This is a classic Fermi problem designed to test your estimation and problem-solving skills. The goal is to break down the problem into manageable parts and make reasonable assumptions to arrive at an order-of-magnitude answer.
1. Understand the Goal: We need to estimate the total bandwidth (data transfer rate in bits per second) of a 747 airplane filled with CD-ROMs crossing the Atlantic.
2. Key Components & Assumptions:
- CD-ROM Capacity: A standard CD-ROM holds about 700 MB (Megabytes) of data. Let's convert this to bits: 700 MB * 1024 KB/MB * 1024 B/KB * 8 bits/B ≈ 6 * 10^9 bits.
- Number of CD-ROMs per Plane:
- A 747 cargo hold is roughly 1000 cubic meters. Let's assume we can fill 70% of this volume with CD-ROMs, so 700 cubic meters.
- A CD-ROM is about 12 cm in diameter and 1 mm thick. Its volume is approximately pi * (6 cm)^2 * 0.1 cm ≈ 113 cubic cm, or 1.13 * 10^-4 cubic meters. However, we need to account for packaging and empty space. Let's assume we can fit 5000 CD-ROMs per cubic meter when packed efficiently.
- Total CD-ROMs = 700 m^3 * 5000 CD-ROMs/m^3 = 3.5 * 10^6 CD-ROMs.
- Total Data: Total data = (3.5 * 10^6 CD-ROMs) * (6 * 10^9 bits/CD-ROM) ≈ 2.1 * 10^16 bits.
- Crossing Time: The Atlantic crossing for a 747 takes about 6 hours. Let's convert this to seconds: 6 hours * 3600 seconds/hour = 21,600 seconds.
3. Calculation:
Bandwidth = Total Data / Time
Bandwidth ≈ (2.1 * 10^16 bits) / (2.16 * 10^4 seconds)
Bandwidth ≈ 1 * 10^12 bits/second
4. Result & Sanity Check:
This estimate is approximately 1 Terabit per second (Tbps). This is a very high bandwidth, comparable to major internet backbones. The assumptions about packing density and CD-ROM capacity are crucial. If we assumed less efficient packing or smaller CD-ROMs, the bandwidth would decrease. Conversely, if we considered newer, higher-capacity discs, it would increase.
Key Takeaway: This problem highlights how physical transport of data, while seemingly slow compared to electronic transmission, can still represent significant bandwidth when dealing with massive quantities of data over a specific duration.
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