Fast Eddie's 8/10 Method of Hand Calculating Blood Alcohol Concentration
California Drunk or Impaired DUI Law for the Public
Fast Eddie's 8/10 Method of Hand Calculating Blood Alcohol Concentration
A Simple Method For Using Widmark's Formula
by Ed Kuwatch, Esq. - deceased
Attorneys with clients accused of drunk driving often are dismayed about Widmark's formula See footnote 1 and don't understand why they should know how to calculate Blood Alcohol Concentrations (BAC's). If you're not interested in using your client's drink history information for the purpose of presenting BAC evidence, you will be interested in doing that the first time the prosecutor's expert witness uses such evidence to call your client a liar.
Typical prosecution experts work backwards from the BAC test result to the amount of alcohol consumed. They state that the defendant had a certain number of "drinks" in his body at the time of the sample was taken. Then, after you carefully cross-examine them about the accuracy of such calculations, they hit you on redirect with how many more drinks the defendant had to have in him to account for the time he spent drinking. Then, in his closing argument, the prosecutor contrasts these "true facts" with what your "lying" client said he drank. Then he tells the jury to ignore all of the defendant's testimony, since he's a liar.
The absurd assumptions behind such ludicrous opinions about the amount of alcohol consumed generally rival those of the Grand Inquisitor. For instance, despite general agreement to the contrary, it is frequently assumed that everyone is a 150 pound male. And it's generally assumed that everyone has an alcohol metabolism rate of 0.02% per hour. These "experts" blind their eyes to reality and instead derive their concepts of truth entirely from the Prosecutor's Book of Facts. If you aren't ready to open the jury's eyes to reality they'll take this dogma as gospel, agree that your client's a liar, ignore all of his testimony and send him to his judgment day.
This article explains Widmark's formula in a simple and understandable fashion, then introduces a new 8/10 short-cut method of using the formula.
A Common Sense Look at BAC Calculation
Common sense is the best approach to explaining Blood Alcohol Concentration (BAC) calculation. And common sense, illustrated in the Equation 1, tells you that if a 150 pound person drinks 0.15 pounds of pure alcohol their BODY Alcohol Concentration will be 0.10%. See footnote 2
But BODY Alcohol Concentration and BLOOD Alcohol Concentration are not the same thing. That's because adipose tissue (fat) and bone don't hold alcohol. In other words, the alcohol does not spread throughout the body evenly. Very little of it is distributed to the fat and bone. Almost all of it is dissolved in the water-rich tissues of the body - muscle, blood and organs. And it's dissolved in these water-rich tissues in just about equal concentration.
Therefore, in order to calculate the Blood Alcohol Concentration, we must divide the weight of the alcohol by the weight of only the portion of the body that holds the alcohol, rather than the weight of the whole body. Widmark's original research, still valid today, found that the average man's body can hold alcohol in even distribution in 68% of its weight. In other words, 68% of a 150 pound man's body holds all the alcohol he consumes, in even distribution. 68% of 150 pounds is 102 pounds (see Equation 2).
Widmark called this "0.68" factor his Widmark `r' factor. See footnote 3 It varies from person to person, but research has shown that among normal men the range of values is 0.50 to 0.90, with an average value of 0.68. For normal women the range of values is 0.45 to 0.63, with an average value of 0.55. See footnote 4 Variations between men and women are due to difference in body fat and the recently discovered differences in the quantity of alcohol metabolizing enzymes in the gastro-intestinal tract. See footnote 5
In our previous example we showed that a 150 pound person who drinks 0.15 pounds of pure alcohol would have a total BODY Alcohol Concentration of 0.10%. But since the 0.15 pounds of alcohol is only dissolved in 102 pounds of water-rich tissue, rather than 150 pounds, that water-rich tissue, including the blood, would have an alcohol concentration of 0.147%. (See Equation 3.)
Equation 4 sums up Widmark's formula so far for this 150 pound man with an `r' factor of 0.68 who drinks 0.15 pounds of pure alcohol.
But since it's a little hard to weigh the alcohol we'll just calculate its volume from the weight. Begin by figuring out the volume consumed: multiply the total number of ounces of beverage times the beverage's alcohol content. For instance, a 12 fluid ounce beer with 3.5% alcohol would be 0.42 fluid ounce of pure alcohol. A 1.25 fluid ounce glass of 80 proof liquor would be 0.50 fluid ounces of pure alcohol. See footnote 6 And let's use "EtOH" (for "ethyl alcohol") from now on to stand for "pure alcohol".
Each fluid ounce of EtOH weighs 0.0514 pounds. After we know the total number of fluid ounces of EtOH consumed we can calculate its weight. Just multiply the total number of fluid ounces of EtOH times the number of pounds per ounce. Equation 5 shows how to calculate the number of pounds of EtOH in six, 1.25 fluid ounce shots of 80 proof liquor.
Equation 6 shows what Widmark's formula looks like as of this point. Up until 1987 this was scientifically accepted by most of experts as correct. But that year Fitzgerald & Hume See footnote 7 pointed out that the specific gravity of blood (1.055 g/ml) must be included in the denominator. Adding that factor, Equation 7 shows Widmark's formula in full, for our sample facts here.
Equation 8 shows the full formula in general terms.
But we're not quite done yet. This formula doesn't take drinking time into consideration. Widmark called the hourly decrease in BAC his Widmark ▀ (beta) Factor. See footnote 8 It's widely agreed now that normal humans metabolize, or burn off, EtOH at a rate of 0.010% to 0.024% per hour, with an average ▀ factor of 0.017% per hour. See footnote 9 To figure the total amount of alcohol metabolism simply multiply the hourly rate (the ▀ factor) by the number of hours.
Subtract this metabolized EtOH from the total BAC to get a BAC which accounts for drinking time. In our example, let's say the client had a ▀ factor of 0.017% per hour and drank his six shots of liquor in 2 hours. His total metabolism, stated in terms of the decrease in his BAC, would be 2 times 0.017%, which equal 0.034% BAC, lost due to metabolism. Equation 9 shows Widmark's formula, with drinking time accounted for, for our example. Equation 10 shows the general Widmark formula, with drinking time accounted for.
The 8/10 Method of BAC Calculation
For an easier-to-use formula that's almost as accurate as that in Equation 10, just do all the multiplication and division of the numbers that don't change. For a man, with a Widmark `r' of 0.68, just multiply 0.0514 times 100 times 1.055, then divide the result by 0.68. If you get 7.97 you did it right. Now round this off to 8 and put it in the equation in place of all the other numbers. For a woman, with an average Widmark `r' of 0.55, the result is 9.86. Round it off to 10. (See Equation 11.)
Now all you have to do is figure the total fluid ounces of EtOH consumed (fluid ounces of beverage times its percent alcohol), multiply that amount by 8 or 10, then divide the result by the person's body weight in pounds, then subtract from that the total metabolism (hours since first drink times ▀ factor) and you have a BAC calculation that's only an insignificant four tenths of a percent less that the BAC result that Widmark's formula would give (1.4% off for a woman).
For example, our 150 pound man, with a ▀ factor of 0.017% per hour, drank 6 shots of 80 proof liquor in two hours. Equation 12 shows the 0.126% BAC result, compared to the 0.125% result in the long version of Widmark's formula
Showing That Your Client Is Not a Liar
Now it's easy to restate the formula so that it tells us how to calculate the amount of alcohol consumed when we already know the BAC. With a little algebra we get the formula in Equation 13. You can see that when the prosecution's "expert" assumes that everyone is a 150 pound male, with a 0.02% ▀ factor, and that all drinks are the same size, that person is making assumptions about many facts that are extremely important to the result. If you don't believe it, try substituting the facts you know about your client into Equation 13.
Play around with the formula in Equation 10 or Equation 11 a bit, using values for the Widmark ▀ and r factors within the range for normal people. You'll see that it's easy to make the BAC come out anywhere within a wide range of values at the time the blood, breath or urine sample was taken. The important thing is that there is nearly always some range of values of ▀ and r, within the range of those values for normal people See footnote 10, that produces a range of calculated BAC's below the legal limit. Then you can explain how defects in chemical testing can produce high chemical test results even though the defendant's BAC was below the limit. Suddenly you have a "story" for the jury that fits everything together - your client drank what he said he drank, his BAC was below the legal limit, and the prosecution's test result is erroneous. One thing's for sure, if you don't successfully make all these points somehow, you're gonna' lose.
The EZ-ALCTM Blood Alcohol Chart Software Program
In 1987 the author developed the EZ-ALCTM Blood Alcohol Chart Software Program. This software runs on IBM and compatible computers and produces calculated BAC charts for courtroom use. The 8/10 method is certainly much simpler than any previously described method of calculating BAC's. But if you have an IBM compatible computer, EZ-ALC is ideal for obtaining calculations of the various ranges of BAC's at the time of driving, arrest and chemical test. In addition the program has the ability to calculate the alcohol in the body based upon a given BAC. It's available from the author's Fast Eddie Publishing Company. You can download a shareware version of EZ-ALC by clicking here.
Whichever method you select to calculate BAC or alcohol consumption, either the long formula, the 8/10 method, or EZ-ALC, you'll find this sort of evidence indispensable in presenting a coherent, well prepared defense.
Footnote: 1 See Principles and Applications of Medicolegal Alcohol Determination (Littleton, Mass: PSG Publishing Co., 1981)
Footnote: 2 Since the percent sign (%) is more commonly recognized among non-scientists as the appropriate label to accompany Blood Alcohol Concentration (BAC) figures, it is used in the text here in order to avoid confusion. Most laboratories and legislatures use confusing terms such as "%w/v" (percent weight per unit volume), or "wt %" (weight percent). Scientists most commonly accept "g/dL" (grams per deciliter) as the proper label.
Connecticut is one state, perhaps the only one, that uses a true % when measuring and expressing BAC. In that state analysts actually weigh out one gram of blood and then measure the alcohol in it. Thus, Connecticut expresses the BAC result as "%w/w" (percent weight of alcohol per unit weight of blood). The Widmark formulas set forth in this article can be used in Connecticut and other states using %w/w, but remove from the equation the 1.055 g/ml factor related to the specific gravity of blood, and change the label to "%w/w", or just plain "%". If you are using the 8/10 method, use 7.6/9.5 instead, for a %w/w result.
In the formulas which accompany this article, BAC is first expressed as "g%/ml" (grams percent per milliliter), since that is the only label left after the others in the numerator and denominator cancel each other out. Then the results are shown as "g/dL" (grams per deciliter), along with the more common "%w/v" (percent weight per unit volume).
The author thanks Randall C. Baselt, Ph.D., DABFT, for his comments on these points.
Footnote: 3 Widmark was Swedish and the original work was written in German. The lower-case "r" stands for "reduced body mass", or "reduzierte k÷rpermasse".
Also note that it's not exactly correct to say that this factor represents the weight of the body to which alcohol is evenly distributed. But it's very close to that, and it works well for our purposes here.
Footnote: 4 ref 1, p.70
Footnote: 5 M. Frezza, C. di Padova, G. Pozzatio et al., High blood alcohol levels in women, New Engl. J. Med. 322:95-99, 1990.
Footnote: 6 Divide proof by two to get percent alcohol. For instance, 80 proof is 40%.
Footnote: 7 Intoxication Test Evidence 2d ed. (Deerfield, IL: Clark-Boardman-Callaghan), for information on EZ-ALC (TM), see: "Use of the EZ-ALC Computer Program by Attorneys and Experts"., Chap. 12.
Footnote: 8 Widmark used [ ] (alpha) to represent the rate constant (decrease in concentration per unit of time) for the vast majority of drugs and chemicals whose elimination is dependent on concentration. It was therefore logical for him to use ▀ (beta) to represent the rate constant for those few substances, such as EtOH and methanol, whose elimination is independent of concentration.
Footnote: 9 R.P. Shumete, R.F. Crowther and M. Zarafshan, A study of the metabolism rates of alcohol in the human body, J. For. Med. 14:83-100, 1967.
Footnote: 10 Widmark r: Men: 0.50 to 0.90, average 0.68. Women: 0.45 to 0.63, average 0.55. Widmark ▀: 0.010%/hr to 0.024%/hr, average 0.17%/hr.
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