Stumbo Method Calculator for Thermal Process Evaluation

The Stumbo Method Calculator is an Excel-based implementation of the tabulated Stumbo method for thermal process evaluation of canned foods.

The calculator automates the tabulated procedure and can determine either:

• the process lethality (F) delivered by a specified process time, or
• the process time (B_b) required to achieve a specified process lethality.

Method Basis

The calculator implements the Stumbo method using tabulated f_h/U:g relationships for specified values of the thermal resistance parameter z and cooling lag factor j_c. The method assumes that the cooling rate f_c equals the heating rate f_h, while allowing the cooling lag factor j_c to vary.

The computer-generated f_h/U:g relationships used in the Stumbo tables were developed for a nominal 307 × 409 cylindrical container, with approximate inside dimensions of 3.30 in diameter × 4.19 in height (H/D ≈ 1.27). Jen et al. (1971) used this geometry in the original finite-difference calculations, which were subsequently refined and expanded by Purohit and Stumbo (1973). Because the internal temperature distribution and resulting cooling response depend on container geometry, the g-to-j_c relationship underlying these calculations is not strictly independent of H/D.

Because the Stumbo tables express temperature-related variables in degrees Fahrenheit, temperature variables in the calculator are likewise expressed in degrees Fahrenheit. This allows the tabulated relationships to be used directly and maintains consistency with the original method.

The calculator uses linear interpolation within an individual f_h/U:g table and j_c column where required. For g values below the lowest tabulated value (g'), the calculator applies the low-g relationship derived by Stoforos (2010) from the treatment of the g < 0.1°F case. The inverse relationship is used when determining g from an f_h/U value below the range represented in the selected table.

The calculator is limited to the discrete z and j_c values represented in the Stumbo tables. Interpolation between z values or between j_c values is not performed.

Heat-Penetration Parameters

The heating lag factor j_h and heating rate f_h are determined from experimental product heat-penetration data plotted on semilogarithmic coordinates as the temperature difference between the retort and product versus heating time. An asymptote is fitted to the long-term linear portion of the heating curve, beyond the initial lag or curved portion, and extrapolated back to zero heating time.

The heating rate f_h is the time required for the fitted asymptote to traverse one logarithmic cycle. The heating lag factor j_h is determined from the intercept of the extrapolated asymptote at zero heating time relative to the initial temperature difference between the retort and product.

For cooling, a line having the same semilogarithmic slope as the heating asymptote is positioned through the point on the experimental cooling curve corresponding to a product temperature of 150°F, consistent with the Stumbo assumption that f_c = f_h. The cooling lag factor j_c is determined from the intercept of this line.

About the Stumbo Method

C. R. Stumbo made a major advance to Ball’s Formula Method by developing process-calculation tables for different cooling lag factors, allowing variations in cooling behavior to be incorporated into process calculations while retaining a practical tabular procedure.

The method was subsequently recalculated using computer-based finite-difference heat-transfer solutions for cylindrical containers. These computer-generated relationships were further refined and expanded and incorporated into the second edition of Thermobacteriology in Food Processing (Stumbo, 1973).

The Stumbo tables relate f_h/U and g for specified combinations of z and j_c, allowing process time or delivered lethality to be determined from experimentally established heat-penetration parameters.

The Excel calculator automates these calculations and table lookups while retaining the basis and assumptions of the tabulated Stumbo method.

Intended Use

This calculator is provided for educational, research, and technical purposes. It implements the tabulated Stumbo method and should be interpreted within the assumptions and limitations of that method.

It is not intended to replace the establishment, validation, or review of commercial thermal processes by a qualified thermal process authority. Users are responsible for determining the suitability of the calculations for their intended application and for compliance with applicable food-safety and regulatory requirements.

Macro Requirement

This calculator uses VBA macros to perform the thermal process calculations. Macros must be enabled for the calculator to function. Depending on Microsoft Excel security settings, users may need to unblock the downloaded workbook or designate its location as trusted before macros can be enabled.

Timothy A. Haley, Ph.D.
Department of Food Science
University of Tennessee

References

Stumbo, C. R., & Longley, R. E. (1966). New parameters for process calculation. Food Technology, 20, 109–114.

Jen, Y., Manson, J. E., Stumbo, C. R., & Zahradnik, J. W. (1971). A procedure for estimating sterilization of and quality factor degradation in thermally processed foods. Journal of Food Science, 36, 692–698.

Purohit, K. S., & Stumbo, C. R. (1973). Refinement and extension of f_h/U:g parameters for process calculation. Journal of Food Science, 38, 726–728.

Stumbo, C. R. (1973). Thermobacteriology in Food Processing (2nd ed.). Academic Press, New York.

Stoforos, N. G. (2010). Thermal process calculations through Ball’s original Formula Method: A critical presentation of the method and simplification of its use through regression equations. Food Engineering Reviews, 2, 1–16. DOI: 10.1007/s12393-010-9014-4.

Custom Applications

For a version supporting broken-heating products, or for modifications tailored to a particular application, contact Timothy A. Haley, Ph.D. at THaley2@utk.edu.

Software © 2026 Timothy A. Haley, Ph.D.