AIR RESISTANCE

• Jurisdiction: Australia

Introduction ................................................................................................... [97.1600]

Terminal velocity ............................................................................................ [97.1650]

Relative velocities ......................................................................................... [97.1700]

Wobble and spin

Oscillations .................................................................................................... [97.1800]

Spin ............................................................................................................... [97.1820]

[97.1600] Introduction

When a body moves relative to liquid or gas, such as a blood droplet moving through air, the fluid exerts a friction-like resistive force on the body. This force (or drag) is a function of the viscosity of the fluid and, at higher speeds, of the turbulence generated in the wake of the body. The retarding force exerted on the body or droplet always acts in a direction tangential to the path of the droplet and, consequently, continuously changes in direction as the droplet arc describes a parabola. Thus, gravity and drag are continually competing. High velocities are dominated by drag until they slow sufficiently for gravitational forces to become prevalent. Similarly, gravity has a significant effect on blood droplets travelling at relatively low velocities. This will mean, in most instances, significant deviation from parabolic motion.

In essence, to a good approximation, the air-resistance force does not depend on the mass of a spherical object (assuming the blood droplet to be spherical as it moves through space), be it solid or hollow, but only on its speed v and radius r. When turbulence is present, as is the case with blood droplets moving through space at a crime scene, experiments have shown that drag force increases proportionally to the square of the speed: Parker (1977). This overall effect may best be described by the formula given by Lock (1982).

Force (air) = A vr + B v² r²

where A and B are constants and v and r represent the velocity and radius respectively. This formula, which is a function of both laminar and turbulent flow, may be used to determine the actual path of the droplets if the initial velocity, trajectory path and droplet radius are known.

[97.1650] Terminal velocity

A droplet in free fall in air reaches a terminal velocity that is clearly a function of the drag. The total drag is...