Aircraft Performance

Flight Mechanics: Steady and Level Flight - Pluto Notebook

Description:

This Pluto.jl notebook provides an interactive tool for analyzing the aerodynamic performance of an aircraft during steady, level flight. It allows users to define key aircraft parameters (like wing area, mass, aerodynamic coefficients) and an operating point (True Air Speed and Altitude). Based on these inputs, the notebook calculates and visualizes crucial flight mechanics parameters, including:

1. Atmospheric Conditions: Calculates pressure, density, temperature, speed of sound, and dynamic pressure at the specified altitude using the International Standard Atmosphere (ISA+0) model.

2. Flight Speeds: Converts between True Air Speed (TAS) and Equivalent Air Speed (EAS), calculates Mach number, and determines the aircraft's stall speed (TAS and EAS).

3. Aerodynamic Coefficients: Calculates the required Lift Coefficient (CL) for level flight and the corresponding Induced Drag Coefficient (CDi) and total Drag Coefficient (CD).

4. Performance Metrics: Determines the Thrust Required and Power Required curves as a function of speed, identifies the minimum thrust/power required points, and calculates the maximum Lift-to-Drag ratio (L/D max).

5. Visualizations: Generates several plots to help understand the aircraft's performance:

   • A flight envelope plot showing dynamic pressure contours, stall speed boundary, and Mach number limits.

   • Plots of Thrust Required (total, parasitic, induced) vs. TAS.

   • A plot of the Lift-to-Drag ratio (L/D) vs. TAS.

   • A plot of Power Required vs. TAS.

   • A plot showing the variation of key ISA atmospheric properties with altitude.

The notebook leverages Julia's capabilities for scientific computing and uses PlutoUI for interactive elements, Plots for visualization, and standard libraries for calculations. It's designed primarily for academic purposes to help students and educators explore the fundamental concepts of aircraft performance in steady, level flight.

Disclaimer: As clearly stated in the notebook, this tool is solely for academic purposes and must not be used for real operational environments or aircraft design.

✈ To use this Pluto (Julia) notebook follow the instructions in "An introduction to the Julia language for Researchers"

Link to GitHub repository Low_speed_AC_performance/21_04_08_Low_speed_perfo_v_0.0.1.jl at main · flt-acdesign/Low_speed_AC_performance 

User's Guide:

1. Running the Notebook:
   
   

   • You need Julia and the Pluto.jl package installed on your system.

   • Save the notebook code to a file (e.g., steady_flight.jl).

   • Start Pluto from the Julia REPL (using Pluto; Pluto.run()) or your system terminal (julia -e 'using Pluto; Pluto.run()').

   • Open the saved notebook file (steady_flight.jl) from the Pluto interface in your web browser.

   • The notebook will automatically install the required packages (PlutoUI, Plots, Colors, ColorSchemes, LaTeXStrings) in a temporary environment if they are not already available in your main Julia environment.

2. Interacting with Inputs:
   
   

   • The notebook uses interactive input fields created with @bind. Simply click on the number field next to a parameter and type in a new value or use the up/down arrows if available.

   • Pluto is reactive: changing any input value will automatically trigger recalculations and update all dependent outputs (text and plots) in real-time.

   • Set Operating Point:

     • TAS(m/s): Enter the desired True Air Speed in meters per second.

     • Altitude(m): Enter the desired flight altitude in meters.

     • Max. Oper. Mach: Enter the aircraft's Maximum Operating Mach number (MMO).

   • Define Aircraft Parameters:

     • Wing area (Sw) m^2: Enter the aircraft's reference wing area in square meters.

     • CLmax: Enter the aircraft's maximum lift coefficient (dimensionless).

     • Aircraft mass (M) kg: Enter the total mass of the aircraft in kilograms.

     • CD0: Enter the aircraft's zero-lift drag coefficient (parasitic drag coefficient, dimensionless).

     • Oswald (e): Enter the Oswald efficiency factor (dimensionless, typically 0.7-0.9).

     • Aspect Ratio (AR): Enter the wing aspect ratio (span²/area, dimensionless).

3. Understanding the Outputs:
   
   

   • Operating Point Summary: Directly below the inputs, you'll see calculated values for the chosen operating point: TAS (m/s and knots), EAS (m/s and knots), Mach number, Altitude (meters and feet), and Reynolds number per meter.

   • Dynamic Pressure Plot:

     • Visualizes the flight envelope. The background color contour shows dynamic pressure (q) variation with TAS and Altitude.

     • The leftmost solid line shows the Stall Speed (TAS) boundary, which increases with altitude. Flying left of this line is generally not possible in level flight.

     • Lines show Mach numbers (M=0.5, MMO, M=1.0). Flying right of the MMO line exceeds the defined maximum operating Mach.

     • The ✈ icon marks your currently selected operating point (TAS, Altitude). It turns red if the selected point is below the stall speed. Associated text labels show TAS, altitude, dynamic pressure (q), and required CL at this point.

     • The circle on the stall line at the operating altitude indicates the specific stall speed (TAS) for that altitude, with its value in knots annotated.

   • Drag Coefficients: Displays the calculated Induced Drag (CDi), the input Zero-Lift Drag (CD0), and the total Drag (CD) at the operating point, shown in "Drag Counts" (DC), where 1 DC = CD of 0.0001.

   • Stall Speeds: Shows the calculated stall speeds (TAS and EAS) in both m/s and knots for the current aircraft configuration and mass at the operating altitude (TAS) or sea level (EAS).

   • Minimum Thrust / Max L/D: Displays the minimum thrust required for level flight and the speed (TAS, kt TAS, KEAS) at which it occurs. This speed corresponds to the maximum Lift-to-Drag ratio (L/D max), which is also displayed.

   • Minimum Power: Displays the minimum power required for level flight and the speed (TAS, kt TAS, KEAS) at which it occurs. Note that this speed is lower than the minimum drag speed.

   • Thrust Required Plot:

     • Shows Parasitic Drag, Induced Drag, and Total Thrust Required (which equals total drag in steady level flight) versus TAS at the selected altitude.

     • A marker indicates the point of Minimum Thrust Required, corresponding to the speed for Maximum L/D (VMD).

   • L/D Plot:

     • Shows the aircraft's Lift-to-Drag ratio versus TAS.

     • A marker indicates the Maximum L/D point and the corresponding speed (VMD).

   • Power Required Plot:

     • Shows the Power Required (Thrust Required * TAS) versus TAS.

     • Markers indicate the Minimum Power Required point (at speed VMDV) and the Power Required at the Minimum Drag speed (VMD).

     • A dashed line from the origin tangent to the curve illustrates how the minimum power required speed (VMDV) is determined graphically.

   • ISA Atmosphere Plot:

     • Shows how pressure, density, speed of sound, and temperature vary with altitude relative to their Mean Sea Level (MSL) values, according to the ISA model. A vertical line marks the selected operating altitude.

4. Exploring Concepts:
   
   

   • Change the altitude and observe how stall speed (TAS) increases, while EAS stall speed remains constant. See how thrust/power required changes.

   • Change the mass and see its effect on stall speed, thrust required, and power required.

   • Adjust CD0 or Oswald factor (e) and observe the impact on L/D max, minimum thrust/power, and the shape of the drag/power curves.

   • Compare the speeds for minimum drag (Max L/D) and minimum power.

5. Code Sections:
   
   

   • The notebook includes cells defining the underlying aerodynamic and atmospheric functions. These have helpful "docstrings" explaining what each function does, its parameters, and examples. You can view these by clicking the "Live docs" button in Pluto or simply reading the comments above each function.

By interactively changing the inputs and observing the resulting calculations and plots, you can gain a deeper understanding of the relationships governing aircraft performance in steady, level flight.