The ill-posed projectile problem of finding the source height from spattereddroplets of viscous fluid is a longstanding obstacle to accident reconstructionand crime scene analysis. It is widely known how to infer the impact angle ofdroplets on a surface from the elongation of their impact profiles. However,the lack of velocity information makes finding the height of the origin fromthe impact position and angle of individual drops not possible. From aggregatestatistics of the spatter and basic equations of projectile motion, weintroduce a reciprocal correlation plot that is effective when the polar launchangle is concentrated in a narrow range. The vertical coordinate depends on theorientation of the spattered surface, and equals the tangent of the impactangle for a level surface. When the horizontal plot coordinate is twice thereciprocal of the impact distance, we can infer the source height as the slopeof the data points in the reciprocal correlation plot. If the distribution oflaunch angles is not narrow, failure of the method is evident in the lack oflinear correlation. We perform a number of experimental trials, as well asnumerical calculations and show that the height estimate is insensitive toaerodynamic drag. Besides its possible relevance for crime investigation,reciprocal-plot analysis of spatter may find application to volcanism and othertopics and is most immediately applicable for undergraduate science andengineering students in the context of crime-scene analysis.
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