# Circular Temperature Recording Chart Measurements

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**DEPT. OF HEALTH, EDUCATION, AND**

**WELFARE PUBLIC HEALTH SERVICE**

**FOOD AND DRUG ADMINISTRATION**

***ORA/ORO/DEIO/IB***

**Date: 2/20/87 Number: 45**

**Related Program Areas:**

All Programs

All Programs

**ITG SUBJECT: CIRCULAR TEMPERATURE RECORDING CHART MEASUREMENTS**

**INTRODUCTION**

Circular temperature recording charts are used in a broad variety of firms from food canneries to medical device manufacturers to drug manufacturers. Investigators currently use draftman's dividers to measure chord (straight line, point-to-point) instead of arc (curve) distances to check process time. There is no easy way to measure arcs in investigational work. Firms also use dividers or stamped metal gauges to do the same chord measurements. When an investigator wants to set dividers to a 25 minute chord, for instance, he/she normally checks the setting by spanning 2 (on charts with 10 minute markings) or 3 (on charts with 15 minute markings) estimated 25 minute chords to come up with an even marked time (50 and 75 minutes on 10 and 15 minute marked charts, respectively). He/she repeats the process until successful. Once the dividers come up on the even markings, the investigator assumes the dividers are properly set. However, estimating odd times such as 13, 19, or 23 minutes is difficult using this method.

In addition to the previous problem, a one minute time difference is only about 0.014 inch on a typical Taylor OP524 chart. Introducing a 0.014 inch error by making 15 spans or misstamping a gauge is easy to envision.

Another problem is the extreme difficulty in extrapolating times from known chord lengths. An investigator cannot calculate a 17 minute chord distance accurately, given either longer (20, 30 minutes) or shorter (10, 15 minutes) chord distances, because of the simple fact that two chords representing shorter times (i.e., 10 minutes each) have a combined length longer than a 20 minute chord.

These chord problems are compounded when a firm uses different process temperatures, handles multiple products and/or containers, or uses different temperature recording charts.

**COMPUTER-CALCULATED CHORDS**

The geometry for determining the arc or chord length of a circle is shown in Appendix 1. A computer can be used to generate reference tables of chord lengths related to times for any circular recording chart at any temperature. An investigator only needs to know: (1) the number of hours on the chart, and (2) the diameter of the circle for the particular temperature desired. Geometric theory is based on the fact that a radius bisecting a chord creates two equal right triangles.

**APPLICATION**

It is suggested that personnel modify the attached computer programs which were written in Microsoft BASIC. Program Listing 1, written for a Tandy 200 laptop portable computer, is compatible on most microcomputers. Program Listing 2 was written for a TRS-80 Model 1 computer. Both programs should run on IBM-PCs unchanged (except possibly for adding spaces where required by GWBASIC). The programs can be adapted to any district computer by knowledgeable personnel. Test the resultant programs by using values from a 24 hour Taylor OP600 chart. The diameter of a circle for 240 degrees F is 7.929 inches. Results should be 0.017299 for 1 minute, 0.034596 for 2 minutes, 0.051895 for 3 minutes, 0.172970 for 10 minutes, and 2.052180 for 120 minutes. Program Listing 2 can be used to print reference tables while Program Listing 1 is primarily a demonstration program. The most useful application of the programs would be to develop reference tables and maintain them in EI files. Once a blank chart is collected and expected process temperatures are run through Program Listing 2, the resultant tables (similar to Table 1 attached) can be kept in EI files and photocopies can be taken to inspection sites. Another possible application is to take laptop computers to inspection sites. A computer used in conjunction with a dot matrix printer can also generate chord gauges on paper similar to the metal gauges made in cannery machine shops.

Ouestions about the geometric theory or computer programming can be addressed to DEIO/IB, (301)443-3340.

Appendix 1. Geometric Theory (Diagram not available)

- An isosceles triangle is formed by connecting a chord (C) with the center of a circle. Call (A) the angle in the center of the circle.
- A line through the center of the circle, perpendicular to the chord, bisects the chord and its arc.
- Since the bisecting line is perpendicular to the chord, each half of the original triangle is a right triangle.
- Each right triangle formed above has a small angle equal to A/2 Let A/2 = a.
- Therefore Sin a = C/2 divided by the radius (R) or, Sin a = C/2R = C/D where D is the diameter of the circle.
- Solving for the chord, C = D Sin a. The chord represents the time which the investigator measures with dividers.
- We want to make chord values equal to minutes. It is simplest to standardize on the fact that there are 360 degrees in a circle. If we assign one minute equal one degree to angle A and its chords, there are 720 angle a's (degrees) in the circle. Thus, we create a formula where a (minutes) = a (degrees) divided by 2, or more apprpriately t (minutes) = a (degrees)/2.
- We must also consider a factor to correct different chart values to minutes because while there are 360 minutes on a 6 hour chart, there are 720 minutes on a 12 hour chart and 1440 minutes on a 24 hour chart. From these figures, factor F = 6/H where H is the number of hours on the chart.
- Combining the above two formulas, t (minutes) = a (degrees) 1/2. Placing this in step 6 above, we get chord = diameter Sin (3t/H) or C = D Sin (3t/H). This is the formula used in Program Listings 1 and 2.

Program Listing 1

1 REM DARRELL LEE, SALT LAKE CITY RESIDENT POST FTS 588-5285

10 DIM C(360): K = .0174533: CLS : REM DIMENSIONS VARIABLES, INSERTS RADIAN CORRECTION FACTOR (K)

100 INPUT "Enter chart name and number"; CH$

110 INPUT "Enter no. hours on chart"; H

120 F = H / 3: REM F IS CORRECTION FACTOR

130 INPUT "Enter target temperature for chord lengths"; TE

140 PRINT "Enter diameter of"; TE; : INPUT " degree circle in inches or millimeters"; D

150 IF D > 15 THEN M$ = "millimeter" ELSE M$ = "inch"

160 INPUT "Is this correct (y/n)"; A$

170 IF LEFT$(A$, 1) = "y" OR LEFT$(A$, 1) = "Y" THEN 200 ELSE 100

200 PRINT "Table of times with corresponding chord lengths for a(n) "; CH$; " chart at "; TE; " degrees (a"; D; M$; " diameter circle)."

210 PRINT : PRINT "Minutes ";

220 IF M$ = "millimeter" THEN S$ = "s" ELSE S$ = "es"

230 PRINT M$; S$: PRINT

240 FOR T = 1 TO 120 STEP 4

250 FOR TT = T TO T + 3

260 C(TT) = D * SIN(K * TT / F)

270 NEXT TT

280 PRINT T; C(T): PRINT T + 1; C(T + 1): PRINT T + 2; C(T + 2): PRINT T + 3; C(T + 3)

290 NEXT T

Program Listing 2

10 ' REPORT CHART PLANNER

20 ' RUNS ON RADIO SHACK TRS-80 COMPUTER. MODIFY FOR OTHER COMPUTERS

NOT USING MICRSOFT BASIC.

30 CLEAR 2000 35 LPRINT CHR$(3): REM PRINTER COMMAND RESETS PAGE

40 DIM C(360): K = .0174533: A$ = "### ###.###### ### ###.###### ### ###.

###### ### ###.###### ### ###.######"

50 ' K = RADIAN CORRECTION FACTOR. NOT USED IF COMPUTER CALUCULATES

SINE USING DEGREES.

60 CLS

70 FOR I = 1 TO 8: PRINT : NEXT I

80 PRINT "********** RETORT CHART PLANNER**********"

90 FOR I = 1 TO 500: NEXT: FOR I = 1 TO 6: PRINT : NEXT I

100 PRINT "***** DARRELL LEE ****"

110 PRINT "* 2073 E. GYRFALCON DR. *"

120 PRINT "* SANDY. UT 84092 *"

130 PRINT "* SALT LAKE CITY RESIDENT POST *"

140 PRINT "* ROOM 1033 ADMINISTRATION BLDG. *"

150 PRINT "* 1745 WEST 1700 SOUTH *"

160 PRINT "* SALT LAKE CITY. UT 84104 *"

170 PRINT "************************************"

180 PRINT : PRINT

190 FOR I = 1 TO 1000: NEXT I

200 INPUT "ENTER RETORT CHART MANUFACTURER'S NUMBER (IE. TAYLOR OP 524)"; O$

210 INPUT "ENTER NUMBER OF HOURS ON RETORT CHART (6,12,24)"; H

220 F = H / 3

260 INPUT "ENTER TARGET TEMPERATURE FOR CHORD LENGTHS"; TE

270 PRINT "ENTER DIAMETER OF"; TE; : INPUT "DEGREE CIRCLE IN INCHES OR MILLIMETERS"; D

280 IF D > 15 THEN M$ = "MM. ": GOTO 300

290 M$ = "INCH " 300 LPRINT "TABLE OF TIMES WITH CORRESPONDING CHORD LENGTHS FOR A(N) ": LPRINT

310 LPRINT O$:' CHART AT";TE; "DEGREES (A";D;M$;"DIAMETER CIRCLE)":LPRINT

320 LPRINT "FOR ADDITIONAL CUSTOM MADE DATA TABLES CONTACT

DARRELL LEE AT SALT LAKE CITY RESIDENT POST.": LPRINT : LPRINT : LPRINT

330 FOR T = 1 TO 120 STEP 4

340 FOR TT = T TO T + 3

350 C(TT) = D * SIN(K * TT / F): NEXT TT

360 LPRINT USINGGA$; T, C(T), T + 1, C(T + 1), T + 2, C(T + 2), T +3, C(T + 3)

370 NEXT T

380 INPUT "DO YOU WISH TO PRINT ANOTHER TABLE"; Q$

390 IF LEFT$(Q$, 1) = "Y" THEN 30 ELSE END

Table 1. Chart Example

TABLE OF TIMES WITH CORRESPONDING CHORD LENGTHS FOR A(N) TAYLOR OP600 CHART AT 240 DEGREES (A 7.929 INCH DIAMETER CIRCLE) FOR ADDITIONAL CUSTOM MADE DATA TABLES CONTACT DARRELL LEE AT SALT LAKE CITY RESIDENT POST

Time Chord(in) Time Chord(in) Time Chord(in) Time Chord(in)

(min) (min) (min) (min)

____ _________ _____ _________ ___ _________ _______ ___________

1 0.017299 2 0.034596 3 0.051895 4 0.069193

5 0.086491 6 0.103787 7 0.121084 8 0.138580

9 0.155675 10 0.172970 11 0.190264 12 0.207557

13 0.224849 14 0.242140 15 0.259429 16 0.276718

17 0.294006 18 0.311292 19 0.328575 20 0.345858

21 0.363140 22 0.380418 23 0.397696 24 0.414972

25 0.432245 26 0.449517 27 0.466787 28 0.484054

29 0.501319 30 0.518582 31 0.535842 32 0.553099

33 0.570354 34 0.587607 35 0.604856 36 0.622102

37 0.639346 38 0.656587 39 0.673824 40 0.691058

41 0.708289 42 0.725516 43 0.742741 44 0.759961

45 0.777178 46 0.794391 47 0.811601 48 0.828807

49 0.846008 50 0.863206 51 0.880400 52 0.897588

53 0.914774 54 0.931955 55 0.949130 56 0.966302

57 0.983470 58 1.000630 59 1.017790 60 1.034940

61 1.052090 62 1.069230 63 1.086370 64 1.103500

65 1.120630 66 1.137750 67 1.154870 68 1.171980

69 1.189090 70 1.206190 71 1.223280 72 1.240370

73 1.257450 74 1.274530 75 1.291600 76 1.308660

77 1.325720 78 1.342770 79 1.359820 80 1.366860

81 1.393890 82 1.410910 83 1.417930 84 1.444950

85 1.461950 86 1.478950 87 1.49540 88 1.512930

89 1.529900 90 1.546870 91 1.563830 92 1.580790

93 1.597740 94 1.614680 95 1.631610 96 1.648530

97 1.665450 98 1.682360 99 1.699260 100 1.716150

101 1.733040 102 1.749910 103 1.766780 104 1.783640

105 1.800490 106 1.817330 107 1.834160 108 1.850990

109 1.867810 110 1.884610 111 1.901410 112 1.918200

113 1.934980 114 1.951750 115 1.968510 116 1.985260

117 2.002010 118 2.018740 119 2.035460 120 2.052180

NOTE: Darrell Lee is now a National Expert in Computers and is located in the SAN-DO office.