Bodyfat Analysis Weights  Pepsi Bottles and PenniesAs with the other Baton sets, you would only need to hold a maximum of two of these Pepsi Batons. This approach should provide an accuracy of around 1% or better regarding the bodyfat percentages. If you intend to regularly measure your bodyfat percentage (every week or every month), and you do not want to go to a YMCA or Health Club and have a swimming pool or (freshwater) lake, this might be a logical choice. The excellent accuracy (and repeatability) can give better feedback about your success in your Progress Chart! If you have your own swimming pool, your friends, relatives and neighbors will certainly want to learn their bodyfat, so you might as well make all 26 of them (Batons A through X and the float and FLOAT)! This particular approach is so simple and fast to make that you might even decide to make the 23 extra Batons that combine float with a Baton. It is our hope that enough YMCAs and Health Clubs near you will have the precision (calibrated) set of PVC bodyfat batons and that they will offer either a free service or a nominal ($1) charge to test bodyfat analysis, such that few people would see reason to need to make their own! There appear to be around 17,000 membershipbased Health Clubs in the USA. There are also many other nonmembershipbased facilities that have swimming pools. That includes around 29,650 Public High Schools, 6010 Private High Schools, 7,000 PostSecondary Schools which have swimming pools. There are also many thousands of (summer) outdoor Municipal Swimming Pools. So we think that there are at least around 74,000 public swimming pools which might choose to provide this service for their communities! Our hope is that one of these pools is near to nearly every American and that they each make or get their own set of these Batons, so that everyone would have the chance to use a publiclyavailable set of this system for no more than a dollar cost.


The Pepsi bottles need to be empty of any Pepsi, and there seems some value in filling them with water and then emptying them just to get rid of some stickiness that seems to sometimes endure! The bottles should then be turned upside down so any water empties out. The Pepsi labels are easily removed.
As an example, we can take one dry 20 ounce Pepsi bottle and put a large A label on its side. Then drop five rolls of pennies into it, which is 250 pennies as long as the Bank was accurate. You can see from the chart below that you need to add 22 additional pennies to have 272 inside it. Securely screw on the top and you are done with that one!
Try to get relatively NEW pennies. Pennies that get worn have some metal worn off and they are not as heavy. Also, ACTUAL COPPER pennies were much heavier than the modern pennies that are 97.5% Zinc, so that could affect the accuracy. We have provided the actual final weights of each Pepsi Baton (and Pepsi Float) in grams, so if you have an accurate metric scale, you could ensure extreme accuracy. In THAT case, you could actually fill many of the Pepsi bottles with sand or nearly anything else that does not change over time! However, sand is not dense enough to fit enough (dry) sand into the Batons for I and above, so you would need to use the pennies or some other more dense material in those.
You can see that you can assemble the entire set of Batons very quickly. There will be NO cost for the discarded Pepsi bottles, maybe $2 cost for the sheet of stickon labels, and no actual cost for the pennies. Not bad, a total of $2 cost! Of course, if neighbors and children visiting your pool realize that there is more than $6 of pennies in some of the Batons, they might occasionally disappear! We don't see that as our problem!
We encourage GLUING on the caps so that kids do not open them up and change the calibrated weight by dumping anything out or adding anything in!
Empty Plastic 20 ounce Pepsi bottles with some pennies in them  Letter  Actual Total Weight 

272 pennies inside  A  705 grams 
290 pennies inside  B  751 grams 
308 pennies inside  C  796 grams 
326 pennies inside  D  842 grams 
345 pennies inside  E  887 grams 
363 pennies inside  F  933 grams 
381 pennies inside  G  978 grams 
399 pennies inside  H  1024 grams 
417 pennies inside  I  1069 grams 
435 pennies inside  J  1115 grams 
454 pennies inside  K  1160 grams 
472 pennies inside  L  1206 grams 
490 pennies inside  M  1251 grams 
508 pennies inside  N  1297 grams 
526 pennies inside  O  1342 grams 
544 pennies inside  P  1388 grams 
562 pennies inside  Q  1433 grams 
581 pennies inside  R  1479 grams 
599 pennies inside  S  1524 grams 
617 pennies inside  T  1570 grams 
635 pennies inside  U  1615 grams 
653 pennies inside  V  1661 grams 
671 pennies inside  W  1706 grams 
690 pennies inside  X  1752 grams 
Precision floats, for people who naturally sink  
an empty oneliter Pepsi bottle with cap  float  
an empty twoliter Pepsi bottle with cap  FLOAT  
The oneliter and twoliter Pepsi bottles are a little
bit heavy for our needs but this float only introduces an error
of around 1/2 of one letter in this system. The FLOAT is farther
off in being too heavy by about 3.5 letters. In other words, the
float is fine for anything short of actual Laboratory accuracy!
If you need to use the FLOAT it might pay to build the FLOAT
for the PVC set of Batons which would be accurate. There is no obvious
way to increase the flotation of these two Pepsi bottles short of
trying to fill them with Helium or Hydrogen gas! And even that would
not have a large enough effect!
 
The float and FLOAT functions can also be handled as a SINGLE Baton, combining the effects of both a Baton and a Float, involving an empty Pepsi bottle and some pennies. The middle column below gives the Designation of the TWO separate Batons (float and a Baton) that is used in the other Baton sets (to reduce the total number of these things that need to be lying around!). So if you use the third one below, which is designated float + B, it would only be a single Baton but to use the automated Calculator, you would have to click on BOTH the float button AND the B button.  
The first 11 Batons below use the Liter or 1000 ml size of the Pepsi bottle.  
NO pennies inside  float alone  50 grams 
12 pennies inside  float + A  79 grams 
30 pennies inside  float + B  125 grams 
48 pennies inside  float + C  170 grams 
67 pennies inside  float + D  216 grams 
85 pennies inside  float + E  261 grams 
103 pennies inside  float + F  307 grams 
121 pennies inside  float + G  352 grams 
139 pennies inside  float + H  398 grams 
157 pennies inside  float + I  443 grams 
176 pennies inside  float + J  489 grams 
The Batons below use the 20 ounce size of the Pepsi bottle.  
17 pennies inside  float + K  70 grams 
35 pennies inside  float + L  116 grams 
53 pennies inside  float + M  161 grams 
71 pennies inside  float + N  207 grams 
89 pennies inside  float + O  252 grams 
108 pennies inside  float + P  298 grams 
126 pennies inside  float + Q  343 grams 
144 pennies inside  float + R  389 grams 
162 pennies inside  float + S  434 grams 
180 pennies inside  float + T  480 grams 
198 pennies inside  float + U  525 grams 
216 pennies inside  float + V  571 grams 
235 pennies inside  float + W  616 grams 
The Batons above are most accurate if you use relatively
new pennies! Older pennies get worn and do not weigh as much, which
could cause very minor changes in the accuracy. The Batons and Floats
will still be fine and extremely accurate, just not quite Laboratory
quality accuracy!
 
These floats can also be made out of 1" thick blue foam building
insulation. The 'float' would be cut as a rectangle of 6" by
12.5". The 'FLOAT' would be cut as a rectangle of 10" by
15". Such floats are not very durable and are fairly easily
damaged, where chunks can get lost and their accuracy then degrades.
If you expect to use this system more than rarely, you should probably
make one of the other types of float and FLOAT
 
An Optional 'Y' baton for larger people  
3" standard PVC pipe 16.375" long  Y  
An Optional 'Z' baton for larger people  
4" standard PVC pipe 13.125" long  Z 
NOTES:
This entire set provides 264 possible different Baton choices that can be used
for determining the Average Body Density and then the Bodyfat Percentage,
72 involving net flotation and 192 that involve net weight. This range
should be sufficient for virtually any person.
In general, the Optional Y and Z batons may not be needed, as they are necessary only for larger people. You might look at the Analysis Charts (linked below) to see if you might need to use a Y or a Z baton.
Brozek formula is: (4.57/(body density)  4.142) * 100
Siri (2compartment) formula is: (4.95/(body density)  4.50) *100
These formulas are a little misleading. First of all, they absolutely require expelling ALL the air possible from the lungs, something that takes some practice to do very well. But then they have to be adjusted for two different effects that they never mention! Even after you expel all the air you can from your lungs, there is still a Residual Volume of air remaining in the lungs. This amount varies from person to person but it is assumed to be 1.2 liters of volume. If a man displaced 91 liters of water, this would represent an adjustment of adding 1.319% (.01319) to the measured body density. It would seem that they could have just adjusted the Siri 2compartment formula to become (4.886/(measured body density)  4.50) * 100. If this man's body density happened to be the same as the water (0.9978 gm/cc), we would therefore have different calculated values of: (Brozek) 36.9% bodyfat or (Siri) 38.6% bodyfat. The adjusted readings are therefore around 6% lower than above, but still VERY high numbers!
I can use myself as an example. After exhaling NORMALLY, I still float. I weigh 202 pounds (and am 6'2") (my waist is around 33", relatively slim). With that NORMAL exhale, I can usually just sink using the X+D Batons but usually still float with the X+C Batons. You can see from the website calculator that my average MEASURED body density is therefore between 0.9891 and 0.9895 (gm/cc). (Note that this is a precision of one part in three thousand!) From our website calculator, that gives an estimate of between 26.2% and 26.5% bodyfat. From the American Council on Exercise guidelines, this is a little above the very top end of Acceptable. I had spent a career as a semipro volleyball player (when it was lower) and the result seems to me to be within a few percent of reality.
Note that our Calculator estimates the correction regarding how much air is still in the lungs and gets 1.0129 as an adjusted average body density. Below, we will see that with an absolute maximum exhale, we will get a very similar figure.
You can calculate that the above (unadjusted) Brozek formula as giving 49.1% and the Siri formula as giving 51.8% for me! Since "morbidly obese" is 35% or higher, those formulas might suggest that I probably don't fit through doorways! (Have you ever seen a winning beach volleyball player who was spectacularly obese?) It seemed obvious that those simple and crude formulas are sometimes very inaccurate! By the way, on the BMI Chart (height/weight) I am at 26, surprisingly close to what seems actually true! However, there is a reasonable explanation! When I really exhale ALL the air I can, I can avoid floating with the 'float' float and 'N' Baton. This means a measured body density of 1.0009. Our website bodyfat calculator gives a value of 26.6%, again in rough agreement with BMI and the other figure. With the adjustment for the Residual Volume of air in the lungs, the adjusted body density is 1.0139. This would give a Siri 2compartment bodyfat value of 36.5%. This is closer but still apparently about 10% higher than we think it really is.
Careful scientific study has been done on such formulas, and it has been found that the Siri 2compartment formula gives results that have a 95% confidence interval ranged from ±8.1% to ±12.0% bodyfat percentage, for different ages and genders studied, as compared to methods that are considered to give reliable results. So even though the Hydrostatic Weighing procedure provides excellent accuracy regarding the Average Body Density, these formulas for converting that to bodyfat percentages can have huge errors! And if the 95% confidence is sometimes off by 12.0%, that means that there are times when it is even worse than that!
When we discovered the large probable errors of such formulas, we developed a complex equation that is based on considering and analyzing each of the many different types of things that are inside our bodies (bone, blood, muscle, fat, organs, brain, skin, etc) and the quantities of each inside us. We feel that our very complex equations (about twenty factors, each of which has a density value and a volume value, or 40 total variables) are far more scientifically based than the popular formulas presented above. However, our bodyfat numbers tend to be less than the Brozek or Siri numbers seem to imply. We are still investigating this matter. Our website bodyfat calculator (linked below) uses our complex formula.
The main concept of our system is to know INCREMENTAL changes in average body density, which our approach certainly does to better than one part in a thousand. We didn't necessarily intend to generate truly precise NUMBERS claiming a specific bodyfat percentage. Once an average body density is determined, the different formulas (and our equations) give different numbers for bodyfat percentage, true. But again, what WE see as important is whether that number goes up or down, and not necessarily the size of that number! See the point? So you really could use the Brozek or Siri formulas with our system, and still see changes, good or bad, just that the numbers will be a lot higher.
As to being able to brag about some specific number as being YOUR bodyfat percentage, our research suggests that nearly any number you might claim has a high likelihood of being substantially incorrect. But we suppose that if it is a number that you LIKE, you will probably want to tell people what it is!
We expect to some day modify our equations, as better figures for organ densities and bone densities, etc, become available. This might especially be true for kids, who tend to have a higher proportion of dense bones! Well, we concede that SOME people will insist on using one or the other of those two popular formulas above, so we are providing (below) analysis charts which use those formulas. You are free to use any of the three, as they will all show improvements or backsliding equally well! Just stay with whichever one you start with!
They are also available as Word (DOC) files which can be printed out
and laminated to be around a swimming pool!:
For body weights of up to 130 pounds
For body weights of between 130 and 230 pounds
For body weights of between 230 and 330 pounds
For body weights of between 330 and 430 pounds
The Analysis Charts based on the Siri formula are:
For body weights of up to 130 pounds
For body weights of between 130 and 230 pounds
For body weights of between 230 and 330 pounds
For body weights of between 330 and 430 pounds
The (blank) Progress Chart is at:
Weekly or Monthly Progress Chart
There is another issue to mention. The Analysis Charts were created using certain assumptions regarding the proportion of different kinds of component materials in the human body, and also assumptions regarding the densities of those component materials. It turns out that some people, such as AfricanAmericans, generally have bones that are of higher density than in others. There are also different proportions of body components in different people, such as bigboned or petite body types. These things can cause a shift in the numbers found in the Analysis Charts. For example, many AfricanAmerican males might normally sink in a pool, due to their highdensity bones. Some kids tend to naturally sink too! That does NOT necessarily mean that they are "professional athletes" as the very low Chart percentages might seem to suggest! They just have different internal body structures from most people. Therefore, the Analysis Charts could possibly provide numbers that are actually lower than their actual bodyfat percentage.
However, for the purposes of this testing, that effect is essentially unimportant! The person will always have the SAME highdensity bones! Therefore, if the following week, a slightly lighter baton is needed (still with the float baton) progress is still shown in a Progress Chart. The actual numbers might be lower than what is real, but any improvements or other changes will still be clearly seen.
For body weights of up to 130 pounds
For body weights of between 130 and 230 pounds
For body weights of between 230 and 330 pounds
For body weights of between 330 and 430 pounds
These values are true and accurate, without any mathematical assumptions regarding proportions of fat, bone, blood, etc, and without any assumptions regarding the precise density of those components. Technically, these values are all that are really needed for this system! However, the general public is less interested in claiming an average body density of 1.0074 gm/cc than in simply claiming a bodyfat percentage! Technically, these charts show WHY this system works and why it is so precise, although we realize that most people will never want to use them!
These density charts, and the other Analysis Charts, were calculated assuming that the the pool water was at around 72°F and therefore had a density of 0.9978 gm/cc. If the pool water was cooled to 39°F, its density would be the 1.00000 gm/cc that books indicate. We note that public pools are nearly always within a few degrees of the same temperature, but even backyard pools rarely change by even 10°F. It turns out that when you DO do the calculations, the difference between doing this in a 70°F pool and an 80°F pool, is less than one part in a thousand. Yes, that might cause the "one part in a thousand density difference" that we described above, but that tiny amount is usually only equal to about one Baton letter difference. And that's for a very cool pool compared to a bathwater pool! NOT a factor!
Have a "normal" amount of air in your lungs, NOT having severely exhaled or inhaled. And then simply float stationary! Your friend sees (or maybe even measures) how much of your head sticks out of the water! If you do NOT float and sink toward the bottom, your bodyfat is likely to be around 13% or lower. If your friend sees TWO INCHES of the top of your head above the water, you are likely to be around 24%. If your friend sees about FOUR INCHES (essentially to the very top of the earlobes), you are likely to be around 40%. If around SIX INCHES (essentially to the earholes, and your eyes are above the water) then you are likely to be around 57%. You might see from the large changes in bodyfat numbers due to rather small differences in the amount of the head being visible, that this method is only very approximate, with plusminus 10% being expected. It only provides a ballpark number!
We mention this because there are a LOT of people who have been told that they have 8% or 4% or 11% bodyfat, due to using the extremely inaccurate bodyfat caliper method or electrical impedance (methods absolutely proven to regularly be 15% off either way, so in other words, meaningless except for bragging purposes.) A person could try to alter this method by intentionally normally exhaling first, which makes you float around one inch lower, which would appear to give an estimate of around 6% lower. By attempting to exhale all the air you can, you can lower your body by about 3 inches, which can give the appearance of around 16% lower estimate. The point is that by simply altering the amount of air in your lungs, you could change this reading by as much as 16%, another indication of why the far more accurate and repeatable Batons and Floats are desirable. If you really want to believe that you are at 8% or 11% so you can brag to your friends, there are many ways you can create such a number. However, if you actually want a REAL number for bodyfat, this very crude method can get you within about plusminus 10%, and the BatonsFloats can get you within about 1%.
The page that has the Bodyfat Percentage  Determining Accurate Bodyfat Easily Bodyfat Calculator which uses the Baton/Float letters and the dry body weight can calculate the correct density and bodyfat values for essentially anyone between 30 pounds and 800 pounds and with essentially any percentage of bodyfat.
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