Balloon rocket — size vs distance

What is happening

The neck points back at the student, so the two halves of the third-law pair are easy to point at on screen: the balloon pushes the air to the right, and the air pushes the balloon to the left. Neither force comes first and neither is bigger. While the balloon is still thrusting the sim labels both arrows, and the escaping air is drawn heading straight back toward the person who let go.

The push lasts only as long as there is air to expel, so a bigger balloon does not push harder, it pushes for longer. That is the heart of this lab: the straw is the same width every time, so the thrust is about the same for every balloon, and what changes is how many seconds it lasts.

Drag is the reason the balloons never get fast. A balloon settles at the speed where drag balances thrust, and because a bigger balloon has a bigger cross-section, it flies slower — but it keeps thrusting long enough to still travel much further. The two effects together give a curve, not a straight line.

Why the string matters

A sagging string costs distance twice over. The straw binds where the string bends, and the balloon has to drag the slack along ahead of it. In the sim a very slack string can cut the distance of a 16 inch balloon roughly in half, and you can see the sag in the 30 m view. It is the clearest example in the whole set of a variable that has nothing to do with the balloon and everything to do with the setup.

Making it a controlled experiment

Three things can change here: balloon size, how full it is, and the string. Only one should change at a time.

• To test size: leave the slider at 100% and the string taut, and work through all five balloons.
• To test how full: pick one balloon and step the slider down from 100%. Note that a half-full 16 inch balloon holds more air than a full 12 inch one, which is worth making students discover.
• To test the string: hold size and fullness fixed and change only the string. On the graph, those points get their own colour, so a series that is not controlled shows up as scattered colours.

Trials that are not fully inflated plot as hollow circles, so mixed data is visible at a glance rather than hidden.

Student questions

• The straw is the same on every balloon. So what is different about a big balloon's push?
• Which balloon reached the highest speed? Is that the same one that travelled furthest? Explain how both can be true.
• Switch the x-axis to air volume. Is that graph straighter than the diameter one? Why would volume be the fairer variable?
• None of the balloons reach the far stand 30 m away. What would you change to get one there, and which of your changes is still a fair test?
• A classmate blew up a 10 inch balloon "as much as it would go" and a 16 inch one "about half". Their data says size does not matter much. What went wrong?

Numbers worth knowing

• Gauge pressure inside is taken as 2.5 kPa, the straw as 9 mm across, drag coefficient 0.47 for a sphere. Balloon latex is scaled from real party balloon masses, and the straw and tape add 1.5 g every time.
• At 100% and taut the sim gives about 6.2 m for the 8 inch balloon rising to about 22 m for the 16 inch. The 30 m spacing you asked for leaves headroom, so nothing is cut off by the far stand — if your own counter run is shorter, that spacing is one constant to change.
• The balloon is drawn a little larger than true scale against the string so that 8 inch and 16 inch are easy to tell apart on screen.