Predicting the position of the source of blood stains for angled impacts

Droplets of pig's blood were dropped onto paper at different angles to the horizontal to produce blood stains. Impact velocities varied from 1.82 to 5.76 m/sec, drop size from 3.7 to 5.0 mm in diameter, and the surface sloped at angles between 22.7 degrees and 90 degrees to the horizontal. From the data a single equation relating stain size to drop size and velocity for all impact angles was produced; ab = 111.74 (Re(1/2)We(1/4))(0.75)D(o)D(o) + 0.00084 with R(2) = 0.88, where a is the stain width, b the stain length, Re the Reynolds number, and We the Weber number. A second equation related the number of spines, N, to drop size, velocity, and surface slope for all impact angles as N = 0.76 We(0.5) sin(3)theta with R(2) = 0.9, where theta is the impact angle. Combining these equations the impact velocity can be determined and hence the position of the stain's source.