E-CodeTI-84 Plus CE engineering programs
62 checked engineering programs for the TI-84 Plus CE. Each one runs in E-Code's virtual calculator in your browser, and you can put it on your own calculator.
The programs
- RC circuit charging transient: Tabulates a capacitor's charging voltage at 5 points in time.
- Cantilever beam deflection: Point-load beam deflection from 5 real engineering inputs.
- Reynolds number / flow regime: Computes the Reynolds number for pipe flow and classifies laminar/turbulent.
- Three-loop circuit (mesh currents): Builds the mesh matrix from 8 inputs, solves it through SOLVE3, and proves the answer by power balance.
- Beam reactions and maximum moment: Simply supported beam with up to any number of point loads: reactions, maximum bending moment, and where it happens.
- Newton's law of cooling: Exact cooling curve versus Euler steps, plus the live rate (nDeriv), the average (fnInt) and the time to a target.
- Polynomial roots and stability: All real roots of a degree 1-5 polynomial by Newton from above plus deflation, a Vieta self-check, and a stable/unstable verdict.
- Tensile test analysis: Least-squares Young's modulus from stress-strain data, fit quality, residual statistics and an outlier count.
- Two-link robot arm (inverse kinematics): Joint angles that put a two-link arm's hand on a target point: 2-D Newton with a Jacobian matrix, in degrees.
- Byte toolkit: binary, hex, checksum: Binary, hex, two's complement and parity of a byte, then an XOR checksum of a typed message, using TOBIN.
- Engineering toolkit hub: One menu that runs all nine tools above through prgm calls, keeps a session log, and summarises it on exit.
- Pin fin with convective tip: Heat rate, fin efficiency, effectiveness, tip temperature and the adiabatic-tip comparison, from sinh/cosh/tanh.
- Transient plane wall (first term): Convective heating/cooling of a plane wall: eigenvalue by bisection, centre and off-centre temperature, heat fraction, validity check.
- 2-D steady conduction, plate series: Rectangular plate, three sides at zero and the top at a uniform temperature rise: separation-of-variables series at any point.
- Stefan melting problem: One-phase melting of a semi-infinite solid: solves the transcendental Stefan equation for lambda, gives interface position, speed and time to melt a depth.
- Radiation exchange, 3-surface enclosure: Gray diffuse enclosure with a re-radiating third surface: radiosities from a 3x3 matrix solve, net heat rates, re-radiating temperature.
- Stefan tube: evaporation by diffusion: Steady diffusion through a stagnant gas film: molar flux, mass flux, and the time for the liquid level in the tube to fall.
- Psychrometrics: wet-bulb and dew point: Humidity ratio, dew point, wet-bulb temperature (energy balance solved by bisection), enthalpy and specific volume of moist air.
- Heat exchanger, effectiveness-NTU: Counterflow, parallel-flow or one-shell-pass exchanger: effectiveness, duty, outlet temperatures, and the LMTD cross-check with its correction factor.
- Semi-infinite solid / diffusion: Temperature (or concentration) profile, surface flux, penetration depth and half-response time after a surface step, via the error function.
- 1-DOF forced vibration: Natural frequency, damping ratio, logarithmic decrement, magnification factor, steady-state amplitude, phase lag and force transmissibility.
- 2-DOF vibration: modes: Two masses, three springs: both natural frequencies from the characteristic quadratic, in rad/s and Hz, and the mode-shape ratios.
- Pipe friction: Colebrook, Darcy-Weisbach: Reynolds number, Darcy friction factor (Colebrook iterated; 64/Re when laminar) beside Haaland's explicit form, head loss and pressure drop.
- Pipe network: series + parallel: One pipe in series with two in parallel, common friction factor: how the flow splits, velocities, and the parallel and total head loss.
- Venturi meter and Pitot tube: Venturi: flow rate from the differential pressure with a discharge coefficient, velocities, and the pressure lost.
- Open channel: Manning, critical depth: Trapezoidal channel: normal depth by bisection on Manning's equation, velocity, Froude number, critical depth, specific energy and the flow regime.
- Hydraulic jump: Rectangular channel: Froude number, sequent depth, downstream velocity and Froude number, head loss, power dissipated and approximate jump length.
- Pump and system operating point: Parabolic pump curve meeting a system curve, with speed scaling by the affinity laws: flow, head, efficiency from a parabolic curve, and shaft power.
- Terminal settling velocity of a sphere: Sphere falling through a fluid with the Schiller-Naumann drag law, solved by bisection: terminal speed, Reynolds number, drag coefficient, and the Stokes-law error.
- Flat-plate boundary layer and drag: Reynolds numbers, laminar or turbulent boundary-layer thickness and local friction at a station, mixed-flow average drag coefficient and total drag on the plate.
- Isentropic flow and normal shock: Perfect-gas tables on demand: Mach to T, p, rho and A/A*; area ratio back to Mach (subsonic or supersonic branch); and every normal-shock ratio.
- Converging nozzle: choking and thrust: Supply and back pressure decide choked or not: exit Mach, pressure and temperature, exit speed, mass flow and thrust for a perfect gas.
- Potential flow past a spinning cylinder: Uniform stream, doublet and vortex: surface pressure coefficient and speed at any angle, Kutta-Joukowski lift, and the stagnation points.
- Hydrostatic force on a gate: Rectangular gate at any incline: resultant force, centroid depth, centre of pressure measured from the top edge, and the moment about the top hinge.
- Impeller velocity triangles (Euler head): Pump impeller exit triangle from speed, radius, width, blade angle and flow: Euler head, hydraulic power and dimensional specific speed.
- Air-standard Otto, Diesel, Brayton: State temperatures, net work, thermal efficiency and mean effective pressure for the ideal engine cycles, with cold-air constants.
- Polytropic process, ideal gas: Any polytropic exponent (n=1 isothermal, n=k adiabatic): end state, boundary work, heat, internal energy change and entropy change.
- Real gas: van der Waals, Redlich-Kwong: Molar volume and compressibility factor from a cubic equation of state (Newton's method from the ideal-gas volume; bisection when that stalls, e.g. for a liquid-like state), compared with the ideal-gas value.
- Entropy generation, lost work: Adiabatic mixing of two streams or heat transfer across a temperature gap: entropy generated and the work destroyed (Gouy-Stodola).
- Chemical equilibrium: N2O4 <-> 2NO2: Van't Hoff shift of the equilibrium constant with temperature, then the degree of dissociation, mole fractions and standard Gibbs energy at a total pressure.
- Radioactive decay chain (Bateman): Parent and daughter activity after any time, the daughter-to-parent ratio, the time of maximum daughter activity, and the kind of equilibrium reached.
- Four-factor formula and criticality: k-infinity from eta, f, p and epsilon; one-group k-effective for a sphere, cylinder or slab from its geometric buckling; reactivity and the critical size.
- Point reactor kinetics, step reactivity: One delayed-neutron group: the two inhour roots, the stable period, the prompt-jump ratio and the neutron level at any time after a reactivity step.
- Gamma shielding and dose geometry: Transmission, half- and tenth-value layers, thickness for a required reduction with and without buildup, and the point-source flux behind the shield.
- Uranium enrichment: SWU and feed: Feed and tails mass for a product assay from a feed and tails assay, separative work in SWU, and the feed and SWU needed per kilogram of product.
- Neutron moderation: xi and collisions: Average logarithmic energy loss per collision for any moderator mass number, collisions needed to thermalise, moderating power and moderating ratio.
- Reactor decay heat after shutdown: Way-Wigner type correlation P/P0 = C[t^-0.2 - (t+T)^-0.2]: decay power fraction, power, and energy released between two times after shutdown.
- Neutron diffusion: critical size, flux: One-group bare reactor: diffusion length, k-infinity, material buckling, critical size (slab, sphere or cylinder) with extrapolation distance, flux shape and peaking.
- RC, RL and RLC transient response: Capacitor volts and current at any instant t for an RC charge, an RL current rise, or a series RLC step (with alpha, omega0, zeta, omega-d and the damping type), from any starting volts and current.
- Series-parallel resistor network reducer: Reduce any series-parallel network step by step: combine a list of resistors in series or in parallel, reuse the running result R (or saved A, B, C) inside the next list, then apply a voltage for the total current and power.
- Pinch analysis: minimum hot and cold utility: Heat-exchanger network targeting by the problem table: type the streams' supply and target temperatures and CP, and dTmin — minimum hot and cold utility and the pinch temperature (shifted, hot side and cold side).
- Two-phase flow pressure drop: Frictional pressure gradient of a gas-liquid flow in a pipe by the homogeneous model and by Lockhart-Martinelli with Chisholm's C (chosen from the phases' laminar/turbulent regimes), plus the homogeneous void fraction.
- Beam deflection by superposition: Simply supported or cantilever beam with any number of point loads plus a uniform load: deflection at the point you choose, the maximum deflection and where it is, and the support reactions — by superposing the standard cases.
- Column buckling: Euler and Johnson: Critical buckling stress and load of a column for the four classic end conditions: slenderness KL/r against the transition Cc, Euler for long columns and the Johnson parabola for intermediate ones, and the allowable load for a safety factor.
- Bode point and stability margins: Type a transfer function as numerator and denominator coefficient lists: magnitude, dB and continuous (unwrapped) phase at any frequency, or the gain and phase crossover frequencies with the phase margin and gain margin.
- Second-order step response metrics: From the damping ratio and natural frequency: damped frequency, peak time, percent overshoot, the exact 10-90% rise time and exact 2% settling time (solved on the true response, not the rules of thumb), with the 4/(ζwn) estimate beside it.
- Discrete PID step response: A first-order plant G/(τs+1) sampled with a zero-order hold, under a positional discrete PID: table of the output at every sample, then the final value, peak, percent overshoot, steady-state error and last control signal.
- Gamma shielding with Taylor buildup: Point isotropic gamma source behind a slab: Taylor buildup factor, unshielded, uncollided and total flux at the detector, and (optionally) the shield thickness that brings the flux down to a target.
- AC circuit: series or parallel RLC phasors: Series or parallel R, L, C on a sine source: impedance magnitude and angle, current, real and reactive power, power factor, and the resonant frequency — leave L or C at 0 when the circuit has none.
- Op-amp stages: gain and output: Ideal op-amp inverting, non-inverting, summing, difference (matched pairs: R1 into each input, R2 as feedback and to ground, Vout = R2/R1·(V2 − V1)) and integrator stages: the gain and the output voltage, clipped at the supply rails with a SATURATED warning (the integrator for a sine input: amplitude and +90° phase).
- Mohr's circle: stress transformation: Plane stress σx, σy, τxy: the stresses on a face rotated by any angle, the principal stresses and their angle, the maximum in-plane shear, the circle's center, and the von Mises stress.
- Thevenin equivalent and maximum power: A source V with R1 in series, R2 across, and R3 out to the terminals: the Thevenin voltage and resistance, the Norton current, the load current and power for your load, and the load that gets maximum power and that power.