ACCURATE MEASUREMENTS by Steve Bodofsky Reading a Vernier Caliper I n the last issue of GEARS, we looked at how to use a vernier caliper. We discussed the different components that make up a caliper, how to zero the caliper, and how to use a caliper to make four different types of measurements. If you re still unsure of any of these concepts, go back and reread that article before going any further. Once you re sure you understand the basics of vernier calipers, you re ready to learn to read the caliper scales. As we go through the various caliper types, we'll compare our measurements with a digital caliper (figure 1). A digital caliper will display in standard numerical format, and will resolve down to about 0.0005, or 0.01 millimeters. That should be more than accurate enough for anything you re likely to measure. And they switch between Imperial (inches) and Metric at the touch of a button. And, while cost might have been an issue in the past, today you can get 48 Figure 1 The easiest way to make accurate measurements is with a digital caliper. There s no need to learn how to read the scale, and the accuracy is better than you re likely to need. GEARS July 2007
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Reading a Vernier Caliper Figure 2 The standard caliper comes in all different forms and formats, making the term standard a huge misnomer. Here are two different types of standard caliper: one that reads in thousandths of an inch and hundreds of a millimeter (A), and a second that reads in fractions of an inch (B). Figure 3 Each inch on the fixed scale breaks into 10 large divisions, or 0.1. Those graduations break into four smaller graduations, equaling 0.025 each. decent digital caliper for just a few dollars. I got the one for this article on line for just under 10 bucks, plus shipping. Harbor Freight offers one for about $16 plus shipping. And I found several others, all for under $30. So before you risk making a costly error while trying to count those little scratch marks on a caliper scale, get a digital and avoid the whole thing. Standard Caliper The term standard is a horrible misnomer for this type of caliper, because there s very little that s standard (figure 2). Some read in thousandths of an inch; others read in fractions, usually down to 1/128th of an inch. Some have a Figure 4 The vernier has 25 graduations on the top (inches) scale. These allow you to refine your measurement. Look for the one that aligns perfectly with a graduation on the fixed scale: That s the measurement, down to 0.001. metric scale, but not all. If your vernier caliper reads in fractions, the best thing you can do is give it to someone you really don t like. Using this type of caliper requires not only reading the different scales, but also adding fractions; that means finding a common denominator and adding the numerator. Then you ll still probably have to convert your measurement to decimals. Not an easy task overall, with lots of steps for a mistake to creep into your measurement. Standard Caliper; Decimal Imperial Scale The better choice is a vernier caliper that measures in decimals; that is, Figure 5 For this measurement, the zero lines up with the third graduation after 0.4 ; that s 0.475. The graduation on the vernier that aligns with the graduations on the fixed scale is 21, so we add 0.021 to 0.475. The total measurement is 0.496. thousandths of an inch and hundredths of a millimeter. Let s look at what each scale means, beginning with the Imperial (inch) scale: The Main or Fixed scale breaks each inch into 10 graduations (figure 3); each graduation equals 1/10th of an inch, or 0.1. Each of those graduations is broken into four smaller graduations, each equaling 0.025. Notice that the adjustment jaw, or vernier, also has graduations: 25 on the Imperial scale (figure 4). Those divisions allow you to refine your measurement down to 0.001. Let s measure the width of this air conditioning feeler gauge and see how to use these calipers: With the feeler gauge held in place, 50 GEARS July 2007
So the measurement is 0.496 based on the standard decimal caliper. How accurate is that? Let s compare it to the digital caliper (figure 6). Not bad. According to the digital caliper, the feeler gauge is 0.4965 ; that s within 0.0005. Can t ask for much better accuracy than that! the measurement appears to be about half an inch (figure 5). But look closer: The zero line on the vernier is just a tiny bit shy of the half-inch mark. That indicates that this feeler gauge is less than half an inch but how much less? This is where those extra 25 graduations come into play. Look along those 25 graduations: Find the one that lines up precisely with a graduation on the fixed scale. Look closely: Some will appear closer than others. You should find a range of about five graduations that look awfully close choose the one in the middle. In this case, the graduation that lines up the best seems to be 21, or 0.021. Now we add the two measurements: 0.475 from the fixed scale 0.021 from the vernier scale 0.496 actual measurement So the measurement is 0.496 based on the standard decimal caliper. How accurate is that? Let s compare it to the digital caliper (figure 6). Not bad. According to the digital caliper, the feeler gauge is 0.4965 ; that s within 0.0005. Can t ask for much better accuracy than that! Standard Caliper; Metric Scale Now we ll look at the bottom scale on the standard caliper: This is the Metric scale (figure 7). Each graduation on the fixed Metric scale is equal to one millimeter. The numbers indicate centimeters, or ten millimeters. Notice the graduations on the Metric side of the vernier: It has 10 Figure 6 A quick check with the digital caliper reveals our measurement was accurate to within 0.0005 ; not bad for counting a bunch of lines on a scale! Figure 7 Each graduation on the fixed Metric scale is equal to one millimeter. The graduations on the Metric side of the vernier are also broken into 10 divisions, with each of them being broken into 5 smaller divisions. So each small division on the vernier lets you measure down to 0.02 millimeters. numbered graduations, and each of those numbered graduations is divided into five smaller graduations. The numbered graduations are tenths of a millimeter; the smaller graduations are each equal to 0.02 millimeters. These graduations work the same way as the ones on the Imperial scale. Let s measure the feeler gauge again and see how the Metric scale works: With the feeler gauge in place, the zero on the vernier scale is just over two millimeters past the 10-millimeter mark on the fixed scale (figure 8). So the feeler gauge is just over 12 millimeters. But how much over? Just as before, look for which graduations on the vernier line up with the graduations on the fixed scale (figure 9). It looks like the graduation at number 6 GEARS July 2007 51
Reading a Vernier Caliper Figure 9 Now when we examine the graduations on the vernier, we see the graduation at number 6 is in perfect alignment. So the measurement is 12.6 millimeters. Figure 8 The zero on the Metric scale is just a little over two graduations past 10 millimeters, so the actual measurement is just over 12 millimeters. Figure 11 This fractional caliper provides measurements in 16ths and 32nds of an inch. And the vernier scale on the 16ths side lets us refine our measurement down to 1/128th of an inch. Figure 10 To measure the feeler gauge in millimeters using the digital caliper, all we need to do is press the inch/mm button. Our measurement was right on the money. Figure 12 At first glance, it appears that the feeler gauge is 1/2 wide. But a closer look reveals that the last graduation on the vernier scale is lined up with the fixed scale, so it s actually 1/128 less than 1/2. Several mathematical steps later shows that it s actually 0.4922 wide. is in perfect alignment with the fixed scale. That means this feeler gauge is exactly 12.60 millimeters across. How does that compare with our previous measurement? If we divide 12.6 by 25.4, we get 0.4961 ; pretty close to the 0.4965 we measured with the digital caliper. To confirm it with the digital caliper, we just press the inch/mm button and measure it again (figure 10). Hmm 12.60 millimeters. Right on the money! Standard Caliper; Fractional Imperial Scale If you re still insistent on learning how to use a fractional caliper, here s how to read the scale (figure 11). This caliper has two basic scales: one in 16ths of an inch, the other in 32nds of an inch. The 16ths scale has eight additional divisions on the adjustable jaw, allowing you to refine your measurement down to 1/128th of an inch. Let s measure that feeler gauge again (figure 12): At first glance, it appears to be an even half inch. But a closer examination reveals that the second to the last line on the vernier jaw 52 GEARS July 2007
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Reading a Vernier Caliper is the one that s actually lined up with the fixed scale. That means this shim is actually 1/128 less than 1/2. Now let s do the math. Remember, to add or subtract fractions, we must first find a common denominator: 1/2 = 64/128 64/128 1/128 = 63/128 So the feeler gauge is 63/128 wide. Great; but how close is that to our earlier measurement? To figure that out, we have to convert the fraction to decimals, by dividing the numerator by the denominator (now do you see why you don t want a fractional caliper?). 63 128 = 0.4922 So the gauge is 0.4922 wide. How does that compare with our earlier measurement? It s within 0.003, which isn t bad, considering what a cheesy caliper it is. And, of course, there s always something lost when rounding the calculation. Not too shabby, all things considered. But was it worth the effort? Probably not: especially for a measurement that was still off by about 0.003. For my money, I d rather go with the digital, and avoid the confusion and the inaccuracy. Dial Caliper CAUTION: Dials such as these are subject to parallax errors; that is, slight errors created by the angle from which you look at the dial. To avoid parallax errors, always keep the dial directly in front of you when reading the measurement; never read it from an angle. Most dial calipers display either inches or millimeters; only a few display both. That s because the conversion ratio would create a problem for using them. Let s look at how to read the dial, and you ll see why. The fixed scale is broken into 10 graduations per inch (figure 13). As you move the vernier, the needle on the dial makes a complete revolution for each 1/10th of an inch it travels. And the dial is broken into 100 graduations. So each graduation on the dial equals 1/1000th (0.001) of an inch. The problem with having a dial caliper that reads in both inches and millimeters is there s no way for a complete rotation to equal both 1/1000th of an inch and 1/100th of a millimeter. Figure 13 The fixed scale on the dial caliper is broken into tenths of an inch, and each graduation on the dial equals 0.001. So when measuring, only one of those measurements can relate to a compete rotation of the needle. The other would be only a part of a revolution, and the zero position would continue to change, depending on the size of the item being measured. The only way to allow both measurements to zero at the same point would be to change the gearing in the dial; possible, but a much more complex and costly construction. So, if you insist on going with a dial caliper, you should probably get two: one Imperial (inches) and one Metric. Now let s try the dial caliper, and see how it compares with the others: As you can see, the fixed scale indicates about 0.5 (figure 14). But the dial is at 96; right near the end of the scale. So this measurement is just under 0.5. The previous measurement on the fixed scale is 0.4, or 0.400. The 96 is 0.096, so we add 0.096 to 0.400 and get 0.496 ; as we said, just under 0.5. The digital scale measured the feeler gauge at 0.4965, so the dial caliper was within 0.0005 ; again, not a bad level of accuracy. Digital Caliper We could get into the whole process of measuring the feeler gauge again, but to be honest, there s no real reason. Once you use the procedures Figure 14 Measuring the same feeler gauge shows the fixed gauge right near the half-inch mark. But the dial is at 96, which indicates the feeler is just under a half inch: 0.496 to be precise. covered in the last article, the measurement appears digitally on the display. You want Metric? Press the button, and it s Metric. Press again and it s back to Imperial (inches). There s nothing we can add that you didn t learn back in 3rd grade. So, in general, each of these calipers provides an accurate measurement, all within about a thousandth of an inch or less of one another (except the fractional caliper, and remember, you re going to give that to someone you dislike!) But when it comes to accuracy, ease of use, and price, these days it s hard to imagine any reason to go any way but digital. Next time, we ll take a look at how to use a micrometer, and compare its accuracy to a caliper. 54 GEARS July 2007
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