BPHO Projectiles

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Atmosphere Density Projectile Model

A projectile model building on Challenge 9, which considers projectile motion in an atmosphere with a model of air density that diminishes with altitude. The original air resistance model (red) can be compared with the new model (orange) along with the drag-free model (purple).
In order to see the difference between the orange and the red, the streamlined body setting works best.

The simulation was based on the molar form of the ideal gas law:

\rho = \frac{p_0 M}{R T_0} \left(1 - \frac{L h}{T_0}\right)^{\frac{g M}{R L} - 1}

Where:

𝑝₀ = sea level standard atmospheric pressure, 101 kPa
𝑇₀ = sea level standard temperature, 288 K
𝑔 = earth-surface gravitational acceleration
𝐿 = temperature lapse rate, 0.0065 K/m
𝑅 = ideal (universal) gas constant, 8.314 J/(mol·K)
𝑀 = molar mass of dry air, 0.02897 kg/mol

Launch conditions

Launch Speed u ms^-1:

Launch Angle from Horizontal θ °:

Strength of Gravity 𝑔 (Nkg^-1):

Launch Height ℎ above sea level (m):

Object Mass (kg):

Air Density (kgm^-3):

Cross-Sectional Surface Area (m²):

Show points