SOP: Calculation of Process Time and Sterilizing Value by the Nomogram Method

GIFSQ — Global Institute for Food Safety & Quality

Principle

The Nomogram Method of Olson and Stevens is a graphical solution of Ball’s Formula Method. Separate nomograms are used for products with a single straight-line heating curve and for products with a broken (two-slope) heating curve; process time or sterilizing value is found by drawing straight lines between the known values on the nomogram scales.

Materials required

• Fig. 25.23 of the book (nomogram for single straight-line heating curve)
• Fig. 25.24 of the book (nomogram for broken heating curve)

Procedure — Process time, simple straight-line heating curve

On Fig. 25.23, connect F₀ (12.1) on scale 1 to RT (250 °F) on scale 4 to get a point on scale 3

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Connect the point on scale 3 to fₕ (60) on scale 2 and extend to get a new point on scale 4

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Follow parallel to the ladder lines between scales 4 and 5 from the new point on scale 4 to a point on scale 5; mark this point

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Connect j (2.0) on scale 5 to RT − IT (250 − 160 = 90) on scale 7 to get a point on scale 6

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Connect the point on scale 6 to the marked point on scale 5 and get a new point on scale 7

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Connect this new point on scale 7 with fₕ (60) on scale 8 and read Bₚ (90.5 min in the book’s Problem 6)

Procedure — Handling nomogram range limits

Bₚ on scale 9 of Fig. 25.23 covers only 0 to 120 min; since a line through a point on scale 7 intersects scales 8 and 9 so that the ratio of Bₚ to fₕ is constant, maintain the same ratio by multiplying or dividing both Bₚ and fₕ by the same number (e.g., for Bₚ = 180 min, draw the line between 180/2 = 90 and fₕ/2)

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A line through a point on scale 3 at any angle intersects scales 1 and 4 so that for every increase of 18 in RT, F₀ increases tenfold — if the retort temperature is 270 °F, take the scale value as 252 °F provided the F₀ value is divided by 10

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There are two scales 8 (8A and 8B); use the one matching the ladder arrangement used between scales 4 and 5 (the A lines start on the lower two-thirds of scale 4, the B lines on the upper third)

Procedure — Process time, broken heating curve (Problem 7)

On Fig. 25.24, connect x_bh (13.65) on scale 1 to f₂ (12.2) on scale 4 and extend to get a point on scale 5

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Connect j (1.2) on scale 7 to RT − IT (240 − 140 = 100) on scale 5 to get a point on scale 6

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Connect the point on scale 6 to the marked point on scale 5 and get g_bh (9.4) on scale 7

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Follow the ladder from g_bh = 9.4 to a point on scale 8

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Connect this point on scale 8 to f₂ − f_h (50 − 12.2 = 37.8) on scale 11 and get U₁ (= 2.75) on scale 9; mark it

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Connect F₀ (10) on scale 6 with RT (240) on scale 8 and get a point on scale 7

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Connect this point on scale 7 with RT (250) on scale 8 and extend to scale 6 to get U₂ (= 35.5)

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Add U₁ and U₂ mentally: Uₜ = 35.5 + 2.75 = 38.25

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Connect Uₜ (38.25) on scale 6 with f₂ (50) on scale 10 and get a new point on scale 7

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Follow the ladder from this point to a point on scale 6; connect this point on scale 6 with g_bh = 9.2 (from the earlier step) on scale 7 and extend to a point on scale 5

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Connect this point on scale 5 with f₂ = 50 on scale 3 and extend to scale 2 to get Bₚ − x_bh (= 50)

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Add Bₚ − x_bh to x_bh mentally: Bₚ = 50 + 13.65 = 63.65 min

Procedure — Sterilizing value, simple straight-line heating curve (Problem 8)

In Fig. 25.23, connect Bₚ (30) on scale 9 with fₕ (12) on scale 8 and extend to scale 7 to get a point

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Connect RT − IT (240 − 170 = 70) on scale 7 with j (1.5) on scale 5 and get a point on scale 6

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Connect this point on scale 6 with the point marked earlier on scale 7 and extend to scale 5 to get a point (if the point falls outside scale 5, scale 8A was the wrong choice — repeat from the first step using scale 8B)

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From this point on scale 5, follow the ladder lines to scale 4 and get a point

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Connect this point on scale 4 with fₕ (12.0) on scale 2 and get a point on scale 3

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Connect the point on scale 3 with RT (240) on scale 4, extend to scale 1 and read F₀ (3.82 in the book’s example, within a few tenths of the figure found by the Formula Method)

Procedure — Sterilizing value, broken heating curve (Problem 9)

Carry out steps 1–5 of the broken-curve process-time procedure above to obtain g_bh (9.2) and U₁ (2.7)

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Connect Bₚ − x_bh (63 − 13.65 = 49.35) on scale 2 to f₂ (50) on scale 3 and extend to scale 5 to get a point

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Connect this new point on scale 5 to g_bh (9.2) on scale 7 and get a new point on scale 6

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From this new point on scale 6, follow the ladder line to a new point on scale 7

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Connect this point on scale 7 to f₂ (50) on scale 10 and extend to scale 6 to get U₂ (40)

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Subtract U₁ (2.7 — the book prints “2.3” at this step, which is a typographical error; the arithmetic requires the Step 5 value 2.7, giving 40 − 2.7 = 37.3) from U₂ (40) mentally to get Uₜ (37.3)

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Connect Uₜ (37.3) on scale 6 to 240 on scale 8 and get a point on scale 7

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Connect this point on scale 7 to RT (240 °F) on scale 8 and extend to scale 6 to read F₀ (10.2)

Precautions

• Careless operation and faulty construction of the nomogram may give rise to erroneous results.
• Different nomograms are required for single straight-line and broken heating curves — do not use one for the other.

References

Ranganna, S., Handbook of Analysis and Quality Control for Fruit and Vegetable Products, 2nd edition.

Olson, F.C.W. & H.P. Stevens, Food Res., 4, 1 (1939) — cited in the book.