Heavy Lift Cargo Plane 2009

Group 6

Calculations

Aerodynamic Calculations

Aerodynamic calculations were performed based on landing and takeoff distance (constraints from the competition, 400 feet and 200 feet respectively), thrust available from the engine, and a number of changeable dimension variables. During the design phase, the Excel sheet allowed the group to try many different configurations of the aircraft by changing the values of a few cells. This lead to a trial and error approach in which educated guesses were used to come up with a design and then the design was tested for its aerodynamic properties.

The user could input various dimensional values including chord, span, height, length, fuselage area, propeller dimensions, and the desired payload. A number of constants were also a part of the calculations. These included the density of the air, a friction factor (friction between the wheels and the runway), and multiple efficiency factors. The drag coefficient was calculated from these values and certain configuration components were determined. Flaps and ailerons were also considered though they were treated as one entity in order to simplify the calculations.

Thrust was determined based on velocity of the aircraft and efficiency of the engine. This data was gathered from a graph that was compiled through various field tests for the appropriate engine and muffler combination. Take-off and landing distances were then calculated. Throughout this whole process, the Excel sheet contained a section used solely for cross-checking the constraints. This box contained the important constraints (i.e. overall dimensions no greater than 175 inches, takeoff distance less than 200 feet, landing distance less than 400 feet, and motor RPM between 2000 and 17000). While the respective value of the constraint was acceptable, the box was green and when a value exceeded the constraints, the box changed to red, signifying that there was a problem with the design. Further information on aerodynamic calculations and formulas used can be found below.

 

Stability Calculations

After the aerodynamic calculations were performed, it was necessary to make sure that the plane would be stable in flight. There were three ways of ensuring this. First, the slope of the moment coefficient curve must be negative; this shows that the airplane model was statically stable. Second, the static margin had to be a positive number. This ensures the aerodynamic center of the airplane is behind the center of gravity, so if a gust of wind disturbs the airplane during flight, the relative locations of the aerodynamic center and the center of gravity restore the plane back to normal flying conditions. Finally, the equilibrium angle of attack must fall within normal flight range.

In order to determine these numbers, the center of gravity of the plane had to be located. The location of the center of gravity was initially determined using weight and location estimates of each component of the plane. Later, this number was modified based on the final SolidWorks model of the aircraft. The location was found to be at 13.5% of the wing chord.

The next step was to determine the slope of the moment coefficient curve. Using information from the airfoil data and wing and tail dimensions and locations, this number was found to be -0.016. Using this number, the equilibrium angle of attack was determined to be 4 degrees. Since the slope is negative, the model is statically stable, and since the angle falls within the reasonable flight range, the model is longitudinally balanced as well.

Finally, the aerodynamic center of the plane was determined to be at 31.4% of the wing cord. The static margin was determined by subtracting 13.5 from 31.4 to get 17.9%. Since this number is positive, this reinforces the static stability of the model. All calculations involving stability can be found below.