Constraint Analysis for Aircraft Design

Welcome to the video on Constant Analysis for Aircraft Design. In this video, we are going to learn how can we determine the design space that meets all given requirements and evaluate appropriate wing sizing and powerplant system. For this purpose, we will be using the Constant Analysis Live Task for Aircraft Design. You can download this as an add-on from File Exchange or the GitHub repository.

In this video, we will discuss how Constant Analysis helps us evaluate design space and determine the required wing area and power plant specifications. We will also have the software demonstration with the Constant Analysis Live Task in Matlab. Finally, we will conclude this video with some of the key takeaways.

Let's start our video by understanding how Constant Analysis helps us with aircraft design. The conceptual aircraft design phase starts with converting multiple design requirements into minimum meaningful ratios. For example, you want to design an aircraft that can carry a weight of X kilograms, take off within Y meters, fly at the maximum cruise speed of V meters per second, at the altitude of 8 meters, and, finally, land within Z meters ground roll.

Handling these requirements will become a more complex task with their increments. Hence, we need some numbers that can represent all these requirements. Constraint Analysis exactly helps us with that.

Constraint Analysis plots the various constraint curves presented in the form of wing loading and power to weight ratio, or thrust to weight ratio. The area bounded by these curves provides feasible design space, which will enable us to meet the design requirements. But how does it do that?

Consider the equation of the take-off ground roll. It can be modified to find a relation between power to weight ratio and wing loading. On plotting this constant, the area above this curve is a feasible solution that represents the design space that will meet this requirement. Similarly, based on the multiple requirements, we can plot the constraints and identify the design space that will meet all given requirements.

This design space is represented in the form of two ratios, which makes it easier to handle these requirements. Also, as these ratios depends on the weight, it adjusts the effect of weight change with other parameters during the design process. If the approximate aircraft weight is estimated with these numbers, we can calculate wing area using wing loading, power required with power to weight ratio, and the thrust required with thrust to weight ratio.

With power required and thrust required numbers, we can identify appropriate power plant, and the wing area can be used to start initial sizing of the aircraft. Let's go back to the Constraint Analysis plot. The plotted constraint curves are feasible design space that can meet given requirements. Let's explore this design space and understand, depending on the location, how the design solution will make a difference.

Let us mark the four major points in the plot. All four points will meet the given requirement, but may result in different performances. In the Constraint Analysis plot, moving across the x-axis will provide us smaller wing area, which may lead to a smaller and so lighter aircraft. Moving across y-axis will require a bigger power plant, which will be costly as well.

With this understanding, we can infer that points A and B will require a smaller wing area compared to point C and D. Points A and B will require bigger engines, which may make aircraft heavy and costly, but the higher engine power will also provide better performance capabilities. Point C is somewhere in between. It will require the lowest power engine and appropriate wing area. Depending on the requirements, we can explore the range of solution points.

Now that we understand how Constraint Analysis can help us to calculate initial parameters, let us move to the Matlab for the software demonstration. For this software demonstration, we will use the Constraint Analysis Live Task. You can download this Live Task from the File Exchange and GitHub.

Once the Live Task is installed, open a new Live Script and start typing Constraint Analysis. It will pop a Constraint Analysis Live Task. Select that. This will add the Live Task to the Live Script, or you can add this Live Script directly from the Insert submenu in the Live Script.

This Live Task has three major sections. First is the Input section, where we need to provide environmental parameters, aerodynamics, and propulsion data. The second section is, Select Appropriate Constants, where we need to select and provide data for required constants. And the third section is Plot Results, where we can select the result type we want to explore.

In the Input section, we can provide the operating environment parameters, which help to customize environmental parameters, including density and gravitational accelerations accordingly. We also need to provide aerodynamic and propulsive parameters. These parameters are based on the research on similar existing aircrafts.

Moving forward, the Select Appropriate Constant section has a total of four constraints. The first constant is the landing distance constant. It makes sure that the designed aircraft lands on the runway within the given landing ground roll limit. This constant solely depends on the wing loading, and so we saw a vertical line on the x-axis in our results. It also puts the right limit on the design space.

This constraint is, by default, enabled, whereas the other three constraints are optional. We can enable them by clicking the checkbox next to them. Similar to the landing distance constraint, take-off distance constant ensures that the designed aircraft flies within the given take-off ground roll limit.

The third constraint, cruise velocity constant, makes sure that the designed aircraft achieves the required maximum speed at a given cruise altitude. Both the take-off distance constraint and cruise velocity constants depends on both wing loading and power to weight ratios, and so we see the polynomial curves. The fourth constraint takes care of the maximum rate of climb at a given altitude. It solely depends on the power to weight ratio, and so we see a horizontal line on the y-axis in our results.

It also puts the bottom limit on the feasible design space. Everything above it is a feasible solution. To make it visually feasible in plots, we have taken the upper limit as 130% of the maximum power to weight ratio.

After selecting the appropriate constraints, we can check the type of results we want to plot. We can plot the power to weight ratio versus wing loading and thrust to weight ratio versus wing loading plots. This generates both plot results and numerical results.

Numerical results can be found in the workspace as CA Structure. It contains all the input data and the superior constraint met up with contribution from various constraints. It also contains information about maximum power to weight limit and maximum thrust to weight limit. The superior constraint information can be further used to explore the design space in an optimization workflow.

Moving back to the Live Task, if you want to perform the Constraint Analysis, but for parameter variations-- for example, you want to perform the Constraint Analysis for multiple climax coefficients-- in that case, you can convert this Live Task into the code and customize it accordingly. Let's move forward and calculate the range of wing area and power required for wing loading at point C, which is around 190 Newton per meter squared.

We can calculate the required wing area by dividing the takeoff weight by wing loading. To calculate the minimum value of power to weight ratio, we can interpolate the constant vector for a given wing loading. Now, by multiplying the minimum power to weight ratio with wing loading, we can calculate the minimum power required. Similarly, the maximum power required and thrust required values can also be calculated.

Now that we have learned how to use the Constant Analysis Live Task, let's move to the key takeaways of this video. In this video, we learned that Constant Analysis plots a feasible design space that meets all given requirements. It converts the multiple design requirements into a few numbers, which are power to weight ratio, thrust to weight ratio, and wing loading. These numbers can be used to calculate initial design parameters.

The Constant Analysis Live Task provides both plot and numerical results, which can be used to explore design space in optimization workflows. We can also convert the Live Task into the Matlab code for customizing the analysis. To download the Live Task, please find the link in the description. In case of any query, please feel free to connect with us at roboticsarena@mathworks.com. Thank you.