Overrun calculations

In looking at calculating overrun in ice cream, it is important to remember the definition of overrun; that is, it is the % increase in volume of ice cream greater than the amount of mix used to produce that ice cream. In other words, if you start off with 1 litre of mix and you make 1.5 litres of ice cream from that, you have increased the volume by 50% (i.e., the overrun is 50%). Equations are as follows:

Figuring plant overrun by volume, no particulates

% Overrun = (Vol. of ice cream - Vol. of mix used)/Vol. of mix used x 100%

Example : 500 L mix gives 980 L ice cream,
(980 - 500)/500 x 100% = 96% Overrun

80 L mix plus 10 L chocolate syrup gives 170 L chocolate ice cream,

(Note : any flavours added such as this chocolate syrup which become homogeneous with the mix can incorporate air and are thus accounted for in this way : )

(170 - (80 + 10))/(80 + 10) x 100% = 88.8% Overrun

Figuring plant overrun by volume, with particulates

Example : 40 L mix plus 28 L pecans gives 110 L butter pecan ice cream,

110 - 28 = 82 L actual ice cream.

% Overrun = (Vol. of ice cream - Vol. of mix used)/Vol. of mix used 
= (82 - 40)/40 x 100% = 105% 

(Note : The pecans do not incorporate air.)

Figuring package overrun by weight, no particulates

 % Overrun = (Wt. of mix - Wt. of same vol. of ice cream )/Wt. of same vol. of ice cream x 100%

Must know density of mix (wt. of 1 L), usually 1.09 - 1.1 kg. /L.

(see example below)

Example : If 1 L of ice cream weighs 560 g,
% Overrun = (1090 - 560)/560 x 100% = 94.6% Overrun

(Note : Figuring package overrun by weight if the ice cream has particulates in it gives very little information because both the ratio of ice cream to particulates and the air content of the ice cream affect the final weight.)

Figuring mix density

The density of mix can be calculated as follows: 

1 / ((% fat/100 x 1.075) + ((% T.S./100 - % Fat/100) x 0.63) + (% Water/100)) = Wt. (kg)/ litre mix

Example - Calculate the weight per litre of mix containing 12% fat, 11% serum solids, 10% sugar, 5% corn syrup solids, 0.30% stabilizer, and 38.3% T.S.

1.0  / ((0.12 x 1.075) + ((0.383 - 0.12) x 0.63) + 0.617) = 1.096 kg/L of mix

Figuring target package weights, no particulates

Weight of given vol. of ice cream = Wt. of same vol. of mix / (Desired overrun / 100 + 1)

Example : Desired 90% Overrun, mix density 1.09 kg/L
net wt. of 1 L = 1.09 kg / ( 90/100 + 1) = 573.7 g

Also, density of ice cream = density of mix / (Overrun/100 + 1)

Example: Density of mix 1100 g/L,

@100% Overrun, density of ice cream = 1100 g/L / (100/100 + 1) = 550 g/L

Figuring target package weights, with particulates

Example : Butter brickle ice cream; density of mix 1.1 kg/L; overrun in ice cream 100%; density of candy 0.748 kg/L; candy added at 9% by weight, (i.e. 9 kg to 100 kg final product)

In 100 kg final product, we have:

9 kg of candy (or 9 kg / 0.748 kg/L = 12.0 L)

91 kg of ice cream (or 91 kg / (1.1 kg/L / (100/100 + 1)) = 165.4 L)

So, 100 kg gives a yield of 12 + 165.4 = 177.4 L

1 L weighs 100 kg / 177.4 L = 564 grams 

(Note : In many cases, ice cream of different flavours is frozen to the same weight. As a result, overrun of actual ice cream in product varies.)

Developing an Overrun Table for Use When Manufacturing Ice Cream

To develop an overrun table to determine overrun quickly by weight when making ice cream, all you need is a cup with a fixed volume that is convenient for filling ice cream into (like a steel measuring cup, for example, with a flat top that would be easy to scrape level) and an ordinary gram balance. Then, using the equation from above, you can calculate what the weight of the cup would be for a series of different overruns, and then make up a table. Then when you are running ice cream, just keep weighing the cup and checking against the table for the overrun in the cup.

% Overrun = (Wt. of mix - Wt. of same vol. of ice cream )/Wt. of same vol. of ice cream x 100%

So, lets say your cup holds 100 mL. Fill the cup with mix and weigh it. Let's say the net weight (minus the weight of the empty cup) is 110 g. Lets say the empty cup weighs 30 g.

The net weight of the cup at 5% overrun would be:
.05 = (110 - x)/x, solve for x and you get 104.8, so the gross weight would be 134.8 g.

{In case your algebra is rusty, to solve for x, follow this example:
.05 = (110-x)/x
x = (110-x)/.05
x = 110/.05 - x/.05
x = 2200 - 20x
x + 20x = 2200
21x = 2200
x = 2200/21 = 104.76}

Likewise for 10%, 0.1 = (110 - x)/x, solve for x and you get 100, so the gross weight would be 130 g.

Keep going up to 150% or so, then make a table:

Overrun%           Weight of cup + ice cream (grams)

0                              140
5                              134.8
10                            130
.
.
.
150                            74