← Back to the archiveSHORT / 078
Watch One Line Carve an 8-Blade Turbine
Curves & geometry

Watch One Line Carve an 8-Blade Turbine

BEHIND THE WORK

Can a single continuous line carve a high-efficiency 3D turbine impeller? In fluid dynamics and turbomachinery, the logarithmic spiral defines the ideal blade curvature to minimize aerodynamic separation and flow losses. Here, 8 swept centrifugal blades radiate from a central conical hub, seamlessly connected into a single unbroken 3D path with exact 0.000mm closure.

Artismathic turns equations into visual art—one function at a time.

#MathArt #Turbine #Kinematics #Engineering #Mechanical #3DArt #Mathematics #Blender3D

THE MATHEMATICAL RULE

Outward blade segments before return paths\text{Outward blade segments before return paths}ϕk(p)=kπ4+0.82p1.25,r(p)=0.55+1.60p0.85\phi_k(p)=\frac{k\pi}{4}+0.82p^{1.25},\quad r(p)=0.55+1.60p^{0.85}z(p)=0.75−1.30p1.4,0≤p≤1, k=0,…,7z(p)=0.75-1.30p^{1.4},\quad0\leq p\leq1,\ k=0,\ldots,7(x,y,z)=(rcos⁡ϕk,rsin⁡ϕk,z(p))(x,y,z)=(r\cos\phi_k,r\sin\phi_k,z(p))
Watch the drawing↗

WATCH IT COME TO LIFE

Watch the drawing

YouTube loads only after you press play.