Lake Ice Thickness and Frost Depth Calculator

Ice growth integrates the one-dimensional latent-heat balance $\rho_i L_i\,dh/dt=(0-T_a)/(h/k_i+R_e)$, with $R_e=1/H+s/k_s$. Thus $h(t)=\sqrt{(h_0+k_iR_e)^2+2k_iF(t)/(\rho_iL_i)}-k_iR_e$, with freezing index $F$ in K·s. This extends Ashton (1989), equations 5–6, with a constant snow resistance in series and nonzero initial ice. The implemented equivalent form avoids subtraction cancellation. Freshwater constants are $k_i=2.2$ W/(m·K), $\rho_i=917$ kg/m³ and $L_i=334$ kJ/kg (Daley, Ice Engineering formula sheet).

The Gold comparison uses measured ice only: $h_e=h_c+0.5h_w$ and $m=A h_e^2$, with $A$ in kg/cm² and thickness in cm. Its inverse $h=\sqrt{m/A}$ is an algebraic comparison, never an access minimum. USACE EM 1110-2-1612 (2002), §8-5, supplies the white-ice convention and independent numerical examples. Gold (1971) reports failure near $50h^2$ lbf for h in inches; this corresponds approximately to the default $A=3.5$ kg/cm². A lower calculated mass is not assurance against failure.

Soil frost depth follows TM 5-852-6 (1988), §3-2: $z=\lambda\sqrt{2\bar{k}F_s/L_v}$, $F_s=nF$, $\mu=\bar C v_s/L_v$, $\alpha=v_0/v_s$. With averaged frozen/unfrozen properties, the dimensionless Neumann root $\eta$ satisfies

The root is solved by bisection, following the two-phase heat-equation basis described in ERDC/GSL TR-12-15 (2012), equations 42–47, specialized to equal averaged properties. This avoids chart-reading error; it does not reproduce the separate-property PCASE model. The animation shows the idealized constant-temperature step solution $z(t)=z_{end}\sqrt{t/t_{end}}$.

Freshwater at 0 °C beneath intact ice; one-dimensional vertical conduction; constant material properties, lake snow and effective surface heat transfer; no basal water heat, solar budget, melting, snow flooding or ice sensible heat. The bare-ice comparison changes only snow resistance.

Initially unfrozen, semi-infinite homogeneous soil freezes sharply at 0 °C. Conductivity and heat capacity are averages of frozen and unfrozen properties. The ground surface index is represented by a constant n-factor. The default 0.7 is the bare-soil value in TM 5-852-6, table 2-4; the default soil properties are illustrative sandy-silt estimates, not a material certification. Soil and lake start from their own stated initial conditions.

Gold's relation is an empirical short-duration load scenario for sound floating ice. It does not model footprint, speed, spacing, flexural strength, fatigue or creep. Input mass includes the complete load.

Always measure ice thickness and quality along the full route. This tool never issues a safe verdict. Modeled lake thickness is excluded from all Gold load calculations. Gold's inverse thickness can be much smaller than local recreational guidance and must never be used as permission to walk or drive onto ice.

Use ice growth only during uninterrupted freezing after freeze-up with fixed, dry snow. Exclude saltwater, currents and warm inflows, rotten or thawed ice, slush, separated layers and pressure ridges. Surface exchange and snow conductivity are uncertain; the two curves are scenarios, not confidence bounds.

Soil results are preliminary seasonal frost estimates or an idealized constant-cold step problem, not daily forecasts, frost-heave estimates or prescribed construction depths. TM 5-852-6, printed p. 3-3, explicitly cautions against using modified Berggren for partial seasons under real weather. Layered soils, water migration, unfrozen bound water, permafrost and building heat need a more complete model. Check against the rules and standard in force before design.

Foundation and utility installation work belongs to qualified people; confirm the required construction depth locally.