Experiment 5
Aim & Theory
Simulation
Reference
Aim & Theory
Aim
To investigate the effect of aerodynamic forces (Thrust, Lift, Drag), mechanical constraints (Friction, Weight), and pilot input (Rotation time, Load factor) on the total takeoff distance of an aircraft.
Apparatus / Tools
Good internet connectivity
Scientific Calculator: For manual verification of kinematic equations.
Formulae & Governing Equations
The takeoff is analyzed as the sum of three distinct horizontal distances: $$S_{TO} = S_g + S_{rot} + S_{tr}$$
| Phase | Formula | Key Variable |
|---|---|---|
| Ground Roll (Sg) | \( S_g = \frac{V_{TO}^{2}}{2a} \) \( a = \frac{g}{W}[T - D - \mu(W-L)] \) | Acceleration \(a\) |
| Rotation (Srot) | \( S_{rot} = V_{TO} \cdot t_{rot} \) | Rotation time \(t_{rot}\) |
| Transition (Str) | \( S_{tr} = R \cdot \sin(\gamma) \) \( R = \frac{V_{TO}^{2}}{g(n-1)} \) | Load factor \(n\) |
| Climb Angle (γ) | \( \sin(\gamma) = \frac{T-D}{W} \) | Excess Thrust \(T-D\) |
Theory & Concepts
Takeoff performance is a balance between Energy Addition (Thrust) and Energy Dissipation (Drag/Friction).
Acceleration Phase: The aircraft must overcome static and rolling friction. As speed increases, Lift (L) reduces the effective weight on the wheels, reducing friction but increasing aerodynamic drag (D).
Rotation: The point where the nose gear leaves the ground. A longer rotation time increases the horizontal distance significantly without gaining altitude.Transition Geometry: The aircraft follows a circular arc. The radius (R) of this arc depends on the "pull-up" load factor (n). A higher n results in a tighter turn but requires more structural strength and pilot skill.
Simulation
Aircraft Take-Off Performance Lab
Input Parameters
Ground Roll 0
Rotation 0
Transition 0
Total Distance 0
Parametric Analysis of Thrust-to-Weight Ratio and Lift-to-Drag Ratio
Reference
Essential Textbooks (Theory & Design)
- Aircraft Performance and Design by John D. Anderson, Jr. (McGraw-Hill): Often considered the standard text for understanding flight mechanics and performance, covering both jet and propeller-driven aircraft.
- Flight Performance of Aircraft (AIAA Education Series): Focuses on the analysis methods for flight performance estimation, including accelerated flight.
- Theory and Practice of Aircraft Performance by Ajoy Kumar Kundu: Bridges the gap between academic theory and practical engineering application.
- Aerodynamics and Aircraft Performance, 3rd Edition by James F. Marchman III: A free, comprehensive textbook covering subsonic performance.
- Elements of Airplane Performance (TU Delft OPEN Books): Covers flight mechanics, propulsion, and performance in various flight phases.