Iron Magnetic Separation (2D) — drum cross-section, release angles and grade/recovery

• Drop the field to 25-30 %: magnetite is released early, falls into tailings and recovery collapses.
• Raise belt speed to 3.6 m/s: the centripetal demand v²/R grows and even magnetite lets go before the sector ends.
• Shorten the magnet sector (130 deg): grains drop on the front side of the drum.
• Move the splitter right to catch more weak hematite in the concentrate: recovery rises, grade drops.

A particle riding the belt around a drum of radius R at belt speed v needs a centripetal acceleration v²/R. The belt pushes it with normal force per unit mass N(φ) = g cosφ + a_m(φ) − v²/R, where φ is measured clockwise from the top and a_m is the magnetic pull towards the drum. The grain leaves when N falls below zero. Non-magnetic rock (a_m ≈ 0) leaves at cosφ = v²/(gR) (immediately at the top when v² ≥ gR); magnetite keeps N > 0 through the magnet sector and is released where the field tapers off.

After release the motion is a parabola: x = x_r + v_xt, y = y_r + v_yt − ½gt², landing on the bin plane; the splitter divides concentrate from tailings. Fe recovery = Fe in concentrate / Fe fed, grade = Fe mass / concentrate mass. The prediction curve integrates the same N(φ) rule over a lognormal spread of magnetic susceptibility.

Simplifications: a_m = 55 m/s² × field × relative susceptibility (illustrative), no air drag, no particle-particle entrainment or bounce, no size/shape effects, flat belt, no field decay with distance from the drum, particles fly as pure projectiles after release. Mass per particle is the same for all types. Real separators have far more complicated field gradients.