This is a classic Fermi problem that requires estimation. To solve it, we need to estimate the volume of a helicopter and the volume of a ping pong ball, and then divide the former by the latter.
1. Estimate Helicopter Volume:
- Shape: Approximate the main body of the helicopter as a cylinder. The tail and other protrusions will be ignored for simplicity, or their volume can be estimated separately and added.
- Dimensions: Let's assume a helicopter's main cabin is roughly 15 feet long and has a diameter of 5 feet (radius of 2.5 feet). We'll also need to estimate the height/width of the cabin, say 5 feet.
- Volume Calculation: Volume of a cylinder = π * r² * h. So, for the cabin: π * (2.5 ft)² * 5 ft ≈ 98 cubic feet.
- Total Volume: We need to account for the cockpit, cargo space, and potentially the rotor housing. Let's roughly double the cabin volume to account for these, giving us approximately 200 cubic feet for the usable internal volume.
2. Estimate Ping Pong Ball Volume:
- Dimensions: A standard ping pong ball has a diameter of 40 mm, which is about 1.33 inches or 0.11 feet.
- Shape: A sphere.
- Volume Calculation: Volume of a sphere = (4/3) * π * r³. Radius = diameter / 2 = 0.11 ft / 2 = 0.055 ft. So, volume ≈ (4/3) * π * (0.055 ft)³ ≈ 0.0007 cubic feet.
3. Calculate the Number of Balls:
- Ratio: Divide the helicopter's volume by the ping pong ball's volume: 200 cubic feet / 0.0007 cubic feet/ball ≈ 285,714 balls.
4. Adjust for Packing Efficiency:
- Ping pong balls are spheres, so they won't pack perfectly. The maximum packing density for spheres is about 74% (for hexagonal close-packing). A more realistic random packing density is around 64%.
- Final Estimate: 285,714 balls * 0.64 ≈ 183,000 balls.
Therefore, a reasonable estimate is around 180,000 to 200,000 ping pong balls.
Google