Claude Skills by ashfordeOU

Use when the task is combustor sizing, burner fuel-air ratio, flame temperature, or heat release for a gas turbine engine. Compute the gas turbine combustor design point: the stoichiometric fuel-air-ratio from the fuel carbon and hydrogen mass fractions, the operating fuel-air-ratio from the fuel and air flows, the equivalence ratio, the combustion efficiency, the heat release from the fuel flow and lower heating value, and the temperature rise across the combustor with the adiabatic flame te...

Use when you must compute the ideal gas turbine (Brayton) cycle: estimate the thermal efficiency, the compressor exit temperature, the turbine exit temperature, and the net specific work from the pressure ratio and the cycle temperature limits. Produces the cycle efficiency, station temperatures, and specific work in SI units that gate the engine cycle assessment. Trigger: gas turbine, brayton cycle, thermal efficiency, pressure ratio, compressor, turbine, engine cycle.

Use when you must analyze a gas turbine cycle with intercooling: split the total pressure ratio into two compression stages with an intercooler between them, compute the intercooler exit temperature from the stage pressure ratio and effectiveness, determine the optimum intercooler pressure ratio minimizing total compressor work, and quantify net specific work and thermal efficiency against the simple non-intercooled cycle. Produces the intercooled cycle efficiency, the simple cycle baseline e...

Use when you must size the gas turbine propelling nozzle: decide the choked or unchoked regime from the nozzle pressure ratio against the critical ratio 1.851, size the throat area from the design mass flow and total conditions under the choked flow relation, and return the choked exit temperature, velocity and static pressure plus the gross thrust with the pressure term, or for an unchoked off-design point the exit Mach number and the actual mass flow the throat passes. Produces the regime f...

Use when you must compute the real-cycle gas turbine performance with component losses: the compressor exit temperature and the turbine exit temperature from the pressure ratio and the component-efficiency (isentropic-efficiency) of each machine, the real-cycle thermal efficiency of the non-ideal Brayton cycle, the actual-SFC from the efficiency and the fuel lower heating value, and the efficiency penalty from the combustor pressure-loss. Produces the actual station temperatures, the real-cyc...

Use when you must analyze a gas turbine cycle with regeneration: compute the regenerative Brayton cycle thermal efficiency from the pressure ratio, temperature limits, and regenerator effectiveness, estimate the optimum pressure ratio at which turbine exhaust heat recovery stops paying off, and quantify the efficiency gain over the simple cycle in percentage points. Produces the regenerative efficiency, the simple cycle efficiency for comparison, the optimum pressure ratio, and the gain, all ...

Use when you must compute subsonic inlet total pressure recovery at a flight condition: the ram recovery ratio from free-stream Mach (unity below Mach 1, MIL-E-5008B style roll-off above), the isentropic stagnation pressure ratio, the engine face total pressure after the duct total-pressure efficiency, the capture area for the engine mass flow at flight speed and density, and the capture verdict against the intake highlight, spillage when the required capture exceeds the highlight. Produces r...

Use when you must analyze an ideal single-stream turbojet core cycle at flight conditions: compute the freestream stagnation temperature from the flight Mach number, the compressor exit temperature from the pressure ratio, the fuel-to-air ratio from the turbine inlet temperature and the combustor efficiency, the turbine exit temperature from the compressor-turbine work balance, the nozzle exit temperature and exit velocity, the net specific thrust as the exit velocity minus the flight velocit...

Use when you must analyze the ideal ramjet cycle: compute the flight stagnation temperature from the speed of sound and Mach number, the total temperature ratio across the combustor from the fuel air ratio and lower heating value, the specific thrust from the Mach number and total temperature ratio, the total thrust from the captured mass flow, and the specific impulse and thermal efficiency from the fuel flow. Produces the specific thrust, thrust, specific impulse, and thermal efficiency tha...

Use when you must analyze the supersonic ramjet inlet: compute the diffuser total pressure recovery at the flight Mach number from the isentropic limit or from the normal shock standing at the cowl lip, convert the freestream stagnation pressure into the diffuser exit total pressure, apply the Kantrowitz starting criterion to the contraction ratio to decide whether the inlet swallows the shock and starts, and report the starting limit Mach number and the maximum startable contraction ratio. P...

Use when you must compute the operating point of a reciprocating compression-ignition aircraft powerplant: the air-standard Diesel cycle thermal efficiency from the compression ratio, the specific-heat ratio and the cutoff ratio of the constant-pressure heat-addition model, the isentropic compression temperature ratio and state temperatures, the four-stroke indicated power from the indicated mean effective pressure, displacement and crankshaft speed, the brake power at the mechanical efficien...

Use when you must compute the operating point of a reciprocating high-speed compression-ignition aircraft powerplant: the air-standard dual-cycle thermal efficiency from the compression ratio, the specific-heat ratio, the pressure ratio of the constant-volume heat-addition phase and the cutoff ratio of the constant-pressure phase, the isentropic compression temperature ratio and state temperatures, the four-stroke indicated and brake power from the indicated mean effective pressure, displacem...

Use when you must compute the operating point of a reciprocating four-stroke aircraft powerplant for general-aviation propulsion: the air-standard Otto cycle thermal efficiency from the compression ratio and the specific-heat ratio, the four-stroke indicated power from the indicated mean effective pressure, the displacement and the crankshaft speed, the brake power at the mechanical efficiency, and the brake specific fuel consumption from the fuel flow and the brake power. Produces the single...

Use when you must size and assess a cold gas thruster for spacecraft reaction control: compute the choked mass flow through the nozzle throat from the plenum pressure and temperature, the thrust from the mass flow and specific impulse, the tank gas mass from the plenum volume and pressure, the isothermal blowdown time constant and pressure history, the operating time to the minimum usable pressure, and the total impulse available over the blowdown. Produces the throat area, mass flow, thrust,...

Use when you must size and assess the combustion chamber of a rocket engine: compute the characteristic velocity (c-star) from the chamber pressure, the throat area, and the propellant mass flow, estimate the theoretical c-star from the chamber temperature, the molecular weight, and the specific heat ratio, size the throat area from the propellant flow and the chamber pressure, compute the thrust coefficient and the thrust from the chamber pressure and the throat area, and derive the chamber ...

Use when you must size and analyze a hybrid rocket motor burning a solid fuel grain with a fluid oxidizer: compute the fuel regression rate from the oxidizer mass flux, solve the oxidizer to fuel ratio, find the chamber pressure equilibrium with the choked nozzle discharge, derive the mass flow, thrust and total impulse, and judge the O/F shift as the port opens. Reference-only typical HTPB grain constants cover the nitrous oxide and liquid oxygen oxidizers. Produces the ballistics summary wi...

Use when you must size and assess a hydrazine monopropellant thruster for spacecraft reaction control: compute the catalytic decomposition products and net decomposition heat release of hydrazine at a documented ammonia dissociation fraction, the adiabatic decomposition temperature from the hydrazine decomposition energy balance, and the frozen composition isentropic nozzle expansion of the decomposed gas mixture to the vacuum exhaust velocity, the vacuum specific impulse and the propellant m...

Use when you must size and assess a hydrogen peroxide monopropellant thruster for spacecraft reaction control: compute the decomposition heat release of H2O2 at a documented concentration with the water dilution, the adiabatic decomposition temperature from the peroxide decomposition energy balance, and the frozen composition isentropic nozzle expansion of the steam-oxygen product mixture to the vacuum exhaust velocity, the vacuum specific impulse and the propellant mass flow at the required ...

Use when you must design the rocket engine injection elements and their atomization basis: orifice discharge flow from discharge coefficient and pressure drop, injection velocity, the momentum flux ratio of impinging unlike-doublet elements, the fuel and oxidizer orifice counts for a chamber mass flow at a given mixture ratio, and the per-element flow balance. Produces per-orifice mass flow, injection velocity, momentum flux ratio, fuel and oxidizer orifice counts, and per-element mass flow f...

Use when you must select the rocket nozzle expansion ratio for a design altitude: solve the inverse isentropic problem for the matched-expansion-ratio whose ideal exit static pressure equals the ambient pressure at the design altitude, using the supersonic-branch area-Mach root and the monotone expansion solve by bisection, and evaluate the sea-level, vacuum and design-altitude delivered isp at the chosen ratio from the ideal rocket relations with the choked mass flow. Produces the design-alt...

Use when you must design a rocket engine nozzle from the chamber conditions: compute the exit Mach number for a target area ratio, the choked mass flow through the throat, the exit velocity and the exit static pressure, and the ideal thrust with the pressure term. Produces the nozzle area ratio, exit Mach number, mass flow, exit velocity, and thrust, plus the expansion verdict against the ambient pressure, all in consistent SI units (Pa, K, kg/s, m/s, N). Trigger: nozzle design, area ratio, e...

Use when you must select and screen rocket propellants for a mission: classify propellant families (cryogenic, storable, hypergolic, solid, hybrid), compare specific impulse and density impulse, compute the mixture bulk density and the O/F ratio optimum, derive the required propellant mass fraction from a delta-v budget with the rocket equation, and judge storability and handling for the mission. Produces the propellant family classification, the density-impulse ranking, the O/F verdict, the ...

Use when you must assess liquid rocket engine feed cycles at a fixed thrust, chamber pressure, and propellant pair: compare pressure-fed against the pump-fed gas-generator, staged-combustion, and expander cycles, compute the pump discharge pressure, the oxidizer and fuel pump powers, the turbine drive power and the cycle power balance, and size the pressure-fed feed-tank mass penalty. Produces the feasible cycle set, pump and turbine power balance, drive mass fraction, tank mass penalty, and ...

Use when you must account for gravity loss in a launch-vehicle powered ascent: compute the burn time from the propellant load and its flow rate, the launch thrust-to-weight ratio from the sea-level thrust and the initial mass, the gravity loss as g0 times the burn time for a vertical ascent or as g0 times the burn time times the sine of a constant mean flight-path angle for a pitched ascent, and the effective ascent delta-v as the ideal delta-v minus the gravity and drag losses. Produces the ...

Use when you must compute the rocket-nozzle-divergence-loss bookkeeping from the nozzle geometry and the ideal attached-flow state: apply the conical divergence factor lambda = (1 + cos(alpha))/2 for the half-angle to the ideal axial momentum thrust, or the bell contour efficiency (0.98 typical for the 80-percent bell) in its place; grow the turbulent boundary layer over the divergent length to the displacement thickness and convert it with the 1-D mass-flux correction to the momentum loss fr...

Use when you must predict flow separation in an overexpanded rocket nozzle: apply the separation-pressure-ratio criterion (wall static pressure falling to K_SEP times ambient, K_SEP 0.4) to decide whether the wall flow separates, find the separation-station area ratio from the isentropic area-Mach relation at the separation pressure, estimate the separation altitude where the nozzle un-separates, and compute the separated-thrust loss and the side-load flag. Produces the separation verdict, se...

Use when you must size launch-vehicle propulsion with the rocket equation: calculate delta-v from specific impulse and the initial and final masses, derive the mass ratio from a delta-v requirement, compute the propellant mass, and sum the delta-v across the stages of a multistage launch vehicle. Produces the stage delta-v, the mass ratio, and the propellant mass that gate the vehicle sizing. Applies to each stage of the launch vehicle in consistent SI units. Trigger: rocket equation, delta-v...

Use when you must analyze multi-stage rocket staging for a launch vehicle: compute the ideal delta-v per stage from the rocket equation, allocate the stage mass ratios and the payload fraction across the stages, derive the structural index from the inert and the propellant masses, and optimize the stage count for a target total delta-v. Produces the per-stage delta-v, the stage mass ratio, the stage payload fraction, the structural index, the optimal stage split, and the minimum stage count, ...

Use when the task is solid rocket motor design, grain sizing, or ballistics estimation. Size and analyze solid propellant rocket motors from first ballistics: compute the Vieille burn rate from the pressure exponent, solve the chamber pressure equilibrium between propellant burn rate and choked throat discharge, evaluate grain geometry with web thickness and burn area, and derive mass flow, thrust, and total impulse from the characteristic velocity c*. Uses typical AP/HTPB composite propellan...

Use when you must estimate the regenerative cooling of a liquid rocket thrust chamber: the throat area and propellant mass flow anchor of the operating point, the Bartz hot gas convective coefficient at the throat, the coolant side convective coefficient from the channel flow with the Dittus-Boelter correlation, the series wall resistance network giving the heat flux and the hot and cold wall temperatures, the coolant mass flux required to hold a copper wall temperature limit, and the film co...

Use when you must size or analyze a rocket thrust vector control (TVC) system: compute the side force from the engine thrust and the nozzle deflection angle, the control torque about the vehicle center of gravity from the side force and the moment arm, and the axial thrust loss from the deflection cosine, and size the actuator authority the gimbal actuators must deliver. Covers the TVC mechanisms: gimbaled engine or nozzle, flex-seal nozzle, jet vanes, and liquid injection, and contrasts thru...

Use when you must size the bypass ratio design trade for a turbofan: compute the thrust split between the fan and core streams, the specific thrust, and the thrust-specific fuel consumption across candidate bypass ratios, and weigh them against the fan pressure ratio trend. Produces the per-stream mass flows and thrust shares, the TSFC versus bypass ratio trend, and the fan pressure ratio verdict that feed the engine trade study. Trigger: bypass ratio, bpr, specific thrust, tsfc, fan pressure...

Use when you must compute the two-stream turbofan design point with a mixing exhaust: traverse the fan and core streams to the mixer entry, close the constant-area mixer by the energy and momentum balance over the two streams' total states to the mixed total temperature and pressure with the mixing loss, expand the mixed stream through the common convergent nozzle, and report the net thrust and TSFC of the mixed-flow configuration against the separate-exhaust baseline. Produces the mixed tota...

Use when you must compute turbofan cycle parameters: calculate the bypass ratio from the fan and core mass flow, the propulsive efficiency from flight and jet velocity, the net thrust from total mass flow and the velocity change, and the specific thrust from net thrust per unit mass flow. Produces the bypass ratio, propulsive efficiency, net thrust, and specific thrust that gate the engine cycle assessment. Trigger: turbofan, bypass ratio, propulsive efficiency, specific thrust, fan mass flow...

Use when you must compute the two-stream turbofan design point at flight Mach and altitude: traverse the fan-stream-station-states and the core stream of the separate-exhaust-cycle down the 0-2-13-2.5-3-4-4.5-5-9/19 station chain from the overall pressure ratio, the turbine-inlet temperature, the bypass ratio and the fan pressure ratio with the component efficiencies; close the two-spool-work-balance of the high-pressure compressor on the HP turbine and of the fan plus booster on the LP turbi...

Use when you must evaluate turbofan performance away from the design point: correct the inlet mass flow and the spool speed to standard-day conditions, scale the sea-level net thrust to altitude with the density ratio and the ram drag penalty, apply the SFC altitude and throttle behavior, sanity-check the throttle setting, and judge the fan and core component matching. Produces corrected mass flow, corrected speed, altitude net thrust, cruise SFC factor, and the matching verdict that gate the...

Use when you must design or assess a centrifugal compressor stage: compute the impeller tip speed from the rotational speed and the impeller diameter, the slip factor from the Wiesner correlation with the blade count and back-sweep angle, the work input coefficient from the Euler work relation, the total temperature rise, and the isentropic stage pressure ratio from the rotor work input, the isentropic efficiency, and the inlet total temperature. Also compute the impeller diffusion ratio and ...

Use when you must size the centrifugal pump inside a liquid rocket engine turbopump: convert the discharge pressure rise and propellant flow into the pump head, compute the dimensionless specific speed from the shaft speed, flow, and head, estimate the impeller tip speed and diameter from the design head coefficient, compute the pump power at the pump efficiency, assess the suction performance with the available net positive suction head and the suction specific speed, and judge the cavitatio...

Use when the task is free-turbine sizing, power-turbine matching, turboprop shaft power, or turboshaft cycle estimates. Size and match a free-turbine turboprop or turboshaft power section: compute the power-turbine exit temperature and shaft power from the gas generator exhaust state (mass flow, inlet temperature, expansion ratio, polytropic efficiency), convert to torque at the power-turbine speed, blade speed from the mean diameter, reduction gearbox ratio to the propeller or rotor, specifi...

Use when you must analyze the turboprop powerplant cycle and propeller performance: compute the propeller (Froude) efficiency from the flight velocity and the slipstream velocity, the thrust delivered from the shaft power at the flight speed, the static thrust from the shaft power and the propeller disk area at zero speed, the equivalent shaft power that credits the residual jet thrust, the advance ratio and the power and thrust coefficients at the propeller speed, the specific fuel consumpti...

Use when a task concerns space systems engineering for European space projects: guide the router to the space-systems pack. ECSS software-engineering criticality, software-verification verification depth, systems-engineering lifecycle gates, power-thermal-budget EPS and battery sizing, communication-link-budget link margin, thermal-design radiator sizing, command-data-handling telemetry, sun-pointing sun vector geometry, star-tracker star identification, attitude-control-sizing reaction wheel...

Use when you must size the attitude control subsystem actuators for a spacecraft: compute the momentum wheel capacity for a commanded slew, check the detumble rate against the allowed rate, and verify the wheel momentum margin before the ADCS design review. Produces the slew momentum requirement, the detumble verdict, and the margin check that gates actuator selection. Trigger: attitude control, momentum wheel, adcs sizing, slew rate, detumble, spacecraft pointing.

Use when you must determine the optimal attitude of a spacecraft from multiple vector observations by the Davenport q-method: minimize the Wahba cost over N >= 2 weighted body and reference direction pairs, form the attitude profile matrix B, assemble the symmetric 4x4 Davenport K matrix, and extract the largest eigenvalue eigenvector with a deterministic fixed-sweep Jacobi iteration. Produces the optimal attitude quaternion, the 3x3 attitude matrix, the per-observation residuals, the achieve...

Use when the task is attitude determination from two vector measurements such as a sun sensor and magnetometer pair, coarse attitude estimation for initial acquisition, or computing the attitude quaternion and rotation angle that gate the ADCS attitude reference before fine pointing. Determine the spacecraft attitude matrix from a pair of non-parallel vector observations with the TRIAD algorithm: normalize the measured body frame directions and the matching reference frame directions, build t...

Use when you must size and analyze a control moment gyro (CMG) cluster for agile spacecraft attitude control: compute the torque from the rotor momentum and the gimbal rate with the CMG torque law, derive the gimbal rates for a commanded torque with the pseudoinverse steering law and its null-space term, judge the torque amplification of the gimbal against a wheel actuator at equal momentum, evaluate the singularity measure and verdict of the gimbal state, and size the cluster momentum envelo...

Use when you must estimate the worst-case environmental disturbance torque budget for a spacecraft: compute gravity-gradient torque from orbit mean motion and principal moment spread at the attitude offset, solar pressure torque from area, incidence cosine and lever arm with reflectivity convention, residual magnetic dipole torque against the local field, and aero drag torque from the free-molecular relation at explicit density. Produces per-source worst-case torques, aligned-axis total with ...

Use when you must design or analyze passive gravity-gradient stabilization: check the inertia-ratio stability criterion I_y > I_x > I_z with y along the orbit normal for a nadir-pointing spacecraft, compute the pitch libration frequency and period from the mean motion and the inertia spread, estimate the gravity-gradient restoring torque at a pitch offset, and size a gravity boom tip mass for a target libration stiffness. Produces the stability verdict, the libration period, the restoring tor...

Use when you must characterize gyroscope noise for ADCS sensor selection: compute the overlapping Allan deviation AD(tau) over a correlation-time grid from a rate sample time series with cumulative sums, fit the log-log noise slope, categorize the noise process from the slope band (white noise or angle random walk at about -1/2, rate random walk at about +1/2, quantization at about -1, bias instability as a flat floor), and extract the angle random walk coefficient in deg/sqrt(h). Produces th...

Use when you must estimate the in-flight magnetometer bias vector with scalar-checking batch least squares: expand |m_k - b|^2 = B_k^2 over the measured body-frame samples m_k and the known field magnitudes B_k, build the 4-unknown rows [-2 m_k, 1] with right sides B_k^2 - |m_k|^2, solve the normal equations A^T A x = A^T y by partial-pivot Gaussian elimination, and recover the bias from the first three unknowns with the fourth unknown |b|^2 as the consistency check. Produces the bias vector,...

Use when the task is magnetorquer control, dipole moment calculation, B-dot detumbling, cross-product torque steering, detumbling rate damping, or torque authority limits. Compute the magnetic dipole moment for spacecraft magnetic attitude control with magnetorquers: solve torque = m x B for the required dipole from a torque demand and the local magnetic field vector, apply the B-dot detumbling law to damp body rates, check the achievable torque against the magnetorquer torque authority limit...