Pepcid Packaging
I take Pepcid Complete chewable tablets for heartburn.
Above, a Pepcid “Berry Flavor” tablet with 2007 US quarter for scale.
Pepcid tablets are 0.695 inches in diameter, and 0.221 inches thick. That’s an aspect ratio of H/D = 0.221/0.695 = 0.32 If a tablet were a perfect cylinder it would have a volume of 0.084 in3, or 1.374 cm3. The real tablet volume is a bit less, since tablets have beveled edges and a slight depression in each end.
I commonly get 50 and 25 tablet bottles. The “Berry Flavor” is the best, tasting more like cupcakes than anything else, but “Cool Mint Flavor” isn’t bad.
Procedure to find volume of bottles
The necks of the bottles are threaded. The lids are interchangeable. I believe the shoulder part of the bottles, a quarter-round knuckle that adapts the cylindrical main bottle to the threaded neck, is the same on both bottles.
I measured the usable volume of each bottle. I did this by weighing an empty bottle, then filling it to the usable volume with water, and weighing again. Since water weighs almost exactly 1 gram per cubic centimeter, the difference in weight in grams is the volume in cubic centimeters.
Scale
I used an Escali brand gram/ounce scale, Model P115C, capacity 5 Kg/175 oz, marked “Not legal for trade”. I guess it’s good I’m doing a Science.
Procedure
To get the “Cylinder full weight”, I filled the bottles to the top of the cylindrical section, ignoring the knuckle and threaded neck volume. I put a needle through the bottles at the cylinder-to-knuckle junction, to get a better visual reference of that junction.
| Outside Dia, inches | Dry weight, grams | Cylinder full, grams | Brim full, grams | |
|---|---|---|---|---|
| 25 tablet | 2.14 | 19 | 157 | 187 |
| 50 tablet | 2.21 | 24 | 208 | 245 |
How many tablets fill a bottle?
I tried a number of methods:
- Counting pepcids one-by-one into the bottle
- pouring handfuls into the bottle, shaking them out, counting
- pouring bowlsful into the bottle, shaking them out, counting
None of these were satisfactory. I felt like repeated manual handling of the tablets would physically degrade them, and make my hands sticky. Dropping tablets in one-by-one led to wildly differing counts.
It was also impossible to only fill the cylinder part of the bottle. Visibility through the opening and neck was sub-optimal. I there considered the whole volume of the 25-tablet bottle.
I ended up cutting the neck and knuckle off a 50-tablet bottle, then using it as a “funnel”. I put 74 tablets in a bowl, set the 25-tablet-bottle in another bowl, fit the “funnel” on to the 25-tablet bottle, then poured the tablets into the 25-tablet bottle via the funnel. By sliding the funnel sideways, I knocked off any tablets that protruded above the lip of the threaded section of the 25-tablet bottle.
The setup appears in the above image. The image portrays the 25-tablet bottle ready to receive tablets. The Pepcid bottle stands in a black bowl which catches any tablets that bounce out of the funnel, and would otherwise cause me to scramble to retrieve them.
Based on 10 “pours” of tablets, The 25-tablet bottle holds a mean of 68.9 tablets. I got a median of 69.5 tablets.
Packing factor
Lots of 3D shapes like Pepcid tablets can’t be packed to completely fill up some volume. Spheres, for example, can be packed carefully to fill up 74% of a volume, but if they’re just tossed in, they fill up 56-64% of volume.
I found a paper, Maximum packing densities of basic 3D objects, by Li ShuiXiang, Zhao Jian, Lu Peng, Xie Yu, Chinese Science Bulletin, Jan 2010, Vol. 55, No. 2, 114-119 They give a graph based on simulation of packing factor versus cylinder aspect ratio.
Unfortunately, Pepcid tablets aspect ratio of 0.32 lies off the left side of the graph. The text of the paper isn’t helpful either, claiming that experimental random cylinder packing got a maximum packing factor of 0.66, when aspect ratio of the cylinders was 1.2. The graph clearly shows a maximum packing factor of at least 0.72. The graph looks like cylinders with an aspect ratio of 0.32 would have a packing factor of about 0.67.
Reduced data
| Usable Volume, cm3 | Neck and knuckle volume, cm3 | ||
|---|---|---|---|
| 25 tablet | 138 | 30 | |
| 50 tablet | 184 | 37 |
Neck and knuckle volumes don’t agree very well, which casts all my results in a bad light.
My measured packing factor is (68.9 * 1.374)/157 = 0.60 That’s a little less than Li and company’s 0.67.
I do know that pouring in some tablets, shaking the container gently, then pouring in a few more, repeat until very full, got me to at least 75 tablets.
(75 * 1.374)/157 = 0.66, almost exactly the Li paper’s cylinder packing factor.
Conclusion
The makers of Pepcid put their product in an outsized container, perhaps as much as 3 times what size it has to be to hold the tablets.
My measured packing factor is pretty close to that reported by other researchers.