How can I create an extended free body diagram of an aircraft during the cruise stage of flight (equilibrium)? The free body diagram should have all the main four forces such as Lift, Weight, Thrust, and Drag. What confuses me is that the question asks to add the tailplane as a vector force (the tailplane is located at the back of the aircraft) and express it mathematically. How can I express this mathematically, as in what equations should I be using? I'm not looking for direct answers, simply explanations to make my research easier!
The Correct Answer and Explanation is:
Key Forces to Include:
- Lift (L): Acts upward, generated by the wings, balances the aircraft’s weight.
- Weight (W): Acts downward, due to gravity, centered at the aircraft’s center of gravity (CG).
- Thrust (T): Acts forward, provided by engines.
- Drag (D): Acts backward, due to air resistance.
- Tailplane force (T_f or L_t): A vertical force generated by the horizontal stabilizer (tailplane), typically acting downward in most conventional aircraft configurations.
Why Tailplane Force Matters:
Although in cruise the net forces are balanced (i.e., no linear acceleration), rotational equilibrium must also be maintained. The tailplane, located behind the CG, provides a moment that balances pitching moments caused by aerodynamic forces on the wing and fuselage.
Mathematical Relationships (Simplified):
1. Vertical force equilibrium:L+Lt=WL + L_t = WL+Lt=W
- If the tailplane produces downward force, then:
L=W+∣Lt∣L = W + |L_t|L=W+∣Lt∣
2. Horizontal force equilibrium:T=DT = DT=D
3. Moment equilibrium about the center of gravity (CG):
Let:
- dwd_wdw = distance from CG to wing’s center of lift
- dtd_tdt = distance from CG to tailplane (positive aft)
- LtL_tLt = force from the tailplane (usually downward)
Then:L⋅dw=Lt⋅dtL \cdot d_w = L_t \cdot d_tL⋅dw=Lt⋅dt
- If LtL_tLt is downward, its moment is nose-up, balancing the nose-down moment from the main wing lift.
Diagram Construction Tips:
- Start at the CG.
- Show Lift acting upward from the wings, Weight downward from the CG.
- Place Thrust forward and Drag backward along the longitudinal axis.
- Add the tailplane force vector acting downward (or upward in canard aircraft) at the tail’s location, clearly labeled with distance from CG.
- Include moment arrows or moment equations if needed.
This extended diagram helps analyze both translational and rotational equilibrium—crucial in aircraft stability.
