Utilize our Free Fall with Air Resistance Calculator to accurately model the motion of objects affected by drag. Input mass, drag coefficient, area, and air density to find terminal velocity, velocity, and distance fallen over time. Ideal for physics students, engineers, and anyone exploring real-world projectile motion.
Formula:
The calculator uses the following formulas, considering an object falling downwards where positive velocity is downwards:
- Drag Force (Fd):
Fd = 0.5 × ρ × v2 × Cd × A - Gravitational Force (Fg):
Fg = m × g - Terminal Velocity (vt):
vt = √((2 × m × g) / (ρ × Cd × A)) - Velocity at Time t (v(t)): (Given initial velocity v0, where α = g/vt)
v(t) = vt × ( ((v0/vt) + 1) × e^(2 α t) - ((v0/vt) - 1) ) / ( ((v0/vt) + 1) × e^(2 α t) + ((v0/vt) - 1) ) - Distance Fallen at Time t (y(t)): (Given initial velocity v0 and y(0)=0, where α = g/vt)
y(t) = (vt2 / g) × ln( ( ((v0/vt) + 1) × e^( α t) + (1 - (v0/vt)) × e^(- α t) ) / 2 )
Where:
m= Mass of the object (kg)g= Acceleration due to gravity (m/s²)ρ= Air density (kg/m³)Cd= Drag coefficient (unitless)A= Reference area (m²)v= Instantaneous velocity (m/s)vt= Terminal velocity (m/s)t= Time elapsed (s)v0= Initial vertical velocity (m/s)y(t)= Distance fallen at time t (m)