Foundry Mold Engineering, Archimedes Metallostatic Core Lift & Chaplet Design
Sand-Casting Core Buoyancy & Top Chaplet Load Formula
Calculate Dry Resin-Sand Core Weight (N), Upward Molten-Metal Archimedes Buoyancy (N), Net Upward Core Float Force (N), and Factored Top-Chaplet Hold-Down Load (N).
Why a 7 kg sand core floats UPWARD with 238 N (24 kgf) of force the instant molten cast iron fills the mold!
Foundry apprentices instinctively place heavy metal chaplets UNDERNEATH an internal resin-sand core (`rho_core ~= 1.60` g/cm³) to support its dry weight—forgetting Archimedes’ principle once dense liquid gray iron (`rho_metal ~= 7.00` g/cm³) or bronze (`8.20` g/cm³) submerges the core! While dry in the open drag flask, a core of submerged volume V_core (cm³) presses downward with Weight W_core = (V_core * 10^-6) * (rho_core * 1,000) * 9.80665 N; once submerged in liquid metal, upward Metallostatic Buoyancy F_buoy = (V_core * 10^-6) * (rho_metal * 1,000) * 9.80665 N overwhelms core weight by ratio (rho_metal - rho_core) / rho_core = (7.0 - 1.6) / 1.6 = **3.375x** its dry weight UPWARD! Without adequately sized TOP chaplets and cope flask clamps rated for F_design = SF * (F_buoy - W_core), the core floats into the cope roof or lifts the entire top flask, spilling white-hot iron!
Verify on a 4,500 cm³ Pump-Volute Internal Resin-Sand Core—Submerged_Core_Volume V_c = 4,500.0 cm³ (B2), Liquid_Cast_Iron_Density rho_m = 7.00 g/cm³ (B3), Resin_Sand_Core_Density rho_c = 1.60 g/cm³ (B4), and Hot_Chaplet_Safety_Factor SF = 2.00 (B5): Dry Bottom Chaplet Weight is only 70.61 N (~7.2 kgf, E2), Upward Metallostatic Buoyancy hits 308.91 N (E3), Net Upward Core Lift equals 238.30 N (~24.3 kgf upward!, E4), and Factored Top-Chaplet / Cope-Weight Design Load demands 476.60 N (E5)!
| Foundry Core Buoyancy KPI (Vcore=4,500 cm³, Iron=7.0 g/cm³, Sand=1.6, SF=2.0) | Formula | Verified Output |
|---|---|---|
| Dry Sand Core Weight Down (N) | (V_cm3 * 1e-6) * (rho_core*1000) * 9.80665 | 70.61 N |
| Molten Metal Buoyancy Up (N) | (V_cm3 * 1e-6) * (rho_metal*1000) * 9.80665 | 308.91 N (119.15 N @ Al 2.70 g/cm³) |
| Net Upward Core Float Lift (N) | Buoyancy_Up_N - Dry_Core_Weight_N | 238.30 N (48.54 N @ Al 2.70 g/cm³) |
| Factored Top-Chaplet Load (N) | Net_Upward_Lift_N * Safety_Factor | 476.60 N (97.09 N @ Al 2.70 g/cm³) |
Archimedes Metallostatic Core Lift & Top-Chaplet Design Load Formula
Validate Core_Volume > 0, Metal_Density > Core_Density > 0 (dense ceramic/zircon cores in light magnesium must check sign!), and Safety_Factor >= 1.25!
=LET(vc_c, B2, rm_g, B3, rc_g, B4, sf_c, B5, IF(OR(vc_c <= 0, rc_g <= 0, rm_g <= rc_g, sf_c < 1.25), "Invalid Core Buoyancy Input", LET(nl_n, (vc_c / 1000000) * ((rm_g - rc_g) * 1000) * 9.80665, ROUND(nl_n * sf_c, 2))))Aluminum A356 Alloy Pour Buoyancy Reduction Check (Set Liquid Metal Density = 2.70 g/cm³)
Pour light Aluminum A356 (rho_m B3 = 2.70 g/cm³) around the exact same 4,500 cm³ sand core: Upward Buoyancy E3 drops from 308.91 N to 119.15 N, slashing Net Upward Core Float E4 nearly 5x from 238.30 N down to 48.54 N (Factored Top-Chaplet Load = 97.09 N in E5)!
=IF(ISTEXT(E5), E5, ROUND((B2 / 1000000) * ((B3 - B4) * 1000) * 9.80665, 2))Try the example
Use the original values or change them to test your understanding.