# 7.1.5: Performances in steady ascent and descent flight

$$\newcommand{\vecs}{\overset { \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$

• Consider a symmetric flight in the vertical plane.
• $$\chi$$ can be considered constant.
• The aircraft performs a leveled wing flight, i.e., $$\mu = 0$$.
• There is no wind.
• The mass, the velocity, and the flight path angle of the aircraft are constant.

The 3DOF equations governing the motion of the airplane are:

$T = D + mg \sin \gamma , \label{eq7.1.5.1}$

$L = mg \cos \gamma,\label{eq7.1.5.2}$

$\dot{x}_e = V \cos \gamma \cos \chi ,$

$\dot{h}_e = V \sin \gamma,\label{eq7.1.5.4}$

Typically, commercial and general aviation aircraft have a relation $$T/(mg)$$ so that flight path angles are small $$(\gamma \ll 1)$$. Therefore, Expression ($$\ref{eq7.1.5.1}$$) can be expressed as

$\gamma \cong \dfrac{T - D}{mg},$

and Expression ($$\ref{eq7.1.5.2}$$) can be expressed as

$L \cong mg, \to n \cong 1.$

Therefore the flight path angle can be controlled by means of the power plant thrust.

Another important characteristic in ascent (descent) flight is the Rate Of Climb (ROC), which is given by Expression ($$\ref{eq7.1.5.4}$$) as:

$V_{ROC} = \dfrac{dh_e}{dt} = V \sin \gamma .$

7.1.5: Performances in steady ascent and descent flight is shared under a CC BY-SA 3.0 license and was authored, remixed, and/or curated by Manuel Soler Arnedo via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.