Skip to main content
SpringerLink
Log in

Formula Methods and Analytical techniques

  • Chapter
  • First Online:
Thermal Processing of Packaged Foods

Part of the book series: Food Engineering Series ((FSES))

Abstract

It is easy today to dismiss the methods developed in the past as no longer relevant. Modern computers can now be used to calculate processes without any knowledge of the background for the calculations. However, it is instructive to see how the methods developed and the problems associated with calculating processes. For this purpose two methods have been selected for more detailed treatment: the Ball methods, because of their ingenuity and widespread use; and the Gillespy method, widely used in the UK canning industry. A number of other methods are mentioned, but in less detail.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Alstrand DV, Benjamin HA (1949) Thermal processing of canned foods in tin containers 5. Effect of retorting procedures on sterilization values for canned foods. Food Res 14:253–257

    Article  CAS  Google Scholar 

  • American Can Co (1950) Calculation of the processes for canned foods. Research Division Staff Memorandum, Maywood, IL

    Google Scholar 

  • Ball CO (1923) Thermal process time for canned foods. Bulletin No. 37. National Research Council, Washington, DC

    Google Scholar 

  • Ball CO (1928) Mathematical solution of problems on thermal processing of canned food. Univ Calif Publ Public Health 1(2):145–245

    Google Scholar 

  • Ball CO, Olson FCW (1957) Sterilization in food technology – theory, practice and calculations. McGraw-Hill, New York, NY

    Google Scholar 

  • Berry MR Jr (1983) Prediction of come-up time correction factors for batch-type agitating and still retorts and the influence on thermal process calculations. J Food Sci 48:1293–1299

    Article  Google Scholar 

  • Berry MR, Bush RC (1987) Establishing thermal processes for products with broken-heating curves from data taken at other retort and initial temperatures. J Food Sci 52(4):556–561

    Article  Google Scholar 

  • Bhowmik SR, Tandon S (1987) A method for thermal process evaluation of conduction heated foods in retortable pouches. J Food Sci 52:201–209

    Article  Google Scholar 

  • Board PW, Cowell ND, Hicks EW (1960) Studies in canning processes. III. The cooling phase of processes for products heating by conduction. Food Res 25:449–459

    Article  Google Scholar 

  • Board PW, Steel RJ (1978) Calculating heat sterilization processes for canned foods. Food Technol Aust 20(5):169–173

    Google Scholar 

  • Bown G (1989) The influence of product and process variability on process control in the thermal sterilization of foods. PhD thesis. University of Leeds, UK

    Google Scholar 

  • Chiheb A, Debray E, Le Jean G, Piar G (1994) Linear model for predicting transient temperature during sterilization of a food product. J Food Sci 59(2):441–446

    Article  Google Scholar 

  • Denys S, Noronha J, Stoforos NG, Hendrickx M, Tobback P (1996) A semiempirical approach to handle broken-line heating: determination of empirical parameters and evaluation of process deviations. J Food Process Preserv 20(4):331–346

    Article  Google Scholar 

  • Downes TW, Hayakawa K-I (1977) A procedure for estimating the retention of components of thermally conductive processed foods. Lebensm-Wiss u-Technol 10:256–259

    Google Scholar 

  • Flambert CMF, Deltour J (1972a) Localization of the critical area in thermally-processed conduction heated canned food. Lebensm-Wiss u -Technol 5:7–13

    Google Scholar 

  • Flambert CMF, Deltour J (1972b) Exact lethality calculation for sterilization process. I. Principles of the method. Lebensm-Wiss u -Technol 5:72–73

    CAS  Google Scholar 

  • Flambert CMF, Deltour J, Dickerson RW, Hayakawa K (1977) Lethal effect of food temperature on linear portion of heating or cooling curve. J Food Sci 42:545–546

    Article  Google Scholar 

  • Ghazala S, Ramaswamy HS, Smith J, Simpson B (1991) Thermal process time calculations for thin profile packages: comparison of formula methods. J Food Process Eng 13:269–282

    Article  Google Scholar 

  • Gillespy TG (1951) Estimation of sterilizing values of processes as applied to canned foods. I. Packs heating by conduction. J Sci Food Agric 2:107–125

    Article  Google Scholar 

  • Gillespy TG (1953) Estimation of sterilizing values of processes as applied to canned foods. II. Packs heating by conduction: complex processing conditions and value of coming-up time of retort. J Sci Food Agric 4:553–565

    Article  Google Scholar 

  • Griffin RC Jr, Herndon DH, Ball CO (1969) Use of computer-derived tables to calculate sterilizing processes for packaged foods. 2. Application to broken-line heating curves. Food Technol 23(4):519–524

    Google Scholar 

  • Griffin RC Jr, Herndon DH, Ball CO (1971) Use of computer-derived tables to calculate sterilizing processes for packaged foods 3. Application to cooling curves. Food Technol 25(2):134–143

    Google Scholar 

  • Hayakawa K (1970) Experimental formulas for accurate estimation of transient temperature of food and their application to thermal process evaluation. Food Technol 24(12):1407–1418

    Google Scholar 

  • Hayakawa K (1971) Estimating food temperatures during various heating or cooling treatments. J Food Sci 36:378–385

    Article  Google Scholar 

  • Hayakawa K (1974) Response charts for estimating temperatures in cylindrical cans of solid food subjected to time variable processing temperatures. J Food Sci 39(6):1090–1098

    Article  Google Scholar 

  • Hayakawa K (1977) Mathematical methods for estimating proper thermal processes and their computer implementation. Adv Food Res 23:75–141

    Article  CAS  Google Scholar 

  • Hayakawa K (1978) A critical review of mathematical procedures for determining proper heat sterilization processes. Food Technol 38(3):59–65

    Google Scholar 

  • Hayakawa K (1982) Advances in thermal process calculation procedures. Food Process Eng AIChE Symp Ser 78(218):42–48

    Google Scholar 

  • Hayakawa K (1983a) Mathematical procedures for estimating thermal processes applied to canned or other packaged food. In: Motohivo T, Hayakawa K (eds) Heat sterilization of food. Koseicha-Koseikaku Co. Ltd., Tokyo, pp 138–147

    Google Scholar 

  • Hayakawa K (1983b) New parametric values for thermal process estimation. In: Motohivo T, Hayakawa K (eds) Heat sterilization of food. Koseicha-Koseikaku Co. Ltd., Tokyo, pp 191–199

    Google Scholar 

  • Hayakawa K (1983c) Heat transfer in canned foods during heat sterilization processes. In: Motohivo T, Hayakawa K (eds) Heat sterilization of food. Koseicha-Koseikaku Co. Ltd., Tokyo, pp 109–120

    Google Scholar 

  • Hayakawa K, Downes TW (1981) New parametric values for thermal process estimation by using temperatures and z values expressed in degree Celsius units. Lebensm-Wiss u -Technol 14:60–64

    Google Scholar 

  • Hayakawa K-I, Wang J, De Massaguer PR (1996) Simplified predictive equations for variable thermal process lethality. J Food Process Eng 19(3):289–300

    Article  Google Scholar 

  • Herndon DH, Griffin RC Jr, Ball CO (1968) Use of computer-derived tables to calculate sterilizing processes for packaged foods. Food Technol 22(4):473–484

    Google Scholar 

  • Hicks EW (1951) On the evaluation of canning processes. Food Technol 5:134–142

    Google Scholar 

  • Hicks EW (1958) A revised table of the P h function of Ball and Olson. Food Res 23:396–400

    Article  Google Scholar 

  • Holdsworth SD, Overington WJG (1975) Calculation of the sterilizing value of food canning processes. Literature review. Technical Bulletin No. 28. Campden BRI, Gloucestershire

    Google Scholar 

  • Hurwicz H, Tischer RG (1952) Heat processing of beef. I. A theoretical consideration of the distribution of temperature with time and in space during processing. Food Res 17:380–392

    Article  Google Scholar 

  • Ikegami Y (1974a) Effect of various factors in the come-up time on processing of canned foods with steam. Rep Tokyo Inst Food Technol 11:92–98 [in Japanese]

    Google Scholar 

  • Ikegami Y (1974b) Effect of “come-up” on processing canned food with steam. Canners J 53(1):79–84 [in Japanese]

    Google Scholar 

  • Jakobsen F (1954) Note on process evaluation. Food Res 19:66–79

    Article  Google Scholar 

  • Kao J, Naveh D, Kopelman IJ, Pflug IJ (1981) Thermal process calculations for different z and j c values using a hand-held calculator. J Food Sci 47:193–197

    Article  Google Scholar 

  • Larkin JW (1989) Use of a modified Ball’s formula method to evaluate aseptic processing of foods containing particulates. Food Technol 43(3):66–72, 75

    Google Scholar 

  • Larkin JW, Berry MR (1991) Estimating cooling process lethality for different cooling ‘j’ values. J Food Sci 56(4):1063–1067

    Article  Google Scholar 

  • Lenz MK, Lund DB (1977) The lethality-Fourier number method: experimental verification of a model for calculating temperature profiles and lethality in conduction-heating canned foods. J Food Sci 42(4):989–996, 1001

    Google Scholar 

  • Merson RL, Singh RP, Carroad PA (1978) An evaluation of Ball’s formula method of thermal process calculations. Food Technol 32(3):66–72, 75

    Google Scholar 

  • National Bureau of Standards (1940) Tables of sine, cosine and exponential integrals, vol I. Federal Works Agency, Work Projects Administration, New York, NY

    Google Scholar 

  • Naveh D, Kopelman IJ, Zechman L, Pflug IJ (1983a) Transient cooling of conduction heating products during sterilization: temperature histories. J Food Process Preserv 7:259–273

    Article  Google Scholar 

  • Naveh D, Pflug IJ, Kopelman IJ (1983b). Transient cooling of conduction heating products during sterilization: sterilization values. J Food Process Preserv 7: 275–286

    Google Scholar 

  • Naveh D, Pflug IJ, Kopelman IJ (1983c) Simplified procedure for estimating the effect of a change in heating rate on sterilization value. J Food Protection 46(1): 16–18

    Google Scholar 

  • Newman M, Holdsworth SD (1989) Methods of thermal process calculation for food particles. Technical Memorandum No. 321 (revised). Campden BRI, Gloucestershire

    Google Scholar 

  • Noronha J, Hendrickx M, Van Loey A, Tobback P (1995) New semi-empirical approach to handle time-variable boundary conditions during sterilization of non-conductive heating foods. J Food Eng 24(2):249–268

    Article  Google Scholar 

  • Olson FCW, Stevens HP (1939) Thermal processing of canned foods in tin containers. II. Nomograms for graphic calculation of thermal processes for non-acid canned foods exhibiting straight-line semi-logarithmic heating curves. Food Res 4(1):1–20

    Article  Google Scholar 

  • Pagurova VI (1961) Tables of the exponential integral. Pergamon Press, Oxford

    Google Scholar 

  • Patashnik M (1953) A simplified procedure for thermal process calculation. Food Technol 7(1):1–6

    Google Scholar 

  • Pflug IJ (1968) Evaluating the lethality of heat processes using a method employing Hick’s table. Food Technol 33(9):1153–1156

    Google Scholar 

  • Pham QT (1987) Calculation of thermal process lethality for conduction-heated canned foods. J Food Sci 52(4):967–974

    Article  Google Scholar 

  • Pham QT (1990) Lethality calculation for thermal process with different heating and cooling rates. Int J Food Sci Technol 25:148–156

    Article  Google Scholar 

  • Ramaswamy HS, Tung MA (1986) Modeling heat transfer in steam/air processing of thin profile packages. Can Inst Food Sci Technol J 19(5):215–222

    Article  Google Scholar 

  • Ramaswamy HS (1993) Come-up time effectiveness for process calculations involving thin-packages. J Food Eng 19(2):109–117

    Article  Google Scholar 

  • Riedel L (1947) The theory of heat sterilization of canned foods. Mitt Kältetech Inst Karlsruhe 1:3–40 [in German]

    Google Scholar 

  • Sablani SS, Shayya WH (2001) Computerization of Stumbo’s method of thermal process calculations using neural networks. J Food Eng 47(3):233–240

    Article  Google Scholar 

  • Shiga I (1970) Temperatures in canned foods during processing. Food Preserv Quart 30(3):56–58

    Google Scholar 

  • Shiga I (1976) A new method of estimating thermal process time for a given F value. J Food Sci 41:461–462

    Article  Google Scholar 

  • Simpson R, Almonacid S, Nuñez H, Urtubia A, Texeira AA (2012) Is there a need for the come-up time correction factor in Ball’s Formula Method? A critical analysis. Food Eng Rev 4:107–113

    Article  Google Scholar 

  • Skinner RH, Jowitt R (1975) A reappraisal of available temperature history models for heat sterilization processes in relation to their suitability for present day computing facilities. In: Proceedings of EFCE mini-symposium – mathematical modelling in food processing. Lund University Technology, Sweden, pp 203–222

    Google Scholar 

  • Skinner RH, Urwin S (1971) Automation of canning process calculations. Process Biochem 6(11):35–38

    Google Scholar 

  • Smith T, Tung MA (1982) Comparison of formula methods for calculating thermal process lethality. J Food Sci 47:626–631

    Article  Google Scholar 

  • Spinak SH, Wiley RC (1982) Comparisons of the general and Ball formula methods for retort pouch process conditions. J Food Sci 47:880–885

    Article  Google Scholar 

  • Steele RJ, Board PW (1979) Amendments of Ball’s formula method for calculating the lethal value of thermal processes. J Food Sci 44:292–293

    Article  Google Scholar 

  • Steele RJ, Board PW, Best DJ, Willcox ME (1979) Revision of the formula method tables for thermal process evaluation. J Food Sci 44:954–957

    Article  Google Scholar 

  • Storofos NG (1991) On Ball’s formula method for thermal process calculations. J Food Process Eng 13:255–268

    Article  Google Scholar 

  • Stumbo CR (1973) Thermobacteriology in food processing, 2nd edn. Academic, New York, NY

    Google Scholar 

  • Stumbo CR, Longley RE (1966) New parameters for process calculations. Food Technol 20:341–345

    Google Scholar 

  • Succar J, Hayakawa K (1982) Prediction of time correction factor for come-up heating of packaged liquid food. J Food Sci 47(3):614–618

    Article  Google Scholar 

  • Teixeira AA, Dixon JR, Zahradnik JW, Zinsmeister GE (1969) Computer optimization of nutrient retention in thermal processing of conduction heated foods. Food Technol 23:137–142

    Google Scholar 

  • Teixeira AA, Tucker GS, Balaban MO, Bichier J (1992) Innovations in conduction-heating models for in-line retort control of canned foods with any j-value. In: Singh RP, Wirakarakusumah A (eds) Advances in food engineering. CRC, Boca Raton, FL, pp 561–574

    Google Scholar 

  • Tucker GS (1991) Development and use of numerical techniques for improved thermal process calculations and control. Food Contr 2(1):15–19

    Article  Google Scholar 

  • Tucker G (2002) Capabilities and pitfalls of computer-based prediction software. In: Tucker GS (ed) Second international symposium, on thermal processing – thermal processing: validation challenges (Session 4:1). Gloucestershire, Campden BRI

    Google Scholar 

  • Tung MA, Garland TD (1978) Computer calculation of thermal processes. J Food Sci 43:365–369

    Article  Google Scholar 

  • Uno J, Hayakawa K (1981) Correction factor of come-up heating based on mass average survivor concentration in a cylindrical can of heat conduction food. J Food Sci 46:1484–1487

    Article  Google Scholar 

  • Vinters JE, Patel RH, Halaby GA (1975b) Thermal process evaluation by programmable computer calculator. Food Technol 29(3):42–44

    Google Scholar 

  • Wiese KL, Wiese KT (1992) A comparison of numerical techniques to calculate broken-line heating factors of a thermal process. J Food Process Preserv 16(5):301–312

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Stretton-on-Fosse, Gloucestershire, UK

    S. Donald Holdsworth

  2. Universidad Técnica Federico Santa María, Valparaíso, Chile

    Ricardo Simpson

Authors
  1. S. Donald Holdsworth
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ricardo Simpson
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Holdsworth, S.D., Simpson, R. (2016). Formula Methods and Analytical techniques. In: Thermal Processing of Packaged Foods. Food Engineering Series. Springer, Cham. https://doi.org/10.1007/978-3-319-24904-9_8

Download citation

Publish with us

Policies and ethics

Search

Navigation