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