Claude Skills by ashfordeOU

Use when a task concerns aerodynamics: guide the router to the aerodynamics pack: airfoil-selection family choice, xfoil-analysis polars, airfoil-geometry NACA geometry, airfoil-optimization shape trade, cfd-convergence residuals, cfd-turbulence-modeling model selection, cfd-mesh-generation grids and y-plus, vortex-lattice-method VLM, panel-method potential flow, normal-shock shock relations, oblique-shock theta-beta-M, prandtl-meyer expansions, swept-wing-aerodynamics sweep, transonic-simila...

Use when you must determine the added-mass-coefficients-potential-flow virtual mass (apparent mass) of a body accelerating through an inviscid irrotational fluid from the kinetic energy of the irrotational flow it sets up: the 2-D circular cylinder rho pi R^2 and normal flat plate rho pi a^2 per unit span, the 3-D sphere two-thirds rho pi R^3, the elliptic cylinder and the prolate and oblate spheroid coefficients, plus the kinetic-energy and acceleration-reaction relations. Produces the added...

Use when you must compute the dynamic aeroelastic response of a flexible two-degree-of-freedom typical wing section to a discrete gust with indicial unsteady aerodynamics: run the Wagner and Kussner lag-state lift model in the time domain, produce the plunge and pitch response histories for a one-minus-cosine gust, and report the dynamic magnification factor of the peak lift over the quasi-steady value plus the peak-load verdict against a limit. Produces response histories, the dynamic magnif...

Use when you must compute the static aeroelastic divergence condition of a lifting surface: calculate the divergence dynamic pressure from the torsional stiffness, the reference area, the chord, the lift curve slope, and the aerodynamic-center-to-shear-center offset ratio, convert it to the divergence speed at sea level, and assess the divergence margin against the design dive speed, flagging risk when the margin falls below the required 1.15 threshold. Produces the divergence dynamic pressur...

Use when the task is classical wing flutter of the two-DOF typical section, the V-g method, damping crossing, frequency coalescence, or flutter clearance. Compute the classical flutter speed of a two-degree-of-freedom bending-torsion wing section: build the typical section with plunge and pitch about the elastic axis, apply Theodorsen unsteady aerodynamics with the complex lift-deficiency function C(k), run the V-g method across the reduced frequency range, locate the flutter speed where the ...

Use when you must compute the frequency-domain gust response of a rigid thin airfoil to a convected sinusoidal vertical gust: evaluate the complex sears-function S(k) from the Bessel series with the Theodorsen lift-deficiency function, the gust gain and the phase lag of the gust load, and the unsteady gust-load amplitude against the quasi-steady 2*pi*rho*V*b*w_g reference, with the |S| = 1 quasi-steady limit at zero reduced frequency, the monotone gain roll-off, and the reduced frequency wher...

Use when you must work with classic NACA airfoil geometry: decode NACA 4-digit, 5-digit, and 6-series designations into camber, camber position, and thickness; compute the 4-digit thickness distribution, mean camber line ordinates and slope; and derive leading-edge radius and section area from the public-domain NACA formulas. Produces the geometry parameters that feed section selection, structural depth checks, and coordinate generation for panel or CFD analysis. Trigger: naca airfoil, camber...

Use when you must optimize an airfoil shape for an aerodynamic objective: set up design variables with NACA or PARSEC parameterization, evaluate objectives such as lift to drag ratio, maximum lift coefficient, and drag bucket width, enforce geometric constraints on thickness and camber, and run trade studies with sensitivity analysis. Produces the parameter sweep, the constraint verdict, the sensitivity ranking, and the recommended design point that feeds section selection and polar analysis....

Use when you must select an airfoil section for a wing design: score candidate airfoils by lift-to-drag ratio at the design condition, filter them by minimum thickness, and choose the best qualified section from classic airfoil data. Produces the candidate scoring, the thickness filter verdict, and the selected airfoil identifier that feeds the wing layout. Trigger: airfoil selection, wing design, lift to drag ratio, thickness, naca airfoils, section selection.

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_...

Use when running XFOIL-style airfoil analysis for a given section: plan viscous and inviscid polar runs, validate lift and drag coefficient points against physical plausibility bands, and check NACA 0012 results at Reynolds number 6 million against the classic wind-tunnel anchor (lift coefficient about 0.82 at 10 degrees, zero-lift drag about 0.0079). Distinguishes inviscid runs (drag meaningless) from viscous runs and flags high-drag cases needing transition or mesh-density checks. Trigger: ...

Use when you must predict boundary layer separation: grow the laminar layer with the Thwaites integral along the edge-velocity distribution of a two-dimensional body, flag the first station where the thwaites lambda parameter crosses minus 0.09 to give the laminar separation point, and apply the Stratford pressure-recovery criterion to the pressure-coefficient distribution to estimate the turbulent separation station and the separation margin below the 0.35 threshold. Produces the laminar sep...

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-...

Use when you must predict the laminar-turbulent transition location on a two-dimensional body from its edge-velocity distribution: grow the laminar boundary layer with the Thwaites integral relation to obtain the boundary-layer momentum deficit at each station, build the local Reynolds numbers from the edge velocity and that deficit, evaluate the Michel transition criterion against them, and interpolate the first station where the criterion is crossed to give the transition location. Produces...

Use when you must compute the two-dimensional laminar far-wake velocity-defect profile and drag downstream of a thin flat plate or slender body at zero incidence, the Goldstein 1933 similarity wake: evaluate the Gaussian cross-stream velocity-defect profile with the spread parameter U/(4*nu*x), the centerline-defect decay as x^-1/2 and the wake half-width growth as x^1/2 downstream of the trailing edge, integrate the momentum deficit across the wake with the wake-momentum-integral drag identi...

Use when you must map the steady laminar boundary layer on a slender axisymmetric body of revolution or a sharp cone into an equivalent 2-D flow with the mangler-transformation: evaluate the Mangler transformed running length xi = integral (r0/L)^2 dx and the transformed normal coordinate from the body radius distribution, the cone-surface radius and the equivalent 2-D length for power-law bodies, and the sharp-cone values at equal running length from flat-plate baseline values passed in: ski...

Use when you must estimate the turbulent skin-friction on a rough flat plate: it computes the smooth-wall turbulent baseline Cf from the local Reynolds number, the friction velocity and the sand-roughness reynolds number k+; classifies the k-plus-regime as smooth, transitional or fully rough; evaluates the Schlichting fully-rough-cf correlation for the fetch; and selects the operative coefficient without iteration, the direct fully-rough value or a log-linear blend. Produces the regime class,...

Use when you must compute the section profile-drag coefficient of a two-dimensional body or airfoil from the boundary-layer momentum state at its trailing edge: evaluate the squire-young-formula c_d,p = 2*(theta_TE/c)*(U_TE/U_inf)^((H_TE+5)/2) with the documented trailing-edge shape factor about 1.4, and the zero-pressure-gradient reduction to the Blasius flat-plate drag 1.328/sqrt(Re_c) when the trailing-edge velocity equals the freestream. Grows the laminar momentum thickness to the trailin...

Use when you must size the laminar boundary layer, wall shear and skin friction at a low-speed 2-D or axisymmetric stagnation point or leading edge: compute the potential-flow stagnation velocity gradient from the body radius and freestream speed (factor 2 in the Hiemenz 2-D regime, 1.5 in the Homann axisymmetric regime), the 99-percent laminar boundary-layer thickness about 2.4 sqrt(nu/a), the wall shear from the Hiemenz or Homann similarity wall-shear constant, and the skin-friction coeffic...

Use when you must compute the steady low-Reynolds-number viscous drag on a sphere in creeping flow, the Stokes solution for the slow motion of a sphere through a viscous fluid: evaluate the stokes streamfunction and the velocity field about the sphere, the surface pressure and wall-shear distributions with their high-pressure-facing-the-stream signature, the total stokes drag F = 6*pi*mu*a*U split one third pressure drag to two thirds friction drag, the drag coefficient Cd = 24/Re_D at the di...

Use when you must compute the exact unsteady laminar Stokes layer of an infinite plate in a quiescent fluid, either impulsively started or oscillating in its own plane: for the stokes-first-problem Rayleigh layer of a plate started at speed U, evaluate the similarity profile u/U = erfc(y/(2*sqrt(nu*t))), the layer edge at 3.64*sqrt(nu*t) where u/U = 0.01, the wall shear decaying as 1/sqrt(t) from rho*U*sqrt(nu/(pi*t)), and the displacement thickness; for the stokes-second-problem oscillating-...

Use when you must judge whether a computational fluid dynamics run has converged: check that residuals drop below tolerance and stay monotone, confirm the Courant number respects the scheme stability limit, and compare mesh refinement levels for answer stability. Produces the residual verdict, the CFL check, and the mesh convergence flag that decide whether results can be trusted. Trigger: cfd convergence, residual convergence, courant number, mesh refinement, solver stability.

Use when the task is CFD mesh generation, grid type selection, prism layer setup, near-wall resolution, domain sizing, or cell quality checking for a solver run. Generate a CFD mesh for an aerospace flow case: choose between structured, unstructured, and hybrid grids, size the near-wall first cell height from a y plus target and skin friction coefficient, build boundary-layer prism layers with a growth ratio, flag cell quality with skewness, orthogonality, and aspect ratio checks, size the fa...

Use when you must estimate the wall-normal first cell height for a CFD mesh: compute the y plus value from the friction velocity and kinematic viscosity, derive the friction velocity from the wall shear stress or the skin friction coefficient, and recommend the turbulence model and wall treatment for the boundary layer. Produces the y plus value, the friction velocity, and the turbulence model recommendation that size the near-wall mesh. Trigger: turbulence model, y plus, friction velocity, b...

Use when you must validate a computational fluid dynamics result against authoritative reference data: select the validation case for the flow regime and application (NACA 0012 or NACA 4412 airfoil, ONERA M6 transonic wing, DLR-F6 transport wing-body, flat plate boundary layer), compute the relative error, RMS error and max local error, run a Richardson extrapolation grid convergence check, judge pass or fail against tolerance bands, and estimate validation uncertainty. Produces the validatio...

Use when you must estimate the vortex lift of a sharp-edged delta wing: apply the Polhamus leading-edge suction analogy to split the total lift into the attached potential term Kp sin(alpha) cos^2(alpha) and the leading-edge-separation vortex term Kv cos(alpha) sin^2(alpha), with the slender-wing potential slope Kp = pi AR / 2 and the vortex factor Kv growing linearly from 3.14 at AR 0 to about 3.45 at AR 4. Produces the total lift coefficient, the potential and vortex lift split, the vortex ...

Use when the task is panel method setup, source or doublet panels, Neumann or Dirichlet boundary conditions, Kutta condition enforcement, pressure distribution on an airfoil or fuselage, or potential flow over 3D bodies. Compute the surface pressure distribution and force coefficients for an airfoil or body in incompressible potential flow with a panel method: build panel geometry from a closed point list, assemble the source panel influence matrix for the Neumann boundary condition, assemble...

Use when you must compute the spanwise loading of a straight trapezoidal wing with the vortex lattice method: build the horseshoe vortex panel lattice at the quarter chord, assemble the influence coefficient matrix at the three-quarter chord control points, solve the linear system for the panel circulations, and derive the spanwise lift distribution, the downwash angles, and the induced drag. Produces the circulation solution, the per-panel lift, and the lift and induced drag coefficients tha...

Use when you must compute the parabolic drag-polar of a wing from the zero-lift-drag coefficient cd0, the Oswald span-efficiency, and the aspect-ratio: calculate the induced-drag factor k with k = 1 / (pi * e * AR), the drag coefficient at a given lift coefficient, the lift-to-drag ratio at a point, and the maximum lift-to-drag ratio with its optimal lift coefficient. Also fit a parabolic drag-polar to two measured lift and drag points to recover cd0 and k. Produces the fitted polar coefficie...

Use when you must estimate the lift curve slope of a wing from section data: compute the thin-airfoil section slope a0 = 2*pi per radian, correct it for finite aspect ratio with the lifting-line formula a = a0 / (1 + a0 / (pi * e * AR)), apply the simple sweep theory cosine correction, apply the Prandtl-Glauert Mach correction a / sqrt(1 - M^2) with a documented M < 0.7 limit, and predict lift coefficient from angle of attack with C_L = a * (alpha - alpha_zero), including an optional stall gu...

Use when the task is drag buildup, zero-lift drag estimation, the wetted-area method, skin-friction coefficients, form factor, interference factor, or equivalent skin-friction coefficient in a preliminary drag assessment. Estimate the parasite (zero-lift) drag of a fixed-wing aircraft with the component buildup method: compute the flat-plate skin-friction coefficient from the Reynolds number for laminar and turbulent flow, apply the form factor and interference factor to each component, conve...

Use when you must estimate the ground effect on a wing operating near the ground: compute the induced drag reduction factor and the induced drag ratio from the height to span ratio, apply the image vortex correction to the downwash and the effective aspect ratio, and estimate the lift increase and lift curve slope change in ground effect for takeoff and landing analysis. Produces the ground effect factor, the corrected induced drag, and the lift curve slope that feed low altitude performance ...

Use when the task is high-lift device selection, flap clmax estimation, slat contribution, wing CLmax, or stall speed with flaps. Estimate high-lift system performance for conceptual design: compute the section clmax increment for trailing-edge flaps (plain, split, slotted, Fowler) and leading-edge devices (slat, Krueger), scale the increment with deflection, flap chord ratio, and flapped span fraction, combine flap and slat increments by superposition, apply the three-dimensional and sweep r...

Use when you must compute the section coefficients of a thin airfoil at supersonic speed by ackeret linearized supersonic theory: evaluate the ackeret parameter sqrt(M^2 - 1), the surface pressure coefficient Cp = 2*theta/sqrt(M^2 - 1) for a deflection theta, the section lift cl = 4*alpha/sqrt(M^2 - 1), the supersonic lift curve slope, and the wave drag of the flat plate, the thin biconvex circular-arc section and a cambered thin plate from the linearized pressure integral over the surface sl...

Use when you must estimate the aerodynamic heating at the stagnation point of a hypersonic body: stagnation-point convective heat flux from the Sutton-Graves correlation using freestream density, flight velocity and nose radius, radiation-equilibrium wall temperature from the Stefan-Boltzmann balance at a chosen surface emissivity, and the nose-radius bluntness trade that scales the flux for blunt versus sharp geometries. Produces the stagnation heat flux, the radiation-equilibrium temperatur...

Use when you must estimate the detached bow-shock standoff distance ahead of a blunt nose: compute the standoff ratio Delta over R with the classical Billig-form correlations for a sphere nose and a circular cylinder leading edge at gamma 1.4, convert the ratio to a physical standoff distance for a given nose radius, and report the trend checks that the standoff decreases with Mach and that the cylinder standoff exceeds the sphere standoff at the same Mach. Produces the standoff ratio, the st...

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 ga...

Use when you must solve the Fanno flow of a steady adiabatic constant-area duct with wall friction: evaluate the fanno-line integral fL*/D that chokes the duct from a Mach number, compute the friction-duct-choking length from the inlet Mach, recover the downstream Mach number for a given friction parameter fL/D on the subsonic or the supersonic branch, find the friction required to choke a duct of given length, and report the total-pressure loss ratio p0/p0* and the static pressure, temperatu...

Use when you must estimate the surface skin friction heating on a flat plate or vehicle skin at high Mach: it computes the recovery factor, adiabatic wall temperature, Eckert reference temperature, Sutherland viscosity, local skin friction coefficient and Reynolds-analogy heat transfer coefficient, then the cold-wall heat flux for a laminar or turbulent boundary layer. Produces the non-stagnation heating report with r, T_aw, T_star, Re_star, Cf, h_c and q_cold_wall in SI units for a thermal p...

Use when you must estimate aerodynamic forces on a body in hypersonic flow with modified Newtonian impact theory: stagnation pressure behind the normal shock (Rayleigh pitot relation), the finite-Mach stagnation pressure coefficient, local pressure by the Newtonian sine-squared law, the hypersonic vacuum limit on shadowed surfaces, and integrals over a sphere, cone and flat plate giving sphere drag, cone axial force, and flat plate lift, drag and lift-to-drag ratio. Produces the stagnation Cp...

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...

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 temper...

Use when you must compute normal shock relations for compressible flow: find the downstream Mach number, static pressure, density, and temperature ratios across the shock, and the stagnation pressure loss from the upstream Mach number. Produces the five shock ratios that gate inlet and high-speed aerodynamic analysis of a supersonic flow. Trigger: normal shock, oblique shock, mach number, compressible flow, pressure ratio, stagnation pressure, supersonic inlet, shock relations.

Use when you must analyze an oblique shock in supersonic compressible flow: compute the wave angle beta from the upstream Mach number M1 and the flow deflection angle theta with the theta-beta-M relation, find the weak and strong solutions, the maximum deflection angle for an attached shock, and the downstream Mach number, static pressure, density, temperature, and stagnation pressure ratios across the shock. Covers shock polar basics: the weak branch keeps the flow supersonic with little sta...

Use when you must compute Prandtl-Meyer expansion relations for supersonic compressible flow: derive the expansion angle from the Mach number, find the downstream Mach number after the flow turns away from itself by a given angle, compute the total turning angle across the expansion fan, and the static pressure ratio across it. Produces the Prandtl-Meyer angle, the downstream Mach number, the turning angle, and the pressure ratio that gate supersonic airfoil, inlet, and nozzle analysis. Trigg...

Use when you must compute the rayleigh-flow state change of a perfect gas heated or cooled in a constant-area frictionless duct: convert the inlet Mach number into the Rayleigh-line ratios against the sonic state T/T*, p/p*, rho/rho*, T0/T0*, p0/p0*; find the maximum heat addition that thermally chokes the duct from a subsonic or supersonic inlet Mach number, q_max = cp*T1*(1 - M^2)^2/(2*(gamma+1)*M^2); recover the exit Mach number after a given heat addition per unit mass on the inlet branch...

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, temper...

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-...

Use when you must determine the four-region state of a shock-tube run from the driver-to-driven diaphragm pressure ratio and driver sound-speed ratio: recover the incident-shock Mach number by deterministic bisection of the implicit diaphragm-match equation, then the post-shock pressure, temperature and density ratios with the region-2 absolute state, the contact-surface velocity shared by shocked driven gas and expanded driver gas with the region-2 and region-3 flow Mach numbers, the driver ...

Use when you must analyze or design a supercritical airfoil for high-speed flight: compute the drag-divergence Mach number from the Korn thickness-lift rule, estimate the terminating shock strength of the upper-surface supersonic pocket, quantify the wave-drag penalty above drag divergence, and size the maximum thickness ratio or cruise lift coefficient that the flat upper surface permits. Produces the drag-divergence Mach, the shock-strength reduction, the wave-drag penalty, and the aft-load...