * A * CL, where L is the lifting force, ρ is the density of air, V is the velocity of air, A is the surface area of the object, and CL is the coefficient of lift.

2. How does the density of air affect the lifting force?

The density of air directly affects the lifting force because it is a factor in the equation. The higher the air density, the greater the lifting force will be on an object.

3. What is the significance of the velocity of air in the equation for lifting force?

The velocity of air is a crucial factor in the equation for lifting force. As the velocity of air increases, the lifting force also increases, meaning that the faster the air is moving, the more lift an object will experience.

4. How does the surface area of an object impact the lifting force of air?

The surface area of an object directly affects the lifting force because it is a factor in the equation. The larger the surface area, the more air molecules will come into contact with the object, resulting in a greater lifting force.

5. What is the coefficient of lift and how does it affect the lifting force of air?

The coefficient of lift (CL) is a dimensionless factor that represents the efficiency of an object in producing lift. It takes into account the shape and orientation of the object, and a higher CL means a greater lifting force. Therefore, a higher CL will result in a greater lifting force of air on an object.

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