Flight metrics

In short

• What it models: the numbers a flight is judged by. These are the apogee, the top speed and Mach number, the peak dynamic pressure (“max q”), the boost’s peak acceleration and, kept apart, the opening shock. It also gives the stability margin from the rail exit to apogee or the first deployment, the largest angle of attack that counts toward the envelope’s high-angle flag (below), whether the rocket is unstable while a motor burns (below), the ejection delay that would fire the charge at apogee, and each landing’s latitude and longitude. Anything that didn’t happen is None, never a zero.
• Sources: the margin is Barrowman’s center of pressure (to Mach 0.8; faster, as Aerodynamics describes) against the center of mass (the CG), defined as RocketPy defines its static margin and stability margin. The peak search is Kiefer’s golden-section search (References). Latitude and longitude come from hpr’s WGS 84 conversions (Geodesy).
• How well it is validated: each number is only as good as the flight it comes from. The flight is checked against RocketPy and OpenRocket (Accuracy), and the metrics add no physics of their own. Tests check each against a hand calculation or against hpr’s own models evaluated directly (Tests). The margin in the weakest plane is checked against hpr’s own scan of 3,600 planes in a test, and against one OpenRocket run that is not committed. None is validated against a real flight.
• What it leaves out:
  • Fin flutter, which has its own page: Fin flutter. Its margin comes from the max q found here.
  • File exports: a later part of the same milestone, M1.10c (CSV, JSON, KML and GeoJSON files).
  • The descent of a separated body, such as a dropped booster. It gets a landing, but no peaks.
  • A damping ratio: how fast a wobble dies out. Both margins here are static quantities.
  • The margin at the flight’s angle of attack. Both margins take the air along the rocket’s axis, in the weakest direction it can cross (Stability margins). In hpr’s model a rocket meeting the air at an angle, as it does leaving a rail in wind, can have a smaller or a larger margin than these, depending on where its body’s lift acts (Stability margins says why they leave it out).

Why these rules

Loft, this project’s predecessor, got four things wrong that these metrics are built to avoid:

• It read peaks off a table of recorded rows and missed them, and it counted the opening shock as the boost’s peak acceleration (L34).
• It printed zeros for things that never happened, and never said which height an apogee was counted from (L35).
• It published margins of ±12 to 15 calibres for rockets where a margin has no meaning (L33).
• Its optimum ejection delay depended on the delay flown (L94).

Each is a numbered lesson with a test (Tests).

Getting the numbers

Fly a Simulation with a FlightMetrics watching it. Then ask the watcher for a FlightSummary:

let mut metrics = FlightMetrics::new();
let flight = simulation.run(&mut metrics)?;
let summary = metrics.summary(&flight, simulation.environment())?;
let best = hpr_sim::metrics::optimum_delays(&simulation)?;

A watcher keeps one flight. Call metrics.clear() before it watches another; summary refuses a flight unless the watcher saw each of its steps once.

The example program flight_metrics.rs does this for Valetudo, the rocket from Getting started. It flies with a 5 m/s wind from the west and one 1.5 m parachute. The charge fires 6 s after burnout (the end of the thrust curve), and the canopy is open 0.5 s later. Run it with cargo run --example flight_metrics -p hpr-sim. It prints:

Valetudo on a K400C, a 1.5 m parachute fired 6 s after burnout, open 0.5 s later
Not yet validated: see the Accuracy page before trusting these numbers.

Heights are the center of mass's above the launch site; it starts 0.94 m up.
Apogee:                714.0 m above the site (713.0 m of climb) at 11.16 s
Top speed:             112.3 m/s at 3.00 s, 188 m up
Top Mach number:       0.337 at 3.02 s, 190 m up
Max q:                  6667 Pa at 2.99 s, 186 m up
Boost acceleration:     47.2 m/s² at 0.03 s, 1 m up
Opening shock:         153.4 m/s² at 9.76 s, 698 m up

Rail exit:            16.2 m/s at 0.37 s, 17.2° off the oncoming air
At rail exit (0.37 s): static margin 3.09 cal, flight margin 3.09 cal at Mach 0.051
Least static margin:    3.09 cal at 0.37 s, 4 m up
Least flight margin:    3.09 cal at 0.37 s, 4 m up

Optimum delay:        10.6 s after burnout at 3.26 s (flown: 6.0 s), for an apogee of 778.7 m at 13.83 s
Landing:              32.990000° N, 106.967084° W: 272.6 m east and 0.0 m north of the site, at 11.6 m/s, at 78.67 s

The 6 s delay is too short:

• The charge fires at 9.26 s, and the canopy opens at 9.76 s: about 4 s (13.83 − 9.76) before the apogee it would have reached.
• The rocket still rises 1.4 s more, to an apogee of 714.0 m.
• With the charge held, it would have coasted to 778.7 m at 13.83 s: the apogee of the Getting started flight, whose drogue fires at apogee.
• So the optimum delay is 10.6 s. The opening shock, 153.4 m/s², is three times the boost’s 47.2 m/s², and it is not counted as the boost’s peak.
• Don’t size a shock cord from the 153.4 m/s²; it is no bound either way. The canopy reaches full drag at line stretch, 0.5 s after the charge, with no filling time (hpr’s default), so the rocket doesn’t slow while it fills: that reads high. hpr also leaves out a canopy’s drag overshoot near the end of filling: that reads low (The opening load).

Top speed comes at 3.00 s, before the 3.26 s burnout, because in the thrust curve’s last moments the motor pushes less than drag and gravity pull back.

Heights

Every height is of the center of mass: its ellipsoidal height above the launch site’s, the same as a flight’s height_above_ground_m. The center of mass starts above the site, because the rocket stands on the rail: 0.94 m for Valetudo. So the summary gives both:

• apogee.height_above_ground_m: 714.0 m, above the site.
• apogee.gain_m: 713.0 m, the climb from where the center of mass stood at launch. OpenRocket’s altitude counts this way. A flight started in the air (Simulation::run_free) has no launch height, and no climb: None.

A flight ends when its center of mass comes back down to the site’s height, so a landing is at height 0 by this measure.

Peaks

Each peak comes with its time and its height. The watcher looks at every step the integrator takes (Time integration and events), not at a table of recorded rows:

1. It evaluates the equations of motion at each step’s start, middle and end.
2. It fits a parabola through the three values. When the parabola bends down with its top inside the step, the peak may lie inside. A golden-section search then looks for it on the step’s dense output, the integrator’s smooth curve through the step, to a billionth of the time since launch (or of 1 s early in the flight).
3. It keeps the largest of what the search finds and the three samples.

Thrust-curve knots, the times where a motor’s tabulated thrust changes slope, end steps. So a spike in the thrust curve is a step’s end, and is never averaged away. Loft took its peak acceleration from a finite difference of the recorded speed, and read it low. Valetudo in a vacuum shows how much: the watcher’s peak matches the hand value from the motor and the masses within the test’s 1e-6, and a finite difference of the speed recorded at 100 Hz reads it more than 1% low.

The accelerations are of the nose tip, which is the body’s origin in hpr’s frames. It differs from the center of mass’s only by the rocket’s turning, which is small in a straight boost, and by the center of mass’s slow drift forward as propellant burns. The accelerations are relative to the launch frame and straight from the equations of motion, so they include gravity’s pull, as a trajectory’s acceleration does. An accelerometer reads something else: it does not feel gravity.

Nothing is kept while the rocket sits on the pad. A rocket that never lifts off has no peaks at all: None, not zero.

Stability margins

The margin is how far the center of pressure lies behind the center of mass, in calibres of the reference diameter d:

margin = (x_cp − x_cg) / d,    x_cp = Σ C_Nα,i x_i / Σ C_Nα,i

Here x is a station measured aft of the nose tip, and C_Nα,i is component i’s normal-force slope. hpr gives two margins at each instant:

• Static margin: the center of pressure at zero angle of attack and Mach 0, against the center of mass of that instant. This is RocketPy’s static_margin. It changes only as propellant burns.

• Flight margin: the center of pressure at the flight’s own Mach number, still with the air along the axis, against the center of mass of that instant. It is defined as RocketPy’s stability_margin is. RocketPy’s min_stability_margin takes the least over its whole flight, on the rail and in the descent too, at its solver’s steps, so it can differ from hpr’s least below. No page compares hpr’s margins with RocketPy’s yet. Against OpenRocket, in calm air at rod clearance, where a rocket is still slow, hpr’s margin at the flight’s Mach number is within 0.016 calibres on 41 of the 53 flights of OpenRocket’s own examples. This comparison takes hpr’s margin with the air along the rocket’s axis (the 0° plane), as OpenRocket’s margin is, not in hpr’s weakest plane (below). On [C6-7; B6-0] of Pods–powered with recovery deployment, hpr’s margin at rod clearance in the report is +3.74 calibres along the axis, while hpr sim prints a least margin of −4.21 in the weakest plane. Where the two programs differ: on the Tube fin rocket hpr’s is 1.08 calibres below OpenRocket’s, tube fins; on the three-stage example’s three flights 0.039 to 0.058 below, cause not yet sized, #185; and on the five of Pods–airframes and winglets 0.071 to 0.076 above, the flattering side, #325 and #326; and on the three of Pods–powered with recovery deployment 0.070 above, also not yet traced. On 35 flights of private designs it is from 0.017 lower to 0.11 higher, cause not yet traced (Accuracy). Near Mach 1 hpr puts the Arcas Robin’s center of pressure up to 2.36 calibres behind the wind tunnel’s (Normal force through Mach 1), so there its flight margin reads high.

  The Mach number moves the center of pressure. On a rocket with fins only at the tail it generally moves aft up to where supersonic theory starts for the fins, Mach 1.2 or later: their slope grows, and from Mach 0.8 their own center moves aft too. Past that their slope falls and the body’s lift can grow, and the center of pressure mostly moves forward again (Your rocket’s center of pressure). Valetudo is slow: at its rail exit, at Mach 0.051, both margins read 3.09 calibres.

Both margins are the weakest direction’s. The air can cross a rocket from any direction around its axis, and for most rockets the margin is the same in every one. A fin set of one or two fins breaks that: it carries Σ sin²(φ − θ_k) of its force in the plane at roll angle φ, for fins at angles θ_k (Niskanen 2009, eq. 3.51, as in Fins). So a rocket with one has a margin for each direction, and hpr gives the least, the direction it was found in as roll_rad. Until #329, hpr’s margins were the 0° direction’s alone, which can be the strongest. A rocket whose fin sets each have three or more fins, or that flies a normal-force table, keeps its one margin, bit for bit.

A worked case: the sustainer of OpenRocket’s Pods–powered with recovery deployment example has a single fin at 0° and a two-fin strake set at 90°. At Mach 0.2, after the booster drops, its margin is +1.86 calibres with the air crossing at 0°, where the single fin lies edge-on and the strakes carry the force. At 45° it is +0.17. At 90° the strakes lie edge-on and only the single fin works: −3.44, unstable. OpenRocket 24.12, asked for that sustainer at 90° in a scratch run (not committed), puts its center of pressure at 0.2954 m with C_Nα 3.49; hpr’s are 0.2993 m and 3.47. For one of its staged configurations, [C6-7; B6-0], hpr sim‘s least margin was +1.56 calibres and is now −4.21, at 0.86 s. That is the sustainer’s margin at the split itself, the moment the booster drops, with its own motor just lit and still full and the air at Mach 0.07; the −3.44 is a later instant, at Mach 0.2. In the conditions of OpenRocket’s record, both programs’ flights of that configuration turn over before apogee: its site is at 28.61° N, where the Earth’s rotation tips hpr’s flight, and hpr’s angle of attack passes 90° at 2.25 s. At hpr sim’s default site, on the equator, nothing tips hpr’s flight: it stays upright and reaches 251.3 m (the format guide).

hpr finds the least in closed form, not by a scan (weakest_margin). Each part’s slope varies as a + b cos 2φ + c sin 2φ, so the net slope S(φ) and its moment M(φ) = Σ C_Nα,i x_i do too. Three directions, 0°, 60° and 120°, give each sum’s a, b and c. The center of pressure M/S is foremost where

P sin 2φ + Q cos 2φ + R = 0,   P = m₀s₁ − m₁s₀,   Q = m₂s₀ − m₀s₂,   R = m₂s₁ − m₁s₂

with m and s the coefficients of M and S. The margin’s conditioning (below) is checked at its own worst direction the same way. Each root and the 0° direction are evaluated through the model, and a direction where no margin can be given wins over any number.

Both margins leave out the angle of attack. In hpr, body lift grows with the angle and acts at each body’s side-view centroid, and the center of pressure moves toward it. Where that centroid lies ahead of the zero-angle center of pressure, the margin at an angle shrinks; on a long body with small fins it can lie behind, and the margin grows. No test pins either direction. But the angle is not a steady property of the rocket. Valetudo leaves its rail 17.2° off the oncoming air in the example’s 5 m/s crosswind, and near apogee the angle swings toward 90° as the rocket slows and tips over. If the least margin followed the angle, it would land wherever hpr chose to stop counting large angles, and hpr models no fin stall that could say where that is. For the margin at a given angle, call margin with Flow::new(mach, angle_rad, roll_rad).

The watcher keeps both margins in FlightMetrics::stability(). The series starts at the rail exit and ends at apogee or when a recovery device opens, whichever comes first. Before the rail exit the rail holds the rocket, so its margin says nothing about how it flies.

The summary’s least margins cover the same span. Each is looked for inside every step, as a peak is (Peaks): wherever the margin is defined at a step’s start, middle and end and the parabola through them bends up with its bottom inside the step, a golden-section search finds the bottom. A later least replaces an earlier one only when lower by more than rounding, so a flat least keeps its first time. A margin with a sharp corner near a step’s end can still hide from the parabola.

• On four test flights, and in the example, both leasts come at the rail exit, where the rocket is heaviest and its center of mass furthest aft. Flown in steps of at most 1 ms, those flights give the same leasts to a millionth of a calibre.
• On a two-stage test flight the least flight margin comes inside a step, after the split. There it matches a scan of every step at 201 points to 1e-7 calibres, and is never above it.

After a powered separation the margins are the sustainer’s, in its own diameter. The split has two entries in the series: the stack’s, then the sustainer’s.

When there is no margin

As the net slope Σ C_Nα,i goes to zero, the air’s loads become a pure couple: a turning moment with no line of action. The quotient x_cp then runs away. That is how Loft came to publish margins of ±12 to 15 calibres.

hpr judges the net slope against the sum of its terms’ sizes:

κ = Σ |C_Nα,i| / Σ C_Nα,i

Each part the model adds up acts at a station x_i on the rocket, within its length L. The center of pressure then lies within κ L of every station. So a fractional error ε in one part’s slope moves the center of pressure by at most about ε κ² L (to first order). A part that is a pure couple on its own (below) has no station, and κ doesn’t count it.

• A rocket whose parts all push the same way has κ = 1, and a 1% error moves its center of pressure by at most 1% of its length. All 13 designs in validation/designs/ stay below 1.5 at Mach 0, 0.3, 0.8, 1.2 and 2 and at angles of attack of 0°, 5°, 10° and 20°.
• At κ = √10 = 3.16, a 1% error in one slope can move the center of pressure by a tenth of the rocket. Past that, or when the net slope is not positive, hpr gives no margin and no center of pressure: None. The limit is a chosen bound on that sensitivity, not a measurement.

The pitch-moment slope about the center of mass is always given, because it stays finite:

C_mα = −(Σ C_Nα,i x_i − x_cg Σ C_Nα,i) / d

A negative C_mα turns the nose back into the wind. With a margin defined, C_mα = −C_Nα · margin.

A worked case, with no fins, pinned by a test:

• The rocket is a conical nose 0.3 m long of radius R = 0.05 m, a 0.5 m tube, and a conical boattail 0.4 m long, narrowing to a radius r. So d = 0.1 m.
• Barrowman gives the nose a slope of 2 at 0.2 m. The boattail gets 2((r/R)² − 1), at 0.8 + (0.4/3)(1 + 1/(1 + R/r)) m.
• So κ = 2/ρ² − 1, with ρ = r/R. The margin is given for ρ ≥ 0.6932, an aft radius of 34.66 mm or more.
• The center of mass is at 0.5 m.

With no fins, every one of these rockets is unstable: its center of pressure lies ahead of its center of mass, and C_mα is positive. The cut is not about how large the margin is. The 35 mm and 34.5 mm rows have margins near −11 calibres; what differs is whether the quotient can be trusted.

A component can be a pure couple on its own. A step down in radius followed by a flare back up cancels its own slope and still turns the rocket. C_mα keeps its moment, which a test also checks.

The largest angle of attack

max_angle_of_attack_rad is the largest angle between the rocket’s axis and the air flowing past it, in radians, over the span the envelope’s high-angle flag watches (Validation plan: the operating envelope; ADR-179):

• from more than 1 s after the rail exit, as the first second off the rail is the expected transient in a crosswind;
• to apogee or the first deployment, the span of the least margins above;
• only at instants where a 15° angle would give a normal force of at least a fifth of the rocket’s weight: q (π d²/4) |C_Nα| · 15° ≥ 0.2 m g, with q the dynamic pressure, d the reference diameter and C_Nα the flight margin’s normal-force slope.

The angle is read at each step’s start, middle and end, without the search between them that the peaks have, so an excursion inside one step can be missed. Above 15°, the flight’s envelope_flags include high_angle_of_attack.

The floor is there because near apogee every flight whose path turns over passes 15°, while the air is too weak to turn it: gravity does. Valetudo, one of RocketPy’s examples, launched off an 84° rail in calm air, passes 15° about 0.9 s before apogee, at 16.7 m/s through the air, a little faster than its 16.2 m/s rail exit. There a 15° angle would give a normal force of 1.0% to 1.5% of its weight, so an error in the aerodynamics at that angle barely moves it. A wind layer met at speed is different: Valetudo climbing into 30 m/s of wind 300 m up passes 15° where that force is 62% of its weight, and the flag is raised. On the tests’ RocketPy rockets, turn-overs give 0.7% to 5.0% and wind layers met at speed 62% to 141%; the fifth, chosen rather than measured, sits between. The tests a_tilted_calm_climb_passes_15_degrees_only_with_too_little_force, a_wind_layer_met_at_speed_raises_the_high_angle_flag and a_wind_layer_met_in_a_fast_coast_raises_the_high_angle_flag (in hpr-sim’s metrics.rs) fly these cases.

Unstable under power

A flight that is unstable while a motor burns raises one of two flags, and its apogee is not a prediction (#335). Unstable means the air turns the rocket away from its path instead of back. Where it ends up then depends on small disturbances, and on aerodynamics that hold only at small angles of attack. hpr still flies it, and the flag changes no number: it marks the flight’s path and apogee as not a prediction. A flight raises at most one of the two flags.

• unstable_under_power: the static margin falls below zero while a motor burns. The center of pressure is then ahead of the center of mass.
• unstable_without_margin: where hpr can give no static margin while a motor burns (When there is no margin), the pitching moment’s slope C_mα is above zero. It is raised only when the first flag isn’t.

min_powered_static_margin_cal is the margin the first flag reads. It is the least static margin, in the weakest plane (Stability margins), from the rail exit to apogee or the first deployment, over the moments a motor burns. It is found inside steps, as the other least margins are. A step counts when the thrust at its middle is above zero. hpr ends a step at every ignition, thrust-curve point and burnout, so a motor that burns at a step’s middle burns through all of it, and the margin at the burnout itself counts. A margin of exactly zero raises nothing; any margin below it does.

max_powered_moment_slope_per_rad is what the second flag reads. Where the parts’ normal-force slopes nearly cancel, or their sum is not positive, hpr gives no margin, since the center of pressure would be noise. The moment about the center of mass is still well defined there:

C_mα = −(Σ C_Nα,i x_i − C_Nα x_cg) / d

with C_Nα,i and x_i the normal-force slope and station of part i, C_Nα their sum, x_cg the center of mass, every station aft of the nose tip, and d the reference diameter. A negative C_mα turns the rocket back toward its path; a positive one turns it away. hpr keeps the largest C_mα at each powered step’s start, middle and end where the margin is undefined, without searching between them. A C_mα of exactly zero raises nothing; any above it does. Without this flag, a rocket so unstable that its margin is undefined would raise no warning at all, while a milder one would.

Only the moments under power count. A rocket that turns then is driven along its new heading by its own motor, so the path flown follows the turn. A rocket that is unstable only in the coast, after its motors burn out, raises neither flag: it has no thrust to carry it off its path, and the least static margin over the whole span, min_static_margin_cal, still prints its margin there.

For example, OpenRocket’s example Pods–powered with recovery deployment, flown on [C6-7; B6-0] or [C6-7; 2× A3-4, B6-0], separates at 0.86 s. The sustainer left has a static margin of −4.21 calibres with its C6 still burning. On [C6-7; B6-0]:

static margin         2.05 calibres off the rail; least -4.21 calibres, at 0.86 s, before apogee
apogee                251.3 m above the site at 5.74 s, not a prediction: unstable under power
warning: unstable: the static margin falls to -4.21 calibres at 0.86 s while a motor burns: the rocket is unstable under power, so the air turns it away from its path rather than back, and its apogee is not a prediction

For the second flag, take RocketPy’s Valetudo with its fins taken off and a conical tail that narrows from the body’s 40.45 mm radius to 22 mm over 0.08 m. At the rail exit its net slope is 0.59 per radian against a sum of sizes of 3.41, too small for a margin, but C_mα is +43.9 per radian:

apogee                399.1 m above the site at 8.46 s, not a prediction: unstable under power
warning: unstable: while a motor burns, the pitching moment turns the rocket away from its path (C_mα +43.9 per radian at 0.25 s) where hpr can give no static margin: the rocket is unstable under power, so its apogee is not a prediction

With the tail ending at 30 mm instead, the margin is defined, −34.37 calibres, and the first flag fires in its place. These figures are from a run on 2026-10-06; the test (sim_flags_a_rocket_unstable_where_it_has_no_margin) pins only the flag and a slope above 1.

hpr sim prints the warning: unstable: line and marks the apogee for either flag, and its JSON lists the flag under flags; the library has it in FlightSummary::envelope_flags, and Python in Flight.envelope_flags. When this was written (2026-10-06), none of the 25 public .ork files and 12 validation designs that hpr sim flies offline raised either flag, on their default configurations off an 85° rail in calm air and in 8 m/s of wind. No test or report pins that count.

What it leaves out:

• A rocket unstable only after its motors burn out raises no flag, as above.
• It reads the static margin and C_mα at Mach 0, not at the flight’s Mach number.
• C_mα is read only at each step’s start, middle and end, not searched between: a moment slope above zero for less than half a step, with no margin, can pass unseen.
• A flight that tips over above 15° raises the high-angle flag (The largest angle of attack) as well; a stable rocket in a strong wind can raise that one alone.

The tests the_powered_margin_counts_only_while_a_motor_burns, a_moment_slope_without_a_margin_counts_only_while_a_motor_burns and a_rocket_without_fins_is_unstable_under_power (in hpr-sim’s metrics.rs), and the_stability_flag_starts_just_below_a_zero_margin and the_moment_flag_starts_just_above_zero_and_only_without_the_margin_flag (in envelope.rs) pin it: a margin of −2⁻³⁰ calibres at a burnout raises the flag, +2⁻³⁰ doesn’t, nor does −1 calibre in the coast that follows; with no margin, a C_mα of +2⁻³⁰ per radian under power raises the second flag, −2⁻³⁰ doesn’t, nor does +2⁻³⁰ after the burnout. In hpr-cli, sim_flags_a_rocket_unstable_where_it_has_no_margin flies the Valetudo example above.

Optimum ejection delay

The optimum delay is the time from a motor’s burnout to apogee: the delay that fires its charge at the top. optimum_delays flies the rocket again with every recovery charge held, so that it coasts to the apogee it would reach untouched. So the answer belongs to the rocket, its motors and its air, not to the delay flown. A charge that fires too early cuts the coast short. Loft’s optimum then came out too short as well, which advised an even shorter delay. hpr gives the same optimum for delays of 1 s and 20 s.

• A separation with nothing ahead of it left to burn is part of the recovery, so it is held too. A two-stage rocket that separates some seconds after its last burnout gets the same optimum for a 3 s delay as for a 30 s one.
• A powered separation still happens. The motors in the booster it drops have no optimum: their charges fire in the booster, which never reaches the sustainer’s apogee.
• A motor that burns out after the apogee, or never lights, has none either. A flight that never reaches an apogee (it never lifts off, or hits its time cap) gives None.

Landing points

A landing is where the center of mass came back down to the site’s height. It is given as a WGS 84 latitude and longitude, as east and north meters from the site in its local frame, and as the speed at the ground hit. The flight’s own landing is the stack’s (the whole rocket before any separation), or after a powered separation the sustainer’s. Each separated body that lands has its own landing, with its body number: 0 keeps the nose, and 1 is the stages aft of the split.

A flight that did not land has no landing and no ground-hit speed: None. A test checks this for a flight stopped by its time cap, and the JSON it writes, where the missing values are null.

Tests

In crates/hpr-sim/src/metrics.rs, unless named otherwise:

References

• J. Kiefer, “Sequential minimax search for a maximum”, Proceedings of the American Mathematical Society 4(3), 502–506, 1953. The golden-section search.
• J. S. Barrowman and J. A. Barrowman, “The theoretical prediction of the center of pressure”, NARAM-8 research and development report, 1966. The slopes and stations, as Aerodynamics uses them.
• S. Niskanen, Development of an Open Source model rocket simulation software, MSc thesis, Helsinki University of Technology, 2009, eq. 3.51. A fin’s share of its force in the plane the air crosses in, which makes a one- or two-fin set’s margin depend on that plane.

The decision behind these choices is ADR-077, from the M1.10a milestone.