Frozen Dairy & Confectionery Engineering, Ice Cream Overrun % & FDA 21 CFR 135.110
Ice Cream Overrun %, Air Fraction & Gallon Weight Formula
Calculate Gravimetric Overrun (%), Dispersed Air Volume Fraction (%), Finished Gallon Net Weight (lb/gal vs FDA 4.50 lb/gal Minimum), and Continuous Freezer Volumetric Yield (L/h).
100% overrun does NOT mean 100% air—it means 50% dispersed air bubbles, and whipping past ~103% violates the US FDA 4.50 lb/gal legal weight floor!
Scraped-surface continuous ice cream freezers whip filtered compressed air into aged liquid dairy mix of **Unfrozen Mix Density `W_{mix}`** (`~1,080–1,110` g/L), expanding volume to **Frozen Finished Density `W_{frozen}`** (`g/L` weighed on a tared `1.000`-L overrun cup!). Dairy technologists define **Percentage Overrun** relative to *unfrozen mix volume* (`(V_{frozen} - V_{mix}) / V_{mix}`), which at constant mass equals **`Overrun% = ((W_{mix} - W_{frozen}) / W_{frozen}) * 100%`** (`25%–35%` Italian gelato, `40%–60%` super-premium pints, `80%–95%` economy tubs), whereas **True Dispersed Air Volume Fraction `phi_{air}% = ((W_{mix} - W_{frozen}) / W_{mix}) * 100% = Overrun% / (1 + Overrun%/100)`**! Crucially, **US FDA `21 CFR 135.110`** mandates that finished ice cream weigh **at least `4.50` lb per US Gallon** (`(W_{frozen} * 3.78541178) / 453.59237 >= 4.50` lb/gal, `~539.3` g/L minimum!) so consumers aren’t sold foam!
Verify on a Continuous Barrel Freezer Line—Aged_Liquid_Mix_Density `W_{mix}` = 1,096 g/L (B2), Tared_1L_Frozen_Cup `W_{frozen}` = 602 g/L (B3), and Liquid_Mix_Pump_Rate `Q_{mix}` = 650 L/h (B4): Overrun equals `82.06%` (E2), Dispersed Air Fraction equals `45.07%` (E3), Finished Gallon Weight hits `5.02` lb/gal (`>= 4.50` FDA legal floor! E4), and Volumetric Tub Filler Output reaches `1,183.4` L/h (E5)!
| FDA 21 CFR 135.110 Ice Cream Overrun KPI (Mix=1,096 g/L, 650 L/h, Frozen=602 vs 505 g/L) | Formula | Verified Output |
|---|---|---|
| Gravimetric Overrun (%) | ((Mix_g_L - Frozen_g_L) / Frozen_g_L) * 100 | 82.06% (117.03% over-whipped @ 505 g/L!) |
| Dispersed Air Volume Fraction (%) | ((Mix_g_L - Frozen_g_L) / Mix_g_L) * 100 | 45.07% (53.92% air foam @ 505 g/L) |
| Finished US Gallon Weight (lb/gal) | (Frozen_g_L * 3.78541178) / 453.59237 | 5.02 lb/gal (4.21 < 4.50 ILLEGAL @ 505 g/L!) |
| Volumetric Freezer Output (L/h) | Mix_Feed_L_h * (Mix_g_L / Frozen_g_L) | 1,183.4 L/h (1,410.7 L/h @ 505 g/L) |
Gravimetric Overrun Cup, Air Volume Fraction & FDA lb/gal Compliance Formula
Validate `Mix_Density W_{mix}` in `[1,000, 1,250]` g/L, `Frozen_Density W_{frozen}` in `[350, W_{mix}]` g/L, and `Mix_Flow Q_{mix} > 0` L/h!
=LET(wm_g, B2, wf_g, B3, qm_l, B4, IF(OR(wm_g < 1000, wm_g > 1250, wf_g < 350, wf_g > wm_g, qm_l <= 0), "Invalid Freezer Input", ROUND(qm_l * (wm_g / wf_g), 1)))Over-Whipped 505 g/L Cup (`117%` Overrun) FDA Short-Weight Rejection Check (Set Frozen Cup B3 = 505 g/L)
Open the dasher air-metering valve until `1`-L cup weight drops to `W_{frozen}` B3 = 505 g/L: Overrun E2 climbs to `117.03%` (`53.92%` air in E3), dropping Finished Gallon Weight E4 to **`4.21` lb/gal**—below the `4.50` lb/gal federal standard of identity, forcing quarantine or downgrading out of "Ice Cream" labeling!
=IF(ISTEXT(E5), E5, ROUND((B3 * 3.78541178) / 453.59237, 2))Try the example
Use the original values or change them to test your understanding.