ashfordeOU

@ashfordeou source repo

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State Machine · ashfordeou bundle
Use when you must model or verify SysML state machine behavior in an aerospace systems engineering model: build state machines with states, transitions, events, guards, and actions, simulate an event sequence to produce the firing trace, compute the reachable state set from the initial state, and detect unreachable states and transition conflicts where two guards enable the same event. Produces the firing trace, the reachable set, and the conflict list that gate the behavioral model review. Trigger: state machine, statechart, transitions, guards, events, reachability, SysML behavior.

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Constraint Analysis · ashfordeou bundle
Use when you must run the aircraft constraint analysis matching chart in conceptual design: compute the stall constraint wing loading from the maximum lift coefficient and the stall speed, the takeoff distance constraint thrust to weight curve, the climb gradient constraint from the excess thrust and the lift to drag ratio, the cruise constraint, and the maneuvering constraint from the load factor, then assemble the feasible design region lower bounds that gate the conceptual design trade. Produces the constraint dict, the feasible region boundary, and the required thrust to weight at the design point. Trigger: constraint analysis, matching chart method, feasible region, stall constraint, takeoff distance, climb gradient, cruise constraint, maneuvering constraint, load factor.

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Operating Cost · ashfordeou bundle
Use when you must estimate the direct operating cost of the aircraft: compute the block fuel cost from the fuel price, the crew cost from the crew complement, the maintenance cost from the man-hours per flight hour, the insurance cost from the annual rate and utilization, and roll the elements into the cost per flight and the cost per flight hour. Produces the DOC breakdown and the per flight hour cost that gate the operating economics assessment. Trigger: direct operating cost, block fuel cost, crew cost, maintenance cost, flight hour cost.

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Bleed Air System Sizing · ashfordeou bundle
Use when you must size the aircraft bleed air system: roll up the total bleed offtake mass flow from the fixed consumer demands (ECS pack flows, wing anti-ice flow, pressurization trim flow), split the offtake per engine, compute the bleed thermal budget the precooler must reject between the bleed supply temperature and the consumer supply temperature, and size each engine bleed duct diameter from compressible pipe flow at a fixed design Mach number. Produces the total and per-engine offtake mass flow, the per-engine and total thermal budget, the duct flow area and diameter, and a fit verdict against the nominal duct diameter limit. Trigger: bleed air sizing, bleed offtake mass flow, per engine offtake, bleed duct diameter, duct Mach sizing, precooler heat load, bleed thermal budget, pneumatic bleed manifold, bleed supply temperature.

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Fuel Feed System Sizing · ashfordeou bundle
Use when you must size the aircraft fuel feed system between the tank and the engine: the per-engine feed flow from the takeoff fuel flow demand, the feed line velocity and Reynolds number, the line pressure loss from the Darcy friction factor (laminar 64/Re, turbulent Blasius) with the major loss over the line length and the minor losses from the fitting loss coefficient, the static head gain from tank to pump, and the net positive suction head available at the engine-driven pump inlet against the required NPSH with the boost pump pressure rise added at cruise altitude. Produces the feed flow, the line pressure loss, the NPSH available with and without the boost pump, the feed PASS/FAIL verdict, and the boost pump hydraulic power that gate the fuel feed system layout. Trigger: fuel feed system sizing, boost pump sizing, feed line pressure loss, engine feed NPSH, fuel pump power.

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Hydraulic System Sizing · ashfordeou bundle
Use when you must size the aircraft hydraulic power system from actuation demand: actuator flow from piston area and rod speed, worst-case simultaneous demand, pump flow and drive power from system pressure, flow and efficiency with leakage make-up, the emergency accumulator gas volume between charged and depleted pressure from the adiabatic gas law given the usable volume, and the reservoir volume from leakage make-up over a hold time with margin. Produces the per-actuator flow, the simultaneous demand group, pump flow and power, the accumulator charged and depleted gas volumes with the p V^n closure check, and the reservoir volume for hydraulic system architecture studies. Trigger: hydraulic pump sizing, actuator flow demand, pump flow and power, accumulator sizing, hydraulic reservoir sizing, system pressure, emergency hydraulic system, hydraulic power sizing.

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Data Control Coupling Analysis · ashfordeou bundle
Use when you must analyze data coupling and control coupling between airborne software components: identify the data-coupling items between component pairs from their written and read variable sets with declared synchronization suppression, identify the control-coupling items across call edges where a caller-written variable is read by the callee, compute the coupling coverage ratio against declared evidence, and return the PASS or FAIL verdict with the uncovered item list. Produces the data-coupling item list, the control-coupling item list, the coupling coverage ratio and the evidence verdict that gate the level A inter-component coupling objective. Trigger: data coupling analysis, control coupling analysis, shared-variable pairs, call-edge coupling items, coupling coverage evidence, level-a coupling objectives, inter-component coupling.

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Rnp Anp Containment · ashfordeou bundle
Use when you must assess the RNP containment of a performance based navigation segment: compute the actual navigation performance (ANP) as the 95 percent containment bound from a lateral position error sigma or accept a directly supplied ANP, apply the required navigation performance (RNP) for the segment with an optional margin fraction, and decide whether the ANP stays inside the RNP. Produces the ANP, the containment margin and the pass or fail verdict that gate FMS navigation dispatch. Trigger: required navigation performance, actual navigation performance, RNP containment, ANP comparison, lateral position error sigma, 95 percent containment, performance based navigation.

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Vertical Navigation · ashfordeou bundle
Use when you must compute the vertical navigation (VNAV) descent path for a flight management system: determine the top of descent distance from cruise altitude to an arrival constraint, compute the descent gradient and flight path angle, and check the resulting altitude against waypoint altitude constraints. Produces the top of descent distance, the descent gradient in feet per nautical mile, the flight path angle in degrees, and the constraint verdict for the descent path. Trigger: vertical navigation, vnav, top of descent, descent gradient, flight path angle, altitude constraints, fms.

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Tcas Resolution Advisory · ashfordeou bundle
Use when you must evaluate a TCAS II resolution advisory for an own aircraft against a single intruder from measured range and altitude state: select the sensitivity level from the own altitude band, compute the modified tau closing time with the DMOD term, apply the horizontal threat test and the altitude test against the tau and ALIM thresholds, and choose the climb or descend advisory sense from the intruder position. Produces the sensitivity level, the modified tau, the threat verdict and the resolution advisory sense that gate a TCAS logic assessment. Trigger: TCAS II, traffic alert and collision avoidance, resolution advisory, modified tau, DMOD, sensitivity level, intruder threat logic, climb descend advisory.

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Engineering Report · ashfordeou bundle
Use when you must draft or review an engineering report and verify its structure: the required sections (abstract, introduction, method, results, discussion, conclusion, references), abstract length against the recommended 150 to 300 word range, completeness of the deliverable, units and uncertainty statements for every reported value, traceability of results to requirements, review gates, and version control. Produces missing-section lists, abstract-length pass or fail, units-statement pass or fail, uncertainty-statement pass or fail, completeness ratios, and requirement traceability closure lists. Trigger: engineering report, report structure, abstract length, required sections, completeness, units statement, uncertainty statement, traceability, review gate, version control.

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Optimization Algorithms · ashfordeou bundle
Use when you must minimize a scalar or multivariate design objective numerically: bracket a smooth one-variable objective and locate the minimum with golden-section search, or apply Newton's method on the derivative; run gradient descent with an Armijo backtracking line search or the derivative-free Nelder-Mead simplex for multivariate problems, and report the converged minimizer, the objective value, and the iteration count at a specified tolerance. Produces the unconstrained minimum, the converged objective value, the iteration count, and the verdict on brackets, learning rates, and tolerances. Trigger: optimization, minimize, golden section search, gradient descent, Nelder-Mead simplex, Newton method, line search, unconstrained minimum.

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Uncertainty Propagation · ashfordeou bundle
Use when you must propagate measurement uncertainties through a calculation with the GUM first order law: combine the sensitivity coefficients and standard uncertainties of the independent inputs into the combined standard uncertainty, expand it with a coverage factor, and identify the dominant contribution. Produces the combined standard uncertainty, the expanded uncertainty, and the per input variance shares that gate the measurement uncertainty budget. Trigger: uncertainty propagation, combined standard uncertainty, expanded uncertainty, coverage factor, sensitivity coefficient, GUM, variance contribution, dominant uncertainty.

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Dimensional Analysis · ashfordeou bundle
Use when you must run dimensional analysis on an engineering relation: check whether equation terms are dimensionally homogeneous, apply the Buckingham Pi theorem to form the dimensionless Pi groups, compute the Reynolds number and Mach number for a wind tunnel model, the required model speed to match full-scale Reynolds number under dynamic similarity, the Froude number, and the full-scale force from a model measurement. Produces the homogeneity verdict, the Pi group set, and the scaled test conditions. Trigger: dimensional analysis, buckingham pi, pi groups, dimensionless, reynolds number, mach number, froude number, dynamic similarity, wind tunnel model, model scale, similarity.

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Breguet Endurance · ashfordeou bundle
Use when you must compute the loiter endurance time of an aircraft with the Breguet endurance equation: combine the specific fuel consumption and the lift to drag ratio with the initial and final weights to produce the holding endurance in seconds, the final weight after an endurance segment, and the fuel burn for the loiter requirement. Produces the endurance time, final weight, and fuel burn that gate the holding performance check. Trigger: loiter endurance, endurance equation, holding time, specific fuel consumption, lift to drag ratio, fuel burn, maximum endurance.

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Climb Performance · ashfordeou bundle
Use when you must compute the climb performance of a fixed-wing aircraft from excess power: derive the rate of climb from thrust, drag, speed, and weight, convert the excess thrust into a climb gradient in percent, estimate the time to climb between two altitudes with the average rate of climb, and locate the service ceiling where the rate of climb decays to 0.5 m/s (100 ft/min). Produces the rate of climb in m/s, the climb gradient, the time to climb, and the service ceiling that gate the climb performance assessment. Trigger: rate of climb, excess thrust, climb gradient, time to climb, service ceiling.

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Glide Performance · ashfordeou bundle
Use when you must compute unpowered glide performance for a fixed-wing aircraft: derive the glide ratio from the lift and drag, convert it into the descent angle, find the sink rate from the airspeed and the descent angle, estimate the time to descend through a given altitude loss, and locate the best glide speed for the maximum lift to drag ratio. Produces the glide ratio, descent angle in degrees, sink rate in m/s, time to descend in seconds, and the best glide speed that gate the glide performance assessment. Trigger: glide ratio, sink rate, best glide speed, descent angle, time to descend, lift to drag.

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Flutter Testing · ashfordeou bundle
Use when you must assess flutter clearance for a flight test: compute the required flutter speed V_F_required as 1.2 times the design dive speed V_D, extrapolate the measured flutter speed from the damping versus test speed trend with a linear least squares fit and its zero crossing, check the frequency separation between structural modes against the 10 percent minimum, and judge the flutter margin ratio and the damping margin at the maximum test speed. Produces the required flutter speed, the extrapolated flutter speed, the frequency separation verdict, and the FAR 25.629 clearance verdict that gate the flutter test assessment. Trigger: flutter margin, damping trend extrapolation, flutter testing, frequency coalescence, frequency separation, design dive speed factor.

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Frequency Response Design · ashfordeou bundle
Use when the task is bode analysis, frequency response, gain crossover, phase crossover, gain margin, phase margin, or stability from the margins. Compute the Bode frequency response of an open loop transfer function for flight control design: evaluate the magnitude and phase at a frequency from the numerator and denominator coefficients at s = j*w, find the gain crossover and phase crossover frequencies, derive the gain margin in dB and the phase margin in degrees, and judge closed loop stability from the margins for the canonical type-1 plant K/(s(s+1)(s+2)). Produces the margins and the stability verdict that gate control law iteration. Trigger: bode plot, frequency response, gain margin, phase margin, gain crossover, phase crossover.

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Rts Smoother · ashfordeou bundle
Use when you must run a fixed-interval Rauch-Tung-Striebel (RTS) smoother over a stored forward Kalman-filter output for a discrete constant-velocity model in SI units: propagate the position and velocity state with the constant-velocity transition matrix, run the linear forward pass that stores the predicted and filtered means and covariances at every step, then execute the backward recursion with the smoother gain to combine each filtered estimate with the future measurements. Produces the smoothed state history, the smoother gains, the smoothed covariance history and the covariance reduction verdict that gate offline trajectory reconstruction and post-processing of navigation data. Trigger: rts smoother, rauch-tung-striebel, fixed-interval smoothing, backward pass, smoothed state, offline trajectory reconstruction, post-processing navigation data, constant-velocity model.

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Command To Line Of Sight · ashfordeou bundle
Use when you must compute a command to line of sight guidance command for a missile intercept: derive the tracker to target line of sight angle, the angular deviation of the missile from the tracker target line, the line of sight rotation rate, the steering acceleration proportional to the LOS error and its rate, the signed cross track offset of the missile from the line, and the on line verdict that gate a CLOS guidance assessment. Produces the LOS angle, wrapped LOS error, LOS rate, steering command, cross track offset, and the on line tracking verdict. Trigger: command to line of sight, CLOS, beam riding, LOS error, LOS rate, line of sight rate, steering command, cross track offset, tracker target line, intercept guidance.

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Gnss Carrier Smoothing · ashfordeou bundle
Use when you must smooth GNSS code pseudoranges with carrier-phase delta ranges before positioning: run the first-order Hatch recursion at a smoothing time constant, carry the smoothed range between epochs on the precise carrier increments, and monitor the code-carrier ionospheric divergence whose trailing-window slope fit predicts the smoothed-minus-code bias that would alarm a diverging range. Computes the noise-reduction verdict from the exact steady-state code-noise closed form sigma_code*sqrt(alpha/(2 - alpha)), its sigma_code/sqrt(2*tau/T) textbook limit and the carrier delta-range term. Produces the smoothed range time series, the verdict (code-only std, quoted limit, carrier term, total std, improvement factor) and the divergence alarm that gate the range before it feeds positioning. Trigger: carrier-phase smoothing, code-carrier smoothing, hatch recursion, smoothing time constant, code-carrier divergence, ionospheric divergence, smoothed range noise reduction.

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Bang Bang Control · ashfordeou bundle
Use when you must compute the time-optimal bang-bang control of a double integrator: the switching curve s = x + v|v|/(2a), the bang-bang command u = -a*sign(s) under a hard input limit |u| <= a, the exact rest-to-rest maneuver time T* = 2*sqrt(d/a), the switch point at half distance with velocity -sqrt(a*d), and the general minimum-time trajectory for nonzero initial velocity. Produces the switch point, the command profile and the maneuver time for single-axis attitude slew and translation bang-bang assessments under torque or rate limits. Trigger: bang bang control, time optimal control, switching curve, minimum time maneuver, rest to rest slew, double integrator, bounded input, torque limit, rate limit.

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Corrective Action · ashfordeou bundle
Use when you must drive a corrective action (CAPA) record for a manufacturing nonconformance to closure: run the eight-discipline (8D) problem-solving workflow, check that a containment action is recorded, validate the five-whys root cause chain, and confirm the corrective action and the effectiveness evidence before the record closes. Produces the closure stage verdict, the missing items, and the effectiveness pass or fail that gate the nonconformance closure. Trigger: corrective action, capa record, 8d report, five whys, root cause analysis, containment action, effectiveness verification, problem solving.

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Management Review · ashfordeou bundle
Use when you must plan and score the periodic top-management review process under an AS9100-style quality management system: compute the management review due date from the last review date and the base interval, check the mandatory review input coverage against the presented input set, track the action items from the review decisions, and issue the review verdict from the interval compliance, the input coverage ratio and the overdue action count. Produces the due date, the input coverage ratio with the missing input list, the action tracking summary and the review verdict that gate the top-management review record. Trigger: management-review, top-management, review-interval, review-inputs, action-item-tracking, review-verdict, qms-review.

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Ndt Method Selection · ashfordeou bundle
Use when you must select a non-destructive testing (NDT) method for an aerospace part from its defect class and material: determine whether the defect is surface, near-surface, or internal, classify the material as ferromagnetic, non-ferromagnetic, or non-conductive, and pick among radiography (RT), ultrasonic (UT), eddy current (ET), liquid penetrant (PT), and magnetic particle (MT) by sensitivity with cost as secondary reporting. Produces the recommended method, the alternates, and the selection rationale that gate the NDT inspection planning for special processes. Trigger: non-destructive testing, ndt, radiography, ultrasonic, eddy current, penetrant, magnetic particle, defect class, ferromagnetic.

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Afterburner Cycle · ashfordeou bundle
Use when you must analyze an afterburning gas turbine cycle with reheat: compute the afterburner fuel-air ratio from the duct energy balance across the turbine exit and the afterburner exit total temperatures with a combustion efficiency, the reheat fuel flow for the core mass flow, the dry and reheat nozzle exit velocities from a fully expanded ideal isentropic nozzle, the dry and reheat gross thrust, the thrust augmentation ratio, and the specific fuel consumption with and without reheat. Produces the reheat fuel flow, augmentation ratio, and dry versus reheat SFC values that gate an afterburner cycle assessment in the FAR-33 engine context. Trigger: afterburner cycle, reheat fuel air ratio, thrust augmentation ratio, reheat temperature rise, dry versus reheat thrust, reheat specific fuel consumption, afterburner nozzle exit velocity.

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Gas Turbine Cycle · ashfordeou bundle
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.

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Intercooled Cycle · ashfordeou bundle
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 efficiency, the optimum intercooler pressure ratio, the specific work gain, and the station temperatures that gate an engine cycle comparison. Trigger: intercooled cycle, two-stage compression, intercooler effectiveness, intercooler pressure ratio, compression work split, cycle work gain.

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Propelling Nozzle · ashfordeou bundle
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 flag, throat area, exit velocity, exit static pressure, gross thrust and expansion verdict. Trigger: propelling nozzle, convergent jet nozzle, nozzle throat area, choked nozzle regime, gross thrust pressure term, air breathing nozzle.

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Hohmann Transfer · ashfordeou bundle
Use when you must size a Hohmann transfer between two coplanar circular orbits of a spacecraft: compute the transfer-orbit semimajor axis and period, the circular-orbit velocity at the departure and arrival radii, the periapsis and apoapsis speeds on the transfer ellipse with the vis-viva equation, and the departure and arrival burn impulses that make up the hohmann-transfer delta-v budget. Produces the transfer time, the two impulse burns, and the total delta-v that gate orbit-raising and orbit-lowering maneuver planning and the rendezvous phase angle for a target in the outer orbit. Trigger: hohmann-transfer, delta-v, transfer-orbit, burn-impulse, vis-viva, coplanar-transfer, orbit-raising, transfer-time.

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Lambert Transfer · ashfordeou bundle
Use when you must solve Lambert's problem for a spacecraft orbit transfer: given two position vectors and a transfer time, find the connecting orbit with the p-iteration method, compute the velocity vectors at both endpoints, the transfer delta-v against circular parking orbits, and the transfer ellipse elements. Produces the semimajor axis, eccentricity, semilatus rectum, the required endpoint velocities, the delta-v budget, and the time-of-flight check, with short-way and long-way branches, the 180-degree case reducing to the Hohmann transfer as a sanity check, and multi-revolution transfers as an extension. Trigger: lambert-transfer, lambert-problem, p-iteration, time-of-flight, two-position, transfer-time, short-way, long-way, multi-revolution.

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Command Data Handling · ashfordeou bundle
Use when the task is command validation, telemetry packetization, CCSDS framing, onboard data storage sizing, downlink budgeting, spacecraft data bus selection, or C&DH redundancy. Design and check spacecraft command and data handling (C&DH): validate telecommands against opcode, length, and CRC-16 checksum; packetize telemetry into CCSDS-style frames with sequence counts and error detection; size onboard storage from per-orbit data volume; and budget downlink time and rate from stored data volume and link capacity. Computes CRC-16 checksums, byte-exact CCSDS packets, storage sizes, and downlink verdicts with deterministic functions. Trigger: command data handling, telemetry, telecommand, CCSDS, packetization, downlink, CRC-16, onboard storage, data bus, SpaceWire, MIL-STD-1553.

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Mmod Shielding Sizing · ashfordeou bundle
Use when you must size meteoroid and orbital debris (MMOD) impact protection: compute the Cour-Palais cratering penetration depth and critical projectile diameter of a single aluminum wall, size a Whipple shield bumper and rear wall so a design projectile at its design impact produces no rear-wall penetration, evaluate the Christiansen ballistic limit across low, intermediate, and hypervelocity regimes with the 3 and 7 km/s normal-velocity transitions and the 65 degree obliquity cap, and grade an impact as penetration or no penetration against the critical diameter. Produces the required rear-wall thickness for the no-penetration condition, the ballistic-limit curve over velocity, and the mission penetration probability from the expected number of penetrating impacts. Debris fluence and expected-impact inputs come from the space environment leaf; no environment model is built. Trigger: micrometeoroid, whipple shield, hypervelocity impact, ballistic limit, bumper sizing.

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Multiaxial Yield Criteria · ashfordeou bundle
Use when you must compute the multiaxial yield margin of an isotropic metal part: evaluate the von Mises equivalent stress in plane stress sqrt(sx^2 - sx*sy + sy^2 + 3*txy^2) and in full 3D, resolve the plane-stress principal stresses from the Mohr circle, compute the Tresca equivalent stress as the maximum principal stress difference including the zero out-of-plane principal, compute the yield margin yield/equivalent - 1, run the von Mises combined bending-plus-torsion margin for a shaft section, and check whether a biaxial tension point falls inside the von Mises yield envelope. Produces the von Mises and Tresca equivalent stresses, the principal stresses, the yield margins and the envelope verdict that gate metallic part hand checks. Trigger: multiaxial-yield-criteria, von-mises-equivalent-stress, tresca-margin.

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Thermal Buckling · ashfordeou bundle
Use when you must compute the thermal buckling of restrained aerospace structure from a temperature rise: the elastic buckling stress of a uniformly compressed flat plate, the compressive stress built by a constrained temperature change under uniaxial or biaxial restraint, the critical-temperature-rise that drives a skin panel to its buckling stress, and the critical-temperature-rise of an Euler column between rigid supports. Produces the buckling stress, the compressive stress at a given rise, and the critical temperature rise, plus the thermal-buckling-margin that gates a thermal-stability check. Trigger: thermal-buckling, critical-temperature-rise, restrained-temperature, thermal-buckling-margin, skin panel, hot structure, Euler column.

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Validation · ashfordeou bundle
Use when you must run requirements validation for an aircraft or system program per ARP4754A: select the validation method, confirm independence is provided where the development assurance level requires it, and score validation closure before the requirements are released to design. Produces the method verdict, the independence flag, and the closure score that gate the validation phase. Trigger: requirements validation, arp4754a, validation method, independent validation, development assurance, closure.

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Sysml Modeling · ashfordeou bundle
Use when you must create or check SysML models for model-based systems engineering in an aerospace program: select the right SysML diagram kind for each modeling purpose (block definition BDD, internal block IBD, parametric, requirement, activity, sequence, state machine, use case), draft block definition and internal block diagrams from the system structure, build requirements diagrams with traceability closure, set up parametric diagrams for constraint-based analysis, and judge model viewpoints complete or missing. Diagram choice follows the modeling purpose; requirements trace through design to verification, and model governance follows the mapped development guidance. Trigger: SysML, block definition diagram, BDD, internal block diagram, IBD, parametric diagram, requirements diagram, traceability.

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Life Cycle Cost · ashfordeou bundle
Use when you must estimate the total life-cycle-cost of an aircraft program: structure the estimate into the RDT&E, production, operations and support, and disposal phases, apply a power-law CER to a phase cost driver, apply the learning curve to get the Nth unit cost and the cumulative average unit cost, escalate costs for inflation, discount future year costs to present value at the discount rate, and bound the result with an uncertainty range. Produces the phase costs, the present value of the operations and support stream and of the disposal cost, and the total life-cycle cost that gates the affordability assessment. Trigger: life cycle cost, present value, discount rate, operations and support, disposal cost, rdt and e, cost driver, uncertainty, inflation.

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Parametric Cost · ashfordeou bundle
Use when you must compute parametric cost estimates for an aircraft development and production program: derive the learning curve exponent from a learning curve percentage, apply the learning curve to get unit cost and cumulative production cost, estimate development cost from airframe mass with a weight-based cost estimating relationship, and roll the recurring and non-recurring pieces into a total program cost. Produces the unit cost, the cumulative learning factor, the production total, and the program total that gate the program cost assessment. Trigger: parametric cost, cost estimating relationship, cer, learning curve, unit cost, development cost, program cost, cumulative average.

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Air Cycle Machine Sizing · ashfordeou bundle
Use when you must size the bootstrap air-cycle cooling pack thermodynamics for the ECS cooling load: compute the compressor exit state from the pack-inlet bleed condition, pressure ratio and isentropic efficiency, cool the discharge through the ram-air heat exchanger at a given effectiveness, expand through the cooling turbine to cabin pressure, close the two-wheel ACM shaft balance, and turn the turbine exit temperature into delivered cooling against the cabin design temperature. Produces compressor and turbine exit temperatures and pressures, heat-exchanger exit temperature, shaft powers, the balance verdict with work deficit or closing effectiveness, delivered cooling power versus the load and the required bleed flow. Trigger: air cycle machine, bootstrap air cycle, ACM shaft balance, cooling turbine exit, compressor exit state, heat exchanger effectiveness, required bleed flow, delivered cooling power.

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Cargo Compartment Sizing · ashfordeou bundle
Use when you must size a freight cargo compartment and its cargo door around standard unit load devices: look up public ULD envelope dimensions from the module catalog, check whether a ULD cross-section passes through a cargo door with the rotated orientation tried, pick the largest-volume ULD that fits a door, lay out ULD positions with a deterministic 2D strip layout and aisle allowance, compute the required cargo volume from payload mass and density, and report the adequacy verdict. Produces the ULD count, the volume utilization, the unused length and width, the door opening width and height with clearance, and the volume adequacy verdict. Trigger: cargo door opening, unit load device, ULD layout, freight hold.

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Shock Expansion Airfoil · ashfordeou bundle
Use when you must compute the supersonic shock-expansion solution for a diamond (double-wedge) airfoil section: patch oblique-shock and Prandtl-Meyer relations over the four planar surfaces at a freestream Mach number and angle of attack, then integrate the panel pressures into the section lift, wave drag, and leading-edge moment coefficients with a surface pressure table. Implements theta-beta-M (weak solution), oblique-shock ratios, and the Prandtl-Meyer function internally for the turn-by-turn surface states. Produces cl, cd_wave, cm_le and per-surface Cp for a given half-angle, angle of attack, and Mach number. Trigger: shock-expansion, supersonic airfoil, diamond airfoil, double-wedge, surface-pressure integration, wave drag coefficient.

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Swept Wing Aerodynamics · ashfordeou bundle
Use when you must apply wing sweep effects for high-speed aerodynamics: compute the simple sweep theory cosine corrections for the lift curve slope and the section Mach number, find the effective Mach number and the velocity components normal and tangential to the leading edge, and estimate the critical Mach number increase that sweep provides over the unswept wing. Produces the swept wing lift slope, the effective Mach number, and the critical Mach estimate that feed transonic cruise and high-speed wing design. Trigger: swept wing, sweep angle, leading edge sweep, simple sweep theory, critical Mach, effective Mach.

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Engineering Margins · ashfordeou bundle
Use when you must compute the margin of safety for a structural element and state it in an engineering report: compare the allowable load against the applied load, express the stress margin as a unitless decimal or a percent, and produce the pass/fail verdict on the limit basis or ultimate basis. Produces the margin of safety, the margin percent, the limit margin, and the one-line report sentence with consistent units in newtons. Trigger: margin of safety, engineering report, allowable load, limit load, ultimate load, stress margin.

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Convergence Verification · ashfordeou bundle
Use when you must verify that a CFD or structural mesh sequence has converged: compute the observed order of accuracy from the finest, medium, and coarse solutions, apply Richardson extrapolation to estimate the exact solution, and report the grid convergence index (GCI) with the 1.25 safety factor. Produces the observed order, the extrapolated value, the GCI, and a monotone converged, oscillatory, or diverging verdict that gate whether the discretization error is acceptable for the assessment. Trigger: richardson extrapolation, grid convergence index, gci, observed order, refinement ratio, discretization error, mesh refinement study.

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Eigenvalue Decomposition · ashfordeou bundle
Use when the task is an eigen-decomposition: spectral analysis, dominant eigenvalue, modal frequencies, covariance or stiffness matrix diagonalization, stability of a linear system, or verifying a pair with the residual A v minus lambda v, and numpy or other numerical libraries are unavailable. Compute eigenvalues and eigenvectors of square matrices with only the Python standard library: the power iteration returns the dominant eigenvalue-eigenvector pair of a general square matrix, deflation exposes the next pairs, and the Jacobi eigenvalue algorithm returns the full spectrum of a real symmetric matrix. Produces the eigenvalue-eigenvector pairs in descending order, unit-norm eigenvectors, and the residual that gates each pair. Trigger: eigenvalue, eigenvector, spectral decomposition, jacobi, power iteration, dominant eigenvalue, deflation, diagonalization, rayleigh quotient.

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Least Squares Regression · ashfordeou bundle
Use when you must fit a straight line to paired measurements by ordinary least squares: compute the slope and intercept of the best fit, the residual standard deviation, and the coefficient of determination, and predict the response at a new input. Produces the fit coefficients, the goodness of fit, and the residual scatter that gate whether the linear model is adequate for the analysis. Trigger: least squares, linear regression, best fit line, slope, intercept, residual standard deviation, coefficient of determination, r squared, prediction.

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Oei Climb Gradient · ashfordeou bundle
Use when you must compute the one engine inoperative climb gradient for a transport aircraft certification analysis: derate the total thrust to the remaining engines, derive the steady climb gradient from the excess thrust over the drag at the aircraft weight, convert the gradient fraction into percent and into a rate of climb, and compare the available gradient against the FAR-25.121 takeoff second segment, approach climb, and landing climb minimum values for the engine count of the twin, trijet, or quad transport. Produces the OEI thrust, the climb gradient in percent, the rate of climb, and the clearance verdict that gate the engine out performance assessment. Trigger: one engine inoperative, OEI, second segment, engine out, approach climb, landing climb, climb gradient.

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Windshear Analysis · ashfordeou bundle
Use when you must assess a low-altitude windshear or microburst encounter on fixed-wing aircraft performance and choose the escape response: compute the windshear F-factor from thrust, drag, weight and the along-track headwind shear rate, or from the headwind gradient and the downdraft; classify the shear severity against the typical escape-guidance thresholds; compute the energy height loss rate and the altitude loss over the encounter; check whether the aircraft can out-climb the downdraft at the current thrust; and find the thrust increment needed for the recovery. Produces the F-factor, the severity class, the energy height loss trend, the out-climb verdict, and the recovery increment that gate the windshear escape decision. Trigger: windshear, microburst, F-factor, downdraft, headwind shear, wind shear hazard, escape guidance, energy height loss, shear encounter.

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Collision Course Guidance · ashfordeou bundle
Use when you must compute the collision-course intercept geometry for a constant-speed pursuer against a constant-velocity target: the lead angle of the pursuer velocity off the line of sight that closes the collision triangle, the closing speed along the line of sight, the time to go to the predicted intercept point, the intercept point coordinates, and the bearing error check against the current pursuer heading. Produces the lead angle, closing speed, time to go, intercept point, and the heading-error verdict that gate a constant-bearing intercept guidance assessment. Trigger: collision-course-guidance, constant-bearing-intercept, lead-angle, collision-triangle, predicted-intercept-point.

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Ultrasonic Inspection · ashfordeou bundle
Use when you must perform ultrasonic inspection (UT) on an aerospace part and turn measured echo data into defect findings: determine discontinuity depth from time of flight, compute wavelength and near-field length for transducer and frequency selection, convert decibel amplitude drops to echo ratios, and apply Snell's law and beam-spread angles for angle-beam shear-wave setups, then size discontinuities against acceptance criteria using reference reflectors such as flat-bottom and side-drilled holes. Produces the inspection math, the scan-planning parameters, and the depth and amplitude results that gate acceptance dispositions. Trigger: ultrasonic, pulse-echo, time of flight, shear wave, transducer, near-field, flat-bottom hole, calibration block.

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Real Cycle Effects · ashfordeou bundle
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-cycle efficiency, the actual-SFC, and the pressure-loss penalty in SI units that gate the engine cycle assessment. Trigger: real cycle, component efficiency, isentropic efficiency, pressure loss, combustor loss, actual SFC, off-ideal Brayton.

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Regenerative Cycle · ashfordeou bundle
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 in SI units, that gate the engine cycle assessment. Trigger: regenerative cycle, regenerator, recuperator, effectiveness, exhaust heat, optimum pressure ratio, thermal efficiency.

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Rocket Nozzle Divergence Loss · ashfordeou bundle
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 fraction; assemble the delivered thrust from the loss-corrected momentum term and the unchanged pressure term. Produces the shape factor, the loss fraction, the effective exit area ratio, the delivered thrust and the nozzle-delivered-isp fraction of the ideal in SI units, replacing the band multiplier. Trigger: rocket-nozzle-divergence-loss, conical-nozzle-thrust-correction, bell-nozzle-efficiency, nozzle-delivered-isp, divergence loss, half-angle thrust loss.

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Rocket Nozzle Flow Separation · ashfordeou bundle
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, separation-station area ratio, separation altitude, corrected thrust and side-load flag. Trigger: rocket-nozzle-flow-separation, separation-pressure-ratio, summerfield-criterion, overexpanded-nozzle, separation-altitude, separated-thrust-loss, side-load-regime.

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Attitude Determination Quest · ashfordeou bundle
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 achieved Wahba cost and the consistency verdict that gate a multi-vector attitude determination. Trigger: wahba problem, davenport q method, quest, optimal attitude quaternion, attitude matrix, observation residuals, body vector, reference vector, multi-vector attitude determination.

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Attitude Determination Triad · ashfordeou bundle
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 the orthonormal triads from the cross products, assemble the 3 by 3 attitude matrix from the triad outer products, and validate the estimate with the rotation angle, the orthogonality error, and the inter observation angle consistency. Trigger: triad algorithm, attitude determination, vector observation, reference vector, body frame, attitude matrix, coarse attitude, sun sensor, magnetometer.

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Low Thrust Spiral · ashfordeou bundle
Use when you must size a low-thrust transfer between two circular orbits under continuous thrust with the Edelbaum approximation, for ion propulsion and other electric-propulsion trajectories: compute the circular-orbit velocity at both radii, the total delta-v budget including the inclination change (no-plane-change spiral case as the di = 0 limit), the propellant mass and final mass from the rocket equation at constant thrust and specific impulse, the spiral transfer time, and the impulsive Hohmann delta-v of the same end orbits as comparison. Produces the delta-v budget, propellant mass, final mass, and transfer time that gate low-thrust transfer sizing and trajectory selection. Trigger: low-thrust transfer, Edelbaum, continuous thrust, spiral transfer, inclination change, ion propulsion trajectory, circular orbit.

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Propellant Tank Sizing · ashfordeou bundle
Use when you must size a spacecraft propellant tank for the propulsion bus: convert the propellant mass into the liquid volume with the propellant density, add the ullage volume for the required tank ullage fraction, compute the spherical tank volume and radius, size the sphere tank wall thickness from the burst pressure and the material allowable, estimate the tank shell mass, and size the helium pressurant mass for the regulated or blowdown pressurization scheme with the blowdown pressure range. Produces the propellant, ullage and tank volumes, the radius, wall thickness, shell mass, pressurant mass, the tank mass fraction and the pass or fail verdict that gate the spacecraft propulsion bus design. Trigger: propellant tank sizing, propellant volume, tank ullage fraction, pressurant mass, blowdown pressure range, sphere tank wall thickness, spacecraft propulsion bus.

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Peel Stress Bonded Joints · ashfordeou bundle
Use when you must compute the peel stress at the overlap end of a single-lap bonded joint: find the Goland-Reissner bending moment factor from the load per unit width, the adherend thickness, modulus and Poisson ratio, and the overlap half length, form the edge moment at the overlap end, resolve the peak peel stress from the adhesive Winkler-foundation beam model with the peel decay coefficient, and rate the peel margin against an allowable peel strength. Produces the bending moment factor, the edge moment, the peel decay coefficient, the peak peel stress and the peel margin that gate the peel-critical joint check. Trigger: goland-reissner peel stress, adherend bending, peel critical joint, overlap end peel stress, bonded joint peel margin.

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Ssa Closure · ashfordeou bundle
Use when you must close out the post-implementation safety assessment over the assessed condition set: look up the quantitative probability target per flight hour for the severity class of each assessed condition, compute the per-condition margin of target over predicted with the strict meets verdict, roll the conditions up into the closure-gate verdict with the closed and open counts, the open condition ids and the per-severity-class closure fraction, and roll the safety requirement verification statuses into the verified and open requirement closure list. Produces the severity-target lookup, the per-condition margins, the closure-gate verdict dict and the requirement closure list that gate the close-out statement. Trigger: ssa-closure rollup, closure-gate verdict, post-implementation-safety-verdict margin, condition-margin, requirement-closure-status.

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Payload Range Diagram · ashfordeou bundle
Use when the task is the payload versus range trade-off, max payload, max fuel, design range, ferry range, or reserve fuel sizing in conceptual aircraft design. Build the payload-range diagram for a conceptual transport aircraft: compute the range at the maximum payload point, the range at the maximum fuel point, the ferry range, and the payload available at the design range from operating empty weight, maximum payload, maximum takeoff weight, and fuel capacity using the Breguet range equation with a reserve fuel policy and fuel fraction. Produces the diagram corner points that gate the payload-range trade assessment. Trigger: payload-range diagram, max payload, ferry range, design range, payload range trade, reserve fuel.

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Fuel Tank Inerting Sizing · ashfordeou bundle
Use when you must size the fuel tank inerting system at the conceptual level: model the ullage as a well-mixed volume washed by nitrogen-enriched air (NEA), compute the required NEA flow from the exponential oxygen decay C(t) = C_NEA + (C0 - C_NEA) exp(-Q t / V), and solve the flow that reaches a target oxygen fraction within a required time Q = (V/t) ln((C0 - C_NEA)/(C_tgt - C_NEA)). Produces the required NEA flow in m3/s and in SCFM, the ullage oxygen fraction at the required time, the washout time at a given flow, and a PASS or FAIL verdict against the NEA generator capacity limit (FAR 25.981 fuel tank flammability reduction context). Trigger: obiggs flow sizing, ullage oxygen washout, nitrogen enriched air, fuel ullage inerting, nea generator capacity.

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Hydraulic Actuator Sizing · ashfordeou bundle
Use when you must size a hydraulic actuator: the piston area and bore diameter from the actuator load and system pressure with the pressure-margin factor and mechanical efficiency, the rod-side annulus area and retract capability, the rod diameter from Euler column buckling over the extended rod length with the design factor, the nearest preferred bore and rod diameters at or above the requirements, and the actuator mass estimate. Produces the bore and rod diameters, the annulus area, the buckling margin, the preferred-size selection and the mass estimate that close the load-to-actuator chain. Trigger: hydraulic actuator sizing, actuator bore diameter, actuator rod buckling, annulus retract check, preferred actuator sizes, actuator mass estimate.

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Thin Airfoil Section Theory · ashfordeou bundle
Use when you must compute the section lift and the quarter-chord pitching moment of a thin cambered airfoil from its camber line: decompose the camber slope into the glauert-sine-series coefficients A0, A1 and A2 by trapezoid quadrature over the theta transform x = (1 - cos(theta))/2, then recover the zero-lift angle alpha_L0, the section lift coefficient cl = 2*pi*(alpha - alpha_L0), the quarter-chord pitching-moment coefficient cm_c4 = (pi/4)*(A2 - A1) and the center-of-pressure location x_cp/c = 1/4 - cm_c4/cl, for a NACA 4-digit mean line, a polynomial camber line or sampled camber stations. Produces the closed-form analytic section aerodynamics that anchor the numerical panel and viscous section tools. Trigger: glauert coefficients, zero lift angle, section pitching moment, camber line analysis, thin airfoil section.

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Hypersonic Piston Theory · ashfordeou bundle
Use when you must estimate the surface pressure on a small-perturbation hypersonic surface by Lighthill piston theory: evaluate the piston-theory pressure ratio p/p_inf = (1 + ((gamma - 1)/2) v/a_inf)^(2 gamma/(gamma - 1)) from the piston velocity ratio, apply the linearized limit p/p_inf = 1 + gamma v/a_inf for a small piston velocity, split the compression side from the expansion side of the inclined surface, compute the surface-pressure coefficient Cp = 2/(gamma M^2) (p/p_inf - 1) from the freestream Mach and inclination on either side, and extend the same law to an unsteady surface whose normal motion adds to the geometric piston velocity. Produces the piston-theory surface-pressure ratios, the linearized limits and the per-side and instantaneous pressure coefficients that gate hypersonic panel pressure, stability derivative and oscillating-surface load estimates. Trigger: piston theory, hypersonic piston analogy, small perturbation hypersonic surface pressure, Lighthill.

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Regular Shock Reflection · ashfordeou bundle
Use when you must compute the regular reflection of an oblique shock impinging on a wall or symmetry plane: solve the weak-branch incident wave angle at the upstream Mach number and deflection, march the state behind it, solve the reflected shock that turns the flow back parallel to the wall, and assemble the post-reflection state from the two shock ratio products. Produces the incident and reflected wave angles, the intermediate and post-reflection Mach numbers, the pressure, density, temperature and stagnation-pressure ratios, the reflected-shock detachment limit and the regular-versus-Mach verdict. Trigger: regular reflection, reflected shock, wall impingement, symmetry plane, two-shock interaction, Mach reflection, post-reflection state.

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Holding Pattern Entry · ashfordeou bundle
Use when you must determine a holding pattern entry: classify the maneuver for joining a holding fix as direct, teardrop, or parallel from the angle between the inbound track and the holding side using the standard 70/110 degree sector rule, compute the outbound leg timing from the holding altitude (1 minute at or below 14000 ft, 1.5 minutes above), correct the outbound heading for crosswind with the 1-in-60 rule, and estimate the first entry lap time. Produces the entry type, outbound leg seconds, wind-corrected outbound heading, and entry-lap time estimate for FMS or manual hold joining. Trigger: holding-pattern-entry, direct-entry-sector, teardrop-entry-sector, parallel-entry-sector, outbound-leg-timing, holding-wind-correction.

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Radio Navigation Aids · ashfordeou bundle
Use when you must compute the radio navigation geometry of conventional navaids for the aircraft navigation solution: derive the VOR radial and the bearing from the aircraft to the station from the planar station and aircraft coordinates, compute the DME slant range from the ground distance and the aircraft altitude, compute the ILS localizer deviation angle from the lateral offset and the distance to the runway threshold, and compute the ILS glideslope deviation from the height above the threshold and the distance to the threshold against the nominal glideslope angle. Produces the VOR bearing and radial, the slant range, and the localizer and glideslope deviation angles that gate radio navigation geometry checks. Trigger: VOR radial, DME slant range, ILS localizer deviation, glideslope deviation, radio navigation geometry, bearing to the navaid station, approach course offset.

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Probability Distributions · ashfordeou bundle
Use when you must fit and characterize a standard probability distribution for aerospace engineering data analysis: estimate the normal, lognormal, exponential, and Weibull distribution parameters from a univariate sample, evaluate the pdf, cdf, quantile, reliability, and hazard functions, score the fit with the chi-square and Kolmogorov-Smirnov goodness-of-fit statistics, and report percentiles plus reliability at a target time. Produces the fitted parameter dict, the fit-quality verdict, and the quantile and reliability values that gate the statistical characterization of scatter data such as loads, life, failure times, and tolerances. Trigger: probability distribution fitting, weibull fit, lognormal, exponential fit, goodness of fit, kolmogorov smirnov, chi-square fit test, quantile estimation, reliability at time, hazard function, parameter estimation.

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Datum Reference Frames · ashfordeou bundle
Use when you must establish the datum reference frame for a part per ASME Y14.5: parse the primary, secondary, and tertiary datum precedence from the drawing callout, compute the datum feature simulators (plane, axis, point), determine the degrees of freedom each datum constrains (translation and rotation), apply the material condition modifiers (MMB, LMB, RMB) to the datum feature references, and build the feature control frame string. Produces the datum reference frame definition, the constrained degrees of freedom table, the datum shift from the material condition modifier, and the feature control frame string that gates the GD&T scheme. Trigger: datum reference frame, datum precedence, primary secondary tertiary, degrees of freedom, datum shift, MMB LMB RMB, feature control frame.

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Temperature Conversion · ashfordeou bundle
Use when you must convert temperatures between the kelvin, celsius, fahrenheit, and rankine scales for a test or an analysis: convert absolute temperatures with the scale offsets and ratios, convert temperature differences with the degree sizes only, and check the result against the absolute zero limit of each scale. Produces the converted absolute temperature or the converted temperature difference that gates the thermal data exchange. Trigger: temperature conversion, kelvin, celsius, fahrenheit, rankine, absolute zero, temperature difference, delta temperature.

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Descent Performance · ashfordeou bundle
Use when you must compute the descent performance of a fixed-wing aircraft for descent planning: convert the glide slope into the descent gradient, find the rate of descent from the groundspeed and the gradient, estimate the glide range from the aerodynamic efficiency and the height to lose, locate the best glide speed from the wing loading, and plan a step-down descent with the descent distance, the time to descend between flight levels, and the fuel burned in the descent segment. Produces the descent gradient, rate of descent in m/s, glide range in meters, best glide speed, descent time, and descent fuel that gate the descent planning assessment. Trigger: rate of descent, descent gradient, glide range, best glide speed, step-down descent, descent fuel, descent time.

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Landing Performance · ashfordeou bundle
Use when you must compute the landing performance of the transport airplane: determine the reference approach speed from the stall speed with the 1.3 factor, size the flare radius, flare height, and flare distance from the approach speed and load factor, estimate the air distance over the 50 foot obstacle, and compute the landing ground roll and total stopping distance from the touchdown speed, braking coefficient, lift and drag ratios, and reverse thrust. Produces the approach speed, air distance, ground roll distance, and certified landing field length that gate the FAR 25.125 and CS 25.125 landing distance check. Trigger: landing distance, landing performance, approach speed, flare, ground roll, stopping distance, 50 foot obstacle, reverse thrust, braking coefficient.

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Takeoff Performance · ashfordeou bundle
Use when you must compute takeoff performance from the aircraft weight, wing area, and thrust: determine the stall speed from wing loading and density, apply the liftoff speed factor, and estimate the ground roll distance with rolling friction. Produces the stall speed, the lift off speed, and the ground roll distance that gate the takeoff field-length check. Trigger: takeoff, ground roll, lift off speed, stall speed, wing loading.

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Spin Recovery · ashfordeou bundle
Use when the task is spin recovery, autorotation, spin modes, incipient spin, flat spin, or post-stall departure recovery. Analyze spin entry, developed spin modes, and recovery controls for a stalled aircraft: compute the post-stall autorotative band and stall penetration, estimate the spin descent rate and rotation rate from weight, wing area, and spin drag, classify the spin mode as steep or flat, and size the altitude lost and rotation stop time during spin-recovery. Trigger: spin recovery, autorotation, flat spin, incipient spin, spin entry, anti-spin controls, post-stall departure.

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Trim Analysis · ashfordeou bundle
Use when you must analyze the stick fixed trim condition of a fixed-wing aircraft: compute the trim lift coefficient from the weight, density, true airspeed, and wing area, derive the elevator deflection required to trim from the pitching moment coefficients and the elevator effectiveness, find the trim speed for a given trim lift coefficient in level flight, and check whether the total pitching moment closes at zero for the trimmed verdict. Produces the trim lift coefficient, the elevator deflection, the trim speed, and the trimmed verdict that gate the pitch trim analysis. Trigger: elevator deflection, trim speed, trim lift coefficient, stick fixed, elevator effectiveness, pitching moment, trim analysis.

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Tightly Coupled Ins Gnss · ashfordeou bundle
Use when you must run a tightly-coupled-ins-gnss integration filter: propagate the eight INS error states (3 position error, 3 velocity error, receiver clock bias in metres, clock drift in m/s) of the constant-velocity-error model between epochs, predict each raw pseudorange from the inertial position estimate plus the clock bias state, build the measurement matrix from the line-of-sight geometry rows with the unit clock column, and apply the raw-pseudorange-update Kalman correction on the residuals. Produces the corrected receiver position and velocity, the clock-state-filter estimates of bias and drift, the per-epoch innovation vector and the propagated and corrected covariance, in SI units, that gate the tightly coupled navigation solution of a moving receiver. Trigger: tightly coupled INS GNSS, raw pseudorange measurement update, ins-gnss-tight-coupling, clock-state-filter, INS error state with clock bias and drift.

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Acceptance Sampling · ashfordeou bundle
Use when you must design an attribute acceptance sampling plan: choose the sample size code letter from the lot size and the inspection level, look up the single-sampling plan (sample size n, accept number Ac, reject number Re) for the required AQL from a small embedded reference table, decide accept or reject from the number of nonconforming units found in the sample, and compute the operating-characteristic probability of acceptance across incoming fraction nonconforming with the binomial model. Produces the code letter, the sample size, the accept and reject numbers, the lot verdict, and the OC curve points that quantify the plan discrimination. Trigger: acceptance sampling, attribute sampling plan, aql, lot size code letter, sample size, accept number, reject number, operating characteristic curve, probability of acceptance, lot acceptance.

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Calibration Control · ashfordeou bundle
Use when you must control calibration of inspection, measuring, and test equipment under an AS9100-style QMS: determine the test accuracy ratio (TAR, 4:1 guidance) between the calibration standard and the unit under test, judge calibration due dates and overdue instruments, check a measured value against nominal and tolerance, and decide recall versus review when a calibrated standard drifts out of tolerance. Covers the calibration system (who calibrates, traceability to national standards), calibration intervals and due dates, out-of-tolerance handling, and calibration records with status labels. Produces the TAR verdict, the due-date verdict, the tolerance verdict, and the out-of-tolerance impact verdict that gate instrument use and product release. Trigger: calibration, TAR, test accuracy ratio, out of tolerance, calibration due, instrument recall, traceability.

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Centrifugal Compressor · ashfordeou bundle
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 the de Haller number to check the inducer-to-exit relative velocity decay. Produces SI velocity triangle and stage performance parameters that gate the compressor stage design review in the FAR-33 engine certification context. Trigger: centrifugal compressor, impeller tip speed, slip factor, Wiesner correlation, work input coefficient, back-sweep angle, diffusion ratio, de Haller number.

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C3 Departure Energy · ashfordeou bundle
Use when you must compute the departure energy of an interplanetary mission from a circular parking orbit: the C3 characteristic energy from a target hyperbolic excess speed and the excess speed back from C3, the injection speed on the departure hyperbola at the parking orbit radius from the vis-viva integral, the injection delta-v above the circular parking speed, the circular parking speed, the parking orbit period, and the declination of the outgoing asymptote from the excess velocity vector. Produces the C3, excess speed, injection speed, injection delta-v, parking period, and asymptote declination that gate the departure-side launch-energy and injection-burn assessment. Trigger: c3 characteristic energy, hyperbolic excess, excess speed, injection delta-v, injection speed, parking orbit, escape hyperbola, asymptote declination, interplanetary departure.

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Clohessy Wiltshire · ashfordeou bundle
Use when you must propagate and analyze the Clohessy-Wiltshire linearized relative motion of a deputy spacecraft about a chief in a circular orbit: compute the chief mean motion, build the 6x6 relative-motion state-transition-matrix, propagate the deputy-chief relative state (x radial, y along-track, z cross-track), check the bounded relative orbit condition y_dot = -2 n x, and size the two-impulse targeting delta-v to a desired final relative state. Produces the propagated relative trajectory, the bounded-orbit verdict, the impulse budget, and a geometry sanity check with singular one-orbit and cross-track-nulling transfer times flagged. Trigger: clohessy-wiltshire, hill equations, relative-motion state-transition-matrix, deputy-chief, two-impulse targeting, along-track drift, cw propagation, relative orbit injection, cross-track offset.

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Keplerian Elements · ashfordeou bundle
Use when you must compute classical orbital elements from a position and velocity state vector: derive the specific angular momentum, node vector and eccentricity vector, then convert to semimajor axis, eccentricity, inclination, right ascension of the ascending node (RAAN), argument of periapsis and true anomaly, and derive the orbital period with periapsis and apoapsis radii for an elliptical Earth orbit. Handles circular and equatorial degenerate cases with documented conventions and raises on parabolic or hyperbolic inputs. Uses Earth gravitational parameter 398600.4418 km^3/s^2 by default. Trigger: keplerian elements, orbital elements, rv2coe, state vector, raan, argument of periapsis, true anomaly, semimajor axis, eccentricity, inclination, orbital period, periapsis, apoapsis.

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Satellite Coverage · ashfordeou bundle
Use when you must analyze satellite ground coverage and access geometry: compute the instantaneous access circle central angle for a satellite from the orbital altitude and the minimum elevation angle constraint, estimate the swath width and the coverage fraction of a region or the globe, derive the maximum off-nadir angle and the elevation and look-angle geometry at a ground station, and evaluate the access time per pass and the revisit time. Produces the central angle, swath width, off-nadir angle, access time, and coverage fraction that gate ground station visibility and constellation coverage analysis. Trigger: satellite coverage, coverage analysis, access circle, central angle, swath width, off-nadir angle, elevation angle, revisit time, coverage fraction, ground station visibility.

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Antenna Aperture Sizing · ashfordeou bundle
Use when you must size the parabolic antenna aperture of a spacecraft communications link: convert a required antenna gain into the reflector diameter through the aperture efficiency, compute the achieved gain of the sized aperture, the half-power beamwidth, the pointing budget with pointing loss, and the receive gain-over-temperature G/T figure of merit. Produces the required gain, the reflector diameter, the achieved gain, the beamwidth, the pointing budget and the G/T that gate an antenna aperture sizing. Trigger: antenna aperture sizing, parabolic reflector gain, aperture efficiency, required antenna gain, half-power beamwidth, pointing loss budget, gain over temperature, spacecraft antenna sizing.

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Laminate Bending Stiffness · ashfordeou bundle
Use when you must assemble the full classical lamination theory stiffness of a composite laminate stack for the bending and coupling response: compute the bending-extension coupling matrix B and the bending matrix D by the z-squared and z-cubed thickness integrals over the ply z coordinates, the full ABD stiffness matrices for symmetric and unsymmetric laminates, the D11 D22 D12 and D66 bending terms the laminate plate buckling analysis takes as given inputs, the exact zero-coupling identity for symmetric stacks, the coupling magnitude of unsymmetric stacks, and the equivalent flexural engineering constants of symmetric stacks with vanishing D16 and D26. Produces the coupling and bending matrices, the four bending terms and the flexural constants in SI units. Trigger: laminate bending stiffness, bending-extension coupling, laminate d matrix, abd matrices, unsymmetric laminate analysis, d11 d22 d12 d66, equivalent laminate bending stiffness.

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Laminate First Ply Failure · ashfordeou bundle
Use when you must compute the first-ply-failure load of a composite laminate: recover the mid-plane strains of a symmetric balanced laminate from its in-plane compliance under applied load resultants, transform the strains to each ply material axis, compute the per-ply Tsai-Wu failure index, and return the critical ply. Produces the mid-plane strains, the per-ply failure indices, the critical ply, the first-ply-failure load scale factor, the FPF load resultant, and the reserve factor. Trigger: first-ply-failure load, first ply failure, critical ply, tsai-wu failure index, reserve factor, mid-plane strain recovery, in-plane load resultant, symmetric balanced laminate, quasi-isotropic laminate, laminate failure envelope, FPF load, per-ply failure index, composite laminate strength.

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Sizing Mission Profile · ashfordeou bundle
Use when defining the design mission profile and estimating block fuel and block time for conceptual aircraft sizing: model mission segments (taxi, takeoff, climb, cruise, descent, loiter, reserve) with their distinct fuel models, compute cruise fuel from the Breguet range equation and loiter and hold fuel from Breguet endurance, model climb and descent on fuel flow and time, apply reserve fuel rules (45 minute hold at 1500 ft plus 5 percent, or FAR 121 alternate plus hold), sum segment fuels into block fuel and segment times into block time, derive the mission fuel fraction, and size required fuel weight including reserves. Produces per-segment fuel burns, block fuel and block time, reserve fuel, mission fuel fraction, payload-range trade point, and total required fuel. Trigger: mission profile, block fuel, block time, breguet range, breguet endurance, reserve fuel, loiter, hold, fuel fraction, required fuel, climb, cruise, descent, taxi, takeoff, FAR 121, payload range.

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Cabin Outflow Valve Sizing · ashfordeou bundle
Use when you must size the cabin outflow valve: compute the choked-flow mass flux G = p sqrt(gamma/(R T)) (2/(gamma+1))^((gamma+1)/(2(gamma-1))) at the cruise cabin condition, divide the governing pack inflow by that flux for the outflow valve effective area, and size the pressure-relief valve effective area to dump the same pack flow at the 8.9 psi differential pressure clamp ceiling. Produces the choked-flow mass flux, the effective area and equivalent diameter for the outflow and relief cases, and a fit verdict against the nominal valve diameter limit. Trigger: cabin outflow valve sizing, outflow valve area, pressure relief valve sizing, cabin choked flow, pressurization valve, differential pressure clamp.

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Landing Gear Height Sizing · ashfordeou bundle
Use when you must select the vertical landing gear geometry of a tricycle-gear aircraft at the conceptual level: solve the static-ground-line from the tail-cone-clearance margin at the design rotation attitude about the main gear contact, compute the main-gear-height and the nose-gear-height that level the cabin waterline over the wheelbase, verify the nacelle and propeller clearances at the level and rotated attitudes, and check the nose gear static load share at the design CG. Produces the static-ground-line, the main and nose gear heights, the achieved tail cone, nacelle and propeller clearance margins at both attitudes, the tail strike margin of the solved geometry, and the height verdict that gates the gear configuration. Trigger: landing-gear-height, static-ground-line, gear-height-selection, tail-cone-clearance, rotation-clearance-margin.

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Boundary Layer Theory · ashfordeou bundle
Use when the task is boundary-layer thickness estimation, displacement or momentum thickness, skin-friction coefficient on a surface, Reynolds-number regime classification, or transition location on a smooth surface. Compute laminar and turbulent boundary-layer thicknesses for a smooth flat plate: estimate the 99-percent thickness, displacement thickness, and momentum thickness from the local Reynolds number with the Blasius and 1/7 power-law correlations, evaluate the local and average skin-friction coefficients, and classify the flow into laminar or turbulent regimes by the transition Reynolds number. Trigger: boundary layer, displacement thickness, momentum thickness, skin friction, transition, Reynolds number, Blasius.

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Compressible Couette Flow · ashfordeou bundle
Use when you must compute the exact constant-property solution for compressible Couette flow in a high-Mach plate gap: the linear velocity profile u = Ue y / h, the Crocco energy-integral temperature profile, the insulated moving-plate temperature from the recovery relation r = Pr, the wall shear tau_w = mu Ue / h, the wall heat flux q_w into the stationary plate and the dissipation energy-balance check at a given plate Mach number, Prandtl number and gap Reynolds number. Produces the full gap solution with velocity and temperature profiles. Trigger: compressible-couette-flow, shear-driven-gap-flow, crocco-energy-integral, gap-reynolds-number, plate-gap, linear-velocity-profile, moving-plate, high-mach-plate-gap.

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Isentropic Flow Relations · ashfordeou bundle
Use when you must convert a Mach number into the isentropic total to static ratios of a compressible flow: the total temperature, pressure and density ratios of a perfect gas at gamma 1.4, rebuild total conditions from a static state and Mach number, recover the Mach number that produces a given area ratio from the area-Mach relation on the subsonic low branch or the supersonic high branch, and compute the choked mass flow a passage passes at its sonic throat from total pressure, total temperature and throat area. Produces the three total to static ratios, both Mach roots for the given area ratio and the choked mass flow in kg/s, the gate numbers for duct and wind tunnel analysis. Trigger: isentropic flow, total to static ratio, mach from area ratio, choked mass flow, sonic throat, wind tunnel contraction, compressible flow, mach number.

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Wind Tunnel Model Design · ashfordeou bundle
Use when you must design the wind tunnel model and the test setup for a wind tunnel campaign on an aircraft configuration: select the model scale as the smaller of the test section blockage limit and the span clearance, compute the model wing area, span and mean aerodynamic chord from the scale, check the model Reynolds number at the maximum tunnel speed against the full scale flight Reynolds number and report the Reynolds mismatch, estimate the maximum dynamic pressure and the model load at the maximum test lift coefficient, rate the force balance capacity against that load, and size the model support sting for the bending moment. Produces the chosen scale, model reference dimensions, blockage ratio, Reynolds ratio, balance verdict and sting diameter that gate the model build. Trigger: wind tunnel model design, model scale selection, blockage ratio, reynolds mismatch, force balance rating, sting sizing, test section.

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Chi Square Goodness Of Fit · ashfordeou bundle
Use when you must test whether observed counts fit a stated categorical model: the chi-square goodness-of-fit statistic as the sum of the squared observed-minus-expected gaps over expected counts, the degrees of freedom k minus 1 minus estimated parameters, and the one-tailed p-value from the chi-square survival function via its own regularized lower incomplete gamma, returning the reject or fail-to-reject verdict at a stated significance level. Produces the statistic, degrees of freedom, p-value and verdict that gate model checks such as uniform defect counts per day or Poisson counts per inspection unit. Trigger: chi-square goodness of fit, observed versus expected counts, categorical model fit, count data fit, goodness-of-fit p-value.

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Cross Correlation Analysis · ashfordeou bundle
Use when you must compute the cross-correlation or autocorrelation of sampled signal sequences to quantify channel similarity and time delay: evaluate the raw cross-correlation over the full lag range with zero padding, normalize it to a correlation coefficient in [-1, 1] from the zero-lag energies, estimate the delay between channels from the peak lag, apply the biased or unbiased convention, and verify the even symmetry of the autocorrelation. Produces the correlation sequence, the peak lag, the normalized coefficient, and the delay in samples that gate time-delay analysis. Trigger: cross-correlation, autocorrelation, time-delay-estimation, lag, normalized-correlation-coefficient, channel-similarity, delay-between-signals.

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Multiple Linear Regression · ashfordeou bundle
Use when you must fit a multiple linear regression model: solve the normal equations for the partial-regression-coefficient vector from two or more predictors, compute each coefficient-standard-error with the two-sided p-value of its t statistic, the overall regression-f-test p-value, R-squared and adjusted-r-squared, and the variance-inflation-factor multicollinearity-check for every predictor, then predict the response at a new design point. Produces the coefficient vector, diagnostic table and prediction that gate whether the linear model explains the data. Trigger: multiple-linear-regression, variance-inflation-factor, adjusted-r-squared, partial-regression-coefficient, regression-f-test, coefficient-standard-error, multicollinearity-check.

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Position Tolerance Calc · ashfordeou bundle
Use when you must compute the position tolerance verification for a hole or pin feature controlled by a true position callout per ASME Y14.5: calculate the radial deviation of the actual feature center from the true position, convert the deviation into the cylindrical zone diameter that contains the actual center, apply the maximum material condition bonus tolerance from the actual feature size, derive the virtual condition boundary for the mating part, and decide whether the feature is acceptable. Produces the deviation, the required zone diameter, the bonus tolerance, the total tolerance, the virtual condition, and the acceptance verdict that gate the GD&T verification. Trigger: position tolerance, true position, MMC, bonus tolerance, virtual condition, feature control frame.

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671 published skills · page 6 of 7