Experiment Results and Conclusions
EXP2: Bomb Drop Trajectory
Case 1: v0 = 10 m/s, θ = 0°, y0 = 5 m
→ The bomb covers a distance x = 10 m
→ Final range: x = 10 m
→ Final height: y = 5 m
Case 2: v0 = 50 m/s, θ = 20°, y0 = 7.5 km
→ Final range: x = 1921 m
→ Final height: y = 7500 m
Case 3: v0 = 0, θ = 0°, y0 = 5 m
→ Final range: x = 0 m
→ Final height: y = 5 m
Conclusion:
→ Higher velocity and angle θ → longer range, greater max height, more stretched curve
→ Lower velocity and θ > 0 → steeper curve, shorter range but still high max height
→ θ = 0 → standard parabolic drop, no initial vertical component
→ v0 = 0 → shortest, steepest trajectory with reduced range and height
EXP3: Beam Vibration Analysis
Result:
The MATLAB code calculates the first five natural frequencies and plots their corresponding mode shapes. These results are consistent with theoretical values for a simply supported beam.
Conclusion:
This experiment demonstrates how MATLAB can be used to analyze the vibrational behaviour of a simply supported beam, including calculating natural frequencies and visualizing mode shape effectively.
EXP4: Lift Distribution with Tail Effect
Result:
Without Tail Effect:
→ z = 0.1000
With Tail Effect:
→ Wing lift = 2392500 / 239
→ Tail lift = -2500 / 239
Conclusion:
The simulation confirms that for the aircraft to maintain a straight, level flight, the forces (lift + weight and thrust + drag) must be balanced and the moment about the centre of gravity (cg) must be zero.
From the results it can be determined that the tailplane introduces a balancing moment, which helps maintain the pitch stability.
In the experiment, the tailplane provides a downward force to counteract the pitching moment caused by the offset of lift & weight.
EXP5: V-n Diagram for Boeing 787-8
Result:
→ Positive stall curve (blue): for n = 0 to 9 → v = 0 to 240 m/s
→ Negative stall curve (red): for n = 0 to -5 → v = 0 to 165 m/s
→ Horizontal limit lines (green):
Top = +9g → between 247 & 370 m/s
Bottom = -3g → between 165 & 370 m/s
→ Dive speed (black) = 370 m/s
→ Unsafe region = > 370 m/s & > +9g
Conclusion:
The safe flight envelope is bounded by stall limits at the lower speeds & structural G-limit at higher speed.
The aircraft must operate within the V-n envelope to ensure aerodynamic stability & structural integrity.
EXP6: Cessna 172 Aerodynamic Performance
Result:
(i) CL vs AOA: CL increases linearly with AOA, stall occurs at 16.5° angle
(ii) CL vs CD: Parabolic curve depicting the drag-polar equation CD = CD0 + kCL²
(iii) Cm vs AOA: Cm increases linearly with AOA, depicts nose-down pitch
(iv) Takeoff vs groundroll:
→ Takeoff distance shows a linear relation till 7000 ft
→ Groundroll shows a curve till 5000 ft