# Air Resistance

Written by Jerry Ratzlaff on . Posted in Classical Mechanics Air resistance, abbreviated as Fa, also called drag coefficient, is a force that opposes an object as it moves through the air.  This force is dependant on the velocity, area and the drag coefficient. As the velocity increases, the force increases by a square.  So if velocity doubles, the resistance increases by four (22).

## Air Resistance formulas

 $$\large{ F_a = k\;v^2 }$$ $$\large{ F_a = \frac{\rho \;C_d\; A}{2} \; v^2 }$$

### Where:

dimensionless
 Units English Metric $$\large{ F_a }$$ = force of air resistance or drag $$\large{ lbf }$$ $$N$$ $$\large{ A }$$ = area cross-section of the object $$\large{ ft }$$ $$\large{m}$$ $$\large{ \rho }$$ (Greek symbol rho) = atmospheric density $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$ $$\large{ C_d }$$ = drag coefficient dimensionless $$\large{ k }$$ = a constant that collects the effects of area, density, and drag $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$ $$\large{ v }$$ = velocity of the moving object $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$

### Solve For:

 $$\large{ v = \sqrt{ \frac{ 2 \; F_a }{ \rho \; C_d \; A } } }$$ 