Alcohol and Driving. The exact amount of alcohol intake to be legally sober.

Introduction

You just left the pub. You are now sitting in the car, wondering how much you drank...

“Oh, god, I forgot I was going to drive. Have I drank too much? Probably not, right? I only had two beer pints, I feel just fine. Uhh. My uncle said that police is more strict with younger people. Shoot. How strict can they be. Even if I drank more, there’s been some time. It’ll be okay, right? Plus, some additional time will pass until police stops me. It will be okay. It will be okay. I’ll go, I guess. I don’t really have a choice... How can I dodge the police? What roads are the safest? If I drive really slowly, they won’t stop me, right? Let’s pray and hope for the best...”

We ALL had these thoughts. The sight of blue lights often sends our hearts racing, and none of us want to be the designated driver on a night-out. We all found ourselves questioning our own sobriety. We all debated with others if we're legally fit to drive. Let's put that debate to rest.

This article aims to clarify, once and for all, the exact amount of alcohol intake, for which someone could not be penalized by law enforcement. By exploring that, the article aims to help readers make informed decisions about responsible alcohol consumption and driving practices. The overall goal is to provide clarity and guidance on this topic, with the hope of promoting greater confidence and safety on the roads.

It is important to clarify that the intention of the article is not to encourage people to break the law and drive under the influence of alcohol. Rather, the purpose is to provide a guidance system for individuals to understand the legal limits of alcohol consumption and the amount of alcohol intake that may lead to impairment.

Blood Alcohol Concentration

Driving under the influence of alcohol is a serious offense that can lead to serious consequences, such as fines, license suspension, and even criminal charges. The exact amount of alcohol intake required to be considered illegally drunk varies depending on the country's laws and the circumstances.

The blood alcohol concentration (BAC) is the most common benchmark used to demonstrate the amount of alcohol in someone's system. BAC is a measurement of the amount of alcohol in a person's bloodstream, expressed as a percentage. It is calculated as mass (grams) of alcohol per volume (100 milliliters) of blood. For example, a BAC of 0.08% means that for every 100ml of blood, 0.08g of alcohol are present [1].

In the majority of countries, the legal limit for BAC is 0.08%, which means that a person is considered to be illegally drunk, if their BAC exceeds this limit. The legal limit may vary depending on the type of license held by the driver. For example, commercial drivers and drivers under the age of 21 may have lower legal BAC limits [1][4].

Widmark’s Formula

In order to be able to calculate BAC, many formulas and algorithms have been utilized over-the-years. However, one of those formulas prevailed, and it is still the most widely used today, the Widmark’s formula.

The Widmark’s formula was invented by a Swedish researcher named -guess what- Erik Widmark. Erik was a pioneer in researching alcohol in the body. He studied how after consumption, alcohol is absorbed, distributed, and eliminated. He also studied the various factors that affect the level of alcohol in the body. Erik’s work remains extremely influential in forensic alcohol analysis even today [2].

Widmark’s General Formula:  $\mathrm{BAC}=\frac{m\times 100}{M\times r}-\beta t$ where:

• m is the mass of alcohol consumed (in kilos)
• M is the body weight (in kilos)
• r is the ratio of body water to total weight. It varies between individuals, but averages about 0.68 for men and 0.55 for women, since women tend to have a higher percentage of fat.
• β is the alcohol elimination rate, the fraction of alcohol eliminated from the body per unit of time. More than 90% of alcohol is eliminated by the liver and the rest is excreted unchanged in urine, sweat, or breath. Females demonstrate a higher average rate of elimination (mean, 0.017) than males (mean, 0.015).
• t is the elapsed time since alcohol consumption (in hours), or more accurately, the amount of time during which alcohol was present in the blood [2].

While Widmark's formula is considered one of the most reliable methods for estimating BAC, it's important to note that it does not account for a number of variables that can affect the levels of BAC. These variables include food intake, current and past medications, other substances in the body, genetics, liver and kidney function, water content (body mass measured instead) and not-so-recent alcohol consumption. Additionally, the accuracy of Widmark's formula may be altered by differences in the rate of alcohol absorption and elimination between individuals, as well as errors in measuring the amount of alcohol consumed. Thus, you should be careful when using the Widmark's formula, as it provides only an estimation of the BAC [2].

Cases

Before we move on to practical examples, we need to establish how to convert the amount of beverage we consumed into the corresponding amount of alcohol in grams. Beverages typically indicate the percentage of alcohol they contain, but this percentage is usually given in milliliters (ml). In order to use Widmark's formula, which calculates BAC based on the amount of alcohol consumed, we must convert the ml of alcohol to grams (g). To do this, we need to take into account the density of alcohol, which is approximately 0.789 g/ml. This means that 1ml of alcohol weighs 0.789g, or conversely, 1g of alcohol equals to 1.27ml of it [1].

Example 1: An 80 kg male drank 2 pints of beer, 2h ago. Is he illegally drank?

A typical pint of beer is around 500ml and 5% alcohol. That means that it contains 5ml of alcohol for every 100ml, and thus it contains 25ml of alcohol. 25ml of alcohol approximately equals to 20g of it.

m=2*20g=40g=0.04kg | M=80kg | r=0.68 | β=0.015 | t=2h

$\mathrm{BAC}=\frac{m\times 100}{M\times r}-\beta t=\frac{0.04\mathrm{kg}\times 100}{80\mathrm{kg}\times 0.68}-0.015\times 2=0.044\%$

In the majority of countries, the legal limit for BAC is 0.08%. Thus, the male is most probably considered legally drank in the majority of countries.

Example 2: A 65kg female drank 1 pint of beer an hour ago. Is she illegally drank?

m=20g=0.02kg | M=65kg | r=0.55 | β=0.017 | t=1h

$\mathrm{BAC}=\frac{m\times 100}{M\times r}-\beta t=\frac{0.02\mathrm{kg}\times 100}{65\mathrm{kg}\times 0.55}-0.017\times 1=0.035\%$

Thus, the female is most probably considered legally drank in the majority of countries.

Example 3: An 70kg male drank 3 shots of vodka an hour ago. Is he illegally drank?

A typical vodka shot is around 50ml and 40% alcohol. That means that it contains 40ml of alcohol for every 100ml and thus it contains 20ml of alcohol. 20ml of alcohol approximately equals to 16g of it.

m=16gx3=48g=0.048kg | M=70kg | r=0.68 | β=0.015 | t=1h

$\mathrm{BAC}=\frac{m\times 100}{M\times r}-\beta t=\frac{0.048\mathrm{kg}\times 100}{70\mathrm{kg}\times 0.68}-0.015\times 1=0.086\%$

Thus, the male is most probably considered illegally drank in the majority of countries.

Example 4: A 70kg female drank 2 shots of vodka 2h ago, and 1 pint of beer an hour ago. Is she illegally drank?

In previous cases, we assumed that the individuals took all the quantities in a very short amount of time surrounding the expressed time. This example is slightly more complex, also more realistic. Usually, we drink a certain beverage over a span of considerable time. We don't drink it immediately. In order to be able to complete this calculation, we have to formulate as many equations as the independent time zones. In this case, two. Then, we shall add the respective BAC, forming the total BAC we need.

2h ago: m=16g*2=32g=0.032kg | M=70kg | r=0.55 | β=0.017 | t=2h

1h ago: m=20g=0.02kg | M=70kg | r=0.55 | β=0.017 | t=1h

${\mathrm{BAC}}_1=\frac{m\times 100}{M\times r}-\beta t=\frac{0.032\mathrm{kg}\times 100}{70\mathrm{kg}\times 0.55}-0.017\times 2=0.049\%$ ${\mathrm{BAC}}_2=\frac{m\times 100}{M\times r}-\beta t=\frac{0.02\mathrm{kg}\times 100}{70\mathrm{kg}\times 0.55}-0.017\times 1=0.034\%$ ${\mathrm{BAC}}_{\text{total}}={\mathrm{BAC}}_1+{\mathrm{BAC}}_2=0.049\%+0.034\%=0.083\%$

Thus, the female is most probably considered illegally drank in the majority of countries.

Breathalyzer Test

Moving on to the essence of this article, which is to provide guidance on whether one is at risk of legal consequences for consuming a set amount of alcohol. Specifically, we want to know if it’s possible to be fined or otherwise penalized, by a patrolling police officer, after consuming a particular amount of beverage.

A breath alcohol test, also known as a breathalyzer test, is the most widely used method by the police to estimate a person's BAC. The test works by analyzing the amount of alcohol present in a person's breath [3].

After the consumption and the absorption of alcohol into the bloodstream, the alcohol infiltrates to almost all body tissues. Some of it is transferred to the lungs and exhaled in the breath. During a breath alcohol test, the individual blows into a device that detects the alcohol in the exhaled breath and displays the results as a BAC level [3].

It's important to note that the accuracy of breathalyzer tests can be affected by various factors, including the calibration of the device, the temperature of the breath, and the presence of other substances in the breath, such as mouthwash or medications. Nevertheless, research has shown that the most accurate breathalyzer devices, when properly calibrated and administered, can provide results that are within +/- 0.01% BAC of a person's actual BAC. This level of accuracy is considered sufficient for most legal and medical purposes. Thus, for all intents and purposes, we may assume that a patrolling officer using a breathalyzer, can detect with almost absolute accuracy, the levels of BAC in our body [3].

Regional Legal Frameworks

As previously mentioned, the exact amount of alcohol intake required to be considered illegally drunk varies depending on the country's laws and circumstances. In this section, a table is displayed that outlines the acceptable limits of BAC for some countries, before a person can be charged with a crime. It's worth noting that the table includes a third row that specifies the acceptable BAC level for younger drivers. While the term "young drivers" can have slightly different definitions across regions, it generally refers to individuals between the ages of 17-25 years old [4][5].

Country	USA	CAN	UK	GER	FRA	AUS	GRC	CYP
BAC limit	0.08	0.08	0.08	0.05	0.05	0.05	0.05	0.05
BAC limit (young drivers)	State	0.08	0.08	0	0.02	0	0.02	0.02

Conclusion

In conclusion, we now have a better understanding of when one can be considered legally or illegally drunk. While some of the presented calculations in this article may have been complex, they were included with the intention of providing fundamental understanding. My overall purpose has always been to make difficult and complicated issues more universally approachable and digestible. I hope I have succeeded in doing so. I also hope this article has helped to clarify the legal limits for alcohol consumption while driving and emphasised the importance of responsible decision-making when it comes to drinking and driving. Remember, the safest approach is always to avoid driving if you have consumed alcohol.

References

1. Blood alcohol content (2023) Wikipedia. Wikimedia Foundation. Available at: https://en.wikipedia.org/wiki/Blood_alcohol_content
2. The Law Office of Denise Kirby. (n.d.). Who is Widmark and What is his Equation? [online] Available at: https://www.denisekirbylaw.com/dwi-faqs/who-is-widmark-and-what-is-his-equation/#:~:text=Widmark.
3. The Law Office of Denise Kirby. (n.d.). I Gave a Breath Test. Now what? [online] Available at: https://www.denisekirbylaw.com/dwi-faqs/i-gave-a-breath-test-now-what/
4. WHO. (n.d.). GHO | By category | Legal BAC limits - by country. [online] Available at: https://apps.who.int/gho/data/view.main.54600.
5. Anon, (n.d.). Drink Driving – All about driving in Cyprus. [online] Available at: https://cyprusdriving.net/drink-driving/