Paper Helicopter Trials: Which Conclusions Are Defensible?
In Ms. Alvarez's eighth-grade class, four groups test how wing length affects the fall time of a paper helicopter. Each group cuts three helicopters with wings 4 cm, 6 cm, and 8 cm wide, drops each from a balcony, and uses a stopwatch. Group 1 drops from 2.0 m and records averages of 1.4 s, 1.7 s, and 1.9 s. Group 2 drops from 2.5 m and records 1.8 s, 1.7 s, and 1.5 s. Group 3 uses a phone slow-motion video and gets 1.5 s, 1.8 s, and 2.0 s. Group 4 times only one trial per helicopter and gets 1.2 s, 2.3 s, and 1.6 s. During the discussion, one student says, 'Group 2 proves longer wings make helicopters fall faster, while Group 1 proves longer wings make them fall slower, so the experiment is worthless.' Another says the class should just average all 12 numbers together. The teacher asks the class to decide which conclusions are defensible and how to revise the investigation.
1. Identify the variables that differ among the four groups and explain how each difference could affect the comparison of fall times.
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The groups differ in at least three ways:
- Release height: Groups 1 and 3 use 2.0 m, while Group 2 uses 2.5 m. A longer fall gives more time for air resistance, spinning, and wing orientation to affect motion, so the 2.5 m data cannot be compared directly with the 2.0 m data.
- Timing method: Groups 1, 2, and 4 use a stopwatch, which includes human reaction time at both start and stop. Group 3 uses slow-motion video, which can be checked frame by frame and should have less timing error.
- Number of trials: Groups 1–3 average three trials, but Group 4 times only one trial per helicopter. One trial cannot show variability caused by release angle, spin, or drafts.
These differences are confounded with wing length. For example, Group 2's pattern might be caused by the greater height or the timing method rather than by wing length alone. A defensible comparison requires holding height, timing method, and trial number constant.
2. Evaluate the student's claim that Group 2 proves longer wings fall faster and that the experiment is worthless.
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Group 2's numbers (1.8 s, 1.7 s, 1.5 s) do show shorter times as wing width increases, but that group also dropped from 2.5 m, so its result is confounded by height and timing method. Groups 1 and 3, both at 2.0 m with more careful timing, show the opposite pattern: longer wings take more time (1.4 → 1.9 s and 1.5 → 2.0 s). That is consistent with longer wings creating more air resistance.
The experiment is not worthless; it is an investigation with uncontrolled variables. The conflicting patterns indicate that the class cannot yet isolate the effect of wing length. Pooling all 12 numbers would be worse because it would mix different heights, timing methods, and trial counts into an average that has no clear physical meaning. The defensible conclusion is that the current data are inconclusive and must be retested under controlled conditions.
3. Describe a revised procedure that would produce more defensible evidence and explain why it addresses the problems.
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Use one drop height, such as 2.0 m, for every helicopter. Use the same paper, paperclip, and release orientation, and have one student release while another records video. Test each wing length five times in random order, then compute the mean and range for each length. Repeat on a second day to check whether the pattern is consistent.
This procedure controls height and timing method, reduces reaction-time error, and quantifies trial-to-trial variability. Random order prevents one helicopter from always being dropped first or last, which could matter if room drafts change. The range shows whether differences between wing lengths are larger than the noise in the measurements.