Flight Mechanics & Space Dynamics • Atmospheric Flight Mechanics • Standard Atmosphere Properties
In the International Standard Atmosphere (ISA), the sea-level temperature is $T_0 = 288.15\text{ K}$ and the standard temperature lapse rate in the troposphere is $\lambda = -6.5\text{ K/km}$. What is the ambient temperature (in K) at a geopotential altitude of $h = 6\text{ km}$?
Answer Key:
249.15
Step-by-Step Verified Solution
### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: ISA Troposphere Modeling:** Altitude $h = 6\text{ km} \le 11\text{ km}$ lies within the troposphere. 2. **Stage 2: Linear Lapse Equation:** $T = T_0 + \lambda h = 288.15 - (6.5)(6)$. 3. **Stage 3: Computation:** $288.15 - 39 = 249.15\text{ K}$. 4. **Stage 4: Correct Value:** 249.15 (range 249.0 to 249.3).