|Enter mass (kg), and diameter (m) of the
|or enter mass (kg) and density (kg/m^3),
e.g. 7874 kg/m^3 for iron,
diameter will be computed
|or enter density (kg/m^3), and diameter
e.g. 7874 kg/m^3 for iron,
mass will be computed
|Enter acceleration (m/s^2), density of the
air (kg/m^3), drag coefficient (dimensionless),
for a sphere the dag coefficient is cD = 0.4 .. 0.5 (0.47)
|enter maximum time (s), or Height (m),
and press button "Apply Input"
You may also use the Parachute mode:
|Enter time (s), or Height (m),
and press button "Apply Input".
|Using mass = 150 kg, diameter = 9 m,
drag coefficient cD = 1.3,
dome-shaped chute cD = 1.3 .. 1.5,
parasheet (flat sheet) cD = 0.75
the rate of descent will be about 5 m/s.
|Using a "Height" input the delay due to air resistance is computed (∆t absolute, and ∆t/T in relation to the time T of free fall).|
The equations without air resistance are quite simple. We assume g=const, s(t=0)=0, and v(t=0)=0:
Taking into account the air resistance force (drag force):
which depends on the drag coefficient cD, the velocity v, the density of air ρ, and the cross section A of the body,
the equation of motion is
The differential equation of motion is solved by
The air resistance force will increase until it equals the gravitational force m.g, and the body will then move at a constant velocity vlimit as the net force is m.a=0
The drag coefficient cD is a function of the non-dimensional Reynolds number Re, defined by
L is a characteristic linear dimension (e.g. diameter of the body/sphere), ρ the density, and μ the dynamic viscosity (for air 17.9 ÁPa.s at 10░C).
>>In theory, the flow is laminar when Reynolds number is below 4,000. However, in practice, turbulence is not effective when Reynolds number is below 200,000; so when the Reynolds number is less than 200,000, you may assume laminar flow. In addition, when the Reynolds number is higher than 2,000,000, you may assume turbulent flow.<< (*).
Using a "Height" input the delay due to air resistance is computed (∆t absolute, and ∆t/T in relation to the time T of free fall).
Ferdinand Reich's experiments were performed at a height of 158.5 m using spheres of 4,034 cm diameter and 270,45 g mass.
The speed limit 86.3 m/s is not reached. The effect of air resistance on time is ∆T = 5.8676s - 5.6845s = 0.1831s, ∆T/T = 3.22%.
Select "∆t - H":
The diagram below is showing the time difference as a function of diameter due to air resistance for iron balls (ρ=7874 kg/m^3) falling from 150 m:
∆t/T ~ 1/diameter (R2=0.999996)
The diagram below is showing the time difference as a function of mass due to air resistance for iron balls (ρ=7874 kg/m^3) falling from 150 m:
∆t/T ~ 1/mass (R2=0.999992)t_95 ~ mass1/6 (R2=0.999997)
The time when 95 % of the terminal velocity (v) is reached as a function of mass (iron balls) is shown in the following diagram:
The diagram is showing the rate of descent (vLimit, terminal velocity) as a function of mass, and the equivalent height at free fall.
Fall mit und ohne Luftwiderstand
(*) Drag Force and Drag Coefficient
2016 J. Giesen
letzte ─nderung: 12. Dez. 2020