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Ways other than the trapezoidal rule for F calc

Printed From: Dairy Science and Food Technology
Category: Thermal processing
Forum Name: Thermal processing
Forum Description: Effects of heat on food, enzymes and microorganisms
Printed Date: 28 Nov 2021 at 3:14am
Software Version: Web Wiz Forums 12.03 -

Topic: Ways other than the trapezoidal rule for F calc
Posted By: beachgirl
Subject: Ways other than the trapezoidal rule for F calc
Date Posted: 07 Nov 2010 at 6:22pm
Im an intern in canning plant. I downloaded your spreadsheet to compare Fo results calculated with it and our software, we get same results with your spreadsheet. Good easy to use.
Our software and your spreadsheet use the the trapezoidal rule. If we did cals using another method would we get different Fo results?
Plaese replyCry

Posted By: Admin
Date Posted: 07 Nov 2010 at 9:23pm
An interesting post and a question that I have never heard from a student. I sincerely hope that you are not trying to find a way out of a production problem; being able to sleep at night is important.
The trapezoidal rule is a commonly used method for estimating the area under the lethality -time graph using simple numerical integration. Generally it gives an acceptable result. This is dependant upon an acceptable number of data points and the use of a constant and small delta time value e.g. 1-5 minutes; smaller is better.
However there are other more accurate ways of obtaining the area under a curve, Simpson's rule and Romberg integration are probably the best known. Of the three methods, Romberg integration gives the most accurate result but Simpson's rule (there are 2 actually) is generally more commonly used.
The differences in the F value calculated by the three methods are often too small to be of any practical significance in food processing;the errors inherent in the trapezoidal rule are small compared with other errors involved in thermal processing e.g.  temperature measurement. When one considers how easy it is to use the trapezoidal rule it is easy to understand why it has become so widely used. However on occasions there can be significant differences.
It is very easy to set up a spreadsheet to calculate F values using the three methods.

Posted By: beachgirl
Date Posted: 08 Nov 2010 at 8:04pm
Thanks! Dont really understand much of this. We have googled methods & thyre to complicted for us. Any more info appreciated. Would u post another spredsheet?

Posted By: Admin
Date Posted: 08 Nov 2010 at 8:25pm
Sorry very busy for the next few weeks so can't help in short term. There are some good articles in Wikipedia. I will try and get back to you later.

Posted By: beachgirl
Date Posted: 08 Nov 2010 at 11:26pm
If I posted some info could you give me Fo with different ways?Pl

Posted By: Admin
Date Posted: 09 Nov 2010 at 7:01pm
OK  post a list of  times and temperatures and confirm your Z and T reference values. I will then calculate  F values using the 3-methods. It is unlikely that they will show much of a difference from your own calculations. Note the trapezoidal rule generally gives slightly higher values than the other two methods.
Please do not provide commercial information with your data.

Posted By: beachgirl
Date Posted: 10 Nov 2010 at 8:31pm
Have chatted to boss. Cant post company data. Thnks for all the help Smile lot happier now.

Posted By: Admin
Date Posted: 10 Nov 2010 at 9:38pm
Glad to have been of some help. You stimulated me to find out more about Romberg integration-surprisingly easy to do but it offers no advantage over Simpsons rule in F calculation.

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