The Hot Air Balloon  

 

For drawings see Mr. Jones

 

Purpose:  to explain the relationship of density and Archimedes' Principle to the flight of a hot air balloon.

 

Background:  Archimedes' Principle states that a body immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced.  In other words, a body immersed in a fluid seems to lose weight equal in amount to the weight of the fluid displaced.  This is the result of the upward pressure of the fluid.  Archimedes' Principle helps us to understand why objects that have a density greater than that of water will sink while those with a density less than 1.00 g/cm³ will float.  Air is fluid; therefore, we can apply the principle to objects immersed in it.  As air is heated, it expands, causing its density to decrease.  The heated air will float upward in the more dense cooler body of air for the same reason a cork will float to the surface of water.

 

Materials:  24 sheets of tissue wrapping paper, string, scissors, glue sticks, wire ring, paper clips

 

Procedure:

1.  Each of the 8 gores is made of 3 sheets of tissue paper, glued end to end.  Place sheet 1 over sheet 2 allowing the bottom sheet to extend 1 cm outward.  Place glue on this extension, fold up and over the top sheet.  Repeat with sheet 3, gluing it to sheet 2.  Unfold, allow to dry, and repeat 7 more times.  (8 x 3 = 24 sheets - arranging for color if you wish).

 

2.  Stack all 8 dry gores on top of teach other and cut out a cigar pattern, to a sharp point at the top and a wider (10-12 cm) opening at bottom.  Cut all 8 gores to this same shape.  Just about any shape will do.

 

3.  The gores will be glued together in a similar fashion to the earlier gores.  Lay sheet 1 on top of sheet 2.  Allow 1 cm of bottom sheet to extend outward.  Place glue here and fold up and over.  Now a key point.   Place sheet 3 on top of sheet 2.  You must glue sheet 2 up and over sheet 3 but on the opposite side.   As you continue you will be creating an accordian of sorts.  You must glue on alternate sides as you add gores.

 

4.  Finally glue the last two ends (free) together.  Tie all 8 gores together with string at the top (twist into an air tight knot and tie a loop around it.)  This loop will be used to hang balloon.

 

5.  At the bottom you must fold, glue, staple, etc. all the bottom into a opening about 10-12 cm across.  This is difficult.  Then inflate your balloon with a hair dryer and check for leaks or tears.  These can be repaired easily.   Be careful not to use flames to check.  This balloon is extremely flammable.

 

6.  Bring the balloon to school for a test flight.  You can complete part 2 at home or at school.

 

Part 2 Calculating Lift Capability

 Purpose: To calculate the lift capability of your balloon.

 Materials: metric ruler or meter stick, lab scales

 Procedure: 1. A cubic meter of air has a mass of about 1.0 kg. this means that a massless bubble can lift about 1.0 kg for each cubic meter of volume. The hot air pumped into your balloon displaces the cooler more dense air, creating a buoyant lifting force. By calculating the volume of the balloon you can determine the force of buoyancy.

 Density = mass/volume or Buoyant Force (mass) = density of balloon x density of air

 If you balloon is assumed to be a sphere , then our formula becomes:

 buoyant Force = 4/3 p r³ x 1.00 kg/m³ (r is the radius)

 2. Determine the radius of your balloon. Radius = ___________cm or __________m

 3. Calculate the buoyant force of your balloon using the formula in step 1 above. Show your math work.

   Buoyant Force =  ________________kg

 4. You hot air balloon, however, is not massless. The paper, glue, wire and even the air have mass. To determine the actual payload which your balloon can lift, you must take into account these masses. By subtracting these from the buoyancy lift force, you can determine if and by how much your balloon will become airborne.

 Determine the mass (kg) of your balloon. Mass = ___________________kg

 5. Now let's determine the mass of the hot air. Since you already know the volume of the air in the balloon, you can multiply that by the density of air to get the mass of the air. Heated air has less density, and therefore, less mass. Multiply the volume of your balloon by the density value given below (this number is an estimate and may need to be changed) to obtain the mass of the air.

 Assuming a mid‑range temperature of 100 ° C, the density of the hot air would be 0.75 kg/m³

 mass of hot air = 4/3 p r³ x 0.75 kg/m³ = _____________kg