totalCompressionRatio
plain-language theorem explainer
totalCompressionRatio N := phi ^ N defines the cumulative compression ratio for N spiral turns in a Tesla turbine at unit pitch κ=1. Fluid dynamicists modeling φ-optimized bladeless turbines cite it when scaling stage gains for Fibonacci disc counts. The definition is a direct exponentiation with no lemmas or reductions applied.
Claim. For a Tesla turbine with $N$ full spiral turns at pitch $κ=1$, the total compression ratio is $φ^N$.
background
The module models Tesla's 1913 bladeless turbine as a φ-spiral engine. Fluid enters tangentially and follows a logarithmic spiral between closely spaced discs, with momentum transfer via boundary-layer adhesion. Optimal parameters follow φ-scaling: disc spacing proportional to φ times boundary-layer thickness, and per-turn compression ratio φ^κ with κ=1 yielding exactly φ (from Spiral.SpiralField lemmas).
proof idea
The declaration is a direct definition setting totalCompressionRatio N to phi raised to N. No tactics or upstream lemmas are invoked; it serves as the base for rfl reductions in the downstream compression theorems.
why it matters
This supplies the ratio used by compression_3_discs, compression_5_discs, compression_8_discs, and fibonacci_compression_step. It realizes the per-turn ratio φ at κ=1 from the RS decipherment of the Tesla patent, linking to the phi self-similar fixed point. The fibonacci_compression_step doc notes that stepping from 5-disc to 8-disc multiplies compression by φ^3, forming a natural hierarchy of φ-scaled improvements.
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