4.1 Equilibrium of Forces in Steady Flight, Climb & Glide

4.1 Equilibrium of Forces in Steady Flight, Climb & Glide

To understand aircraft performance and controllability, an aircraft maintenance engineer or aerodynamicist must first examine the vector forces acting on an aircraft in flight. Under EASA Part-66 Module 08 specifications, flight dynamics are modeled by analyzing how Lift ($L$), Weight ($W$), Thrust ($T$), and Drag ($D$) interact across various steady-state operational modes.

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1. Straight-and-Level Unaccelerated Flight

In straight-and-level unaccelerated flight, an aircraft moves at a constant true airspeed ($V$) and constant altitude along a straight path. Because acceleration is zero ($\vec{a} = 0$), Newton's First Law dictates that the vector sum of all forces and moments acting on the aircraft must equal zero:

$\sum \vec{F} = 0, \quad \sum \vec{M} = 0$

Vertical and Horizontal Equilibrium

Assuming the thrust line is parallel to the flight path:

• Vertical Axis Equilibrium: Aerodynamic Lift acts perpendicular to the flight path and opposes gross Weight: $L = W$
• Horizontal Axis Equilibrium: Engine Thrust acts along the flight path and opposes total aerodynamic Drag: $T = D$

                    Lift (L)
                       ^ 
                       |
                       |   
   Thrust (T) <--------+--------> Drag (D)
                       |   
                       |
                       v
                   Weight (W)

If Thrust exceeds Drag ($T > D$), the aircraft accelerates. If Drag exceeds Thrust ($D > T$), the aircraft decelerates. Similarly, if Lift exceeds Weight ($L > W$), the flight path curves upward, introducing vertical acceleration.

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2. Forces in a Steady Climb

When an aircraft enters a steady, constant-airspeed climb at a flight path angle $\gamma$ (gamma) relative to the horizontal plane, the force equilibrium changes fundamentally. Weight ($W$) always acts vertically downward toward the center of the Earth. Consequently, when the flight path is inclined upward by angle $\gamma$, Weight must be resolved into two orthogonal components:

1. Component Perpendicular to the Flight Path: $W_{\perp} = W \cos \gamma$
2. Component Parallel to the Flight Path: $W_{\parallel} = W \sin \gamma$

                     Lift (L)
                        ^
                       / 
                      /  
   Thrust (T) <------+------> Drag (D) + W*sin(gamma)
                    / \
                   /   \
                  v     v
         W*cos(gamma)   Weight (W)

Steady Climb Force Equations

Applying equilibrium conditions along and perpendicular to the inclined flight path:

• Perpendicular Equilibrium: $L = W \cos \gamma$ Critical Exam Note: Because $\cos \gamma < 1$ for any positive climb angle $\gamma > 0^{\circ}$, aerodynamic lift in a steady climb is strictly less than the total weight of the aircraft ($L < W$). The remaining portion of weight support is provided by the vertical component of thrust.

• Parallel Equilibrium: $T = D + W \sin \gamma$ Thrust must overcome both aerodynamic drag ($D$) and the rearward component of weight ($W \sin \gamma$).

Angle of Climb vs. Rate of Climb

EASA examinations frequently test the aerodynamic distinction between Angle of Climb and Rate of Climb:

• Best Angle of Climb Speed ($V_x$): Occurs at the speed where Excess Thrust ($T - D$) is maximized. For a jet aircraft, this is near $(L/D)_{\max}$.
• Best Rate of Climb Speed ($V_y$): Occurs at the speed where Excess Power ($(T - D) \cdot V$) is maximized.

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3. Forces in a Steady Power-Off Glide

In an unpowered descent (glide), engine thrust is zero ($T = 0$). The energy required to overcome aerodynamic drag is supplied entirely by the loss of gravitational potential energy as the aircraft descends along a flight path inclined downward by angle $\gamma$.

                 Lift (L)
                    ^
                     \ 
                      \  
   Drag (D) <----------+  
                      / \
                     /   \
                    v     v
           W*cos(gamma)   Weight (W)

Steady Glide Force Equations

Resolving forces parallel and perpendicular to the downward flight path:

• Perpendicular Equilibrium: $L = W \cos \gamma$
• Parallel Equilibrium: $D = W \sin \gamma$

Dividing the parallel equation by the perpendicular equation eliminates Weight ($W$):

$\frac{D}{L} = \frac{W \sin \gamma}{W \cos \gamma} = \tan \gamma \implies \tan \gamma = \frac{D}{L} = \frac{1}{L/D}$

Key Glide Aerodynamic Principles

1. Minimum Glide Angle ($\gamma_{\min}$): To achieve the shallowest glide angle and cover maximum horizontal distance, the aircraft must operate at the speed corresponding to the maximum Lift-to-Drag ratio $(L/D)_{\max}$.
2. Independence from Aircraft Weight: The maximum glide distance in calm air depends solely on $(L/D)_{\max}$ and initial altitude. An increase in gross weight does NOT alter the glide distance or glide angle. However, a heavier aircraft will glide at a higher true airspeed along the exact same flight path angle, resulting in a higher rate of descent ($RoD$).

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4. Pitching Moments and Longitudinal Equilibrium

Equilibrium of forces ensures linear acceleration is zero, but rotational stability requires equilibrium of pitching moments about the aircraft Center of Gravity ($CG$):

$\sum M_{CG} = 0$

In conventional aircraft layouts, the main wing center of pressure ($CP$) or aerodynamic center ($AC$) is located behind the $CG$. This configuration generates a continuous nose-down pitching moment ($M_{\text{wing}} = L \times d$). To maintain trim, the horizontal tailplane is designed as an inverted airfoil, generating a downward aerodynamic force (tailplane downforce, $L_t$).

$\sum M_{CG} = (L \cdot d_{\text{wing}}) - (L_t \cdot d_{\text{tail}}) = 0$

        Lift (L)
           |
   CG      v (CP)
   o-------|---------
   |                 \
   v                  v Tailplane Downforce (Lt)
 Weight (W)

When maintenance engineers adjust ballast or alter cabin seating configurations, moving the $CG$ forward increases tailplane load requirements, increasing total trim drag and slightly elevating stall speeds.

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Glide Ratio and Unpowered Descent

Glide ratio is the horizontal distance travelled per unit of altitude lost in steady unpowered flight. Numerically it equals the lift-to-drag ratio at the chosen airspeed:

$\text{Glide Ratio} = \frac{L}{D} = \frac{\text{Distance Forward}}{\text{Altitude Lost}}$

• Best glide distance occurs at $(L/D)_{max}$ (minimum total drag speed $V_{MD}$).
• Flying faster or slower than $V_{MD}$ reduces glide range.
• Configuration (gear, flaps, speedbrakes) raises parasite drag and worsens glide ratio — a critical Part-66 performance fact when assessing in-flight emergency capability after maintenance alterations to drag devices.