A smoke streak visualization technique is employed to observe the steady flow field over a cone of a half angle of $$\theta _c = 30^\circ $$, spinning at an angular speed of $$\varOmega = 5 \text { revs/s}$$, at angles of attack of $$0 \le \alpha \le 36^\circ $$, in an axial flow of $$U_\infty = 1 \text { m/s}$$. The Reynolds number is $${\sim }10^4$$ based on the generator of the cone. Streaklines highlight increasing asymmetry of the flow and formation of vortices at increasing angles of attack. The rotation direction of the cone shapes the streaklines ingested into the boundary layers. Good agreement in streakline patterns between potential flow theory and experiment is observed over the cone at $$\alpha = 0$$, the agreement getting better near the tip of the cone. No signs of boundary layer instabilities are noted as the Reynolds number is not sufficiently high, except at the highest angle of attack $$\alpha =36^\circ $$ where a wave pattern is observed on the rolled-up streamwise vortex. Streaklines over a $$60^\circ $$ cone at angle of attack $$\alpha $$ in an axial flow of 1 m/s.