CONSTRAINT ANALYSIS The two parameters (i) wing loading and (ii) power loading are the most important parameters that affect the airframe design and its performance. Wing loading and power loading are interconnected for a number of design parameters and because of this interconnection it is difficult to use historical data to independently select these values. Hence a different approach needs to be followed. The team decided to use sizing matrix plots to find the optimum value of the two parameters. For calculating the optimum values, the most important design requirements must be decided. The design requirements that have the highest weightage are: (i) (ii) (iii) (iv) Stall speed Take off distance Landing distance Sustained turn

All the above design requirements were written in terms of wing loading and power loading.

Since in the design requirements parameters are given in the inequality form, hence a region of point is obtained instead of single point of intersection. This region of favorable points is known as design space. On putting values of all parameters and then plotting in matlab, design space is obtained. The code for plotting the sizing matrix plot is given in Appendix A(a). In the design space the optimum design point is obtained by calculating the score of the point based on its weightage. (The weightage of various design parameters is given in Appendix A(b).

REGRESSION ANALYSIS A regression analysis was done to find out the statistical relation between empty weight fraction of an airplane and various design driving parameters such as wing loading, power loading, aspect ratio, dash speed etc. The regression was done by obtaining the values of various design parameters of aircrafts of the same class. The code for regression is given in Appendix B.

INITIAL SIZING Initial sizing of weight is one of the first calculations done in early design phase. The weight is calculated from the following equation.

, where Wfuel =weight of the fuel/gross takeoff weight Wempty=empty weight of airplane/gross takeoff weight

In the above equation the unknowns are Wfuel and Wempty.

To calculate fuel weight fraction: Breguet’s Endurance equation is used to calculate the mission weight fractions of various mission segments.

Using the above equation mission weight fractions of various mission segments such as take-off, landing, loiter etc. When mission weight fractions of all mission segments is known then (initial weight/final weight) fraction is calculated by multiplying weight fractions of various mission segments. Fuel weight is obviously initial weight-final weight Hence fuel weight = 1-(final weight/initial weight)

Calculation of empty weight fraction: The equation obtained through the regression analysis is

Note that in the above equation gross take-off weight (W0) is also included. So initially a Gross take-off weight must be guessed(which is known as Wguess). We put Wguess in above equation along with other known parameters and calculate empty weight fraction. Then empty weight fraction is put in the following equation to obtain Wcalculated and the process is iterated till Wguess is equal to Wcalculated.. If Wguess is not equal to Wcaculated then a new guess weight is selected which is equal to (Wguess +Wcalculated)/2. Another method for calculating Gross take-off weight is to plot graph between Wguess and Wcalculated and then find the point of intersection of the graph and line y=x which eventually gives the point where Wguess=Wcalculated. The matlab code for the initial sizing is given in Appendix C and its algorithm is given below.