Nomenclature
| Latin | Definition | Unit |
| a | Local speed of sound | m/s, ft/s |
| a | Semimajor axis of inlet elliptic lip (internal) | m, ft |
| a | Swirl profile parameter | — |
| at | Speed sound based on total temperature | m/s, ft/s |
| A | Area | m2, ft2 |
| An | Projection of area in the normal direction | m2, ft2 |
| A9 | Nozzle exit flow area | m2, ft2 |
| Aref | Reference area | m2, ft2 |
| Ao | Inlet (freestream) capture area | m2, ft2 |
| A1 | Inlet capture area | m2, ft2 |
| A8, A8geo | Nozzle throat area (geometrical area) | m2, ft2 |
| A8eff | Effective nozzle throat area | m2, ft2 |
| AB | Blocked area (due to boundary layer) | m2, ft2 |
| Ab | Burning area of grain in solid rocket motors | m2, ft2 |
| AE | Effective area | m2, ft2 |
| AHL | Inlet highlight area | m2, ft2 |
| AM | Maximum nacelle area | m2, ft2 |
| Ath | Inlet throat area | m2, ft2 |
| A* | Sonic throat, choked area | m2, ft2 |
| b | Semiminor axis of inlet elliptic lip (internal) | m, ft |
| b | Swirl profile parameter | — |
| B | Blockage | — |
| B | Compressor instability parameter due to Greitzer | — |
 |
Absolute velocity vector in turbomachinery | m/s, ft/s |
| C | Absolute flow speed, i.e.,  |
m/s, ft/s |
| c | Chord length | m, ft |
| c | Effective exhaust velocity in rockets | m/s, ft/s |
| c* | Characteristic velocity in rockets | m/s, ft/s |
| Cr, Cθ, Cz | Radial, tangential, axial velocity components in the absolute frame of reference | m/s, ft/s |
| CD | drag coefficient, discharge coefficient | — |
| Cf | Friction drag coefficient | — |
| cf | Local skin friction coefficient | — |
| Cf | Force coefficient | — |
| Cp | Pressure coefficient | — |
| CPR | Diffuser static pressure recovery coefficient | — |
| CA | Nozzle flow angularity loss coefficient | — |
| CD8 | Nozzle (throat) discharge coefficient | — |
| Cfg | Nozzle gross thrust coefficient | — |
| CV | Nozzle exit velocity coefficient | — |
| Cd | Sectional profile drag coefficient | — |
| CDi | Induced drag coefficient | — |
| Cl | Sectional lift coefficient | — |
| Ch | Enthalpy-equivalent of the static pressure rise coefficient due to Koch | — |
| cp | Specific heat at constant pressure | J/kg · K |
| cv | Specific heat at constant volume | J/kg · K |
 |
Molar specific heat at constant pressure | J/kmol · K |
| d | Flameholder width | m, ft |
| D | Diameter, drag | m, N |
| D | Liquid fuel droplet diameter | micron |
| Dflameholder | Flameholder drag | N, lbf |
| Dadd | Additive drag | N, lbf |
| Dnacelle | Nacelle drag | N, lbf |
| Dpylon | Pylon drag | N, lbf |
| Dr | Ram drag | N, lbf |
| Dspillage | Spillage drag | N, lbf |
| Daft-end | Nozzle aft-end drag | N, lbf |
| Dboattail | Nozzle boattail drag | N, lbf |
| Dplug-friction | Friction drag on the plug nozzle | N, lbf |
| D | Diffusion factor in turbomachinery | — |
| D′ | Two-dimensional or sectional profile drag | N/m |
 |
Unit vector | — |
| e | Specific internal energy | J/kg |
| ec, et | Polytropic efficiency of compressor or turbine | — |
| E | Internal energy | J |
| Ea | Activation energy | kcal/mol |
| f | Fuel-to-air ratio | — |
| fstoich | Stoichiometric fuel-to-air ratio | — |
| Fg | Gross thrust | N, lbf |
| Flip | Lip suction force | N, lbf |
| Fplug | Axial force on the nozzle plug | N, lbf |
| Fn | Net thrust | N, lbf |
| F | Force | N, lbf |
 |
Tangential force, axial force | N, lbf |
| fD | D’Arcy (pipe) friction factor | — |
| g | Staggered spacing (s.cos β in a rotor and s.cos α in a stator) | m |
| g0 | Gravitational acceleration on the surface of the earth | m/s2, ft/s2 |
| h | Specific enthalpy | J/kg |
| ht | Specific total enthalpy | J/kg |
| h | Heat transfer rate per unit area per unit temp. difference | W/m2K |
| h | Altitude above a planet | km, kft |
| ht | Specific total (or stagnation) enthalpy in the absolute frame; h + C2/2 | J/kg |
| htr | Specific total enthalpy in relative frame of reference; h + W2/2 | J/kg |
| hlg | Latent heat of vaporization | J/kg |
| HHV | Higher heating value | J/kg, BTU/lbm |
| H | Enthalpy | J, ft-lbf |
| H | Afterburner duct height | m, ft |
| i | Blade section incidence angle | deg |
| iopt | Optimum incidence angle | deg |
| Is | Specific impulse | s |
| It | Total impulse | N · s, lbf · s |
| I | Impulse | N, lbf |
| Kp | Equilibrium constant based on partial pressure | (bar)x |
| Kn | Equilibrium constant based on molar concentration | — |
| L | Length | m, ft |
| L | Lift | N, lbf |
| L | Flameholder length of recirculation zone | m, ft |
| L | Diffuser wall length | m, ft |
| L | Diffusion length scale in a blade row | m, ft |
| LHV | Lower heating value | J/kg, BTU/lbm |
| L/D | Aircraft lift-to-drag ratio | — |
| Mb | Blowing parameter in film cooling,  |
— |
| MT | Blade tangential Mach number U/a | — |
| Mz | Axial Mach number, Cz/a | — |
| Mr | Relative Mach number (in turbomachinery);  |
— |
| M | Mach number | — |
| M* | Characteristic Mach number | — |
| Ms | Gas Mach number upstream of a shock inside a nozzle | — |
| m | Parameter in Carter’s rule for deviation angle | — |
| m | Mass | kg, lbm |
 |
Mass flow rate | kg/s, lbm/s |
 |
Corrected mass flow rate | kg/s, lbm/s |
 |
Air mass flow rate | kg/s, lbm/s |
 |
Fuel mass flow rate | kg/s, lbm/s |
 |
Propellant (oxidizer and fuel) mass flow rate | kg/s, lbm/s |
 |
Mass flow rate through the side of the control volume | kg/s, lbm/s |
 |
Coolant flow rate | kg/s, lbm/s |
| MW | Molecular weight | kg/kmol |
| n | Exponent of superellipse | — |
| n | Polytropic exponent; parameter in general swirl distribution | — |
| N | Number of blades; shaft rotational frequency; number of stages | — |
| N | Number of bluff bodies in a flameholder | — |
| N | Diffuser axial length | m, ft |
| Na | Avagadro’s number (6.023 × 1023 molecules per gmole) | — |
| NB | Inlet lip bluntness parameter | — |
| Nc | Corrected shaft speed | rad/s, rpm |
 |
Unit normal vector (pointing out of a surface) | — |
| Nu | Nusselt number | — |
| Pr | Prandtl number | — |
| p | Static pressure | bar, Pa, psia |
| pt | Total pressure | bar, Pa, psia |
| ps | Static pressure upstream of a shock (in nozzle) | bar, Pa, psia |
 |
Power | W, hp |
 |
Shaft power | W, BTU/s |
| PF | Pattern factor | — |
| Pf | Profile factor | — |
| Q | Heat exchange | J, BTU |
| q | Dynamic pressure | bar, atm |
| q | Heat transfer rate per unit area (heat flux) | W/m2, BTU/s.ft2 |
| q | Heat transfer rate per unit mass flow rate | J/kg, BTU/lbm |
| QR | Fuel heating value | kJ/kg, BTU/lbm |
 |
Heat transfer rate | W, BTU/s |
 |
Aircraft range | nm |
| Re | Reynolds number | — |
| R | Gas constant | J/kg · K, BTU/lbm-°R |
| Rl.e. | Blade leading-edge radius | m, in |
 |
Universal gas constant | J/kmol · K |
| r | Mixture ratio (oxidizer to fuel) in liquid propellant rockets | — |
| r | Burning rate in solid propellant rockets | cm/s, in/s |
| r | Radius | m, ft |
| r | Cylindrical or spherical coordinate | — |
| rh | Hub radius | m, ft |
| rt | Tip radius | m, ft |
| rm | Pitchline or mean radius (rh+rt)/2 | m, ft |
| °R | Stage degree of reaction in turbomachinery | — |
| S | Entropy | J/K |
| SL | Laminar flame speed | m/s, ft/s |
| ST | Turbulent flame speed | m/s, ft/s |
| St | Stanton number | — |
| SN | Smoke number | — |
| s | Specific entropy | J/kg · K |
| s | Blade spacing | m, ft |
| t | Blade thickness | m, ft |
| t | Time | s, hr |
| tmax | Maximum blade thickness | m, ft |
| treaction | Reaction time scale in a combustor | ms |
| ti | Ignition delay time | ms |
| te | Evaporation time scale in a combustor | ms |
| T | Static temperature | K, °R, °C, °F |
| Tt | Total temperature | K, °R, °C, °F |
| Tf | Reference temperature, 298.16 K | K, °R, °C, °F |
| Tg | Gas temperature | K, °R, °C, °F |
| Tc | Coolant temperature | K, °R, °C, °F |
| Taf | Adiabatic flame temperature | K, °R, °C, °F |
| Taw | Adiabatic wall temperature | K, °R, °C, °F |
| Tu | Turbulence intensity,  |
— |
| u | Speed, velocity normal to a shock | m/s, ft/s |
| u | Gas speed | m/s, ft/s |
| u′rms | Turbulent fluctuating speed (root mean square) | m/s, ft/s |
 |
Rotational velocity vector of rotor; v-reg | m/s, ft/s |
| UT | Blade tip rotational speed, ωrt | m/s, ft/s |
 |
Root mean square of fluctuating velocities in 3 spatial directions | m/s, ft/s |
 |
Average gas speed in the mixing layer | m/s, ft/s |
| V | Volume | m3, ft3 |
| V | Speed | m/s, ft/s |
| Vm | Mean speed (used in stall margin or turbulence intensity) | m/s, ft/s |
| V′ | Relative speed used in the stall margin analysis | m/s, ft/s |
| Vc | Compressor or chamber volume | m3, ft3 |
| Vp | Plenum volume | m3, ft3 |
| W | Weight | N, lbf |
| W | Flame width in afterburner | m, ft |
| W | Width | m, ft |
 W |
Relative velocity vector, relative flow speed | m/s, ft/s |
| Wr, Wθ, Wz | Radial, tangential and axial velocity components in relative frame of reference | m/s, ft/s |
| wc | Rotor specific work (rotor power per unit mass flow rate; ) |
J/kg, BTU/lbm |
| w | Specific work | J/kg, BTU/lbm |
| w | Tangential speed to an oblique shock | m/s, ft/s |
| wp | Propellant weight | N, lbf |
| Wvisc. | Rate of work done by the viscous force | W, BTU/s |
| X | Solid flow fraction in a rocket nozzle | — |
| X | Semimajor axis of an elliptic external cowl | m, ft |
| Y | Semiminor axis of an elliptic external cowl | m, ft |
| z | Axial coordinate in the cylindrical coordinate system | — |
| z | Airfoil camber | m, ft |
| zmax | Maximum airfoil camber | m, ft |
| x, y, z | Cartesian coordinates | — |
| Greek | Definition | Unit |
| α | Bypass ratio in a turbofan engine | — |
| α | Angle of attack | deg |
| α | Absolute flow angle with respect to the axial direction in turbomachinery | deg |
| Δα | Flow turning angle across a stator blade section | deg |
| Δp | Pressure drop | Pa, psi |
| β | Plane oblique shock wave angle | deg |
| β | Relative flow angle with respect to the axial direction in turbomachinery | deg |
| βm | Mean flow angle corresponding to an average swirl across a blade row | deg |
| Δβ | Flow turning angle across a rotor blade section | deg |
| δ | Boundary layer thickness | m, ft |
| δ* | Boundary layer displacement thickness | m, ft |
| δ | Ratio of total pressure to reference (standard sea level) pressure; p/pref | — |
| δT | Thermal boundary layer thickness | m, ft |
| δ* | Deviation angle defined at the blade trailing edge, a cascade parameter | deg |
 |
(Standard) molar heat of formation | J/kmol |
 |
(Standard) specific heat of formation | J/kg |
 |
Tip clearance; slip factor in turbomachinery | — |
|
A small quantity ( 1) |
— |
| g |
Emissivity of gas | — |
| κ | Coefficient of thermal conductivity | W/m · K |
| κ1 | Blade leading-edge angle in turbomachinery | deg |
| κ2 | Blade trailing-edge angle in turbomachinery | deg |
| π | Total pressure ratio | — |
| ω | Angular speed | rad / s, rpm |
 |
Total pressure loss parameter in a cascade;  |
— |
 |
Spherical coordinate | — |
|
Equivalence ratio | — |
|
Diffuser wall divergence angle | deg |
|
Flow coefficient;  |
— |
 |
Camber angle, κ1 — κ2 | deg |
 |
Cooling effectiveness parameter | — |
 |
Ratio of specific heats | — |
 |
Circulation (of a vortex filament), blade circulation | m2/s, ft2/s |
| γ° | Cascade stagger angle or blade setting angle | deg |
 |
Fluid density | kg/m3, lbm/ft3 |
 |
Coefficient of viscosity | N · s/m2 |
|
Mach angle | degree |
| v | Kinematic viscosity  |
m2/s, ft2/s |
| v | Prandtl-Meyer angle | radians, degree |
 |
Compressor total pressure ratio | — |
 |
Burner total pressure ratio | — |
 |
Inlet total pressure recovery | — |
 |
Nozzle total pressure ratio | — |
 |
Temperature sensitivity of chamber pressure in solid rockets | %/K, %/F |
 |
Mach index  |
— |
 |
Flow angle, cylindrical or spherical coordinate | deg |
|
Nozzle exit flow angle (from axial direction) | deg |
|
Ratio of total temperature to the reference (standard sea level) temperature;  |
— |
|
Circumferential extent of the inlet spoiled or distortion sector | deg |
| * |
Momentum deficit thickness in the boundary layer | m |
 |
Cascade or blade solidity; c/s, in turbomachinery | — |
|
Stefan–Boltzmann constant | W/m2K4 |
 |
Temperature sensitivity of burning rate in solid propellant grain | %/K, %/F |
 |
Shear stress | Pa, lbf/ft2, psi |
|
Total temperature ratio | — |
|
Characteristic timescale | s |
 |
Rotor torque, stator torque in turbomachinery | N · m, ft-lbf |
 |
Turbine total temperature ratio,  |
— |
 |
Cycle limit enthalpy ratio,  |
— |
 |
Limit enthalpy ratio with afterburner,  |
— |
 |
Resident timescale | ms |
 |
Burner efficiency | — |
 |
Overall efficiency | — |
 |
Propulsive efficiency | — |
 |
Propeller Efficiency | — |
 |
Ideal Propeller Efficiency | — |
 |
Cycle or engine Thermal efficiency | — |
 |
Adiabatic efficiency of a diffuser | — |
 |
Adiabatic efficiency of a nozzle | — |
 |
Coordinate along the vortex sheet | — |
 |
Stage loading parameter;  |
— |
|
stream function | m2/s, ft2/s |
 |
Vector operator, Del | m—1 |
 |
Pressure gradient | bar/m |
 |
Mole fraction | — |
 |
Propellant mass fraction | — |
| Subscripts | |
| 1, 2 | Stations up- and downstream of a shock, or inlet and exit of a duct |
| C.S. | Control surface |
| C.V. | Control volume |
| e | Boundary layer edge |
| h | Hydraulic (in hydraulic diameter) |
| max | Maximum |
| n | Normal to an oblique shock |
| net | Net |
| r | Rotor, relative |
| rev | Reversible |
| s | Shock, shaft, stator |
| s | Isentropic |
| t | Total or stagnation |
| w | Wall |
 |
Free stream |
| Superscripts | |
| * | Sonic or critical state |
| Abbreviations and acronyms | |
| ADEN | Augmented-Deflector Exhaust Nozzle |
| AGARD | Advisory Group for Aeronautical Research and Development |
| AGT | Allison Gas Turbine |
| AIAA | American Institute of Aeronautics and Astronautics |
| AR | Blade aspect ratio |
| AR | Diffuser area ratio |
| ASME | American Society of Mechanical Engineers |
| ATF | Altitude Testing Facility |
| ATP | Advanced Turboprop |
| AVGAS | Aviation Gasoline |
| BDC | Bottom Dead Center |
| BLING | Bladed ring |
| BLISK | Bladed disk |
| BMEP | Brake Mean Effective Pressure |
| BPR | Bypass ratio |
| BTDC | Before Top Dead Center |
| C–D | Convergent–divergent |
| CEV | Crew Exploration Vehicle |
| C.G. | Center of gravity |
| CFD | Computational fluid dynamics |
| CHT | Cylinder Head Temperature |
| CLP | Combustor Loading Parameter |
| CO | Carbon monoxide |
| C.V. | Control volume |
| C.S. | Control surface |
| CDA | Controlled-diffusion airfoil |
| CDP | Compressor Discharge Pressure |
| CR | Compression Ratio |
| DCA | Double-circular arc blade |
| DOC | Direct Operating Cost |
| E3 | Energy efficient engine |
| EGT | Exhaust Gas Temperature |
| EPA | Environmental Protection Agency |
| EPNL | Effective Perceived Noise Level |
| ET | External tank |
| FADEC | Full-Authority Digital Electronic (or Engine) Control |
| FMEP | Friction Mean Effective Pressure |
| GE | General Electric company |
| GNC | Guidance–navigation–control |
| GTF | Geared Turbofan |
| HPC | High-pressure compressor |
| HPT | High-pressure turbine |
| IC | Internal Combustion |
| IGV | Inlet guide vane |
| ICAO | International Civil Aviation Organization |
| IMEP | Indicated Mean Effective Pressure |
| IPC | Intermediate Pressure Compressor |
| ITAR | International Traffic in Arms Regulation |
| K–D | Kantrowitz–Donaldson inlet |
| LCA | Life Cycle Assessment |
| LE | Leading edge |
| LEO | Low-Earth Orbit |
| LHS | Left-hand side |
| LOX | Liquid oxygen |
| LPC | Low-pressure compressor |
| LPT | Low-pressure turbine |
| MAP | Manifold Absolute Pressure |
| MEP | Mean Effective Pressure |
| MFR | Inlet mass flow ratio |
| MCA | Multiple-circular arc blade |
| MEMS | Micro-electro-mechanical systems |
| MIT | Massachusetts Institute of Technology |
| MR | Mass ratio |
| NACA | National Advisory Committee on Aeronautics |
| NASA | National Aeronautics and Space Administration |
| NPR | Nozzle pressure ratio |
| NOx | Nitric oxide(s) |
| N.S. | Normal shock |
| OPR | Overall pressure ratio |
| O.S. | Oblique shock |
| PDE | Pulse detonation engine |
| PR | Pressure ratio |
| PS | Pressure surface |
| P&W | Pratt & Whitney |
| P&WC | Pratt & Whitney Canada |
| RBCC | Rocket-based combined cycle |
| RJ | Ramjet |
| RMS | Root mean square (of a fluctuating signal, e.g. turbulence or total pressure distortion) |
| RR | Rolls-Royce |
| RAE | Royal Aeronautical Establishment |
| RHS | Right-hand side |
| RPV | Remotely Piloted Vehicle |
| SABRE | Synergetic Air Breathing Rocket Engine |
| SCRJ | Scramjet |
| SERN | Single Expansion Ramp Nozzle |
| Sfc | Specific fuel consumption (same as TSFC) |
| SM | Stall margin |
| SPL | Sound Pressure Level |
| SS | Suction surface |
| SSTO | Single-Stage to Orbit |
| STOL | Short Takeoff and Landing |
| SSME | Space Shuttle Main Engine |
| TBC | Thermal Barrier Coating |
| TDC | Top Dead Center |
| TE | Trailing edge |
| TF | Turbofan |
| TJ | Turbojet |
| TP | Turboprop |
| TPC | Thermal protection coating |
| TO | Takeoff |
| TSFC | Thrust specific fuel consumption |
| UAS | Uninhabitted Aerial System |
| UAV | Uninhabited aerial vehicles |
| UCAV | Uninhabited combat air vehicle |
| UDF | Unducted fan |
| UHB | Ultra-high bypass |
| UHC | Unburned hydrocarbons |
| VCE | Variable Cycle Engine |
| VTOL | Vertical takeoff and landing |
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