Bloody Traces: Criminal Physics
The forensic scientist looking for traces of a possible crime must reckon with the fact that this task is often difficult. Attackers tend to get rid of evidence, but even without it, blood is clearly not visible on any surface. In addition, traces of blood can change color over time - right down to greenish. In difficult cases, the rich arsenal of modern science comes to the rescue. The main sign of blood is the presence of hemoglobin or its derivatives in the test material. Their search is carried out by spectroscopic and luminescent methods, chromatography and electrophoresis. A serious difficulty is that any method allows you to confidently ascertain the presence of blood, but you can’t guarantee its absence, even having tested the entire arsenal on a controversial sample. In such a situation, the expert only concludes that no blood was detected. Remember, Sherlock Holmes used to say that traces of gunpowder are evidence, but their absence is not. This principle is applied quite widely in forensics.
If we are talking about examining a suspect, then priority is traditionally given to the nails and what is under them. Parts of clothes that are difficult to completely clean often promise a positive result: seams, pockets and flap pockets, button loops, fastener on trousers, buttons, cuffs, etc. On shoes, these are seams, rings, buckles and laces. As they say in textbooks, "attempts to clean clothes from traces of blood rarely lead to complete success."
The next step is to determine the species of blood: is it human? After making sure that the affected party was not a chicken or a pig, the examination can further determine the blood type, gender, and also whether the blood belongs to an adult or a newborn and whether it is menstrual.
Modern molecular biology based on the study of DNA and other blood characteristics allows you to draw a generalized portrait of the "owner". You can determine race and nationality, judge the color of eyes and hair, health, etc. More recently, a method for determining age from one drop of blood has been proposed - although so far, with an accuracy of up to ten years. But there are still many unresolved problems. So, there is still no way to conclusively determine the age of blood traces. Another problem solved with a large error is determining the height of the drop of blood drop.
Since the time of Holmes, forensic scientists have developed many approaches to the classification and analysis of blood puddles, drops, drips, splashes and other marks. Comparing the amount of blood in a puddle under the corpse with the nature of the injuries, one can fairly accurately say whether the victim has been in this place since the moment of injury. By the shape of the puddle and the nature of blood coagulation, one can judge where the source of the bleeding was. From the drops that fell on the floor, much can be said about the intensity of the bleeding, the location of the victim and whether she stood still: if the wounded man moved relatively quickly, then the spots from the fallen drops will have a characteristic shape, called a “bear paw” in the textbooks.
If blood does not drip vertically, then the angle of incidence to the surface can be determined by lengthening the track. The sine of the angle between the drop and the surface is equal to the ratio of the transverse and longitudinal sizes of the wake.
If several traces of drops are found at the crime scene, the work of the forensic scientist is greatly facilitated. The intersection of the directions of the elongation of the drops will indicate the projection of the drop's starting point on the horizontal plane, that is, it will make it possible to determine the position of the vertical axis passing through the point of departure. But not the height of this point.
It is known from the school physics course that without data on the initial velocity of the body it is impossible to establish the exact trajectory of its movement. Perhaps an infinite number of trajectories leading to a meeting with a horizontal surface at the same angle. This means that to determine the height it is necessary to attract additional data - to analyze the drop trail. Its shape depends on the speed at the time of "landing", and therefore on the height of the fall. The more the shape of the track differs from the circle, the more blood is sprayed, the greater the speed (and height). The matter is further complicated by the fact that the shape of the track depends on the surface: on tile, cardboard and asphalt, the tracks will look different. The criterion of truth is practice: for a reliable assessment, you need blood, the same surface and a series of experiments with different heights of fall, one of which should give us exactly the same trace. No need to explain that this approach is rather inconvenient. In addition, it is applicable to free fall - but a drop can fly out of the wound with a non-zero initial velocity.
Meanwhile, the question of height is sometimes extremely important. So, when considering situations related to self-defense, a lot depends on whether the victim was sitting or standing: a seated person is less dangerous.
Physicists - Experts
Physicists Christopher Vorney and Fred Gittes from Washington University, people who are far from detective problems, tried to solve the problem not so long ago. They managed to do this with "little blood" - without complex instruments, using classical methods of mechanics. Their work, Locating the source of projectile fluid droplets, was published by the famous scientific journal American Journal of Physics.
It turned out that it is possible to determine the height of the point of departure of blood drops based on a study of the statistics of the dispersion of their traces - under the assumption that different drops escaped from the wound at approximately the same angle. The spread of departure angles should be small. It must be said that in forensic practice this condition is not often fulfilled.
The authors of the study initially modeled the situation using mathematical methods and came to the conclusion that reliable estimates of the height are possible if the distance from the source of the droplets to the point of incidence of each of them is proportional to the tangent of the angle of incidence. We will not bore readers with formulas, we only note that sensation did not happen: the conclusion follows from Newton's laws in the case of uniformly accelerated motion, more specifically, in the field of gravity. It is important that, in order for the tangent (in fact, the angle of incidence itself) and the flight range to be related by this rule, the drops should shoot in approximately the same direction. If not, then the linear dependence on the graph will not work. Its points will be located randomly, and in this case the authors method cannot be used.
To test the method, American physicists built a “device” similar to the device used in the training of forensic scientists. It was a vessel with a viscous liquid, which was placed between two collapsing boards. By placing the boards in different planes, it was possible to change the direction of the droplets and the dispersion of their velocities. Instead of blood, scientists used an equivalent viscosity mixture of chicken wings sauce and dishwashing liquid.
By changing the various parameters of the experiment, they were able to comprehensively study the phenomenon and collect statistics. Drops incident on inclined and vertical planes were also considered. All angles of incidence, determined by the shape of the frozen drops, through trigonometric transformations are simply converted into meeting angles relative to the horizon, appearing in theoretical formulas and graphs.
The experimental results confirmed theoretical assumptions. The authors illustrated this with a pair of graphs, comparing them with the results of applying forensic methods. Where the tangent of the angle of incidence linearly depended on the distance, determining the height from the shape of the tracks gave acceptable results. Where the points did not lie on a straight line, the method did not work. But according to him, court decisions are made!
It turned out that a fairly simple kinematic approach works very reliably. Physicists were surprised by the fact that air resistance did not affect the position of the experimental points on the graphs.
Therefore, it was decided to evaluate the effect of air resistance on droplet flight and to calculate nonlinear equations of motion taking into account friction against air. The calculations confirmed the insignificance of the resistance force to determine the departure heights. Friction introduced distortions only at the very beginning of the line on the graph and slightly shifted it upwards, which was not reflected on the slope of the line. Note that Galileo in the experiments also neglected the influence of air resistance on the fall of bodies.
Drops in the sea
For criminologists, the presence of a linear dependence on the graph also serves as a simple and reliable criterion for the applicability of the method. If, after analyzing the traces of a few drops, linearity is not detected, the method cannot be used. But if nothing was found at the crime scene, except for traces of blood, on the basis of this criterion we can judge the reasons for its occurrence and the likelihood of the fact of the crime.
I must say that the forensic community took the study without much enthusiasm. The reasons are clear: the methods adopted in forensic science have a long history, are well developed and, of course, take into account more details. Whether the statistics of two Washington physicists will find a place among the proven methods, time will tell. The requirements for evidence in court are strict and conservative.
Finally, we note that the results of the study are applicable to any liquid that forms drops. At the end of the work, it was modestly indicated that the method may be needed in many cases, in particular when studying volcanic activity and the expansion of lava drops. Other applications are possible: metallurgy, chemical production, painting, military research.