Experiment 2: Paper Airplanes — Variables and Fair Tests

Every physics experiment in this course — and every honest experiment anywhere — stands or falls on one discipline: change one thing at a time. This lesson is about that discipline itself. You will race two paper airplane designs, learn to name the independent, dependent and controlled variables in any setup, and discover why scientists repeat trials and report ranges, not just averages.

The physics behind the practical

A paper airplane is a glider: its wings generate lift from forward motion, and drag steals that motion away. Wing shape trades the two against each other — a dart's narrow wings slice the air with little drag but make little lift, while a glider's broad wings make generous lift at low speed but drag more. Which design flies farther is a genuine empirical question, and it can only be answered cleanly if everything except wing shape is held fixed. That is the fair test: the independent variable (wing shape) is the only difference between conditions, the dependent variable (flight distance) is what you measure, and the controlled variables (same paper, same thrower, same launch height and effort, same still indoor air) are pinned down so they cannot explain the result instead.

Repeating each throw three times matters because launches vary randomly — a slight wrist flick can add or steal a metre. The mean estimates the typical flight, and the range (largest − smallest) measures consistency. A difference between designs is only convincing if it is clearly bigger than the ranges within each design.

Variables and controls

In the virtual lab

The simulator isolates a different variable: with wing angle and throw speed sliders, readouts for Distance, Flight time and Max height, and a Launch plane button. Follow its Guided Procedure: hold the angle at 10° and launch three times at one speed — those are control runs, and their small scatter is the sim's built-in launch noise. Then sweep the angle through 0°, 5°, 15°, 20°, 25°, 30°, one variable at a time, and watch the orange dot trace the distance-vs-angle curve: it rises to a hump near the middle angles and falls away as the wing becomes a drag brake. The curve is the lesson in one picture — a trade-off with an optimum, not "more is better". Finish by raising the throw speed and re-finding the best angle: you are now testing whether the optimum itself depends on a second variable, which is a two-variable question and needs its own careful design.

Hands-on: racing the two designs

Build three identical darts and three identical gliders from the same paper stock. Mark a launch line, throw each plane three times with the same effort, and measure to the first touchdown with a tape measure. Record every flight — a nosedive is data about consistency, not a mistake to delete. Throw away from people and never toward faces.

A worked investigation

One group's honest results:

Step 1 — Means. Dart: (7.8 + 9.0 + 8.4) ÷ 3 = 25.2 ÷ 3 = 8.4 m. Glider: (6.0 + 6.1 + 6.2) ÷ 3 = 18.3 ÷ 3 = 6.1 m.

Step 2 — Ranges. Dart: 9.0 − 7.8 = 1.2 m. Glider: 6.2 − 6.0 = 0.2 m. The glider is far more consistent even though it flies shorter.

Step 3 — Judge the difference. Difference of means = 8.4 − 6.1 = 2.3 m, which is bigger than either range (1.2 m and 0.2 m). The dart's advantage is larger than the launch-to-launch wobble, so it is reasonable to claim a real difference for these conditions.

Step 4 — Claim, evidence, next test. Claim: the dart flies farther, the glider more steadily. Evidence: means 8.4 m vs 6.1 m; ranges 1.2 m vs 0.2 m. Next test: does a paperclip on the nose change the dart's consistency? That changes one new variable — mass distribution — while design, paper and thrower stay controlled.

Conclusion and evaluation

The conclusion is deliberately narrow: *for these planes, this thrower and this hall*, the dart wins on distance. The biggest threats to fairness were throw effort (hard to keep identical — a simple lever launcher would fix it) and air currents (one flight near an open door should be repeated, not deleted silently). Notice what would invalidate the test entirely: using different paper for the two designs, or letting a stronger thrower launch the darts. One changed variable you did not intend becomes a rival explanation for the whole result.

Safety

Throw only in the agreed direction, away from faces and walkways; retrieve planes between rounds rather than darting across the flight path; keep launch lines clear of anyone bending to measure.

Common mistakes

• Changing two things at once — a bigger glider made from card instead of paper tests size and material together, and answers neither question.
• Deleting bad flights — cherry-picking destroys the range, which is half the evidence.
• Comparing single throws — one flight each is a coin toss, not a measurement.
• Reporting only the mean — 8.4 m with range 1.2 m and 8.4 m with range 0.2 m are very different claims.
• Letting the thrower "try harder" for a favourite design — effort is a variable whether you name it or not.

Exam Experience

Question 1 — analysis [4 marks]. Two new designs are tested with three flights each. Design X: 5.2 m, 5.6 m, 5.4 m. Design Y: 5.5 m, 4.9 m, 5.8 m. Calculate each mean and range, and state, with justification, whether either design has been shown to fly farther.

Scoring guide:

• Mean of X = 5.4 m; mean of Y = 5.4 m [1]
• Range of X = 0.4 m; range of Y = 0.9 m [1]
• The means are equal, so no design has been shown to fly farther [1]
• Y is less consistent (larger range); more repeats would be needed to detect any small difference [1]

Question 2 — evaluation and design [4 marks]. Design a fair test of whether paper type (printer paper vs card) changes flight distance, using one airplane design. State the variables and two features that make the test fair.

Scoring guide:

• Independent variable: paper type; dependent variable: flight distance measured the same way each time [1]
• Identical design/folds for every plane, several planes per paper to allow for build variation [1]
• Controlled: same thrower or launcher, same launch height, same indoor conditions [1]
• At least three flights per plane, all recorded, comparing means against ranges [1]

Multiple choice 1. In the airplane test, flight distance is the:

• A. Independent variable
• B. Dependent variable
• C. Controlled variable
• D. Hypothesis

Answer: B. Distance is what you measure in response to the change you deliberately make (wing shape or angle).

Multiple choice 2. A scientist repeats each measurement three times mainly to:

• A. Make the experiment last longer
• B. Average out random variation and reveal how consistent the results are
• C. Guarantee the hypothesis is correct
• D. Use up spare materials

Answer: B. Repeats cannot fix a biased method, but they expose random scatter and let the mean settle near the typical value.

Going deeper: what "best design" really means

Engineers rarely ask "which went furthest once?" — they ask "which performs best, reliably, for the brief?" Watch how the verdict changes with the brief. Suppose three designs each fly three times:

For a one-throw distance record, the Sprinter's 10.5 m wins and its wild range is forgiven. For delivering a message to a target 8 m away every time, the Cruiser is the only serious choice — its whole distribution sits within 0.2 m of 8.4 m, while the Sprinter sometimes lands at 7.9 m and the Tanker never arrives. Mean without range is half a result; the pair together is the engineering answer. Real reports add one more column: the conditions (indoor still air here), because a design crowned indoors may fold outdoors in a crosswind.

The physics under the stability is worth naming: a paper plane stays nose-first when its centre of mass sits ahead of its centre of pressure — gravity acts at the front, aerodynamic forces push at the back, and the pair works like a weathercock, forever swinging the nose back into line. That is why a paperclip on the nose transforms a tumbling sheet into a dart, and why the Tanker (rear-heavy) wobbles: its mass sits too far back. When you tune your design in the next round, move mass forward before you reshape wings — trim first, sculpt second.

One more angle: when is a difference real?

A working rule for small data sets: a difference between two means is trustworthy only when it clearly exceeds the sum of the spreads behind it. Apply it to the Going deeper table: Sprinter mean 9.1 m (range 2.6) vs Cruiser mean 8.4 m (range 0.2). The means differ by 0.7 m, but the ranges sum to 2.8 m — the distributions overlap heavily, so three throws each cannot separate these designs for distance. The honest report says "Sprinter probably throws further, but the evidence is weak; ten throws each would settle it." Judging when data *cannot* answer the question is as scientific as answering it.