The Relationship Between Shoe Size and the Amount of Sand that Enters the Shoe

Abstract

This study examines how shoe sizes affect the amount of sand that enters the shoe. By building a simple mathematical model that compares ankle size and ankle-collar size, we show that sand inflow can be approximated as proportional to the difference between the area of the shoe opening and the cross-sectional area of the ankle. For non-custom-made shoes produced in fixed sizes, the model suggests that size intervals may affect sand intake because larger size intervals can create larger ankle gaps. A small pilot observation using five shoe cases is included to connect the theoretical model to non-hypothetical data. The results do not provide a directly prescriptive industrial recommendation, but they suggest a conceptual way to think about shoe-size intervals, ankle-collar geometry, and wearer comfort.