"48 flux-units," she whispered.
Lyra raced to the control platform. She encoded the function into the harmonic resonators, and as the monsoon winds arrived, the great whirlpool shuddered—then dissolved into a spiral of calm, glimmering water.
Now came the integral calculus. The total destructive potential ( P ) was the integral of velocity across the whirlpool’s radius ( R ) (which was 4 meters):
Lyra recognized the form. It was a first-order linear ODE. She rewrote it:
The integrating factor ( \mu(r) ) was:
The Churnheart wasn’t a normal vortex. Its radial velocity ( v(r) ) at a distance ( r ) from the center obeyed a differential equation that had baffled engineers for decades:
"Here," said her master, old Kael, handing her a data slate. "This equation models how the spin changes with radius. The whirlpool’s total destructive potential is the area under the velocity curve from ( r=0 ) to ( r=R ). Solve for ( v(r) ), then integrate it. That area is the energy you must dissipate."