SYPT Cat A: Problem 1: Invent Yourself – Paper Boomerang Task: Create a returning boomerang using only a sheet of paper through folding and/or cutting techniques. Investigate how its motion depends on relevant parameters.

 Dear SYPT Jurors,

 Name         Count Round 1 Round 2 Round 3 Round 4

Lawrence Wee 3 C         -             B             B

Thank you for making time to be a juror at SYPT Category A. Please find below essential details for the event.

 

	Category A
Date	22 Feb 2025, Saturday
Reporting Venue	Atrium, National Junior College
Reporting Time	7.40 am   A briefing will be conducted for all jurors upon arrival.

 

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Problem 1: Invent Yourself – Paper Boomerang Task: Create a returning boomerang using only a sheet of paper through folding and/or cutting techniques. Investigate how its motion depends on relevant parameters.

1. Aerodynamics & Flight Mechanics of Boomerangs

1.1. Basic Principles

• Rotating Airfoil: A boomerang works as a rotating wing. Each wing (or “arm”) acts as an airfoil. When thrown with spin, the boomerang’s rotation creates differences in relative airflow speed between its arms.
• Lift Differential: The wing advancing in the direction of the throw moves through the air faster than the retreating wing. This speed difference generates more lift on the advancing side, creating a net force that causes the boomerang to turn.
• Gyroscopic Stability: The spinning motion gives the boomerang gyroscopic stability. This means that when an external torque (from aerodynamic forces) is applied, the boomerang responds by precessing (rotating its axis), contributing to its curved, returning path.

1.2. Key Forces

• Lift: Generated perpendicular to the airflow and is affected by wing shape and angle of attack.
• Drag: The force opposing the motion, influenced by the surface area and shape.
• Torque & Precession: Differences in lift create torque about the boomerang’s center of mass. Gyroscopic precession then causes the boomerang to turn, eventually curving its flight back toward the thrower.

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2. Design Considerations with Paper

Since you are limited to a single sheet of paper and techniques such as folding and cutting, here are important design elements to consider:

2.1. Wing Geometry & Shape

• Wing Curvature: Introducing curves or tapered edges via cuts can mimic the airfoil shape, enhancing lift. Curved wings promote a differential in lift between the arms.
• Wing Length & Width: Longer wings may provide more lift but can also increase drag. Experiment with various dimensions to find a balance that supports stable rotation and a predictable turning radius.

2.2. Angle of Attack & Dihedral Angle

• Folding to Set Angles: By folding along the wing edges, you can adjust the angle at which the wing meets the airflow (angle of attack). A slight upward tilt (dihedral angle) can contribute to roll stability.
• Asymmetry for Precession: Slight differences in the wing angles or shape can amplify the effect of aerodynamic precession, ensuring the boomerang follows a returning path rather than flying off in a straight line.

2.3. Weight Distribution & Stiffness

• Folding as Reinforcement: Creases and folds can add rigidity to your paper boomerang, ensuring the wings maintain their shape during flight.
• Center of Mass: By strategically folding (or even layering parts of the paper), you can shift the center of mass. Ideally, the center of mass should be positioned such that it supports smooth rotation and proper aerodynamic response.
• Material Properties: Although paper is relatively uniform in density, how you fold or cut it can locally alter stiffness and weight distribution, affecting the moment of inertia and, thus, the gyroscopic stability.

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3. Investigating Relevant Parameters

When experimenting with your paper boomerang design, consider these parameters and methods to investigate their effects:

3.1. Wing Shape & Cut Patterns

• Variable Edge Profiles: Try different cutting patterns to alter the curvature and edge shape of the wings. Document how these changes influence lift generation and flight stability.
• Symmetry vs. Controlled Asymmetry: While a symmetric design is a good starting point, slight asymmetries (intentional variations between the two wings) may be necessary to trigger the returning behavior.

3.2. Folding Angles & Dihedral Effects

• Angle Adjustments: Experiment with different folding angles along the wing’s leading and trailing edges. Record changes in flight path curvature, distance, and stability.
• Dihedral Angle Variations: Adjust the upward tilt of the wings. A greater dihedral angle might improve lateral stability but can also change the turning radius.

3.3. Throwing Technique & Spin Rate

• Initial Conditions: The success of the flight depends not only on design but also on the throw. Vary the spin rate (angular velocity) and launch angle to see how these interact with your boomerang’s design.
• Gyroscopic Effects: A higher spin rate tends to increase stability due to stronger gyroscopic effects. However, if spun too fast, drag forces may become more significant. Balance is key.

3.4. Measurement & Analysis

• Flight Path Tracking: Use video recordings or mark the flight path (if indoors, a controlled environment works best) to study the turning radius, flight duration, and return accuracy.
• Data Collection: Record parameters such as wing angles, spin rate (if measurable), and weight distribution. Use these data to correlate specific design choices with flight performance.

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4. Experimental Procedure Outline

1. Prototype Design:

   • Start with a basic symmetric design.
   • Introduce simple folds to create slight wing curvature.
   • Make minimal cuts to experiment with edge shapes.

2. Initial Testing:

   • Throw the boomerang with moderate spin.
   • Observe the flight path and note any deviations from a straight trajectory.

3. Parameter Variation:

   • Change one variable at a time (e.g., increase dihedral angle, adjust wing length, modify cut shape).
   • Test under similar conditions to isolate the effects of each change.

4. Data Analysis & Iteration:

   • Analyze the recorded flight paths and compare performance metrics.
   • Use the findings to refine the design iteratively.

5. Final Optimization:

   • Combine the best features observed during testing.
   • Fine-tune the design for the most consistent returning behavior.

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Conclusion

Designing a paper boomerang that reliably returns involves a delicate balance between aerodynamic principles and practical design choices achievable with paper. By understanding how wing geometry, angle of attack, weight distribution, and spin rate contribute to flight stability and turning behavior, you can methodically experiment with folding and cutting techniques to create an effective paper boomerang. This research provides a framework for exploring the complex interplay of forces that make returning flight possible and encourages iterative testing to hone your design.