# Butter Yield Calculations

Technological limits to yield efficiency are defined by separation efficiency, churning efficiency, composition overrun, and package over fill.

# Separation efficiency (Es)

- represents fat transferred from milk to cream

Es = 1 - fs/fm
where fs = skim fat as percent w/w
fm = milk fat as percent w/w

Separation efficiency depends on initial milk fat content and residual fat in the skim. Assuming optimum operation of the separator, the principal determining factor of fat loss to the skim is fat globule size. Modern separators should achieve a skim fat content of 0.04 - 0.07%.

# Churning Efficiency (Ec)

- represents fat transferred from cream to butter

Ec = 1 - fbm/fc
where fbm = buttermilk fat as percent w/w
fc = cream fat as percent w/w

Maximum acceptable fat loss in buttermilk is about 0.7% of churned fat corresponding to a churning efficiency of 99.3% of cream fat recovered in the butter. Churning efficiency is highest in the winter months and lowest in the summer months. Fat losses are higher in ripened butter due to a restructuring of the FGM (possibly involving crystallization of high melting triglycerides on the surface of the globules). If churning temperature is too high, churning occurs more quickly but fat loss in buttermilk increases. For continuous churns assuming 45% cream, churning efficiency should be 99.61 - 99.42%.

# Composition Overrun

% Churn Overrun

= (Kg butter made - Kg fat churned)/Kg fat churned x 100 %

% Composition Overrun
= (100 - % fat in butter)/% fat x 100 %

# Package Fill Control

= (actual wt. - nominal wt.)/nominal wt. x 100%

An acceptable range for 25 kg butter blocks is 0.2 - 0.4% overfill. Overfill on 454 g prints is about 0.6%.

# Other factors affecting yield

• shrinkage due to leaky butter (improperly worked).
• shrinkage due to moisture loss; avoided by aluminum wrap.
• loss of butter remnants on processing equipment; % loss minimal in large scale continuous processing.

# Plant Overrun

Plant efficiency or plant overrun is the sum of separation, churning, composition overrun and package fill efficiencies. In summary the theoretical maximum efficiency values are:

Separation Efficiency 98.85
Churning Efficiency 99.60
Composition overrun (% fat) 23.30
Package overfill 0.20

These values can be used to predict the expected yield of butter per kg of milk or kg of milk fat received.

# Example

3.6% m.f. milk

0.05% m.f. in skim
40% m.f. in cream
0.3% m.f. in buttermilk
81.5% m.f. in butter

Es = 1 - .05/3.6 = 98.6
Ec = 1 - .3/40 = 99.25
% Composition Overrun = (100-81.5)/81.5 = 22.7%
If 100 kg of milk was used, 8.9 kg of cream would be produced (from a Pearson Square mass balance) and 4.35 kg butter would be produced from that. This is the theoretical yield based on no losses. The mass balance of fat shows that 98.3% of the fat ended up in the butter, 0.4% of the fat ended up in the buttermilk and 1.3% of the fat ended up in the skim.
The % Churn Overrun = (4.35 - 3.6)/3.6 = 20.8%