Claude Skills by ashfordeOU

Use when you must run the Wald-Wolfowitz runs test: determining whether the ordering of a two-sign sequence (plus and minus signs, or 1/0 flags recoded as plus and minus) is random by counting the runs of identical signs, computing the expected number of runs and its variance under the randomness null from the two sign counts, forming the standard normal z statistic, and returning the randomness verdict against the two-sided 95 percent normal critical value. Produces the run count, expected r...

Use when you must compute the singular value decomposition of a general real rectangular matrix into its singular value factors: the economy U diag(s) Vh form with orthonormal factors from deterministic one-sided Jacobi rotations, singular values in descending order, the 2-norm condition number, the numerical rank at a relative tolerance and the Moore-Penrose inverse. Pure Python standard library, offline. Produces the SVD factors, the condition assessment and the pseudoinverse that control-a...

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, com...

Use when you must author a NEW conformant SKILL.md for the agentskills.io format under SEP-2640-style delivery: build the frontmatter template from the required fields (name kebab-case matching the folder, description with action and use-when and trigger clauses, Apache-2.0 license, compliance flag, standards references, gated boolean, metadata version and author), then run the deterministic pre-publish conformance check that reports missing or invalid required fields before a leaf is publish...

Use when packaging or delivering domain skills over MCP per SEP-2640: check that a skill package carries a conformant SKILL.md (kebab-case name, description), build the skill URI (skill:// namespace and path), and verify the MCP server exposes the delivery model (resources/read and directory listing behind the directoryRead capability). SEP-2640 serves skills as resources and stays an adapter over the agentskills.io content format, an emerging spec not yet stable. Trigger: SEP-2640, skills ov...

Use when you must evaluate a delivered skill against SEP-2640-style conformance and quality criteria: run conformance checks on the package (frontmatter, description with trigger, license, standards references), judge whether the skill's contract test exercises the core logic, score deterministic quality criteria (offline, no network, stdlib only), compute coverage ratio of tested versus total behavior, and issue an acceptance verdict (accept, rework, or reject). SEP-2640 stays an emerging sp...

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 const...

Use when you must size positional tolerances or clearance holes for mating fastener patterns: compute the total positional tolerance budget as the clearance hole MMC diameter minus the fastener maximum diameter, split the budget between the two mating members with the floating fastener formula, apply the fixed fastener formula when the threaded member share acts through a projected tolerance zone, and invert the formula to find the minimum clearance hole MMC diameter for a given fastener and ...

Use when the task is GD&T fundamentals: feature control frames, datum reference frames, form tolerances such as flatness, straightness, circularity, and cylindricity, orientation tolerances such as perpendicularity, parallelism, and angularity, position tolerance, profile, runout, or material condition and bonus tolerance on drawings. Interpret geometric dimensioning and tolerancing callouts per ASME Y14.5: parse a feature control frame into its symbol, tolerance, and datum references, identi...

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 accep...

Use when you must compute the assembly tolerance stack-up from the part tolerances with the worst case and root sum square methods: sum the absolute tolerances for the worst case total, take the root sum square for the statistical total, sum the signed nominals into the assembly nominal dimension, and produce the assembly limits and the dominant variance share. Produces the worst case total, the RSS total, the assembly limits, and the dominant contributor that gate the fit assessment. Trigger...

Use when you must convert airspeeds through the compressibility-corrected air-data chain: calibrated airspeed from impact pressure, calibrated airspeed from true airspeed at altitude, true airspeed from calibrated airspeed at altitude through the compressible inversion on the local static pressure, equivalent airspeed from true airspeed and the density ratio, Mach number from calibrated or true airspeed, and impact pressure from Mach number or calibrated airspeed. Produces the full calibrated...

Use when you must compute the density altitude from the pressure altitude and the outside temperature: the ISA deviation, the density ratio sigma from the ISA pressure ratio and the temperature ratio, and the density altitude via the troposphere closed-form inverse with the stratosphere branch. Produces the density altitude in meters and feet for hot-day and cold-day takeoff and performance checks. Trigger: density altitude, pressure altitude, outside air temperature, non-standard day, ISA de...

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...

Use when you must apply the international standard atmosphere in aerospace calculations: read temperature, pressure, and density at altitude from the ISA model, from sea level through the tropopause and lower stratosphere. Produces the atmospheric state values at the requested altitude for performance and flight mechanics work. Trigger: standard atmosphere, isa, atmospheric density, temperature lapse, pressure altitude, troposphere.

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, fahren...

Use when you must convert aerospace quantities between SI and imperial or aviation units: length (m, ft, NM), speed (m/s, kt, ft/s, Mach), temperature (K, C, F, R), pressure (Pa, hPa, psi, inHg), density (kg/m3, slug/ft3), mass (kg, lb, slug), and force (N, lbf). Converts with a deterministic factor table, handles offset temperature scales, computes Mach from true airspeed and speed of sound, and relates pressure altitude to geometric altitude. Trigger: unit conversion, convert units, knots, ...

Use when a task concerns aircraft flight mechanics: guide the router to the flight-mechanics pack. breguet-range cruise range, breguet-endurance loiter endurance, specific-range cruise fuel economy, takeoff-performance takeoff distance, climb-performance rate of climb, oei-climb-gradient OEI climb gradient, energy-height specific excess power, descent-performance descent, turn-performance turn rate and load factor, glide-performance glide ratio and sink rate, wind-effects wind triangle and gr...

Use when you must simulate the point-mass trajectory of an aircraft climbing out in the vertical plane: propagate speed, flight-path angle and altitude with the energy-state point-mass equations, integrate the state with a fixed time-step RK4 scheme, apply the thrust altitude lapse and parabolic drag polar, and report the speed-altitude history, load factor and steady-climb consistency versus the closed-form excess-thrust climb angle. Produces the time histories of V, gamma, h and x with per-...

Use when you must simulate the rigid body motion of an aircraft with the six degree of freedom body axis equations of motion: compute the body axis accelerations from the applied aerodynamic forces and moments, compute the angular accelerations from the moments and the inertia tensor, form the state derivative of the state vector u v w p q r phi theta psi, and propagate the state one step with a fourth order Runge Kutta integrator to integrate the equations of motion over the simulation step....

Use when the task is handling qualities assessment, pilot rating, flyability evaluation, or certification flight test analysis framed by FAR-25 and CS-25 flight characteristics requirements. Determine a Cooper-Harper handling qualities rating (1 to 10) for an aircraft from a pilot-in-the-loop evaluation: walk the decision tree (controllability, adequate performance with desired or adequate tolerances, pilot compensation required), classify the rating band (1-3 satisfactory without improvement...

Use when the task is flying qualities assessment, handling qualities level classification, or MIL-STD-1797A compliance review. Assess the flying qualities of a piloted aircraft against MIL-STD-1797A level criteria: classify the flight phase category (A precision tracking, B gradual nonterminal, C terminal), select the aircraft class (I small light, II medium, III large heavy, IV high maneuverability), and grade each dynamic mode against the level tables: short period damping and frequency by ...

Use when you must assess pilot-induced oscillation (PIO) susceptibility and pilot-in-the-loop coupling for a piloted aircraft: categorize the oscillation into Category I (linear aircraft response), Category II (quasi-linear response with rate-limited actuators), or Category III (nonlinear response with mode transitions or control logic changes), identify the typical causes: excessive phase lag, high control sensitivity, actuator rate limiting, structural notch filters, run a phase-lag-at-cros...

Use when you must assess the pitch-axis flying qualities of an aircraft with the MIL-STD-1797A bandwidth and phase-delay criterion: model the pitch attitude response as a short period transfer function with a control anticipation numerator time constant and an actuator lag, evaluate the frequency response, find the bandwidth frequency omega_BW as the lower of the 45 degree phase margin frequency and the 6 dB gain margin frequency, read the -180 degree frequency, compute the phase delay tau_p ...

Use when you must compute the balanced field length and V1 decision speed of a multi-engine transport: derate the total thrust to the remaining engines, derive the constant ground accelerations and the braking deceleration, trace the accelerate-stop distance (roll on all engines to V1, react, brake to a stop) and the accelerate-go distance (roll to V1, continue on the remaining engines to lift-off, rotate, and climb over the 35-ft obstacle on the engine-out climb gradient), solve the quadrati...

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...

Use when you must estimate the cruise range of a transport aircraft with the Breguet range equation: combine speed, thrust specific fuel consumption, and lift to drag ratio with the initial and final masses to produce the cruise range in meters, the cruise time from range and speed, and the final mass from the fuel fraction. Produces the range, cruise time, and final mass that gate the mission performance assessment. Trigger: cruise range, TSFC, lift to drag, fuel fraction, cruise time.

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 cl...

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 t...

Use when you must compute the energy state of an aircraft for performance and maneuverability analysis: derive the specific excess power Ps from thrust, drag, speed, and weight, express the total energy as the energy height combining the geometric altitude with the kinetic height from the airspeed, convert between kinetic and potential energy in climb and cruise trades with the zoom climb gain and the speed bleed for an altitude gain, and recover the speed from a target energy height. Produce...

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 per...

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 dis...

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, tr...

Use when you must compute the cruise range of a propeller or turboprop aircraft: form the range with the propeller Breguet equation from power specific fuel consumption and propeller efficiency at a given lift to drag ratio, convert a pounds per horsepower hour PSFC into SI kilograms per watt second when needed, and derive the final mass from the fuel fraction. Produces the cruise range in meters and kilometers for fuel planning between the initial and final mass. Covers the propeller branch ...

Use when you must estimate the power-off autorotative descent performance of a single-rotor helicopter: the energy-method sink rate from the minimum level-flight power and the weight, the empirical minimum descent rate from the Talbot-Schoers correlation of NASA TM 78452 (public domain), its equivalent power-based entry, and the feet-per-minute conversion. Produces the energy-method sink rate, the empirical minimum descent rate and the power-to-weight ratio entry that gate an autorotative des...

Use when you must classify the axial flow state of a rotor in vertical descent: hover at zero rate, the vortex-ring band from zero to twice the hover induced velocity, and the windmill-brake momentum state at and above that boundary. Computes the band limits, the windmill-brake induced velocity from the momentum-theory closed form, the signed rotor power and torque in descent (negative when the rotor absorbs power from the airstream), and the torque-reversal condition c = P_profile over k T v...

Use when you must determine the blade-element hover performance of a helicopter main rotor: the thrust coefficient from the collective pitch schedule, rotor solidity, lift-curve slope and Betz tip loss factor, the inflow ratio from the uniform-inflow hover closure, the collective pitch required to hover at a target thrust coefficient, the torque coefficient with its induced and profile split, and the rotor shaft torque, shaft power and hover figure of merit from the coefficients. Produces a h...

Use when you must compute the blade-flapping dynamics of a helicopter main rotor: the blade Lock number from the air density, the section lift-curve slope, the blade chord, the rotor radius and the blade flap moment of inertia, the steady hover coning angle from the Lock number, the collective pitch and the uniform inflow ratio, and the rotating flap natural frequency ratio for a flap hinge offset. Produces the Lock number, the coning angle in radians and degrees and the flap frequency ratio ...

Use when you must compute the cyclic-pitch trim of a helicopter main rotor blade in forward flight under uniform inflow: the steady first-harmonic (1/rev) flapping equilibrium of the idealized centrally hinged blade with the control channel added, longitudinal cyclic theta1s and lateral cyclic theta1c about the collective, in the standard rotor convention, and the trim inversion for the cyclic pitch and equivalent swashplate tilt that hold the tip-path plane at a target longitudinal and later...

Use when you must compute the steady first-harmonic (1/rev) flapping equilibrium of a helicopter main rotor blade in forward flight under uniform inflow: the longitudinal flapping angle a1s (the tip-path-plane aft tilt, negative few degrees at cruise) and the lateral flapping angle b1s of the idealized centrally hinged untwisted blade from the advance ratio, the inflow ratio, the collective pitch and the blade Lock number gamma, with the forward-flight coning angle a0 that reduces to the hove...

Use when you must compute the forward-flight power required of a rotorcraft rotor with momentum-theory inflow: the Glauert induced velocity at a given flight speed, the induced power, the parasite power from the equivalent flat-plate drag area, the profile power from rotor blade solidity and tip speed, and the total power, then find the best endurance speed (minimum total power) and the best range speed (minimum power per unit speed) over a speed sweep. Produces the forward induced velocity, ...

Use when you must compute the hover-in-ground-effect performance of a rotorcraft rotor: the Cheeseman-style ground-effect reduction factor for the rotor induced power from the height above the ground and the rotor radius, the in-ground-effect induced power, the in-ground-effect total hover power from the induced-power factor and the unchanged profile power, the power margin against an available power, and the maximum rotor height at which the rotorcraft can still hover with that available pow...

Use when you must compute the hovering performance of a rotorcraft rotor with momentum theory: the ideal induced velocity through the rotor disk, the ideal hover power, the profile power from blade solidity and tip speed, the total hover power through an induced-power factor or through the figure of merit, and the disk loading. Produces the induced velocity, ideal power, profile power, total power, figure of merit, and disk loading that gate a hover performance check at a chosen density altit...

Use when you must compute the lead-lag dynamics of a helicopter main rotor: the lead-lag frequency ratio from the lag-hinge offset of an idealized uniform blade or as a measured or design input, the fixed-frame lag mode frequencies of a 3+ bladed rotor (collective, regressing, advancing), and the coincidence rotor speed where the regressing lag mode meets the airframe lateral frequency, with a ground-resonance clearance verdict at the operating rotor speed. Produces the lag frequency ratio, m...

Use when you must size the main rotor of a single-main-rotor rotorcraft from the takeoff weight and design ceilings: the main-rotor-disk-loading ceiling sets the disk area and radius, the rotor-thrust-coefficient follows from momentum theory at the chosen rotor tip speed, the rotor solidity closes from the ct-over-sigma hover design point, the blade area and chord follow from the blade count on constant-chord blades, and the rotor-tip-mach number checks the tip speed against the speed of soun...

Use when you must determine the rotorcraft fuel closure into hover endurance and cruise range and endurance: the hover power from the weight, the rotor disk area and the figure of merit, the exact weight-decay integration of the fuel burn into a closed-form hover endurance, and the cruise range and endurance at a chosen speed from an input power-required curve scaled with the average weight, together with the best-range and best-endurance speed picks. Produces the hover power and endurance, t...

Use when you must size the anti-torque tail rotor of a single-main-rotor rotorcraft from the main rotor torque balance: main rotor shaft torque from the main rotor power input and rotor speed, tail rotor thrust to balance that torque about the tail arm with a yaw margin factor, tail rotor disk area and radius for a chosen maximum disk loading, ideal induced velocity and ideal power from momentum theory, and tail rotor total power from the induced-power factor and a tail-rotor profile power es...

Use when you must determine the banked-turn power of a helicopter rotor from momentum theory: the turning-flight inflow solved for the n-times-weight thrust of the banked level turn, the banked-turn-power breakdown into induced, profile and parasite terms, the sustained-load-factor an available power supports at the turn speed, the power-limited bank angle, and the turn rate and radius of the sustained maneuver. Produces the turn induced velocity, the turn power breakdown, the sustained-load-...

Use when you must compute the vertical climb performance of a rotorcraft rotor with axial momentum theory: the climb induced velocity from the hover induced velocity and the climb rate, the induced power through an induced power factor, the total rotor power required in a vertical climb as induced plus profile power, and the maximum vertical rate of climb for an available shaft power. Produces the induced velocity in climb, the climb power required, the climb power margin and the maximum vert...

Use when you must compute the specific air range of an aircraft in cruise: divide the true airspeed by the fuel flow to produce the specific air range in meters per kilogram, derive the fuel flow from the thrust specific fuel consumption and the required thrust, estimate the instantaneous range from speed, thrust specific fuel consumption, weight, and lift to drag ratio, and convert a block distance into the fuel burn for the sector. Produces the specific air range, fuel flow, and fuel burn t...