| 🚩 Keywords: Full Factorial Design, ANOVA, Response Surface, Interaction Effects | GitHub |
This project was completed with Zhihao Chen for the Fall 2025 section of STA 522: Study Design and Causal Inference at Duke University.
Overview
Using a 2⁴ full factorial experiment, we systematically investigated which physical properties of a paper helicopter most affect flight duration — and identified the optimal design configuration for maximum airtime.
Experimental Design
We tested four binary factors across 16 treatment combinations, each replicated 5 times for a total of 80 flights:
| Factor | Low Level | High Level |
|---|---|---|
| Rotor length | 7.5 cm | 8.5 cm |
| Leg length | 7.5 cm | 12.0 cm |
| Leg width | 3.2 cm | 5.0 cm |
| Paper clip | None | Attached |
- Response variable: Flight duration (seconds), measured from drop to landing
- Randomization: Flight order randomized within each replicate block
Statistical Methods
- Full factorial ANOVA including all main effects and two-way/three-way interactions
- Nested F-tests for model comparison and interaction significance
- Model diagnostics: residual normality (Shapiro-Wilk), constant variance (Levene’s test)
- 95% Confidence intervals for individual treatment effects
Key Findings
| Factor / Interaction | Effect on Flight Time | p-value |
|---|---|---|
| Rotor length (high) | +0.220s | < 0.001 |
| Paper clip | −0.315s | < 0.001 |
| Leg length (high) | −0.159s | < 0.01 |
| Leg width (high) | −0.152s | < 0.05 |
| Rotor × Leg length | Significant interaction | < 0.05 |
| Rotor × Clip | Significant interaction | < 0.05 |
Interpretation: Rotor length is the most important design factor — a longer rotor increases lift and slows descent. Paper clips add weight without aerodynamic benefit, sharply reducing flight time. The significant rotor × clip interaction suggests that clipping a long-rotor helicopter is especially detrimental.
Optimal Configuration
The best-performing treatment (treatment “a”) used:
- ✅ High rotor length (8.5 cm)
- ✅ Low leg length (7.5 cm)
- ✅ Low leg width (3.2 cm)
- ✅ No paper clip
Predicted flight time: 2.47 seconds (95% CI: 2.31 – 2.63s)
Technical Stack
- Language: R
- Packages:
tidyverse,dplyr,ggplot2,kableExtra