Aircraft Performance Fundamentals PDF

# Aircraft Performance Fundamentals ## Basic Disciplines of Aircraft Performance - Aerodynamics - Aircraft Structure - Aircraft Propulsion ## Aircraft Performance and Its Parameters - The subject of aircraft performance is a part of the mechanics of flight ## Flight Phases - Flight consists of v...

# Aircraft Performance Fundamentals ## Basic Disciplines of Aircraft Performance - Aerodynamics - Aircraft Structure - Aircraft Propulsion ## Aircraft Performance and Its Parameters - The subject of aircraft performance is a part of the mechanics of flight ## Flight Phases - Flight consists of various phases: - Takeoff - Climb - Cruise - Turn - Descent - Landing ## Takeoff Performance Parameters ### Takeoff Flight - Begins from the start of A/C ground roll on the runway and ends when the lowest portion of the A/C during its climb has reached the height of 35 ft (10.67 m) above ground. - This 35 ft height is called the screen height or obstacle height which is taken to be the height of an imaginary obstacle. - The screen height is sometime taken as 50 ft (15.24 m) depending on flight regulations and aircraft. - Performance parameters of takeoff flight: - Ground roll distance and time - Rotation distance and time ### Generally - A/C first roll on the ground until it has reached a specified speed. - It is then rotated about the rear wheels for a short time (3s). - It then finally becomes airborne when both the front and rear wheels are above ground. - Thereafter, the A/C climbs and soon reaches a height of 35 ft (or 50 ft) above ground to complete the takeoff phase. ## Climb Performance Parameters - Start from the height of 35 ft (or 50 ft as the case may be) above the ground and ends when the aircraft has completed climbing. ## Performance Parameters of the Climb Phase 1. Angle of climb 2. Rate of climb 3. Airspeed or Mach number of climb 4. Time taken during climb 5. Horizontal distance covered in climb 6. Fuel consumption in climb 7. Absolute and service ceilings ## Cruise Performance Parameters - The cruising phase starts soon after the completion of the climbing phase and ends when the aircraft has started descending or maneuvering. - During cruise, the aircraft moves steadily along a straight line in the horizontal plane. - Aircraft is a steady (no acceleration) straight and level (horizontal) flight. ## Turning Performance Parameters - In the cases of turning flight, the important performance parameters of the flight are: - Air speed or Mach number of turn - Bank angle (phi) - Load factor n (= L/W) - Rate of turn - Radius of turn. ## Descent Phase - The descent phase starts when the aircraft has started losing height with the purpose of descending toward the ground and ends when the aircraft is 35 ft (or 50 ft) above the ground. ## Descent Performance Parameters 1. Rate of descent 2. Angle of descent 3. Air speed of descent 4. Time taken in descent 5. Fuel consumption in descent ## Landing Phase - The landing phase can be regarded as the reverse of the takeoff phase . - The landing phase starts when the aircraft is at 35 ft (or 50 ft) above the ground. - As soon as the airborne distance of the landing phase is completed, the rear wheels of the aircraft first touch the ground, soon after the nose wheels are also on the ground. - Thereafter, a rapid deceleration of the aircraft takes place, first due to aerodynamic drag and then by braking friction until it comes to a standstill. ## Performance Parameters of the Landing Phase 1. Airborne distance and time 2. Rotation distance and time 3. Ground roll distance and time ## Performance Analysis - Optimizes different phase parameters: - Best range - Maximum endurance - Maximum rate of climb - Fastest turn rate - Etc - These are some of the very important performance parameters called figures of merit (FOM) of the aircraft. ## Mission for Commercial Aircraft Sizing (A diagram of the flight phases is depicted, including takeoff, climb, cruise, descent, and landing). ## Aircraft Drag ### Parasite Drag - There is friction between the air and the skin of the aircraft. - This is called "parasitic drag". - It increases as airspeed increases. ### Induced Drag - As the aircraft produces lift, it also creates drag. - This is called "induced drag". - It decreases as airspeed increases. ### Total Drag - The sum of parasite and induced drags gives total drag of the aircraft. - In order to maintain airspeed, the thrust provided by the aircraft must equal the total drag (T=D). ### Power - To get the power curve multiply drag and thrust by airspeed (P=TV). ## Basic Equations ### Steady Level Flight (A diagram depicts the relation between lift, weight, and the horizontal plane) - Lift = Weight. (L=W) ### Stall Speed (Vstall) - A diagram shows the relation between lift coefficient (CL) and airspeed. - L= (1/2) pV^2SC1 = W - V = ( SQRT (2W) /( pSC1) - Vstall = Vmin = Vcc = ( SQRT (2W) / ( pSC1max) ) ### Drag Polar - CD = CD0 + ( (CL^2)/(πARε) )--- (2.4) - CD0 is the parasite drag coefficient at zero lift. - e = Oswald efficiency factor - AR = aspect ratio. ## Drag vs velocity - CL= W/ (1/2) pV^2S - CD = CDO + (πARε(1/2)pS^2V^2)--- (2.5) - Increase of velocity results in decreasing induced drag. - At low speed it is very important the induced drag must be less as possible, to do this increase the aspect ratio. - At high speed: - D1 is not needed to change aspect ratio. - D0 is to decrease by decreasing S. ## Total Drag - D = (1/2)pV^2SC1 - D = (1/2)pV^2S(CD0 + CD1) --- (2.6) - D = (1/2)pV^2S[CD0 + (πARε(1/2)pS^2V^4)] --- (2.7) - CD0 = cos tan - D0 increases parabolicady with V. - D1 decreases parabolicaly with V. - (D/dV) = 0 ===> V = V|Dmin ## Schematic of drag polar (A diagram shows the relation between drag force and flight velocity) - Parasitic drag - Lift - induced drag - Total drag ## Other representation of Drag Polar (A diagram shows two different representations of Drag Polar. The first shows the relationship between CD and CL. The second shows the relationship between CD and CL') - CD = CD0 + (CL^2/πAR) ## Course Road Map (A diagram shows the different aspects of aircraft performance, including static performance, dynamic performance, the equations of motion, and how the various flight phases are interconnected). - **Static performance (zero acceleration)** - Thrust Required - Thrust Available - Maximum Velocity - Power Required - Power available - Maximum velocity - Rate of climb - Gliding flight - Time to climb - Maximum Altitude - Service ceiling - Absolute ceiling - Range and endurance - **Dynamic performance (finite acceleration)** - Takeoff - Landing - Turning Flight - V-n diagram - Accelerated rate of climb - (energy method) ## Equations of Motion (A diagram depicts the forces acting on an airplane in flight). - **The flight path (direction of motion of airplane)** is inclined at angle θ with respect to horizontal. - **Four physical forces are acting on the airplane:** 1. Lift (L), which is perpendicular to the flight path direction. 2. Drag (D), which is parallel to the flight path direction. 3. Weight (W), which acts vertically toward the center of the earth (and hence is inclined at angle φ with respect to the lift direction). 4. Thrust (T), which in general is inclined at the angle αT with respect to the flight path direction. ## Applying Newton's law along the flight path - ΣFii = ma = mdV/dt--- (2.8) - ΣFii is the summation of all forces parallel to the flight path. - ΣFii = TcosaT – D – W sine --- (2.9) ## Applying Newton's law perpendicular to the flight path - ΣF1 = mV^2 /r --- (2.10) - ΣF1 is the summation of all forces perpendicular to the flight path. - V^2/r is the acceleration normal to a curved path with radius of curvature r. - ΣF1 = L + TsinaT –W cose --- (2.11) - TcosaT – D – Wsine = mdV/dt --- (2.12) - L + TsinaT –W cose = mV^2/r --- (2.13) ## Equations of motion for level unaccelerated flight - Level flight means that the flight path is along the horizontal, that is, θ= 0. - The airplane at constant altitude - (dh/dt) = h = 0.0 - Unaccelerated flight that the right sides of equations 2-12 and 2-13 are zeros. - TcosaT = D --- (2.14) - L + TsinaT = W --- (2.15) - For most conventional airplanes αT is small enough that: - cosaT ≈ 1 - sinaT ≈ 0 - T = D --- (2.16) - T= thrust produced by the power plant of an airplane or thrust available. - L = W ==> n= load factor = 1. --- (2.17) ## Kinetic Equations - dx/dt = V, h = 0.0 --- (2.18) - **Equations 2-16 and 2-17 are the equations of motion for level, unaccelerated flight.**' - Solution of these equations gives V, a, or C1 for level unaccelerated flight. - In next sections, we will apply these results to the static performance analysis of an airplane to answer: - How fast, how far, how long, and how high a given airplane can fly? ## Thrust Required for Level, Unaccelerated Flight - T = D = (1/2)ρV^2SCD --- (2.19) - L = W = (1/2)ρV^2SC1 --- (2.20) - T/W = CD/CL --- (2.21) - TR = W/C1CD = W/L1D --- (2.22) ## Variation of TR with airplane velocity (at given altitude) (A diagram shows the variation of thrust required (TR) with airspeed (V). It highlights that the minimum thrust required occurs around the maximum L/D point. The red line shows the thrust required at different airspeeds) - It highlights that the minimum thrust required occurs around the maximum L/D point. ## Steps to Plot TR vs V - To calculate a point on this curve, proceed as follows: 1. Choose a value of V∞ 2. For this V∞, calculate the lift coefficient, given by CL = W/((1/2)ρV∞^2S) 3. Calculate CD from the known drag polar for the airplane: CD = CD0 + ( (CL^2)/(πARε) ) 4. Form the ratio CL/CD 5. Calculate the thrust required from equation 2.22 - The value of TR obtained from Step Five is the thrust required to fly at the specific velocity chosen in Step One. - In turn, the curve in above Figure is the locus of all such points taken for all velocities in the flight range of the airplane. ## Example 2-1 (An image of a single-engine Cessna Skylane aircraft is included) - A light, single-engine, propeller-driven, private airplane, approximately modeled after the Cessna Skylane shown in Figure 2-1. - For convenience, we will designate our hypothetical airplane as the CP-1, having the following characteristics: - Wingspan = 35.8 ft - Wing area = 174 ft^2 - Normal gross weight = 2950 lb - Fuel capacity = 65 gal of aviation gasoline. - Power plant: one-piston engine of 230 hp at sea level. - Specific fuel consumption = 0.45 lb/(hp)(h). - Parasite drag coefficient CD0 = 0.025 - Oswald efficiency factor ε= 0.8 - Propeller efficiency = 0.8 - Calculate the TR curves at sea level for this airplane (CP-1) ## Solution - For the CP-1, assume that V∞ = 200 ft/s = 136.4 mi/h. - CL = W/((1/2)pV∞^2S) = 2950/((0.002377)(200)^2(174)) = 0.357 - AR = (b^2)/S = (35.8)^2/174 = 7.37 - CD = CD0+ ( (CL^2)/(πARε) ) = 0.025 + ( 0.357^2)/(π(0.8)(7.37) ) = 0.0319. - L/D = 0.357/ 0.0319 = 11.2 - TR = W/L1D = 2950/ 11.2 = 263 lb. - To obtain the thrust-required curve, the preceding calculation is repeated for many different values of V∞. Some sample results are tabulated as follows: | V∞ (ft/s) | Cl | CD | L/D | TR (lb) | |:----------:|:----:|:----------:|:------:|:-------:| | 100 | 1.43 | 0.135 | 10.6 | 279 | | 150 | 0.634 | 0.047 | 13.6 | 217 | | 250 | 0.228 | 0.028 | 8.21 | 359 | | 300 | 0.159 | 0.026 | 6.01 | 491 | | 350 | 0.116 | 0.0.26 | 4.53 | 652 | (A diagram shows the thrust required (TR) curves for different airspeeds at sea level for CP-1) ## Example 2-2 (An image of a jet-powered Cessna Citation 3 aircraft is included) - A jet-powered executive aircraft, approximately modeled after the Cessna Citation 3, shown in Figure 2.2. - For convenience, we will designate our hypothetical jet as the CJ-1, having the following characteristics: - Wingspan = 53.3 ft - Wing area = 318 ft^2 - 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 CD0 = 0.02 - Oswald efficiency factor ε = 0.81 - Calculate the TR curves at sea level for this airplane (CJ-1) ## Solution - Assume that V∞ = 500 ft/s = 341 mi/h - CL = W/((1/2)pV∞^2S) = 19,815/((0.002377)(500)^2(318)) = 0.210 - AR = (b^2)/S = (51.3)^2/318 = 8.93 - CD = CD0 + ( (CL^2)/(πARε) ) = 0.02 + ( 0.21^2)/(π(0.81)(8.93) ) = 0.022. - L/D = 0.21/0.022 = 9.55 - TR = W/L1D = 19,815/9.55 = 2075 lb - A tabulation for a few different velocities follows: | V∞ (ft/s)| Cl | CD | L/D | TR (lb)| |:---------:|:----:|:-------:|:------:|:-------:| | 300 | 0.583| 0.035 | 16.7 | 1188 | | 600 | 0.146 | 0.021 | 6.96 | 2848 | | 700 | 0.107 | 0.021 | 5.23 | 3797 | | 850 | 0.073 | 0.020 | 3.59 | 5525 | | 1000 | 0.052 | 0.020 | 2.61 | 7605 | (A diagram shows the variation of thrust required (TR) with airspeed (V∞) for CJ-1. It shows that as airspeed increases, the thrust required rapidly increases, and the maximum L/D point is near the lowest airspeed). # Conclusion This document provides a comprehensive overview of aircraft performance fundamentals, covering various flight phases, performance parameters, and drag considerations. The document also includes examples showcasing the calculation of thrust requirements for specific aircraft scenarios.