This document discusses airplane performance analysis. It covers static and dynamic performance topics like thrust required, thrust available, maximum velocity, rate of climb, takeoff, landing, equations of motion, drag polar, and drag types. It provides equations and examples to calculate thrust required, lift-to-drag ratio, and velocity for minimum thrust required.
Atmosphere: Properties and Standard Atmosphere | Flight Mechanics | GATE Aero...Age of Aerospace
For Video Lecture of this presentation: https://youtu.be/DqaoNt0LoIE
The topics covered in this session are, Properties of Atmosphere, International Standard Atmosphere (ISA) definition and derivation, ISA Chart. The formula for obtaining ISA Chartar completely derived from basic equations.
Attention! "Gate Aerospace Engineering aspirants", A virtual guide for gate aerospace engineering is provided in "Age of Aerospace" blog for helping you meticulously prepare for gate examination. Respective notes of individual subjects are provided as 'Embedded Google Docs' which are frequently updated. This comprehensive guide is intended to efficiently serve as an extensive collection of online resources for "GATE Aerospace Engineering" which can be accessed free of cost. Use the following link to access the study material
https://ageofaerospace.blogspot.com/p/gate-aerospace.html
Airspeeds | Q & A | Question Analysis | Flight Mechanics | GATE AerospaceAge of Aerospace
Question Analysis, Book Reference, Important Concepts, Formulae and topic wise Solutions for the topic "Airspeeds" are time-stamped below. Access the study materials, presentation, links to previous and next lectures and further information in the description section.
What are the elements of aircraft performance?
How much thrust do you need?
How fast and how slow can you fly?
#WikiCourses
http://wikicourses.wikispaces.com/Topic+Performance+of+aerospace+vehicles
Mechanics of Aircraft Structures solution manual C.T. Sun 2nd edDiego Fung
Designed to help students get a solid background in structural mechanics and extensively updated to help professionals get up to speed on recent advances This Second Edition of the bestselling textbook Mechanics of Aircraft Structures combines fundamentals, an overview of new materials, and rigorous analysis tools into an excellent one-semester introductory course in structural mechanics and aerospace engineering. It's also extremely useful to practicing aerospace or mechanical engineers who want to keep abreast of new materials and recent advances. Updated and expanded, this hands-on reference covers: * Introduction to elasticity of anisotropic solids, including mechanics of composite materials and laminated structures * Stress analysis of thin-walled structures with end constraints * Elastic buckling of beam-column, plates, and thin-walled bars * Fracture mechanics as a tool in studying damage tolerance and durability Designed and structured to provide a solid foundation in structural mechanics, Mechanics of Aircraft Structures, Second Edition includes more examples, more details on some of the derivations, and more sample problems to ensure that students develop a thorough understanding of the principles.
Atmosphere: Properties and Standard Atmosphere | Flight Mechanics | GATE Aero...Age of Aerospace
For Video Lecture of this presentation: https://youtu.be/DqaoNt0LoIE
The topics covered in this session are, Properties of Atmosphere, International Standard Atmosphere (ISA) definition and derivation, ISA Chart. The formula for obtaining ISA Chartar completely derived from basic equations.
Attention! "Gate Aerospace Engineering aspirants", A virtual guide for gate aerospace engineering is provided in "Age of Aerospace" blog for helping you meticulously prepare for gate examination. Respective notes of individual subjects are provided as 'Embedded Google Docs' which are frequently updated. This comprehensive guide is intended to efficiently serve as an extensive collection of online resources for "GATE Aerospace Engineering" which can be accessed free of cost. Use the following link to access the study material
https://ageofaerospace.blogspot.com/p/gate-aerospace.html
Airspeeds | Q & A | Question Analysis | Flight Mechanics | GATE AerospaceAge of Aerospace
Question Analysis, Book Reference, Important Concepts, Formulae and topic wise Solutions for the topic "Airspeeds" are time-stamped below. Access the study materials, presentation, links to previous and next lectures and further information in the description section.
What are the elements of aircraft performance?
How much thrust do you need?
How fast and how slow can you fly?
#WikiCourses
http://wikicourses.wikispaces.com/Topic+Performance+of+aerospace+vehicles
Mechanics of Aircraft Structures solution manual C.T. Sun 2nd edDiego Fung
Designed to help students get a solid background in structural mechanics and extensively updated to help professionals get up to speed on recent advances This Second Edition of the bestselling textbook Mechanics of Aircraft Structures combines fundamentals, an overview of new materials, and rigorous analysis tools into an excellent one-semester introductory course in structural mechanics and aerospace engineering. It's also extremely useful to practicing aerospace or mechanical engineers who want to keep abreast of new materials and recent advances. Updated and expanded, this hands-on reference covers: * Introduction to elasticity of anisotropic solids, including mechanics of composite materials and laminated structures * Stress analysis of thin-walled structures with end constraints * Elastic buckling of beam-column, plates, and thin-walled bars * Fracture mechanics as a tool in studying damage tolerance and durability Designed and structured to provide a solid foundation in structural mechanics, Mechanics of Aircraft Structures, Second Edition includes more examples, more details on some of the derivations, and more sample problems to ensure that students develop a thorough understanding of the principles.
FM-Basics Topics Wise Solutions | Q & A | Flight Mechanics | GATE AerospaceAge of Aerospace
For Video Lecture of this presentation: https://youtu.be/XNsIdHUx7q8
The topics covered in this session are, Airplane (fixed wing aircraft) configurations and various parts of airplane. A detailed list of airplane configuration is discussed with general insight about airplane parts.
Attention! "Gate Aerospace Engineering aspirants", A virtual guide for gate aerospace engineering is provided in "Age of Aerospace" blog for helping you meticulously prepare for gate examination. Respective notes of individual subjects are provided as 'Embedded Google Docs' which are frequently updated. This comprehensive guide is intended to efficiently serve as an extensive collection of online resources for "GATE Aerospace Engineering" which can be accessed free of cost. Use the following link to access the study material
https://ageofaerospace.blogspot.com/p/gate-aerospace.html
Airplane (fixed wing aircraft) configuration and various parts | Flight Mecha...Age of Aerospace
For Video Lecture of this presentation: https://youtu.be/uD_qWvTZEhY
The topics covered in this session are, Airplane (fixed wing aircraft) configurations and various parts of airplane. A detailed list of airplane configuration is discussed with general insight about airplane parts.
Attention! "Gate Aerospace Engineering aspirants", A virtual guide for gate aerospace engineering is provided in "Age of Aerospace" blog for helping you meticulously prepare for gate examination. Respective notes of individual subjects are provided as 'Embedded Google Docs' which are frequently updated. This comprehensive guide is intended to efficiently serve as an extensive collection of online resources for "GATE Aerospace Engineering" which can be accessed free of cost. Use the following link to access the study material
https://ageofaerospace.blogspot.com/p/gate-aerospace.html
Takeoff and Landing | Flight Mechanics | GATE AerospaceAge of Aerospace
For Video Lecture of this presentation: https://youtu.be/ieQYv7p-tnQ
The topics covered in this session are, takeoff performance (ground roll & airborne distance), landing performance (approach distance, flare distance & ground roll). The equations are completely derived from basics and physical significance of the concept is also discussed.
Attention! "Gate Aerospace Engineering aspirants", A virtual guide for gate aerospace engineering is provided in "Age of Aerospace" blog for helping you meticulously prepare for gate examination. Respective notes of individual subjects are provided as 'Embedded Google Docs' which are frequently updated. This comprehensive guide is intended to efficiently serve as an extensive collection of online resources for "GATE Aerospace Engineering" which can be accessed free of cost. Use the following link to access the study material
https://ageofaerospace.blogspot.com/p/gate-aerospace.html
Pressure Distribution on an Airfoil
The team conducted the experiment to determine the effects of pressure distribution on lift and pitching moment and the behavior of stall for laminar and turbulent boundary layers in the USNA Closed-Circuit Wing Tunnel (CCWT) with an NACA 65-012 airfoil at a Reynolds number of 1,000,000. The airfoil was tested in a clean configuration at angles of attack of 0, 5, 8, 10, and 12 degrees. Tape added to the leading edge tripped the boundary layer, and pressure distributions were taken at 8, 10, and 12 degrees angle of attack. Experimental results showed a suction peak at less than 1% of chord, providing a beneficial test article for contrast between smooth and laminar boundary layer behavior at the stall condition. The maximum lift coefficient for the clean airfoil was 0.9 at 10 degrees angle of attack, and tripped airfoil reached a maximum lift coefficient of 1.03 at 12 degrees angle of attack, a 14% increase. These data were 10% lower than the empirical airfoil data found in Theory of Wing Sections from Abbott and von Doenhoff. Pitching moment coefficient about the quarter chord remained near zero below stall as expected for a symmetrical airfoil, but rapidly became negative after stall for experimental and empirical data. The airfoil exhibited a leading edge stall for both laminar and turbulent boundary layers.
Angle of attack | Flight Mechanics | GATE AerospaceAge of Aerospace
For Video Lecture of this presentation: https://youtu.be/GXKgH0guKqg
The topics covered in this session are, Definition: Angle of Attack (AOA), Insights,FoilSim AOA effect Visualization: Symmetric Airfoil, Cambered Airfoil, Flat Plate,Special Question: Why Airfoil?, Why not flat plate?
Attention! "Gate Aerospace Engineering aspirants", A virtual guide for gate aerospace engineering is provided in "Age of Aerospace" blog for helping you meticulously prepare for gate examination. Respective notes of individual subjects are provided as 'Embedded Google Docs' which are frequently updated. This comprehensive guide is intended to efficiently serve as an extensive collection of online resources for "GATE Aerospace Engineering" which can be accessed free of cost. Use the following link to access the study material
https://ageofaerospace.blogspot.com/p/gate-aerospace.html
Angle of Attack | Q & A | Question Analysis | Flight Mechanics | GATE AerospaceAge of Aerospace
Question Analysis, Book Reference, Important Concepts, and topic wise Solutions for the topic "Angle of Attack" are time-stamped below. Access the study materials, presentation, links to previous and next lectures and further information in the description section.
For Video Lecture of this presentation: https://youtu.be/NAjezfbWh4Y
The topics covered in this session are, drag, categories of drag, drag polar equation and drag polar graph, drag polar derivation, induced drag coefficient.
Attention! "Gate Aerospace Engineering aspirants", A virtual guide for gate aerospace engineering is provided in "Age of Aerospace" blog for helping you meticulously prepare for gate examination. Respective notes of individual subjects are provided as 'Embedded Google Docs' which are frequently updated. This comprehensive guide is intended to efficiently serve as an extensive collection of online resources for "GATE Aerospace Engineering" which can be accessed free of cost. Use the following link to access the study material
https://ageofaerospace.blogspot.com/p/gate-aerospace.html
Fighter Aircraft Performance, Part II of two, describes the parameters that affect aircraft performance.
For comments please contact me at solo.hermelin@gmail.com.
For more presentations on different subjects visit my website at http://www.solohermelin.com.
FM-Basics Topics Wise Solutions | Q & A | Flight Mechanics | GATE AerospaceAge of Aerospace
For Video Lecture of this presentation: https://youtu.be/XNsIdHUx7q8
The topics covered in this session are, Airplane (fixed wing aircraft) configurations and various parts of airplane. A detailed list of airplane configuration is discussed with general insight about airplane parts.
Attention! "Gate Aerospace Engineering aspirants", A virtual guide for gate aerospace engineering is provided in "Age of Aerospace" blog for helping you meticulously prepare for gate examination. Respective notes of individual subjects are provided as 'Embedded Google Docs' which are frequently updated. This comprehensive guide is intended to efficiently serve as an extensive collection of online resources for "GATE Aerospace Engineering" which can be accessed free of cost. Use the following link to access the study material
https://ageofaerospace.blogspot.com/p/gate-aerospace.html
Airplane (fixed wing aircraft) configuration and various parts | Flight Mecha...Age of Aerospace
For Video Lecture of this presentation: https://youtu.be/uD_qWvTZEhY
The topics covered in this session are, Airplane (fixed wing aircraft) configurations and various parts of airplane. A detailed list of airplane configuration is discussed with general insight about airplane parts.
Attention! "Gate Aerospace Engineering aspirants", A virtual guide for gate aerospace engineering is provided in "Age of Aerospace" blog for helping you meticulously prepare for gate examination. Respective notes of individual subjects are provided as 'Embedded Google Docs' which are frequently updated. This comprehensive guide is intended to efficiently serve as an extensive collection of online resources for "GATE Aerospace Engineering" which can be accessed free of cost. Use the following link to access the study material
https://ageofaerospace.blogspot.com/p/gate-aerospace.html
Takeoff and Landing | Flight Mechanics | GATE AerospaceAge of Aerospace
For Video Lecture of this presentation: https://youtu.be/ieQYv7p-tnQ
The topics covered in this session are, takeoff performance (ground roll & airborne distance), landing performance (approach distance, flare distance & ground roll). The equations are completely derived from basics and physical significance of the concept is also discussed.
Attention! "Gate Aerospace Engineering aspirants", A virtual guide for gate aerospace engineering is provided in "Age of Aerospace" blog for helping you meticulously prepare for gate examination. Respective notes of individual subjects are provided as 'Embedded Google Docs' which are frequently updated. This comprehensive guide is intended to efficiently serve as an extensive collection of online resources for "GATE Aerospace Engineering" which can be accessed free of cost. Use the following link to access the study material
https://ageofaerospace.blogspot.com/p/gate-aerospace.html
Pressure Distribution on an Airfoil
The team conducted the experiment to determine the effects of pressure distribution on lift and pitching moment and the behavior of stall for laminar and turbulent boundary layers in the USNA Closed-Circuit Wing Tunnel (CCWT) with an NACA 65-012 airfoil at a Reynolds number of 1,000,000. The airfoil was tested in a clean configuration at angles of attack of 0, 5, 8, 10, and 12 degrees. Tape added to the leading edge tripped the boundary layer, and pressure distributions were taken at 8, 10, and 12 degrees angle of attack. Experimental results showed a suction peak at less than 1% of chord, providing a beneficial test article for contrast between smooth and laminar boundary layer behavior at the stall condition. The maximum lift coefficient for the clean airfoil was 0.9 at 10 degrees angle of attack, and tripped airfoil reached a maximum lift coefficient of 1.03 at 12 degrees angle of attack, a 14% increase. These data were 10% lower than the empirical airfoil data found in Theory of Wing Sections from Abbott and von Doenhoff. Pitching moment coefficient about the quarter chord remained near zero below stall as expected for a symmetrical airfoil, but rapidly became negative after stall for experimental and empirical data. The airfoil exhibited a leading edge stall for both laminar and turbulent boundary layers.
Angle of attack | Flight Mechanics | GATE AerospaceAge of Aerospace
For Video Lecture of this presentation: https://youtu.be/GXKgH0guKqg
The topics covered in this session are, Definition: Angle of Attack (AOA), Insights,FoilSim AOA effect Visualization: Symmetric Airfoil, Cambered Airfoil, Flat Plate,Special Question: Why Airfoil?, Why not flat plate?
Attention! "Gate Aerospace Engineering aspirants", A virtual guide for gate aerospace engineering is provided in "Age of Aerospace" blog for helping you meticulously prepare for gate examination. Respective notes of individual subjects are provided as 'Embedded Google Docs' which are frequently updated. This comprehensive guide is intended to efficiently serve as an extensive collection of online resources for "GATE Aerospace Engineering" which can be accessed free of cost. Use the following link to access the study material
https://ageofaerospace.blogspot.com/p/gate-aerospace.html
Angle of Attack | Q & A | Question Analysis | Flight Mechanics | GATE AerospaceAge of Aerospace
Question Analysis, Book Reference, Important Concepts, and topic wise Solutions for the topic "Angle of Attack" are time-stamped below. Access the study materials, presentation, links to previous and next lectures and further information in the description section.
For Video Lecture of this presentation: https://youtu.be/NAjezfbWh4Y
The topics covered in this session are, drag, categories of drag, drag polar equation and drag polar graph, drag polar derivation, induced drag coefficient.
Attention! "Gate Aerospace Engineering aspirants", A virtual guide for gate aerospace engineering is provided in "Age of Aerospace" blog for helping you meticulously prepare for gate examination. Respective notes of individual subjects are provided as 'Embedded Google Docs' which are frequently updated. This comprehensive guide is intended to efficiently serve as an extensive collection of online resources for "GATE Aerospace Engineering" which can be accessed free of cost. Use the following link to access the study material
https://ageofaerospace.blogspot.com/p/gate-aerospace.html
Fighter Aircraft Performance, Part II of two, describes the parameters that affect aircraft performance.
For comments please contact me at solo.hermelin@gmail.com.
For more presentations on different subjects visit my website at http://www.solohermelin.com.
A Good Effect of Airfoil Design While Keeping Angle of Attack by 6 Degreepaperpublications3
Abstract: Airfoil is a shape of wing or blade of (a propeller, rotor or turbine) by which a fluid generates an aerodynamic force. The component of this force perpendicular to the direction of its speed is called lift force and the component parallel to its speed is called drag forces. Here we see that if we set the angle of attack by 6 degree in fluid NACA0012 we found the aerodynamic forces with suitable positive result our research is totally based on iterations method and based on the help of cfd software.
Banked turn and its effects on Stall speed of an AirplaneJagrataBanerjee
This presentation is totally meant to show that -- Why an airplane needs to roll to the side of the turn? And, what are the effects of such banked turns on Stall Speed (minimum airspeed required to stay airborne) of an airplane.
Not only that, this slide also covers that why and how Stall speed will change with respect to the bank angle. Also, it shows the derivation of the formula to calculate the stall speed in a banked turn.
Hope, you will enjoy it and understand & learn a lot.
The International Journal of Engineering and Science (IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
AIRCRAFT PITCH EECE 682 Computer Control Of Dynamic.docxgalerussel59292
AIRCRAFT PITCH
EECE 682
Computer Control Of Dynamic System
Project Report
Boeing Aircraft- Pitch Controller
Example: Dynamics, Modeling, Simulation, Analysis
Instructor:
Dr. Adel Ghandakly
Dept. Electrical and Computer Engineering
California State University, Chico
Submitted By:
Nasser Al Ahbabi
AIRCRAFT PITCH
BOEING AIRCRAFT- PITCH CONTROLLER
Example: Dynamics, Modeling, Simulation, Analysis
by
Nasser Al Ahbabi
California State University, Chico.
NOVEMBER 2014
Abstract
Though airplane has a number of important factors, its stability and control is a key design parameter that must be met. In an airplane
the stability is defined in three angles i.e. pitch, yaw, and roll. In this paper I have focused on the pitch. The system transfer was
AIRCRAFT PITCH
obtained through analyzing the various parameter involved in the pitch control. In all the designs, I considered the design parameter
requirements i.e. the percentage overshoot, steady state error, settling time, and rise time of Boeing aircraft. The designs of pitch
controller using various techniques have been implemented on the system transfer function. I have provided an extension of to these
techniques by using MATLAB/Simulink models that plays an important role in monitoring the results of designed controllers. In
addition, I have also provided a descriptive analysis of the system response to the designed controllers and their conclusions.
Keywords: Aircraft, Pitch, Ackerman, Digitized PID, Diophantine, Optimal Control, Controller , Simulink and MATLAB design.
CONTENTS:
INTRODUCTION
� INTRODUCTION
MATHEMATICAL MODEL
� BOEING AIRCRAFT: PHYSICAL SETUP AND SYSTEM EQUATIONS
� TRANSFER FUNCTION AND STATE-SPACE MODEL
� DESIGN REQUIREMENTS:
CONTROLLER DESIGN
AIRCRAFT PITCH
� DESIGN 1 : DIGITIZED PID
� DESIGN 2 : DIRECT METHOD ( CLOSED FORM)
� DESIGN 3 : DIRECT METHOD ( DIOPHANTINE)
� DESIGN 4 : POLE PLACEMENT (ACKERMAN’S FORMULA)
� DESIGN 5 : OPTIMAL CONTROL
CONCLUSION
REFERENCES
1. INTRODUCTION
Aircrafts are perfect and good examples of a Controller system. They possess unique characteristics that make their controller design a
more challenging problem. On linearization of the model we can attain results with simplified controller designs.
Major parameter in the design of aircrafts entails the horizontal speed, pitch control and the throttle. The throttle controls the main
motor revolutions per minute; the pitch controls the magnitude of the motor thrust. There are two inputs that are independent; the
longitudinal input and the lateral cyclic input. These controls
An aircraft in flight is free to rotate in three dimensions: pitch, nose up or down about an axis running from wing to wing, yaw, nose
left or right about an axis running up and down; and roll, rotation about an axis running from nose to tail. In this .
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
An Approach to Detecting Writing Styles Based on Clustering Techniquesambekarshweta25
An Approach to Detecting Writing Styles Based on Clustering Techniques
Authors:
-Devkinandan Jagtap
-Shweta Ambekar
-Harshit Singh
-Nakul Sharma (Assistant Professor)
Institution:
VIIT Pune, India
Abstract:
This paper proposes a system to differentiate between human-generated and AI-generated texts using stylometric analysis. The system analyzes text files and classifies writing styles by employing various clustering algorithms, such as k-means, k-means++, hierarchical, and DBSCAN. The effectiveness of these algorithms is measured using silhouette scores. The system successfully identifies distinct writing styles within documents, demonstrating its potential for plagiarism detection.
Introduction:
Stylometry, the study of linguistic and structural features in texts, is used for tasks like plagiarism detection, genre separation, and author verification. This paper leverages stylometric analysis to identify different writing styles and improve plagiarism detection methods.
Methodology:
The system includes data collection, preprocessing, feature extraction, dimensional reduction, machine learning models for clustering, and performance comparison using silhouette scores. Feature extraction focuses on lexical features, vocabulary richness, and readability scores. The study uses a small dataset of texts from various authors and employs algorithms like k-means, k-means++, hierarchical clustering, and DBSCAN for clustering.
Results:
Experiments show that the system effectively identifies writing styles, with silhouette scores indicating reasonable to strong clustering when k=2. As the number of clusters increases, the silhouette scores decrease, indicating a drop in accuracy. K-means and k-means++ perform similarly, while hierarchical clustering is less optimized.
Conclusion and Future Work:
The system works well for distinguishing writing styles with two clusters but becomes less accurate as the number of clusters increases. Future research could focus on adding more parameters and optimizing the methodology to improve accuracy with higher cluster values. This system can enhance existing plagiarism detection tools, especially in academic settings.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
Water billing management system project report.pdfKamal Acharya
Our project entitled “Water Billing Management System” aims is to generate Water bill with all the charges and penalty. Manual system that is employed is extremely laborious and quite inadequate. It only makes the process more difficult and hard.
The aim of our project is to develop a system that is meant to partially computerize the work performed in the Water Board like generating monthly Water bill, record of consuming unit of water, store record of the customer and previous unpaid record.
We used HTML/PHP as front end and MYSQL as back end for developing our project. HTML is primarily a visual design environment. We can create a android application by designing the form and that make up the user interface. Adding android application code to the form and the objects such as buttons and text boxes on them and adding any required support code in additional modular.
MySQL is free open source database that facilitates the effective management of the databases by connecting them to the software. It is a stable ,reliable and the powerful solution with the advanced features and advantages which are as follows: Data Security.MySQL is free open source database that facilitates the effective management of the databases by connecting them to the software.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
Heap Sort (SS).ppt FOR ENGINEERING GRADUATES, BCA, MCA, MTECH, BSC STUDENTS
Performance.pdf
1.
2. We will talk about
static and dynamic
performance.
3. We will answer questions such as:
How fast?
How high?
How far?
How long can an aircraft fly?
4. Coverage Airplane Performance
Static Performance
(zero acceleration)
Dynamic Performance
(finite acceleration)
Thrust Required
Thrust Available
Maximum
Velocity
Power Required
Power Available
Maximum Velocity
Rate of Climb
Takeoff
Landing
Equations of Motions
V-n Diagram
Turning Flight
Range and Endurance
Time to Climb
Maximum Altitude
Gliding Flight
Service Ceiling
Absolute Ceiling
Drag Polar
7. What is a drag polar?
It is a term coined by Eiffel.
The same monsieur of Eiffel tower fame.
The same guy who designed Quiapo bridge
(a.k.a. Quezon bridge)
It is a graph or an equation that accounts for all types of drag
in an airplane and how it relates to lift.
12. Pressure drag due to flow separation (form drag):
The drag due to the pressure imbalance in the
drag direction caused by separated flow.
Drag Types
13. Profile drag. The sum of skin friction drag and
form drag. (The term profile drag is usually used
in conjunction with two-dimensional airfoils; it is
sometimes called section drag.)
Drag Types
14. Interference drag. An additional pressure drag
caused by the mutual interaction of the flow
fields around each component of the airplane.
The total drag of the combined body is usually
greater than that of the sum of its individual
parts; the difference is the interference drag.
Drag Types
15. Parasite drag. The term used for the profile drag
for a complete airplane. It is that portion of the
total drag associated with skin friction and
pressure drag due to flow separation, integrated
over the complete airplane surface. It includes
interference drag.
Drag Types
16. Induced drag. A pressure drag due to the
pressure imbalance in the drag direction
caused by the induced flow (downwash)
associated with the vortices created at the tips
of finite wings.
Drag Types
17. Zero-lift drag. (Usually used in conjunction
with a complete airplane configuration.) The
parasite drag that exists when the airplane is
at its zero-lift angle of attack, that is, when the
lift of the airplane is zero.
Drag Types
18. Drag due to lift. (Usually used in conjunction with a
complete airplane.) That portion of the total airplane
drag measured above the zero-lift drag. It consists of
the change in parasite drag when the airplane is at an
angle of attack different from the zero-lift angle, plus
the induced drag from the wings and other lifting
components of the airplane.
Drag Types
19. Wave drag. The pressure drag associated with
transonic and supersonic flow (or shock waves,
hence the name). It can be expressed as the
sum the zero-lift wave drag and wave drag
due to lift.
Drag Types
20. Total Drag
Skin Friction Drag Pressure Drag
Induced Drag Wave Drag
Note : Profile Drag = Skin Friction Drag + Form Drag
Total Drag
Form Drag (Drag due to flow separation)
drag
induced
drag
profile
drag
total +
=
22. Drag Polar
eAR
C
C
C L
e
D
D
2
, +
=
parasite drag coefficient
-profile drag of wing
-friction and pressure drag of:
tail surfaces
fuselage
engine nacelles
landing gear
other components exposed to the flow
-a function of angle of attack
lift span
efficiency factor
induced drag coefficient
23. Drag Polar
2
0
,
, L
D
e
D rC
C
C +
=
2
0
, )
1
( L
D
D C
eAR
r
C
C
+
+
=
eAR
π
C
C
C L
e
D
D
2
, +
=
eAR
π
C
C
C L
D
D
2
0
, +
=
24. Drag polar of a complete airplane
i
D
D
L
D
D C
C
eAR
C
C
C ,
0
,
2
0
, +
=
+
=
induced drag
coefficient
parasite drag
coefficient at
zero lift
Oswald’s
efficiency
factor
25. Drag polar of a complete airplane
eAR
C
C
C L
D
D
2
0
, +
=
37. D
TR =
NOTE:
Thrust Required is a
function of velocity.
It has two
components.
It has a minimum.
Thrust Required for Level, Unaccelerated Flight
at a given velocity
38. Thrust Required for Level, Unaccelerated Flight
D
TR =
)
(
2
1
)
(
2
1
2
1
2
2
2
2
eAR
C
C
S
V
C
C
S
V
SC
V
D
T L
D
D
D
D
R o
i
o
+
=
+
=
=
=
)
)
2
/
1
(
(
2
1
2
2
2
eAR
S
V
L
C
S
V
T o
D
R
+
=
)
1
)(
2
1
(
2
1
2
2
2
eAR
S
V
W
C
S
V
T o
D
R
+
=
40. Applying a first and a second derivative test to this function
will confirm the existence of a minimum. This minimum will
exist at velocity,
2
/
1
1
2
min
,
=
S
W
eAR
C
V
o
R
D
T
)
(
)
1
)(
2
1
(
2
1
2
2
2
=
+
= V
f
eAR
S
V
W
C
S
V
T o
D
R
Thrust Required for Level, Unaccelerated Flight
42. Thrust Required: Alternative Approach
D
TR =
L
D
R
C
C
W
T
W
L
=
=
Since
D
L
R
C
C
W
T
/
=
Since we have already established the existence of a minimum
thrust required, this equation implies the existence of a
maximum lift-to-drag ratio.
43. Thrust Required: Alternative Approach
Indeed there is a
maximum L/D ratio
exhibited by every
aircraft.
You will see how this
ratio is an indicator of
performance
(aerodynamic efficiency)
of an aircraft.
45. Different
points on TR
curve
correspond to
different
angles of
attack.
+
=
=
=
=
=
eAR
C
C
S
q
SC
q
D
SC
q
SC
V
W
L
L
D
D
L
L
2
0
,
2
2
1
At a:
Large q∞
Small CL and a
D large
At b:
Small q∞
Large CL (or CL
2) and a to support W
D large
Thrust Required: Alternative Approach
46. Thrust Required Computation
TR is thrust required
to fly at a given
velocity in level,
unaccelerated flight
1. Select a flight speed,V∞ and calculate CL.
S
V
W
CL
2
2
1
=
eAR
C
C
C L
D
D
2
0
, +
=
2. Calculate CD.
3. Calculate CL/CD and calculateTR.
=
D
L
R
C
C
W
T
47. CP-1: A light, single-engine, propeller-driven, private airplane,
approximately modelled after the Cessna Skylane, having the following
characteristics:
Wingspan = 35.8 ft
Wing area = 174 ft2
Normal gross weight = 2950 lb
Fuel capacity: 65 gal of aviation gasoline
Power plant: one-piston engine, 230 hp (SL)
Specific fuel consumption= 0.45 lb/(hp)(h)
Parasite drag coefficient CD,o = 0.025
Oswald efficiency factor, e = 0.8
Propeller efficiency = 0.8
Example
51. CJ-1: A jet-powered executive aircraft, approximately modelled after
the Cessna Citation 3, having the following characteristics:
Wingspan = 53.3 ft
Wing area = 318 ft2
Normal gross weight = 19,815 lb
Fuel capacity: 1119 gal of kerosene
Power plant: two turbofan engines of 3650-lb thrust each at sea level
Specific fuel consumption = 0.6 lb of fuel/(lb thrust)(h)
Parasite drag coefficient CD,o = 0.02
Oswald efficiency factor e = 0.81
Example
55. How do we compute for (L/D)max?
At TRmin we found (by differentiating TR with
respect to V and equating to zero),
2
/
1
1
2
min
,
=
S
W
eAR
C
V
o
R
D
T
i
D
L
D C
eAR
C
C ,
2
0
, =
=
From this formula for V at TRmin, the following
relationship (which has already been revealed in
the graph) can be derived:
0
,
0
,
0
, 4
/
2
/
/ D
D
D
D
L C
eAR
C
eAR
C
C
C
=
=
Thus,
and this is a maximum
because an (L/D)max is simultaneous with a TRmin.
56. i
D
L
D C
eAR
C
C ,
2
0
, =
=
How do we compute for (L/D)max?
0
,
max
4
/ D
D
L C
eAR
C
C
=
At TRmin
Thus,
57. How do we compute for TRmin?
You can substitute
Or you can substitute
0
,
max 4
/
)
/
( D
D
L C
eAR
C
C
=
)
1
)(
2
1
(
2
1
2
2
2
eAR
S
V
W
C
S
V
T o
D
R
+
=
=
D
L
R
C
C
W
T
to to
2
/
1
1
2
min
,
=
S
W
eAR
C
V
o
R
D
T
59. Effects of altitude onTR
)
1
)(
2
1
(
2
1
2
2
2
eAR
S
V
W
C
S
V
T o
D
R
+
=
Note that the minimum thrust required is independent of altitude.
2
/
1
1
2
min
,
=
S
W
eAR
C
V
o
R
D
Lower
T
2
/
1
1
2
min
,
=
S
W
eAR
C
V
o
R
D
Higher
T
max
min
,
=
D
L
R
C
C
W
T
64. Example
Calculate the maximum velocity for the sample jet plane.
Vmax = 975 ft/s
= 665 mi/h
Intersection of TR
curve and maximum
TA defines maximum
flight speed of airplane.
65. Example
Some remarks. Computation of TR
curve assumed constant CD,o
At this speed, drag
divergence effects are
significant, and adds to
the CD,o
66. Maximum Velocity: Analytical
+
=
=
=
eAR
C
C
S
q
SC
q
T
D L
D
D
2
0
,
S
q
W
CL
=
eAR
S
q
W
SC
q
eAR
S
q
W
C
S
q
T D
D
+
=
+
=
2
0
,
2
2
2
0
,
0
2
0
,
2
=
+
−
eAR
S
W
T
q
SC
q D
Steady, level flight:T = D
Steady, level flight: L =W
Substitute into
drag equation
Turn this equation into a
quadratic
equation (by multiplying by q∞)
and rearranging.
68. Maximum Velocity: Design Considerations
2
1
0
,
0
,
2
max
max
max
4
−
+
=
D
D
A
A
C
eAR
C
W
T
S
W
S
W
W
T
V
• TA,max does not appear alone, but only in ratio: (TA/W)max
• S does not appear alone, but only in ratio: (W/S)
• Vmax does not depend on thrust alone or weight alone, but rather on
ratios
• (TA/W)max: maximum thrust-to-weight ratio
• W/S: wing loading
69. Maximum Velocity: Design Considerations
• Vmax also depends on density (altitude), CD,0, eAR
• Increase Vmax by
• Increase maximum thrust-to-weight ratio, (TA/W)max
• Increasing wing loading, (W/S)
• Decreasing zero-lift drag coefficient, CD,0
2
1
0
,
0
,
2
max
max
max
4
−
+
=
D
D
A
A
C
eAR
C
W
T
S
W
S
W
W
T
V
70. Example
CalculateVmax for the CP-1.
2
lb/ft
95
.
16
174
2950
=
=
S
W
Wingspan = 35.8 ft
Wing area = 174 ft2
Normal gross weight = 2950 lb
Fuel capacity: 65 gal of aviation gasoline
Power plant: one-piston engine, 230 hp (SL)
Specific fuel consumption= 0.45 lb/(hp)(h)
Parasite drag coefficient CD,o = 0.025
Oswald efficiency factor, e = 0.8
Propeller efficiency = 0.8
3
-
2
0
,
10
x
4066
.
5
]
174
/
)
8
.
35
)[(
8
.
0
(
)
025
.
0
(
4
4
=
=
eAR
CD
3
5
0
,
slug/ft
10
x
9425
.
5
)
025
.
0
(
002377
.
0
−
=
=
D
C
2
1
0
,
0
,
2
max
max
max
4
−
+
=
D
D
A
A
C
eAR
C
W
T
S
W
S
W
W
T
V
71. Example
CalculateVmax for the CP-1.
lb)/s
(ft
10
x
012
.
1
)
550
)(
230
(
8
.
0 5
=
=
=
=
P
P
V
T A
A
( )
max
max
V
P
TA
=
For maxTA and PA,V∞ =Vmax
max
max
max
305
.
34
1
V
V
W
P
W
TA
=
=
?
max
=
W
TA
2
1
0
,
0
,
2
max
max
max
4
−
+
=
D
D
A
A
C
eAR
C
W
T
S
W
S
W
W
T
V
72. Example
CalculateVmax for the CP-1.
2
/
1
3
2
max
max
max
max
max 10
x
4066
.
5
305
.
34
305
.
34
97
.
558
−
+
= −
V
V
V
Solve this by trial and error.
73.
74. Jets Engines are usually rated inThrust
Thrust is a Force with units (N = kg m/s2)
For example, the PW4000-112 is rated at 98,000 lb of thrust
Piston-Driven Engines are usually rated in terms of Power
Power is a precise term and can be expressed as:
Energy /Time with units (kg m2/s2) / s = kg m2/s3 = Watts
Note that Energy is expressed in Joules = kg m2/s2
Force *Velocity with units (kg m/s2) * (m/s) = kg m2/s3 =Watts
Usually rated in terms of horsepower (1 hp = 550 ft lb/s = 746W)
Why is there a need for a new parameter?
75. PR vs. V∞ curve qualitatively
resembles TR vs. V∞ curve.
Power Required
PR = TRV∞
78. Power Required, Minimum
)
(
)
1
)(
2
1
(
2
1 2
3
=
+
= V
f
eAR
S
V
W
C
S
V
P o
D
R
Get f’(V∞).
Equate to zero.
Solve forV∞ in f’(V∞)=0 to getVPR,min.
Substitute V∞ in f(V∞) to get PR,min.
The results are…
81.
=
= V
C
C
W
V
T
P
D
L
R
R
Power Required: Alternative Approach
L
SC
V
W
L
2
2
1
=
=
L
SC
W
V
=
2
L
D
L
R
R
SC
W
C
C
W
V
T
P
=
=
2
C
1
2
2
/
3
L
3
2
3
D
L
D
R
C
SC
C
W
P a
= x
87. How do we compute for (L3/2/D)max?
eAR
C
C
C L
D
D i
2
0
,
3 =
=
( ) 4
3
3
1
0
,
0
,
4
3
0
,
max
2
3
3
4
1
4
3
=
=
D
D
D
D
L
C
eAR
C
eAR
C
C
C
eAR
C
C D
L
0
,
3
=
88. i
D
D C
C =
0
,
3
How do we compute for (L3/2/D)max?
At PRmin
Thus,
4
3
3
1
0
,
max
2
3
3
4
1
=
D
D
L
C
eAR
C
C
91. How do we compute for PR,min?
You can substitute
Or you can substitute
to to
2
1
0
,
,
3
1
2
min
,
=
S
W
eAR
C
V
D
PR
)
1
)(
2
1
(
2
1 2
3
eAR
S
V
W
C
S
V
P o
D
R
+
=
4
3
3
1
0
,
max
2
3
3
4
1
=
D
D
L
C
eAR
C
C
C
1
2
D
2
3
L
3
=
C
S
ρ
W
PR
92. Effects of altitude on PR
2
1
0
0
,
,
2
1
0
0
=
=
R
ALT
R
ALT
P
P
V
V
C
1
2
D
2
3
L
3
=
C
S
W
PR
2
1
0
,
,
3
1
2
min
,
=
S
W
eAR
C
V
D
PR
93. Effects of altitude on PR
2
1
0
0
,
,
2
1
0
0
=
=
R
ALT
R
ALT
P
P
V
V
94. Effects of altitude on PR
2
1
0
0
,
,
2
1
0
0
=
=
R
ALT
R
ALT
P
P
V
V
95. SUMMARY
thrust required
power required
)
1
)(
2
1
(
2
1 2
3
eAR
S
V
W
C
S
V
P o
D
R
+
=
C
1
2
D
2
3
L
3
=
C
S
W
PR
)
1
)(
2
1
(
2
1
2
2
2
eAR
S
V
W
C
S
V
T o
D
R
+
=
D
L
R
C
C
W
T
/
=
96. SUMMARY
At minimum thrust required At minimum power required
i
D
D C
C ,
0
, =
0
,
max
4
/ D
D
L C
eAR
C
C
=
i
D
D C
C =
0
,
3
2
1
0
,
,
3
1
2
min
,
=
S
W
eAR
C
V
D
PR
2
/
1
1
2
min
,
=
S
W
eAR
C
V
o
R
D
T
( ) 4
3
3
1
0
,
0
,
4
3
0
,
max
2
3
3
4
1
4
3
=
=
D
D
D
D
L
C
eAR
C
eAR
C
C
C
109. Rate of Climb
sin
+
= WV
DV
TV
sin
W
D
T +
=
sin
/
=V
C
R
sin
=
−
V
W
DV
TV
W
DV
TV
C
R
−
=
/
110. Rate of Climb
W
DV
TV
C
R
−
=
/
Power Available ~ Power Required
(for small Ѳ)
sin
W
D
T +
=
−
= DV
TV
power
excess
W
C
R
power
excess
/ =
113. Example
Calculate the rate of climb vs velocity at sea level for (a) the CP-1
and (b) the CJ-1.
ft/min
1398
ft/s
3
.
23
2950
32600
-
10120
2950
P
P
power
excess
)
/
( R
A
=
=
=
−
=
=
W
C
R
AtV = 150 ft/s PR = 32,600 ft-lb/s and PA = 10,120 ft-lb/s. Hence,
117. R/Cmax: Analytical
( ) ( )2
max
2
max /
/
3
1
1
W
T
D
L
Z +
+
=
( ) ( )
( ) ( )
−
−
=
Z
D
L
W
T
Z
W
T
C
Z
S
W
C
R
D
2
max
2
max
2
/
3
max
2
/
1
0
,
max
/
/
2
3
6
1
3
/
/
( )
( ) 2
/
3
max
0
,
max
max
/
1
/
8776
.
0
/
D
L
C
S
W
W
P
C
R
D
−
=
For a piston-propeller aircraft:
For a jet aircraft:
Where:
121. Example
Calculate the absolute and service ceilings for (a) the CP-1 and (b) the CJ-
1.
W
C
R
power
excess
maximum
)
/
( max =
122. Example
Calculate the absolute and service ceilings for (a) the CP-1 and (b) the CJ-
1. (a) the CP-1 (b) the CJ-1
service ceilings = 25,000 ft
absolute ceilings = 27,000 ft
service ceilings = 48,000 ft
absolute ceilings = 49,000 ft
126. Time to Climb
b
mx
y +
=
0
max
0
max,
0
)
/
(
)
/
(
H
C
R
C
R
H
H +
−
=
0
H
0
max,
)
/
( C
R
=
H
C
R
dh
t
0 max
)
/
(
)
(
)
/
(
)
/
( 0
0
0
max,
max H
H
H
C
R
C
R −
=
−
=
H
H
H
dh
C
R
H
t
0 0
0
max,
0
)
/
(
−
=
H
H
H
C
R
H
t
0
0
0
max,
0
ln
)
/
(
Altitude,
H
Maximum Rate of Climb, (R/C)max
131. How do we compute for (L/D)max?
At TRmin we found (by differentiating TR with
respect to V and equating to zero),
2
/
1
1
2
min
,
=
S
W
eAR
C
V
o
R
D
T
i
D
L
D C
eAR
C
C ,
2
0
, =
=
From this formula for V at TRmin, the following
relationship (which has already been revealed in
the graph) can be derived:
0
,
0
,
0
, 4
/
2
/
/ D
D
D
D
L C
eAR
C
eAR
C
C
C
=
=
Thus,
and this is a maximum
because an (L/D)max is simultaneous with a TRmin.
132. Gliding Flight
To maximize range, glide at smallest (at (L/D)max )
A modern sailplane may have a glide ratio as high as 60:1
So = tan-1(1/60) ~ 1°
133. Example
Calculate the minimum glide angle and the maximum range measured
along the ground covered by the CP-1 and the CJ-1 in a power-off glide
that starts at an altitude of 10,000 ft.
10,000 ft
134. CP-1: A light, single-engine, propeller-driven, private airplane,
approximately modelled after the Cessna Skylane, having the following
characteristics:
Example
Aspect Ratio = 7.37
Parasite drag coefficient CD,o = 0.025
Oswald efficiency factor, e = 0.8
135. Example
Calculate the minimum glide angle and the maximum range measured
along the ground covered by the CP-1 in a power-off glide that starts at
an altitude of 10,000 ft.
( )
=
=
= −
2
.
4
61
.
13
1
1
tan
max
1
min
D
L
ft
136,000
)
61
.
13
(
10000
)
( max
max
=
=
=
D
L
h
R
10,000 ft
136. CJ-1: A jet-powered executive aircraft, approximately modelled after
the Cessna Citation 3, having the following characteristics:
Example
Aspect Ratio = 8.93
Parasite drag coefficient CD,o = 0.02
Oswald efficiency factor e = 0.81
( )
9
.
16
)
02
.
0
(
4
/
)
93
.
8
)(
81
.
0
(
4
/ 0
,
max
=
=
=
D
C
eAR
D
L
137. Example
Calculate the minimum glide angle and the maximum range measured
along the ground covered by the CJ-1 in a power-off glide that starts at
an altitude of 10,000 ft.
( )
=
=
= −
39
.
3
9
.
16
1
1
tan
max
1
min
D
L
ft
169,000
)
9
.
136
(
10000
)
( max
max
=
=
=
D
L
h
R
10,000 ft
138. Example
For the CP-1, calculate the equilibrium glide velocities at altitudes of
10,000 ft and 2,000 ft, each corresponding to the minimum glide angle.
L
SC
V
W
L
2
2
1
cos
=
=
S
W
C
V
L
=
cos
2
i
D
L
D C
eAR
C
C ,
2
0
, =
=
CL corresponding to
(L/D)max
At
(L/D)max
eAR
C
C D
L
0
,
=
634
.
0
)
37
.
7
)(
8
.
0
(
)
025
.
0
(
=
=
L
L
C
C
139. Example
For the CP-1, calculate the equilibrium glide velocities at altitudes of
10,000 ft and 2,000 ft, each corresponding to the minimum glide angle.
S
W
C
V
L
=
cos
2
2
lb/ft
95
.
16
174
2950
=
=
S
W
= 2
.
4
min
)
634
.
0
(
0017556
.
0
)
95
.
16
)(
2
.
4
cos
2
(
=
V
ft
10,000
h
at
ft/s
3
.
174 =
=
V
)
634
.
0
(
0022409
.
0
)
95
.
16
)(
2
.
4
cos
2
(
=
V
ft
2,000
h
at
ft/s
3
.
154 =
=
V
140.
141. f
W
W
W +
= 1
dt
dW
dt
dW f
=
Weight Equation
W –Weight of the airplane at any instant during flight.
W0 – Gross weight of the airplane, including everything: full fuel
load, payload, crew, structures, etc.
Wf – Weight of fuel: this is an instantaneous value, and it
changes as fuel is consumed during flight.
W1 –Weight of the airplane when the fuel tanks are empty.
f
W
W
=
142. ( )( )
hour
BHP
fuel
of
lb
SFC =
SFC VS TSFC
( )( )
hour
thrust
of
lb
fuel
of
lb
TSFC =
P
dt
dW
P
W
c
f
f
−
=
−
=
T
dt
dW
T
W
c
f
f
t −
=
−
=
pr
t
V
c
c
=
143. Range: Piston-Propeller
( )( )
=
=
V
mile
(HP)
fuel
of
lb
hour
HP
fuel
of
lb
SFC
( )
( )
R
T
SFC)
(
V
HP
SFC
mile
fuel
of
lb
To cover longest distance use minimum pounds of fuel per mile.
To cover longest distance fly at minimum thrust required.
144. Range: Piston-Propeller
dt
V
ds
dt
ds
V
=
=
T
c
dW
dt
T
dt
dW
c
t
f
f
t −
=
−
=
−
=
T
c
dW
V
ds
t
f
f
W
W
=
−
=
T
c
dW
V
ds
t
W
W
T
c
dW
V
ds
t
−
=
W
dW
D
L
c
V
W
L
D
c
dW
V
ds
t
t
−
=
−
=
145. Range: Piston-Propeller
W
dW
D
L
c
V
ds
t
−
=
−
=
=
1
0
0
W
W t
R
W
dW
D
L
c
V
ds
R
−
=
=
1
0
0
W
W
t
R
W
dW
D
L
c
V
ds
R
Assumptions made: level,
unaccelerated flight with
constantTSFC and L/D.
1
0
ln
W
W
D
L
c
V
R
t
=
BREGUET RANGE
EQUATION
1
0
ln
W
W
D
L
c
R
pr
=
pr
t
V
c
c
=
146. Range: Piston-Propeller
1
0
ln
W
W
D
L
c
R
pr
=
To maximize range:
Fly at largest propeller efficiency
Lowest possible SFC
Highest ratio of W0 toW1 (fly with the largest fuel weight)
Fly at maximum L/D (minimumTR)
propulsion
aerodynamics
structures
and materials
147. Example
Estimate the maximum range for the CP-1.
Normal gross weight = 2950 lb
Fuel capacity: 65 gal of aviation gasoline
Specific fuel consumption= 0.45 lb/(hp)(h)
Parasite drag coefficient CD,o = 0.025
Oswald efficiency factor, e = 0.8
Propeller efficiency = 0.8
1
0
max
max ln
W
W
D
L
c
R
pr
=
148. Example
Estimate the maximum range for the CP-1.
( ) 61
.
13
4
/ 0
,
max =
= D
C
eAR
D
L
1
-
7
ft
10
x
27
.
2
s
3600
h
1
lb/s
-
ft
550
hp
1
(hp)(h)
lb
45
.
0 −
=
=
c
lb
367
)
64
.
5
(
65 =
=
f
W
Since aviation gasoline weighs 5.64 lb/gal,
lb
2583
367
2950
1 =
−
=
W
mi
1207
ft
10
x
38
.
6
2583
2950
ln
)
62
.
13
(
10
x
27
.
2
8
.
0
ln 6
7
1
0
max
max =
=
=
= −
W
W
D
L
c
R
pr
149. Range: Jet Aircraft
( )
V
T
TSFC A
)
(
mile
fuel
of
lb
To cover longest distance use minimum pounds of fuel per mile.
To cover longest distance fly at maximum L1/2/D.
( )( ) ( )
=
=
V
miles
thrust
of
lb
fuel
of
lb
hour
thrust
of
lb
fuel
of
lb
TSFC
D
L
D
L
R
C
C
C
SC
W
S
V
T
2
1
1
2
2
1
=
150. Range: Jet Aircraft
−
=
1
0
W
W t W
dW
D
L
c
V
R
L
SC
W
V
=
2
−
=
1
0
2
1
2
1
2
W
W t
D
L
W
dW
c
C
C
S
R
)
(
2
2 2
1
1
2
1
0
2
1
W
W
C
C
S
c
R
D
L
t
−
=
Assumptions made: level,
unaccelerated flight with
constantTSFC and L1/2/D.
151. Range: Jet Aircraft
To maximize range:
Fly at minimumTSFC
Maximum fuel weight
Maximum L1/2/D
Fly at high altitudes (low density)
)
(
2
2 2
1
1
2
1
0
2
1
W
W
C
C
S
c
R
D
L
t
−
=
152. How is (L1/2/D)max computed?
)
(
2
0
,
2
/
1
2
/
1
L
L
D
L
D
L
C
f
KC
C
C
C
C
=
+
=
( )
( )
0
)
2
(
)
2
/
1
(
)
(
' 2
2
0
,
2
/
1
2
/
1
2
0
,
=
+
−
+
=
−
L
D
L
L
L
L
D
L
KC
C
KC
C
C
KC
C
C
f
( ) 0
)
2
(
)
2
/
1
(
2
/
1
2
/
1
2
0
, =
−
+
−
L
L
L
L
D KC
C
C
KC
C
i
D
L
D C
KC
C ,
2
0
, 3
3 =
=
πeAR
K /
1
Where =
153. How is (L1/2/D)max computed?
K
C
C
KC
C D
L
L
D 3
3 0
,
2
0
, =
=
0
,
0
,
0
, )
3
/
4
(
)
3
/
1
( D
D
D
D C
C
C
C =
+
=
0
,
,
,
0
, )
3
/
1
(
3 D
i
D
i
D
D C
C
C
C =
=
( ) 4
/
1
3
0
,
0
,
2
/
1
0
,
max
2
/
1
)
(
1
256
27
)
3
/
4
(
3
=
=
D
D
D
D
L
C
K
C
K
C
C
C
155. Example
Estimate the maximum range for the CJ-1.
)
(
2
2 2
1
1
2
1
0
max
2
1
max W
W
C
C
S
c
R
D
L
t
−
=
Normal gross weight = 19,815 lb
Fuel capacity: 1119 gal of kerosene
Specific fuel consumption = 0.6 lb of fuel/(lb thrust)(h)
Parasite drag coefficient CD,o = 0.02
Oswald efficiency factor e = 0.81
156. Example
Estimate the maximum range for the CJ-1.
1
-
4
s
10
x
667
.
1
s
3600
h
1
(lb)(h)
lb
6
.
0 −
=
=
t
c
lb
7463
)
67
.
6
(
1119 =
=
f
W
Since kerosene weighs 6.67 lb/gal,
lb
12352
7463
19815
1 =
−
=
W
4
.
23
)
02
.
0
(
)
93
.
8
)(
81
.
0
(
256
27
)
(
1
256
27
4
/
1
3
4
/
1
3
0
,
max
2
/
1
=
=
=
D
D
L
C
K
C
C
157. Example
Estimate the maximum range for the CJ-1.
)
(
2
2 2
1
1
2
1
0
max
2
1
max W
W
C
C
S
c
R
D
L
t
−
=
)
12352
19815
)(
4
.
23
(
)
318
(
001184
.
0
2
10
x
667
.
1
2 2
1
2
1
4
max −
= −
R
miles
3630
ft
10
x
2
.
19 6
max =
=
R
158.
159. Endurance: Piston-Propeller
( )( )
hour
HP
fuel
of
lb
SFC =
To stay in the air for the longest time,
fly at minimum pounds of fuel per hour.
For maximum endurance, fly at minimum power required.
( )
)
(SFC)(P
hour
fuel
of
lb
R
a
160. Endurance: Piston-Propeller
/
= DV
P
cP
dW
dt
P
dt
dW
c −
=
−
=
1
=
=
=
0
1
0
1
0
W
W
W
W
E
DV
dW
c
cP
dW
dt
E
L
SC
W
V
=
2
=
0
1
2
3
2
W
W
L
D
L
W
dW
SC
C
C
c
E
W
dW
DV
L
c
E
W
W
=
0
1
( ) ( )
2
1
0
2
1
1
2
1
2
3
2
−
−
−
= W
W
S
C
C
c
E
D
L
Assumptions made: level, unaccelerated
flight with constant SFC, η and L3/2/D.
161. Endurance: Piston-Propeller
( ) ( )
2
1
0
2
1
1
2
1
2
3
2
−
−
−
= W
W
S
C
C
c
E
D
L
To maximize endurance, fly at:
Largest propeller efficiency, η
Lowest possible SFC
Largest fuel weight
Fly at maximum CL
3/2/CD
Flight at sea level
162. How do we compute for (L3/2/D)max?
eAR
C
C
C L
D
D i
2
0
,
3 =
=
( ) 4
3
3
1
0
,
0
,
4
3
0
,
max
2
3
3
4
1
4
3
=
=
D
D
D
D
L
C
eAR
C
eAR
C
C
C
eAR
C
C D
L
0
,
3
=
163. i
D
D C
C =
0
,
3
How do we compute for (L3/2/D)max?
At PRmin
Thus,
4
3
3
1
0
,
max
2
3
3
4
1
=
D
D
L
C
eAR
C
C
166. SUMMARY
At minimum thrust required At minimum power required
i
D
D C
C ,
0
, =
0
,
max
4
/ D
D
L C
eAR
C
C
=
i
D
D C
C =
0
,
3
2
1
0
,
,
3
1
2
min
,
=
S
W
eAR
C
V
D
PR
2
/
1
1
2
min
,
=
S
W
eAR
C
V
o
R
D
T
( ) 4
3
3
1
0
,
0
,
4
3
0
,
max
2
3
3
4
1
4
3
=
=
D
D
D
D
L
C
eAR
C
eAR
C
C
C
167. CP-1: A light, single-engine, propeller-driven, private airplane,
approximately modelled after the Cessna Skylane, having the following
characteristics:
Example
Aspect Ratio = 7.37
Parasite drag coefficient CD,o = 0.025
Oswald efficiency factor, e = 0.8
168. Example
Estimate the maximum endurance for the CP-1.
81
.
12
3
4
1
4
3
3
1
0
,
max
2
3
=
=
D
D
L
C
eAR
C
C
( ) ( )
2
1
0
2
1
1
2
1
max
2
3
max 2
−
−
−
= W
W
S
C
C
c
E
D
L
−
= − 2
/
1
2
/
1
2
1
7
2950
1
2583
1
)
174
)(
002377
.
0
(
2
)
81
.
12
(
10
x
7
.
2
8
.
0
E
h
4
.
14
s
10
x
19
.
5 4
=
=
E
169. Endurance: Jet Aircraft
( )( )
hour
thrust
of
lb
fuel
of
lb
TSFC =
To stay in the air for the longest time,
fly at minimum pounds of fuel per hour.
For maximum endurance, fly at minimum thrust required.
( )
)
(TSFC)(T
)
(TSFC)(T
hour
fuel
of
lb
R
A a
a
170. Endurance: Jet Aircraft
A
t
A
t
T
c
dW
dt
T
dt
dW
c −
=
−
=
1
−
=
=
1
0
0
W
W A
t
E
T
c
dW
dt
E
−
=
1
0
1
W
W t W
dW
D
L
c
E
1
0
ln
1
W
W
C
C
c
E
D
L
t
=
Assumptions made:
level, unaccelerated
flight with constant
TSFC and L/D.
172. Example
Estimate the maximum endurance for the CJ-1.
h
3
.
13
s
10
x
79
.
4 4
=
=
E
1
0
max
max ln
1
W
W
C
C
c
E
D
L
t
=
12352
19815
ln
)
9
.
16
(
10
x
667
.
1
1
4
max −
=
E
174. Coverage Airplane Performance
Static Performance
(zero acceleration)
Dynamic Performance
(finite acceleration)
Thrust Required
Thrust Available
Maximum
Velocity
Power Required
Power Available
Maximum Velocity
Rate of Climb
Takeoff
Landing
Equations of Motions
V-n Diagram
Turning Flight
Range and Endurance
Time to Climb
Maximum Altitude
Gliding Flight
Service Ceiling
Absolute Ceiling
175.
176. Ground Roll (Liftoff Distance)
Preliminary (purely kinematic) considerations
dt
dV
m
ma
F =
=
dt
m
F
dV =
t
m
F
dt
m
F
dV
V
t
V
=
=
=
'
'
0
0
tdt
m
F
Vdt
ds =
=
2
'
'
'
2
0
0
t
m
F
dt
t
m
F
ds
s
t
s
=
=
=
F
m
V
F
Vm
m
F
s
2
2
1 2
2
=
=
177. Ground Roll (Liftoff Distance)
Rolling resistance
mr = 0.02 relatively smooth paved surface
mr = 0.10 grass field
( )
dt
dV
m
L
W
D
T
R
D
T
F r =
−
−
−
=
−
−
= m
Forces in an aircraft during takeoff ground roll
180. Ground Roll
L
SC
V
L
2
2
1
=
Is the assumption of a
constant force
reasonable?
+
=
eAR
C
C
S
V
D L
D
2
2
0
2
1
( )
( )2
2
16
1
16
b
h
b
h
+
=
181. Ground Effect
( )
( )2
2
16
1
16
b
h
b
h
+
=
Reduction of induced drag
by a factor Φ≤1.
+
=
eAR
C
C
S
V
D L
D
2
2
0
2
1
183. Ground Roll
Is the assumption of a
constant force
reasonable?
T is approximately constant
(especially for a jet)
The difference between the
drag and friction combined
and the thrust is also
approximately constant
( ) constant?
=
−
−
−
= L
W
D
T
F r
m
184. Ground Roll
AssumeT is constant.
Assume an average value
ofT-[D+μR(W-L)].
( ) ave
r
eff L
W
D
T
F ]
[ −
−
−
= m
Shevell suggests computing
this average atV=0.7VLO.
eff
LO
LO
F
g
W
V
s
2
)
(
2
=
187. Example
Estimate the liftoff distance for the CJ-1 at sea level. Assume a paved
runway; hence, μr = 0.02. Also, during the ground roll, the angle of
attack of the airplane is restricted by the requirement that the tail not
drag the ground; therefore, assume that CL,max during ground roll is
limited to 1.0. Also, when the airplane is on the ground, the wings are 6
ft above the ground.
( )
( )
764
.
0
16
1
16
2
2
=
+
=
b
h
b
h
192. Balanced Field Length
A + B
Distance up toV1
Additional distance travelled =
Distance required to clear an obstacle
= Distance required for a full stop
193. Distance to clear obstacle
sin
R
sa =
Where,
g
V
R stall
2
)
(
96
.
6
=
)
1
(
cos 1
R
h
−
= −
h is the obstacle height.
Analysis is based on pull up maneuver
197. Landing Roll
( )
dt
dV
m
L
W
D
F r =
−
+
−
= ]
[ m
Assume a constant
effective force,
( ) ave
r
eff L
W
D
F ]
[ −
+
−
= m
Compute this average by
evaluating the quantity at
0.7VT , where VT is the
touchdown velocity.
200. Example
Estimate the landing ground roll distance at sea level for the CJ-1. No
thrust reversal is used; however, spoilers are employed such that L = 0.The
spoilers increase the zero-lift, drag coefficient by 10 percent.The fuel
tanks are essentially empty, so neglect the weight of any fuel carried by
the airplane.The maximum lift coefficient, with flaps fully employed at
touchdown, is 2.5.
ft/s
6
.
148
)
5
.
2
)(
318
(
002377
.
0
)
12353
(
2
3
.
1
2
3
.
1
3
.
1
max
,
=
=
=
=
L
stall
T
SC
W
V
V
ft/s
104
7
.
0 =
T
V
022
.
0
)
02
.
0
(
1
.
0
02
.
0
0
, =
+
=
D
C
206. W
L =
cos
Load Factor
Turn Radius
Turn Rate
Level Turn
−
=
=
V
n
g
R
V
dt
d 1
2
2
2
W
L
Fr −
=
W
L
n
1
2
−
= n
W
Fr
R
V
m
Fr
2
=
1
2
2
−
=
n
g
V
R
207. Constraints on n and V∞
At any given velocity the maximum possible load factor for a
sustained level turn is constrained by the maximum thrust
available.
2
/
1
0
,
2
max
2
max
/
2
1
)
/
(
2
1
−
=
S
W
C
V
W
T
S
W
K
V
n D
eAR
K
1
=
208. Constraints on n and V∞
2
/
1
0
,
2
max
2
max
/
2
1
)
/
(
2
1
−
=
S
W
C
V
W
T
S
W
K
V
n D
max
max
=
W
T
D
L
n
n is also constrained by
CLmax
S
W
C
V
n L
/
2
1 max
,
2
max
=
max
max
1
cos
n
=
209. Constraints on n and V∞
V∞ is constrained by stall.
max
,
2
L
stall
C
n
S
W
ρ
V
=
n is also constrained by regulation. Example:
category)
(utility
4
.
4
=
n
210. Minimum Turn Radius
Minimum R occurs at the right combination of n and V∞.
)
/
(
)
/
(
4
)
( min
W
T
S
W
K
V R
=
2
0
,
)
/
(
4
2
min
W
T
KC
n D
R −
=
2
0
,
min
)
/
/(
4
1
)
/
(
)
/
(
4
W
T
KC
W
T
g
S
W
K
R
D
−
=
1
2
2
−
=
n
g
V
R
211. Maximum Turn Rate
Maximum ω occurs at the right combination of n and V∞.
4
/
1
0
,
2
/
1
)
/
(
2
)
( max
=
D
C
K
S
W
V
2
/
1
0
,
1
/
min
−
=
D
KC
W
T
n
−
=
2
/
1
0
,
max
2
/
/ K
C
K
W
T
S
W
q D
−
=
V
n
g 1
2
214. For large load factors
gn
V
R
2
=
=
V
gn
R for level turn, pull-up and pull down
ω for level turn, pull-up and pull down
215. For large load factors
S
W
gC
R
L max
,
min
2
=
)
/
(
2
max
max
,
max
S
W
n
C
g L
=
Minimum R for level turn, pull-up and pull down
Maximum ω for level turn, pull-up and pull down
218. Topics Discussed Airplane Performance
Static Performance
(zero acceleration)
Dynamic Performance
(finite acceleration)
Thrust Required
Thrust Available
Maximum
Velocity
Power Required
Power Available
Maximum Velocity
Rate of Climb
Takeoff
Landing
Equations of Motions
V-n Diagram
Turning Flight
Range and Endurance
Time to Climb
Maximum Altitude
Gliding Flight
Service Ceiling
Absolute Ceiling
219. • John D. Anderson. Introduction to Flight
• John D. Anderson, Airplane Performance and Design
References