Engineering Geometry: Mastering the Center of Gravity in Trailmakers

Materials Needed

• Xbox One console or compatible device with "Trailmakers" installed.
• Access to the "Stranded in Space" or "Race Island" game modes (for building and testing tracks).
• Paper, pencil, or digital spreadsheet for calculations and design notes.
• One simple physical object (e.g., a sturdy book, a block, or a stack of coins) for the initial demonstration.
• Measuring tool (ruler, optional, for physical demonstration).

Learning Objectives

By the end of this lesson, learners will be able to:

1. Define Center of Gravity (CoG) and explain its role in vehicle stability and physics.
2. Apply basic geometric calculations (perimeter and area) to the structure of their virtual vehicle.
3. Design, iterate, and modify a vehicle in Trailmakers to successfully balance speed and structural stability on a challenging course.

Success Criteria

You have succeeded when:

• You can clearly explain to the educator/peer why your final vehicle is more stable than your first attempt.
• You correctly calculate the block area of your final vehicle's base.
• Your vehicle successfully completes the designated obstacle course without flipping or losing major parts.

Lesson Introduction (10 minutes)

Hook: Why Do Things Tip?

Educator Prompt: Imagine you are carrying a stack of books. Which stack is easier to walk with: one that is very tall and narrow, or one that is short and wide? Why? (Wait for responses focusing on balance.)

The secret is the Center of Gravity (CoG). The CoG is the average location of the weight of an object. The lower the CoG, the harder it is to tip over!

Demonstration: The Tipping Point (I Do - Modeling)

Take a sturdy book or block. Place it upright on its short edge. Gently push the side until it tips. Now, lay the book flat and push it—it’s much harder to tip!

Key Concept: Stability increases when the CoG is lowered (closer to the ground) and when the base is widened.

Relevance

Engineers use CoG principles for everything: skyscrapers, ships, race cars, and even roller coasters. In Trailmakers, understanding CoG will allow you to build vehicles that dominate the rough terrain instead of ending up upside down!

Lesson Body: Applying Math and Engineering Principles

Phase 1: Initial Build & Geometry (We Do - Guided Practice) (20 minutes)

Activity 1: Building the Basic Frame

1. Launch Trailmakers and enter the build mode (or load a basic chassis).
2. Build a simple, four-wheeled vehicle frame (e.g., 6 blocks long by 3 blocks wide, using standard blocks).

Activity 2: Calculating the Footprint

We need to quantify the size of the stable base, or the "footprint," of our vehicle. We will measure using the blocks as our units.

Math Task: Record the length (L) and width (W) of your basic frame in block units.

• Perimeter Calculation (Distance around the frame): P = 2(L + W)
• Area Calculation (Base footprint): A = L x W (in square blocks)

Example: If your frame is 6 blocks long and 3 blocks wide: P = 2(6+3) = 18 blocks. A = 6x3 = 18 square blocks.

Phase 2: Testing the High CoG (I Do/We Do - Application) (15 minutes)

Activity 3: The Instability Test

1. Add a single seat, engine, and four basic wheels to your frame.
2. Introduce Instability: Place a large, heavy block (like a large ballast or a decorative box) 4 blocks high directly above the seat. This dramatically raises the CoG.
3. Drive the vehicle through a moderately challenging section of the terrain (or a pre-built ramp/turn track).

Formative Assessment: What happened? Did the vehicle tip easily, especially in turns or over bumps? Why? (Expected answer: Yes, because the CoG is too high.)

Phase 3: Redesigning for Stability (You Do - Independent Practice) (30 minutes)

Challenge: The Low Rider

Your goal is to redesign your vehicle to complete the challenge course successfully. You must achieve better stability by lowering the CoG and potentially widening the base. Your final vehicle must use no more than 50 total blocks (excluding wheels/engines).

Engineering Task Steps:

1. Lower the Mass: Remove the high-mounted heavy block. Place the engine and heavier components (batteries, spring blocks) as low as possible on the frame, ideally flush with the axle line.
2. Widen the Base: Increase the width (W) of your frame by at least 2 blocks on each side.
3. Re-calculate: Calculate the new perimeter and area of your redesigned vehicle's base. Record both the original and new calculations. (Note to learner: How much did the base area increase?)
4. Retest and Iterate: Drive the new vehicle on the same challenging course. If it fails, make small adjustments (e.g., add weight lower down, move the seat forward or backward) and retest until stable.

Lesson Conclusion (15 minutes)

Recap and Reflection

Educator Prompt: Look at your starting numbers and your ending numbers. How did changing the L x W footprint affect the stability? What did you notice about where you placed the heavy parts?

Key Takeaway Reinforcement: A low CoG and a wide base create a stable platform, which allows for higher speed and better handling—essential for complex engineering designs.

Summative Assessment: Design Pitch

The learner will complete the final challenge and then verbally present their design choices to the educator (acting as a review board).

1. Successfully complete the designated course without flipping.
2. Present the "before and after" calculations (Original Area vs. Redesign Area).
3. Explain which specific engineering principle (lowering CoG, increasing base width) was most effective and why, using the appropriate vocabulary (stability, mass, CoG).

Differentiation and Adaptability

Scaffolding (For learners needing extra support)

• Pre-Built Frames: Provide the learner with a simple, pre-built high-CoG frame in Trailmakers to save building time and jump straight into testing and modification.
• Visual Aids: Use simple real-world pictures of stable structures (pyramids, wide ships) versus unstable ones (tall towers, narrow canoes) to reinforce the geometry visually.
• Simplified Math: Focus only on the Area calculation (L x W) instead of perimeter.

Extension (For advanced learners)

• Constraint Challenge: Introduce a new variable: the vehicle must be narrow (W=3 blocks) but still stable. How must they manipulate the mass (CoG) to maintain stability despite the narrow base? (This requires very precise placement of heavy components and potentially the use of springs/shocks.)
• Efficiency Calculation: Require the learner to calculate the block-to-speed ratio (Total number of blocks used / Average speed over the track) and attempt to optimize for the best efficiency score while maintaining stability.
• Flight Dynamics: Challenge them to build a stable flying machine (using wings/props) and discuss how CoG differs in 3D air movement versus 2D ground movement.