How to Calculate the Angle of Impact

How to Calculate the Angle of Impact
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The angle of impact is a mechanics concept that defines the acute angle formed by the plane tangent to the ground surface and the tangent to the trajectory. These two are defined in terms of the point of impact of a projectile. In other words, the angle of impact represents the angle formed with the horizontal axis by an object hitting a plain surface. One very useful application is in bloodstain pattern analysis, where the angle of impact has to be computed for each blood spatter.

General Analysis

    Write down the vertical motion equation, “y(t) = v0 * t – 1/2 * g * t^2” , which will be very useful for this process. y(t) is the measure of how far the object is away from impact. t denotes the time between the moment when the object is being thrown and the actual impact. g is the gravitational acceleration. v0 is the initial velocity, or the velocity at which the object is thrown.

    Use the equation in the previous step at the moment of impact, i.e. when y(t) = 0. For example, if an object is thrown with a speed of 18 m /s, from a height of 50 m, you would obtain t = 3.193 seconds after applying 18 * t – 1 / 2 * 9.81 * t^2 = 0.

    Compute the vertical speed of the object at the moment of landing using the conservation of energy law, i.e. (1/2) Vf^2 = V0^2 / 2 + g * h, where Vf and V0 represent the final and initial speed, respectively, h denotes the height and g the gravitational acceleration. In this example you will obtain Vf = 31.3 m / s after using 18 m/s for V0, 9.81 m/s^2 for g and 50m for h.

    Compute the angle of impact, knowing that it is equal to atan(Vf / V0). The example above produces a value of atan(31.3 / 18) = 60.1 degrees.

Blood Spatter Analysis

    Locate the spatter. It should be in the shape of an ellipse. An oval shape with one diameter that is longer than the other. These two diameters are known as the major and minor axes.

    Use a rule to measure the length of the major axis and minor axis of the ellipse. The major axis is the longest length of the ellipse. The minor axis is the shortest length, or width, of the ellipse.

    Calculate the angle of impact with the following equation: "i = asin (w/l)." Replace "w" with the length of the minor axis and "l" with the length of the major axis. "Asin" is the arcsin or inverse sine function and is available on most calculators. If the calculator is programmed in degrees, the angle of impact is produced in degrees. If the calculator is programmed in radians, the angle of impact is produced in radians.