Aerodynamics Notes PDF

Okay, here is the transcription of the images you sent, converted into a structured markdown format. I have focused on preserving the information, mathematical formulas, and the overall structure of the notes. ### Page 1 so the flow upstream doesn't feel pressure dist and reduce it remains in the...

Okay, here is the transcription of the images you sent, converted into a structured markdown format. I have focused on preserving the information, mathematical formulas, and the overall structure of the notes. ### Page 1 so the flow upstream doesn't feel pressure dist and reduce it remains in the free flow stage SHOCK WAVES, divides undisturbed and disturbed flow. * As the sweep angle increases after a certain threshold there is a sudden increase in drag, i e the Drag divergence Mach Number, It increases! * shock wave * wind tunnel testing on scaled down models $C_l$ and $C_D$ & other non-dimensional numbers $C_L (Re, \alpha, M)$ $Re = \frac{\rho_{\infty} V_{\infty} L}{\mu}$ for test on $\frac{1}{100}$ scale ie $\frac{L-L}{100}$ $\implies$ to maintain $Re$ we increase $V_\infty$ to $100 V_\infty$ $C_L = \frac{L}{\frac{1}{2}\rho(V_\infty \times 100)^2 (\frac{L}{100})^2}$, we find lift using the test rente we can find $C_L$ * if we scale way too much $\implies$ Mach no. $> 0.3$ which will give wrong results. to solve this problem there are variable density wind tunnels so that to maintain $Re$ there wouldn't be a need to inc vel drastically. Part testing $\implies$ Testing wings with part of fusela Instruments $\implies$ static ports on the nose to find the altitude. Pitot tube: to measure velocity by Bernoullis eg $P_{\infty} + \frac{1}{2}\rho V^2_{\infty} = P_0$ ### Page 2 * Pitotstatic tube to measure to towe for accurate measurement. Also used to check angle of attack by $aogh$ sensor on the pitot tube. * Propulsions deals with power requirements for thrust. 4-stroke $IC$ engines $\implies$ work done depends on compressibility factor. For aircrafts Power: wt ratio is cheulad * Configurations: Radial, in-line Flywheel $\implies$ moving $\implies$ kinetic energy stored to move the pistons Propeller $\implies$ to transfer power from the engine to the air. Engine - chemical to mechanical Propeller- mechanical to Propulsive $\eta$, $\eta_{prop} = \frac{useful \ power}{Kt \ input}$ $= TV_{\infty}$ $(T = \dot{m}(V_e-V$ $\frac{\frac{1}{2}\dot{m}(V_e^2-V_{\infty}^2)}{2}$ ($KE = \frac{1}{2}m(V_e$ $=\frac{\dot{m}(V_e-V_{\infty})V_{\infty}}{\frac{1}{2}\dot{m}(V_e^2-V_{\infty}^2)} = \frac{2V_{\infty}}{V_e+V_{\infty}}$ $\implies \eta_{prop} = \frac{2}{1+\frac{V_e}{V_{\infty}}}$ or $\frac{V_e}{V_{\infty}} \approx 1 \implies \gamma \approx 1$ i. e less kinetic energy wasted. Thus engines are made bigger a bigger to inc the $V_e$ uptill $V_{\infty}$. ### Page 3 \# Mach no. = $\frac{V}{a}$ - speed of sound Incompressible Low speed M<0.3 Subsonic <0.8 Transonic 0.8<M<1.2 \#SHOCK WAVES - very thin regions of flow. Mach(1.4 - supersonic) (Doppler effect) Sonic M=1 Supersonic M>1 Very thin regions of flow, acros The Mach no. $\downarrow$ Static pressure $\uparrow$ Static temp $\uparrow$ flow velocity $\downarrow$ Total pressure $\downarrow$ Variable sweep * By changing the area of airfoil, facing the flow, we can change the is required. As the curvature of airfoil will reduce on retracting the wings. **winsweep-high pressure * SHOCK WAVE formation disturbances in the flow are communicated to further regions by weak pressure waves, ie pressure waves for $V < V_s$, the "sound waves upstream". $(i e M>1) \implies$ pressure disturbances can't propagate upstream coalesce to for SHOCK WAVE ### Page 4 if $V_e$ is close to $V_{\infty}$ the thrust is zero, thus $\dot{m}$ us increased by using bigger engines. $\\$Blade pitch - $\beta$ $\\$airspeed $\\$Rotational Speed \$(r\omega)$ $\\$Relative wind $\\$Plane of rotation $C_T = \frac{T}{\frac{1}{2}\rho V_{\infty}^2 s}$ $G(J=Adv \ Ratio = \frac{V_{\infty}}{(rpm)\pi nD}$. decides d $\eta_t = \frac{Mech \ output}{Heat \ Input}$ $\eta_{total} = \frac{useful \ mech \ output}{Heat \ input}$ As advance ratio changes the $\alpha$, the propeller eff. will peak and then stall. To maintain that Blade rotation can be changed, & $\alpha$ varies changed, which that * Propeller driven aircrafts are slower as the rotational speed will increase the drag divergence, even for lower $V_{\infty}$ * combo * Arrangement of Rotors and stators in the compressors of the engine, rotors impart KE, gases while at stators convert KE to pressure by. Bernoulli's $eqn$ ### Page 5 causes drag used to change shape and characteristic of airfoil. * airfoil to be designed by taking in account Re value by cruise * the flaps helps to mitigate any issue Helps in reducing $c_l$ and thus cover angle of attack/lis sufficient for lift. Deployed during take-off and landing when velocity is much us spoils the lift and generates more drag, to stop or bring down the aircraft. Rough surface to make flow turbulent, for Same (Re), smooth objects have laminar flow around them, and rough crave turbulent. ### Page 6 * Turbojet engines eff. - independent of $V_{\infty}$ * the thrust to weight ratio is much higher * directly converts to rotary motion * thrust produced by the jet flow in the nozzle * Turboprop engines - fly at low velocity * propeller rotates but as $V$ increases, the propeller off dec * on inc the $R$ of propeller blade, thrust inc but vel$\uparrow$, leads to $\downarrow$ eff * Turbofan engines- an intermediate of turboprop and turbojet. * Since temp ratio varies with pressure ratio, the temp (highest) should be bearable by the turbine blades. * to protect the blade, it has holes and are coated with heat resistant ceramic coating $\eta = 1 - \frac{T_2}{T_1} = 1-(\frac{p_1}{p_2})^{\frac{\gamma -1}{\gamma}}$ Brayton cycle when secondary combustion chamber as after burner is utilised, it is just after the turbines blades. This will be $\less$ energy due to energy extraction by the turbine The energy in the gas is converted to ke by the nozzle. ### Page 7 when after burner is switched on, the mass-flow rate inc, thus nozzle area is inc to prevent thermal choking. $\dot{m}_{intot} = \dot{m}_{bypass} + \dot{m}_{comb}$. the bypass ratio = $\frac{\dot{m}_{bye pass}}{\dot{m}_{nicohib}} \approx 11$ on inc this ratio, propulsive eff is increased. although the thrust is decreased $\implies$ for fighter aircrafts, $\frac{Thrust}{wt}$ ratio should be higher $(than \ 1)$ * variable pitch propeller can be used to maintain $\eta prop$ at a const. for turbojet and turbofan, thrust always remains almost coust. Troo-const KE * All the drag due to machinary is reduced. in the ramjet engines, it is simplified but can't work alone, as it works only at higher Mach numbers. much higher range for less amount of mass *sor breathing engine -oxygen is taken in from the air flow itself \#Turbo-Ramjet engines at low mach numbers, the air is passed into the compressor-turbine machivary and the after-burner. St High mach numbers, the air avoids the compressor- turbine machinary and enters directly in the combustion chamber of the afta burner ### Page 8 * Aircraft Performance $\implies$Steady Level flight Drag polar $C_D = C_{D0} + C_{0i}$ $C_D = C_{D0} + \frac{C_L^2}{\pi e AR}$ $\frac{D}{q_{\infty} S} = C_{D0} + \frac{L^2}{\frac{1}{2} \rho_{\infty} V_{\infty}^2 (\pi e AR)}$ $\implies D = C_{D0} q_{\infty} S + \frac{W^2}{q_{\infty} \pi e AR}$ (as for steady level $L=W=m$) $C_o.$ ($\alpha + Re$) $\implies$ for diff velocities both $\alpha$ and $Re$ will vary as $Re \alpha V_{\infty}$ and $\alpha$ is adjusted to maintain $L=W.$ for min Drag $V_{\infty j}$ $\frac{dD}{dq_{\infty}} = 0 = C_{D0} S + \frac{-W^2}{q_{\infty}^2 \delta \pi eAR}$ $\implies C_{D0} = \frac{W^2}{q_{\infty}^2 s^2 \pi e AR}$ $C_{D0} = \frac{C_L^2}{\pi e AR}$ ### Page 9 For different densities $V_{\infty min}$ will be different $C_L = \frac{w}{\frac{1}{2} \rho V_{\infty} S}$ = $\implies W = C_L q_{\infty} S.$ $= C_{L max} (q_a)_{min} S.$ Now,$C_{Lmax} \implies fixed$ for a particular aircraft $q_{\infty min} =\frac{1}{2}\rho V_{\infty min}$ $if \ \rho \downarrow \ V_{\infty min} \uparrow$ $So \ V_{\infty min} \downarrow$ *for $C_L, opt.$ $\frac{D}{W} = \frac{D}{L/D}$ $\implies \frac{CD}{CL} max$ $\# \frac{L}{D} \implies {(\frac{CL}{CD})}_{max}$ min drag FOR $\frac{d}{d(C_L} (\frac{C_D}{C_L}) = 0$ $\impliesemin$ drag $4 \frac{C_D}{C_L} = \frac{CDO}{C_L} + C L a$ ${*C_{DO} = C_{Di}, \ C_L^2 = C_{DO}\pi e AR. }$ \# min power condition minimise fuel $\implies$ maximize Range $\implies min \ drag \implies min work \ required \implies mint thrust$ $as \ W=CDR \ Range.$ Work Drag \# Endurance for an amt. of fuel, time spent in flight. Maximize endurance $\implies$ minimize fuel ### Page 10 $\eta_{th} = \frac{Mech \ Power}{\dot Q} = \dot{m}_f x CV \implies calorific \ value \ of \ fuel$ Power req = drag x vel =$DV_\infty$ = $\frac{W C_\infty}{(CL/CD)}$ $C_D = C_{D0} + a C_L^2$ $\implies C_L = L=W/C_aS \implies V_{\infty} = \frac{2w}{(\rho_{0}SL)^{\frac{1}{2}}}$ P req =$\frac{W}{C_LICD}(\frac{2W}{\int \varphi CL})^{1/2}$ $\implies Preq \propto \frac{CD}{{CL}^{3/2}}$ $\implies P_{Rmin } \propto {(/ \frac{CD}{{CL}^{\frac{3}{2}}});min}$ $\implies \frac{CD}{{P_1}^{3/2}+2 +ACl^{2 }} \implies \frac{CD_0}{{Cl_0}^3 +aCl^{2}}{} $ to minimize $\frac{d}{dc_2}(\frac {CD_0}{{Cl_0}^3}=0 $ ${CD}_0(-\frac{3}{2}{P_1}^{3/2} +\frac{1a}{0} + {} = $ CD_0 + = -3CD_0 ### Page 11 \# Altitude effect min drug $ \implies C L = \sqrt{\frac{{CD}_{\sigma}}{a}}$ since CL= const. Q = $\frac{W}{1/2pV_o^{-2}{S}}$ min a $\implies$ $\frac{40}{5}$=w=const. $W = \frac{e_zs}{w}$ Algo as $r^{os} \downarrow $ +Vo=$9^2$ and $ b q_{1}$ Pruch a * Full theotte- maximum fuel consumtion rate . * Flight Envelope