# Where is the mistake in this air density calculation?

I intend to compute the air density, $\rho$ at an altitude of $h=15000ft=4572m$, with an ISA deviation of $\Delta_{ISA}=18^{\circ} F=10\,K$.

Well I first computed the real temperature of the air at $h$ altitude with the following ISA temperature realtions:

$$T_{ISA}[K]=288.15-0.0065\,h[m]=258.432\,K$$ $$T=T_{ISA}+\Delta_{ISA}=268.432\,K$$

I then computed the temperature altitude, i.e. the $ISA$ altitude for a temperature $T$:

$$h_T[m]=\frac{T[K]-288.15}{-0.0065}=3034m$$

With $h_T$ computed I got the air density by the respective ISA relation:

$$\rho[kg/m^3]=1.225\left(1-0.0065\frac{h_T [m]}{288.15}\right)^{4.25588}= 0.906kg/m^3$$

The problem is that this value is different from what I got here ($\rho=0.742 kg/m^3$)

What did I do wrong?

• Are you comparing different atmosphere models by any chance? – user7241 Dec 26 '17 at 19:53