Aerospace engineering research starters

These five ordinary Grid models cover four aerospace topics. Each exposes bounded inputs, named results, assumptions, a reference case, and a guided parameter change. The parameters describe synthetic teaching cases.

Topic	Model and reference case	Guided change
Orbital transfer and propellant	Hohmann transfer: from 400 km altitude to radius 42164 km, total delta-v 3.853957053 km/s; propellant 2414.759372 kg for 1000 kg dry mass and 320 s Isp	Change altitude to 800 km: delta-v 3.706172704 km/s and propellant 2257.675399 kg. Restore 400 km.
Aircraft performance and drag fitting	Aircraft performance: 1200 kg, density 1.225 kg/m³, 50 m/s gives drag 916.3266173 N; minimum-drag speed about 41.56522388 m/s	Change flight speed to 60 m/s. Inspect drag and power. Changing density or mass changes the curve and optimum; the separate synthetic fit data stay fixed.
Nozzle branches	Isentropic nozzle: area ratio 2.5 and gamma 1.4 give Mach 0.2395428431 and 2.442764846	Set area ratio to 1: both branches return Mach 1 explicitly. Values below 1 are rejected by the input contract.
Structures and dynamics	Beam and modes: tip deflection 0.009142857143 m and first beam frequency 20.56304413 Hz. Vibration and impact: 101 vibration samples, with an independent ballistic impact at 11.909590765 s	Change beam length from 2 to 3 m: deflection multiplies by 27/8 and frequency by 4/9. In the separate vibration model, vary damping and inspect the complete trajectory.

Work through a scenario

Open a model's source and read Assumptions and ScenarioGuide in I/O. Save a Baseline scenario before editing inputs. Apply the guided change, check the affected outputs, save the alternative, and restore Baseline. Reset returns inputs to their authored defaults. Export a .gridoc document and reopen it when a handoff needs source, scenarios, and surfaces together. The .grid examples themselves contain source defaults, without prepopulated scenarios.

Use Expose output to give a calculation a meaningful identifier and an optional description. For example, expose DeltaV_m_s as TransferDeltaV_m_s and describe the impulsive-burn assumptions. Descriptions are ordinary ## source notes on the output alias. I/O displays available unit metadata and offers navigation to the named source. A unit in an identifier documents the working convention; it does not perform conversion or validate external data.

Select DragCurve or the numeric Trajectory array and choose Plot selection. Review the source preview, X/Y choices, and axis units. The drag curve contains seven calculated speeds from 30 to 90 m/s; vibration contains all 101 requested times. The supplied line charts set smooth = false. Connecting samples is presentation, not an additional fit, optimum, or solver evaluation. Change a physical input that affects the plotted data before saving and reopening the chart.

Keep units and mathematical intent explicit

The orbit model works in kilometers and seconds until CONVERT changes delta-v to m/s for the rocket equation. A physical tag does not rescale a number: 1km + 500m retains legacy numeric arithmetic and warns about the scale conflict. Normalize explicitly, for example:

unit_scales strict
output Distance = CONVERT(1, "km", "m") + 500m

This yields 1500 m. The independent unit_scales axis can be warn, strict, or off. Without the directive, proven conflicts warn. Explicit warn also reports relevant unverified uses; strict refuses reported conflicts and unverified uses. Existing strict retains its dimensional/coercion meaning. The analysis does not prove unit safety for unannotated working-unit names or arbitrary functions. See coercion and scale checking.

For decay, write EXP(-(2^2)) when the intended exponent is negative four. EXP(-2^2) warns because Grid interprets the negative base before the power. EXP((-2)^2) explicitly chooses positive four. Warnings do not rewrite source.

Interpret numerical results within their assumptions

The orbital model excludes plane change, finite burns, perturbations, reserves, and staging. Its input range keeps the transfer outward. The aircraft model assumes steady level flight and a fixed parabolic drag polar. It exposes stall flags separately; scalar minimization does not impose an aircraft envelope or power limit. The fitted drag polar uses five synthetic observations and does not validate an aircraft design.

The nozzle uses separate subsonic and supersonic brackets. A NO_BRACKET failure means the selected endpoints did not bracket the target; it does not establish that no root exists elsewhere. Inspect the endpoint evidence and specific recovery in I/O, Inspector, or Errors. A domain error, invalid control, or exhausted iteration budget calls for a different repair. Downstream errors remain inspectable through the existing bounded source search.

The cantilever formula assumes a uniform slender beam and small deflection. Its deflection indicator is a simple teaching check, not a structural design criterion. The two-mass eigenproblem is separate from the continuous beam; the model deliberately sorts the two frequencies. The vibration trajectory uses rtol = 1e-9, atol = 1e-12 and 101 samples. Compare time, displacement, and velocity across the trajectory when changing tolerances. The independent ballistic model neglects air resistance and has its own analytic reference.

Hand off the right artifact

An Excel formula export must preserve all referenced names and formulas for the receiving spreadsheet to recalculate. Cached values alone are insufficient. Review export diagnostics: lambdas, numerical solvers, charts, validation, or other model behavior may require a Grid archive or the explicitly labeled values export. See Excel export. Test a parameter change in the actual receiving application and record its version before describing a handoff as live or portable.