# Blood Loss After Severing an Artery (CAREFUL: GRAPHIC CONTENT)

Recently I’ve been going through stabbing videos from Kaotic and I found an excellent example that allows an estimation of the rate of blood loss after an artery has been cut. The video shows an altercation in the open-dining area of a bar. A middle-aged man approaches and antagonizes a young man, who can be seen sitting at a table. The young man gets up, draws a knife and stabs the middle-aged man. One of the stabs hits an artery and blood can be seen pouring out. In some frames one can even see the parabolic trajectory of the massive blood stream, which can be used to estimate the flow speed and volume flux.

The initial path of the trajectory seems to be about alpha = 20° down, hitting the floor at a distance of roughly one and a half feet lengths, so about d = 0.45 m. This translates to an ejection speed of v = 0.9 m/s = 90 cm/s. Given that an artery has a cross-section of around A = 3 cm², the volume flux should be Q = 270 cm³/s = 16 Liter/Min = 0.25 Liter/s. Note that since blood pressure decreases as blood is lost, we should expect that ejection speed to decrease as well. So instead of a linear model (constant loss of 0.25 L/s) one should favor an exponential model (constant loss of 5 %/s). Given that we begin at 5 L of blood, which was also used to calculate the aforementioned percentage, we get the following formula for the remaining blood in the body after t seconds:

V = 5*0.95^t

Roughly speaking, people enter a state of limited motor function after 30 % of blood is lost (1.5 L lost or V = 3.5 L) and collapse once 40 % of blood is lost (2 L lost or V = 3 L). So after an artery has been severed, we should expect the two events to occur after the following time span:

• Limited Motor Function: 7 s
• Collapse: 10 s

This calculated blood loss and the predictions made from it seem to agree quite well with what can be seen in the video. The severing of the artery occurs at the time stamp 1:18. The victim starts to make disoriented / wobbly motions at around 1:26, so 8 seconds after the stabbing. He collapses at 1:30, which is 12 seconds after the stabbing. Any signs of life end very soon after that. From the calculations and the video it’s easy to see why severing of arteries has a near 100 % mortality even in the best of circumstances.

Here are some key moments of the fatal altercation: