Can One Cup of Alcoholic Coffee Keep You Out of DUI? A Widmark Formula Analysis

Widmark Formula

The Widmark formula estimates blood alcohol concentration (BAC) based on the amount of alcohol consumed, body weight, gender-specific distribution ratio, and elimination rate.

C = BAC (g/dL)

A = total alcohol ingested (g)

r = alcohol distribution ratio (0.68 for men, 0.55 for women)

W = body weight (kg)

β = elimination rate (typically 0.010–0.015 g/dL per hour)

t = time since drinking began (hours)

When Can You Drive Safely

In China, a BAC below 0.02 g/dL is not considered drink‑driving. Using a 388 ml coffee with an assumed alcohol content, we calculate the initial BAC and the time required to drop below 0.02 g/dL for different body weights and genders.

<code>import numpy as np
import matplotlib.pyplot as plt
plt.rcParams['font.family'] = ['SimHei']
plt.rcParams['axes.unicode_minus'] = False
# Parameters
weights = [50, 60, 70, 80]
r_male = 0.68
r_female = 0.55
A = 1.9725  # total alcohol (g)
beta = 0.015
C_target = 0.02
A_new = 388 * 0.005 * 0.789
time_to_target_new_male = [(A_new/(r_male*weight)-C_target)/beta for weight in weights]
time_to_target_new_female = [(A_new/(r_female*weight)-C_target)/beta for weight in weights]

def alcohol_concentration(t, A, r, W, beta):
    return A/(r*W) - beta*t

time_points = np.linspace(0, max(max(time_to_target_new_male), max(time_to_target_new_female))+2, 500)
for i, weight in enumerate(weights):
    plt.plot(time_points, alcohol_concentration(time_points, A_new, r_male, weight, beta), label=f'Male {weight}kg')
    plt.plot(time_points, alcohol_concentration(time_points, A_new, r_female, weight, beta), '--', label=f'Female {weight}kg')
plt.axhline(y=0.02, color='r', linestyle='--', label='Legal limit 0.02g/dL')
plt.xlabel('Time (hours)')
plt.ylabel('BAC (g/dL)')
plt.title('BAC Over Time')
plt.legend(loc='upper right')
plt.grid(True)
plt.show()
</code>

The graph shows that all subjects exceed 0.02 g/dL immediately after drinking. An 80 kg man drops below the limit in about 0.5 hour, while a 50 kg woman needs roughly 2.4 hours.

If Alcohol Concentration Is Not That High

We also model scenarios with lower beverage alcohol percentages (0.1%–0.5%) for a 60 kg male and female.

<code># Define parameters for the specific scenario
weight = 60  # kg
alcohol_concentrations = [0.1, 0.2, 0.3, 0.4, 0.5]  # percentages
max_time = 10  # hours
time_points = np.linspace(0, max_time, 500)
for concentration in alcohol_concentrations:
    A_current = 388 * (concentration/100) * 0.789
    plt.plot(time_points, alcohol_concentration(time_points, A_current, r_male, weight, beta), label=f'{concentration}%')
plt.axhline(y=0.02, color='r', linestyle='--', label='Legal limit 0.02g/dL')
plt.xlabel('Time (hours)')
plt.ylabel('BAC (g/dL)')
plt.title('Male (60kg) – BAC Over Time')
plt.legend(loc='upper right')
plt.grid(True)
plt.show()
# Female plot (similar loop omitted for brevity)
</code>

The results show that higher initial alcohol percentages lead to higher peak BAC and longer elimination times. Concentrations below 0.2% generally stay under the legal limit, but caution is still advised.

How Many Sips?

We provide tables indicating how many 15–30 ml sips of the coffee would raise BAC to the legal limit for different body weights and genders.

Male version (sips needed to reach ≥0.02 g/dL): 50 kg – 9 sips of 20 ml; 60 kg – 10 sips of 20 ml; 70 kg – 12 sips of 20 ml; 80 kg – 14 sips of 20 ml.

Female version (sips needed to reach ≥0.02 g/dL): 50 kg – 7 sips of 20 ml; 60 kg – 8 sips of 20 ml; 70 kg – 10 sips of 20 ml; 80 kg – 11 sips of 20 ml.

Yesterday various media performed breath tests; most showed zero alcohol. Subsequent tests by police in several cities sometimes detected low levels, confirming that even small amounts can be measurable.