Desmos Graph for Corrected Reynolds/Hermite Activation Bridge

Copy these equations into Desmos (https://www.desmos.com/calculator):

1. Normalized activation curve:
A(x) = 3x^2 - 2x^3

2. Offset physical bridge:
f_A(x) = 0.0278 + 0.012(3x^2 - 2x^3)

3. Reynolds number to x conversion:
x(Re) = clamp((Re - 2300) / 1700, 0, 1)

4. Direct Reynolds to activation:
A_Re(Re) = 3 * clamp((Re - 2300) / 1700, 0, 1)^2 - 2 * clamp((Re - 2300) / 1700, 0, 1)^3

5. Direct Reynolds to physical bridge:
f_A_Re(Re) = 0.0278 + 0.012 * (3 * clamp((Re - 2300) / 1700, 0, 1)^2 - 2 * clamp((Re - 2300) / 1700, 0, 1)^3)

Set x-axis range: 0 to 1 (for x) or 2000 to 4500 (for Re)
Set y-axis range: 0 to 0.05

Key points:
- Re = 2300 → x = 0 → A(0) = 0 → f_A(0) = 0.0278
- Re = 4000 → x = 1 → A(1) = 1 → f_A(1) = 0.0398
- Re = 3150 → x = 0.5 → A(0.5) = 0.5 → f_A(0.5) = 0.0338

Properties:
- A(x) is monotone increasing on [0,1]
- A'(x) = 6x(1-x) ≥ 0 for 0 ≤ x ≤ 1
- A'(0) = 0, A'(1) = 0 (smooth endpoints)
- f_A(x) maps [0,1] to [0.0278, 0.0398]