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Charles Law (Hot Air Balloon)

Concepts to Investigate
: Charles's Law, hot air balloons, buoyancy, density, temperature-volume relationships in gases, Archimedes' Principle.

Materials: Tissue paper, scissors, glue or tape, construction paper or other heavy paper, hair dryer.

Principles and Procedures: Frenchmen Joseph and Étienne Montgolfier are credited with the development of the first practical hot air balloon. In September of 1783 they sent a sheep, rooster and duck aloft over Versailles, and two months later sent three men (Jean-François Pilâtre de Rozier, François Laurent, and Marquis d'Arlandes) on a 5.5 mile (approximately 9 km) flight over Paris! Later, hot air balloons were used in the Napoleanic and American Civil Wars to perform reconnaissance of enemy positions and movements. Ballooning is a popular sport today, although propane has replaced hay as a heating fuel, and lightweight nylon and other synthetics have replaced silk, cotton and wool as balloon fabric. In this activity you will employ the principles used by the Montgolfier brothers and modern ballooning enthusiasts in the construction and flight of your own hot air balloon.
Four years after the success of the Mongolfier brothers, fellow countryman Jacques Charles formalized the principle
responsible for balloon flight. Charles's Law states that at constant pressure, the volume of a fixed mass of gas is directly proportional to the absolute temperature (V=kT). For example, if the absolute temperature of a fixed mass of gas (at constant pressure) is doubled, the volume doubles and the density is cut in half (density = mass/volume). If the temperature is raised from room temperature (20˚C, 68˚C, 293 K) to 50˚C (122˚F, 323 K), the volume of the heated air increases 10% (323K/293K= 1.10). Since a hot-air balloon is an open system at constant pressure, this can be accomplished only if air leaves the balloon. Thus, the mass of air remaining in the balloon decreases, leading to a decrease in the composite density of the balloon (balloon and the air it
contains). The balloon rises because it now has a lower density than the air surrounding it.

The BalloonFigures Q-U shows the plans for a pentadecahedronal (15-sided) balloon. You can read the instructions about how to make this balloon here: Instructions. Your task however, is not to simply make the same balloon as listed here but to design you own balloon. Some things to think about in your design process: how big will your balloon be (are you going to make the biggest balloon you can or the smallest)? How much weight (payload) can it carry? How high will it go? How long will it stay aloft? 

For you to do:
  • Create a rough draft of your design. Should be complete with details on size/dimensions (in cm) and the materials needed. Your drawing should show multiple views and parts of your balloon. List the materials you will be using. (10 points)
  • Using your rough draft create your balloon. Make note of changes to your plans and materials as necessary. (40 points)
  • Launch your balloon. Successful launch of your balloon with the class on the given launch day. (20 points)
  • Final Draft of plans. The final draft should be drawn to scale (for example 1 graph square could equal 10cm), and show the dimensions of the individual sides/pieces of your ballon as well as a diagram of those pieces in context of the whole balloon. (20 points).
  • Final reflection. A couple of paragraphs which answers the questions below and reflects on the design process and building of you balloon. Think about how your final balloon changed from your initial plans, how well you group worked together, what you would do differently next time, and what you learned from the process? (20 points).
Your refection should include answers to the following questions:
  1. How high did your balloon travel? How long did it stay aloft?
  2. Will your balloon rise faster on a cool day or a warm day? Explain.
  3. Why does the hot air balloon eventually fall back to earth? 
  4. Why does the density of the air in the balloon decrease as it is heated? 

Optional Tasks
  • Upload a photos of your balloon to a shared PicasaWeb Album (see Mr. Fazio for instructions)
  • Upload a movie of you balloon to YouTube and share with the class.
  • Modify your balloon, to make it better in some way (flight height, payload, time aloft, etc). Document the making of a new balloon and it's launch.