How Much Ink Do You Need?

Learn how to calculate the total amount of ink needed for any job based on mesh parameters and run length.

It's inventory time, and with pen and notebook in hand, you set out for the ink department. As you near the inkroom, however, your progress begins to slow. Ink buckets of every shape and size--none of them empty--litter the corridor. Hurdling a final stack, you push through the inkroom door and find yourself confronted with an even larger collection of containers filling every available inch of shelf space and stacked to the ceiling everywhere else. "We have enough ink in here to cover Texas!" you cry. "Where did it all come from?" From behind a wall of half-full five-gallon containers pops the head of your ink technician. "Hi Boss!" he answers. "Just leftovers from the jobs we've been running." If this sounds like a visit to your own inkroom, then you've been paying the price for inaccurate ink estimating. And the price is likely a high one. Not only do you have an expensive inventory that may rival your supplier's, there's no guarantee that you'll find a use for those 13 extra gallons of hot pink Pantone 812 or other custom-color leftovers before the ink goes bad. Poor estimating works in the opposite direction, too. If you're constantly coming up short on a particular color during a long run, you'll see costly consequences in the press time you lose while another batch is whipped up. Then there's the problem of getting the second batch to match the first. It doesn't have to be this way, though. A few details about your screens and a little bit of math can help you avoid the whole dilemma. It just adds up I'll admit it--I'm writing this article because I like math (must be hereditary). But even if you suffer from calcu-phobia, there's really no reason to be intimidated by a few mesh measurements and simple equations, which is all you need to get accurate ink estimates. Most of the numbers you require are readily available from mesh suppliers or sources like our Comparative Screen Fabric Guide (available through ST Publication's online bookstore at www.stpubs.com/stbin/quikstore.cgi). The best place to start when figuring out how much ink you need to run a job is to determine how much ink you'll need per print. The volume of ink that gets printed per image through a particular mesh is determined by five factors: * mesh count (M) * thread diameter (D) * fabric thickness (F) * coverage area (A) weave Stencil thickness may increase this printed ink volume. But with the thin stencils used in most graphics applications, the contribution to ink deposit is small enough to overlook for basic estimating purposes. How Much Ink Do You Need? Your first goal is to determine the wet ink-deposit height (I) delivered by a particular mesh. Wet ink-deposit height is defined as the thickness of a printed ink layer on a substrate after the mesh is no longer in contact with the substrate and the ink has flowed to a smooth, even layer. Over the years, mesh manufacturers and research groups including the Screen Printing Technical Foundation have developed several formulas that can be used to calculate theoretical wet ink-deposit heights for the fabrics they offer. None of these formulas will work with all meshes, but when used with specific mesh-count ranges and mesh types as shown in Table 1, they can be very accurate.

 

Table 1: Formulas for calculating wet ink-deposit height
Thread count
(threads/cm) Weave Formula
0-42 plain 1.82D (1-MD)2
43-139 plain 0.285 x F
140 and up plain 0.35 x F
all counts twill 0.31 x F
Key:
M = mesh count
D = thread diameter
F= fabric thickness

Before you start sticking numbers into these formulas, you need to note a couple of things. Despite the fact that you buy mesh specified in threads/in., the fabrics you purchase are woven according to metric measurements. The counts per inch are really just approximations, so for accuracy you need to use the metric counts (threads/cm). Figure 1 shows sample calculations for wet ink-deposit height. Note that most of the other measurements provided by mesh manufacturers are also given in metric units (usually microns), so the sample calculations you'll see in this article also use metric values. You'll learn how to convert your final ink-volume estimate back into a standard value near the end of this article.

 

Figure 1: Calculating wet ink-deposit height (I)
Mesh: M = 39 threads/cm (100 thread/in.), D = 55 microns
Formula: I = 1.82D(1-MD)2
  M = 39 threads/cm x (1 cm/10,000 microns) = 0.0039 threads/micron
  I = 1.82 x 55 x (1-(0.0039 x 55))2
  I = 100.1 x (1-0.2145)2
  I = 100.1 x 0.617
  I = 61.76 microns
Mesh: M = 120 threads/cm (205 threads/in.), F = 50 microns
Formula: I = 0.285 x F
  I = 0.285 x 50
  I = 14.25 microns

Determining Image Area Knowing the height of the ink layer that a particular mesh will deposit only represents one piece of the estimating puzzle. Remember, you're trying to determine the volume of ink that you'll need for a job. The height of the ink deposit is a one-dimensional measurement--volume is three dimensional. So to get the value you're after, you need to multiply the ink height by the area the image will cover. Here's where the estimating process can get a little tricky. If you're printing a flood coat of ink through your mesh, determining the image area is no problem: Just multiply the length of the open mesh area by the width. Most jobs, however, don't involve flood coats--they involve a mixture of open and blocked mesh cells across the entire screen. As you might expect, halftones pose the greatest challenge. To help you determine the area covered by complex images, you have a few options. First, your design programs may have features for determining image area. Photoshop, for example, will provide coverage data, functioning somewhat like an automatic densitometer. But you can only measure specific areas of the image. For total coverage over the entire image, you have to take multiple measurements across the image and average the results. Another option is to invest in software and equipment designed specifically to measure coverage area and other halftone characteristics. One such system is the Dot*Spec product offered by Quality Imaging Products, Marietta, GA (http://qip.com/dotspec/dotspec.html). The system, which features a microscope, digital camera, dedicated PC, and special software, provides a wide assortment of data on halftones, including average dot size, percentage of coverage, and line spacing. You can also use an image area calculator. This is a clear film with a grid pattern that you can place over the image (generally on your film positive). Once the grid is positioned, you can estimate how much of each square is filled with image areas, then add up the results to get total coverage. Most of these solutions, however, are too complex, time consuming, or expensive for the average screen shop. So most printers attempt to "guesstimate" the percentage of this area that is actually covered by image elements. While visually estimating coverage is not the most precise method, it can provide reasonably accurate results if you take a systematic approach. For example, you may be looking at the magenta separation for a particular process-color job. The image for this screen falls inside an area that is approximately 50 x 50 cm. Image elements show up over roughly 80% of the screen, and most of the halftone dots fall in the midtone range. So you can estimate the coverage area per dot at about 50%. So now you have 80% coverage of the image area with 50% dots, which would be equivalent to covering 40% of the total image area with 100% dots. In other words, 40% of your 50 x 50-cm image area, or 1000 cm2, would actually contain image elements. Putting it all together Once you've determined how thick your ink deposit will be and how large an area it will cover, you can calculate the approximate ink volume (V) for a single print. Simply multiply the ink-deposit height by the coverage area (V = I x A). Note that your ink-deposit height will likely be in microns, while your coverage area will be in square centimeters. So before you complete the multiplication, you'll need to convert all the values to the same units. The easiest option is to divide the micron measurement by 10,000, which will give you the ink height in centimeters. You then multiply the image area and deposit height to get an ink volume per print in cubic centimeters. Next, you want to project this volume across the total run length to get the total amount of ink necessary for the job. Simply multiply the volume per print times the number of images you expect to print. You'll end up with a very large value in cubic centimeters. Obviously, you don't buy ink by the cubic centimeter. It's much more likely that you're buying it by the gallon. So you'll need to do that final metric-to-standard conversion I mentioned earlier. To simplify the task, just divide the volume in cubic centimeters by the factor 3785 (the number of cubic centimeters in a gallon). The result will be the total volume of ink you'll need. To cover test prints, setup, and slight overage, it's generally wise to inflate the final number by another 5%--just in case. The entire sequence of calculations is illustrated in Figure 2.

 

Figure 2: Calculating total ink required
Print quantity: 10,000 pieces
Image size: 76 x 102 cm (approx. 30 x 40 in.)
Coverage: 35%
Mesh: M = 140 thread/cm (355 thread/in.), F = 58 microns
Calculate wet ink-deposit height (I)
Formula: I = 0.35 x F
  I = 0.35 x 58
  I = 20.3 microns
Convert ink-deposit height to centimeters
Formula: I = height (microns) x 1 cm/10,000 microns
  I = 20.3/10,000
  I = 0.00203 cm
Calculate coverage area (A)
Formula: A = width x length x coverage
  A = 76 cm x 102 cm x 35%
  A = 7752 cm2 x 0.35
  A = 2713.2 cm2
Calculate ink volume per print (V)
Formula: V = I x A
  V = 0.00203 cm x 2713.3 cm2
  V = 5.51 cm3
Calculate ink volume for total job
Formula: Total ink = V x # of pieces
  Total ink = 5.51 cm3 x 10,000
  Total ink = 55,100 cm3
Convert volume to gallons
Formula: Total ink = volume (cm3) x 1 gal/3785 cm3
  Total ink = 55,100/3785
  Total ink = 14.6 gal (15.3 gal with 5% extra)

Keep in mind that your results will be approximations of the ink you'll need. Nevertheless, they are approximations based on actual mesh characteristics, so they'll be much closer to your actual needs than the arbitrary guesses you may have relied on in the past.

View more from this Screen Printing issue