The Physics of Propagation Delay
Velocity Factor and Signal Speed
The Hard Floor: What is the Velocity Factor (Vf)?
The velocity of an electromagnetic wave in a vacuum is one of the universe's fundamental constants: meters per second. However, information rarely travels in a vacuum. Whether it is drifting through a glass core or racing along a copper wire, it is slowed down by its interaction with the medium's atoms.
The Velocity Factor (Vf) is the ratio of the signal speed in a medium to the speed of light in a vacuum. It is expressed as a decimal or a percentage.
For standard single-mode fiber optic cable, the Vf is approximately 0.67. This means information travels at roughly 200,000 km/s. While this seems instantaneous, at global scales, this delay becomes the primary driver of latency.
PROPAGATION PHYSICS ENGINE
Modeling Velocity of Information in Physical Media
Medium Property
Light slowed by silica glass atoms.
Media Comparison: How Speed Varies
Different cable constructions use different dielectric materials (insulation), which directly dictates the velocity factor. As a rule of thumb, the less the electric field interacts with the insulation, the faster the signal travels.
| Medium | Typical Vf | Delay (ns/m) |
|---|---|---|
| Vacuum / Air | 0.99 - 1.00 | 3.33 |
| RG-6 Coaxial (Foam PE) | 0.82 - 0.85 | 4.00 |
| Cat6 Ethernet (UTP) | 0.65 - 0.70 | 4.80 |
| Single-mode Fiber (G.652) | 0.67 | 5.00 |
Refractive Indices and the Fiber Barrier
In fiber optics, light is contained within the core through Total Internal Reflection. The core glass has a specific refractive index (). The relationship between the refractive index and the speed of light in that medium is inverse:
As increases, the signal slows down. Modern silica glass has a refractive index of approximately 1.468. Solving for gives us the result of .
This leads to a fascinating engineering reality: Radio waves in air are faster than light waves in glass. This is why long-distance microwave links are still used by high-frequency traders to beat fiber-optic competitors by several milliseconds, despite the lower bandwidth of radio.
Fiber Optic Refraction Simulator
Total Internal Reflection & Signal Velocity
Snell's Law: When light enters a denser medium (higher n), it slows down and bends toward the normal. In fiber optics, if the incident angle exceeds the critical angle (θc = arcsin(n₂/n₁)), total internal reflection occurs, trapping light within the core. This is the foundation of optical fiber transmission.
Dispersion: Why Fast Signals Get Blurry
Velocity Factor tells us when a signal arrives, but Dispersion tells us in what condition it arrives.
- Chromatic Dispersion: Different wavelengths (colors) of light travel at slightly different speeds in glass. Over long distances, the pulse "spreads out," eventually overlapping and causing bit errors.
- Modal Dispersion: In multi-mode fiber, different paths (modes) taken by light rays result in different arrival times. This is why multi-mode fiber is limited to short distances.
The Chicago-NY "Speed of Light" Tunnel
One of the most extreme examples of propagation optimization occurred in 2010. Spread Networks spent $300 million to drill a direct, straight-line fiber route through the Allegheny Mountains between Chicago and New York. By shortening the physical path and reducing the number of bends, they reduced the RTT from 16ms to 13ms.
For a trader, that 3ms difference—shaved off simply by acknowledging the Velocity Factor—was worth hundreds of millions in competitive advantage.
Theoretical RTT Calculation
To set a "Golden Baseline" for any network link, calculate the minimum theoretical RTT. If your actual ping is vastly higher, the issue is at Layer 2 or 3 (congestion/queuing), not Layer 1.
Example: London to New York (approx 5,500km)