Glossary

This page defines the terms the other pages use, each in a sentence or two, with a link to the page that models the term or uses it most. Terms are listed alphabetically, and each has its own heading, so any page can link straight to one. Where hpr uses a term in a particular way (a sign, a frame, a reference point), the entry says so. The definitions follow the model pages; if this page and a model page ever disagree, the model page is the authority.

6-DOF (six degrees of freedom)

A simulation that follows all six ways a rigid body can move: its position along three axes and its rotation about three. hpr flies a rocket in 6-DOF from rail exit on. On the rail it has one degree of freedom, along the rail, and under an open parachute it is a point mass whose attitude is frozen. See Rigid-body flight.

Accuracy census

The count of the numbers the validation reports hold hpr to, one row each, kept as it was last accepted. CI fails when a row moves by more than its slack (a small share of the bound it is judged by), changes its standing (pass, within target, not flown and so on), or comes or goes, until the change is accepted with a written reason. It holds a number to where it was, not to the truth. See Accuracy: the census.

Adaptive time step

A time step the integrator (the part that steps the equations forward in time) chooses for itself. It estimates each step’s error, and shrinks or grows the next step to keep that error within a tolerance. hpr’s default method, Dormand–Prince 5(4) at rtol = atol = 1e-8, puts Valetudo’s apogee (one of RocketPy’s example rockets) within 1.1e-6 m of a far tighter run. See Time integration and events.

Added mass

The air a canopy has to push along with it while it speeds up or slows down relative to the air, counted as extra mass that carries no weight; in steady descent it changes nothing. RocketPy includes it in its parachute descent and hpr doesn’t. For NDRT 2020’s main, one of the example rockets, RocketPy’s added mass is 15.9 kg against the rocket’s 20.8 kg, which makes it the likely cause of the largest difference between the two codes’ descents. See Recovery.

AGL (above ground level)

Height above the launch site. A recovery device’s altitude trigger is a height above the launch site, and a flight ends when the center of mass comes back down to the site’s height. See Recovery and Rigid-body flight.

Air start

A motor lit in flight, some time after launch, rather than on the pad. It can be in the same stage as a motor lit at launch: OpenRocket’s Airstart timing example lights a 3-ring of I211W motors 1, 2, 4 or 6 s after launch (and, in one configuration, at launch), beside a K550W lit at launch. In hpr each motor has an ignition: at launch, at a time, a delay after another motor’s burnout, or a delay after its stage separates. A .ork file’s ignitions are read into these (.ork design files), and each flight of OpenRocket’s air-start example is within 5% of OpenRocket’s apogee and largest speed (M1.9c, a two-stage and a cluster design against OpenRocket). See Staging.

Angle of attack

The angle between the rocket’s axis and the airflow it meets. In hpr it is the total angle α between the body axis, pointing to the nose, and the rocket’s velocity relative to the air, from 0 to π (180°). hpr’s aerodynamics are small-angle models, so results at large angles, off the rail in a strong crosswind and near apogee, are the least trustworthy. See Frames and Aerodynamics.

API reference

The documentation of hpr-sim’s code: every public type, function and constant, generated from the source by rustdoc, Rust’s documentation tool. It is part of this site, and on GitHub it has to be built; see The API reference.

Apogee

The highest point of a flight, where the rocket stops climbing. hpr finds it as the moment the center of mass’s rate of climb above the WGS 84 ellipsoid falls through zero. It does not use the launch frame’s up axis, whose flat plane rises above the curved Earth with distance (7.8 m at 10 km). See Rigid-body flight.

Average thrust

A motor’s total impulse divided by its burn time, in newtons (N), as ThrustCurve.org defines it. It is the number in a motor designation. See Solid motors.

Barometric altimeter

A flight computer that finds its height from the air pressure it measures. It converts the pressure to an altitude with the standard atmosphere and subtracts the pad’s. The air of the day is rarely standard: on a hot day a column of air is taller, pressure falls more slowly with height, and the altimeter reads less than the height climbed, 6.5% on a day 20 K warmer than the standard (worked example). On a cold day it reads more. hpr reads its own flight the same way when it compares with a log; see Accuracy: real flights.

Barrowman’s method

J. S. Barrowman’s 1966–67 method for the normal-force slope and center of pressure of a slender finned rocket: each nose, transition and fin set is worked out on its own, and the results are summed. hpr follows it, with extensions from Niskanen’s 2009 thesis. Four of Barrowman’s five printed examples agree within 1%, and the six-fin Recruiter’s slope is 2.87% high. See Aerodynamics.

Base drag

The drag on a rocket’s flat aft end, its base. hpr works it out on the base’s area, with a coefficient of 0.12 + 0.13 M² below Mach 1 and 0.25/M above it (M the Mach number). While a motor burns, hpr subtracts the burning motors’ cross-section from that area (power-on drag), following Niskanen, who takes from Fleeman that a base the size of the motor has no base drag. OpenRocket keeps the whole base’s drag, and hpr can fly that rule for a comparison (Aerodynamics). Neither rule has been checked against a measured flight. On one private design’s supersonic flight, C06/1, the choice moves hpr’s apogee difference from OpenRocket’s by about 24 percentage points, more than any other known cause (#222). Behind a boattail, faster than sound, the base’s pressure is higher and hpr lowers the base drag to match (Boattails faster than sound). See Aerodynamics.

BATES grain

A cylindrical propellant grain with a hole along its axis (the bore), which burns on the bore and, unless inhibited, on both ends. hpr can place a motor’s propellant as a stack of identical BATES grains, which sets how its center of mass and inertia change as it burns. See Solid motors.

Bearing

A direction on the ground, measured clockwise from true north: 0° is north, 90° east, 180° south and 270° west. Getting started gives the landing point as a distance and a bearing from the pad. A wind direction is a bearing too: the one the wind blows from. A compass gives a magnetic bearing; add the declination to make it true.

Boattail

A transition at the tail that narrows toward the aft end. Its normal-force slope is negative, so it moves the center of pressure forward. Below Mach 0.8 hpr counts its pressure drag as a share of the base drag on the area it removes: all of it for a short, steep boattail and none for a long, gentle one. Faster than sound a boattail has its own wave drag, which hpr takes from a handbook chart that matches measured boattails of 3° to 10° within about a quarter, and reads high for steeper ones. See Boattails faster than sound.

Body frame

The axes fixed to the rocket. The origin is the nose tip, on the axis. z_B points along the axis toward the nose, x_B is the design’s zero direction around the body (the one fins and rail buttons are placed from), and y_B completes a right-handed set, so every part lies at z_B ≤ 0. See Frames.

Body lift

A sideways force on the body itself, not the fins, when the rocket flies at an angle to the airflow. It grows with the square of the sine of the angle of attack, so it is nothing at small angles and large at steep ones, such as a slow rocket leaving the rail into a crosswind. hpr sizes it by Jorgensen’s crossflow drag, which depends on the body’s length over its diameter and on how fast the air crosses it; before M1.8e6 it used Galejs’s constant. RocketPy leaves it out. See Aerodynamics.

Booster

The aft part of a staged rocket: the stages behind the separation, whose motor lights first and which are dropped when the stack separates. After a powered separation hpr flies it as a point mass under its own recovery devices, one of which must be open from the separation: hpr sim tumbles it from the split until its own parachute opens. Its motors must have burned out by then. See Staging. Boosters can also be strapped beside the core instead of behind it, a parallel stage.

Boundary layer

The thin layer of air next to the rocket’s skin, slowed by friction with it. It grows thicker toward the tail: on a model rocket a meter long it can be a centimeter or more thick at the base. Skin friction comes from it, and where it is thick it softens what the outer flow does, such as the expansion around a boattail. hpr takes it as turbulent everywhere. See Aerodynamics.

Burn time

How long a motor burns, by the NFPA 1125 rule that ThrustCurve.org uses: from the moment the thrust first reaches 5% of its peak to the moment it last falls to 5% of its peak, in seconds. It is not the time of the thrust curve’s last point, which is burnout. See Solid motors.

Burnout

The moment a motor stops producing thrust. In hpr it is the time of the thrust curve’s last point: from then on the thrust, the propellant flow and the propellant left are all zero. A flight records a burnout event and steps exactly to it, because the equations change there. See Solid motors.

Calibre (caliber)

A length measured in body diameters. A stability margin is usually quoted in calibres, and a nose cone three calibres long is three times as long as its base diameter. See Shapes.

Canard

A fin set near the nose, ahead of the main fins. Its normal force acts well forward, so it moves the center of pressure forward, and as speed rises its slope grows too. See Aerodynamics.

Cant

The small angle at which fins are set to the rocket’s axis, turning each about its own span so that the air pushes it sideways and the rocket spins. hpr measures it in radians, positive turning fin 0’s leading edge (fin 0 is the one along +x_B) toward −y_B (Body frame); a positive cant spins the rocket clockwise seen from ahead of the nose, looking aft. See Roll: forcing and damping.

Center of dry mass

The center of mass of the rocket with its motor’s propellant gone: the empty rocket, motor casing included. It does not move during the flight, so RocketPy follows this point, and the comparisons with RocketPy measure speeds and drifts there. The center of gravity of the loaded rocket lies aft of it while the motor burns. See Accuracy.

Center of gravity (CG)

The point where the rocket’s mass balances. The model pages call it the center of mass, which in uniform gravity is the same point. It moves as the propellant burns, and hpr recomputes it at every instant from the parts and the motors. See The design tree and Mass properties.

Center of pressure (CP)

The point along the rocket where the normal force acts, given as a station aft of the nose tip. hpr finds it by averaging each component’s own center of pressure, weighted by its normal-force slope, at small angles of attack. A rocket is statically stable when its CP is behind its center of gravity. See Aerodynamics.

CIPM-2007

The formula for the density of moist air, from its temperature, pressure and humidity, that the International Committee for Weights and Measures (CIPM) adopted in 2007. hpr’s humid-air density is checked against it, within 0.047% over 15 to 27 °C. See Atmosphere.

Closed form

An answer written as an exact formula, such as the parabola a body follows in a vacuum, rather than one computed step by step. hpr’s analytic tests compare the code with closed forms, the first of the four kinds of evidence on Accuracy.

Cluster

Several motors in one rocket, burning side by side: in one mount of several like tubes (an OpenRocket 3-ring, say), or each in its own mount. hpr lights each motor at its own ignition (at launch unless told otherwise). It sums their thrusts and masses, and adds the turning moment of any motor set off the axis, as when one motor of a cluster fails to light (a “motor out”). Tests check this against hand calculations, and OpenRocket’s cluster example, read from its .ork file with a motor in every tube, flies within 5% of OpenRocket’s apogee and largest speed. Three of its apogees are compared with OpenRocket’s flight with no parachute, since its parachute opened before apogee (M1.9c, a two-stage and a cluster design against OpenRocket). See Clusters.

CMA-ES

The covariance matrix adaptation evolution strategy, N. Hansen’s optimization method. It samples designs from a cloud (a normal distribution), moves the cloud toward the better ones, and learns from them which way and how far to step next. It needs only the order of the results, not their slopes. See Optimization.

Code-to-code comparison

Flying the same rocket, or the same part of a flight, in hpr and in another simulator from the same inputs, and comparing the numbers. It is the third of four kinds of evidence, and it shows that two codes agree, not that either matches a real flight. hpr’s parachute descents match RocketPy’s within 3% on all 30 numbers compared; whole flights come next. See Recovery.

Configuration

One choice of motors for a rocket design, at most one in each motor mount, named by an id such as h54. A design can hold several, such as the same rocket on different motors, and a flight names the one it flies. Each motor lights at launch unless its ignition says otherwise (Staging). See Your own rocket and The design tree.

Coriolis acceleration

The sideways acceleration that anything moving over the rotating Earth appears to have, −2Ω × v, with Ω the Earth’s rotation (7.292115e-5 rad/s) and v the velocity in the Earth-fixed launch frame. It is the only rotating-Earth term hpr adds, since the centrifugal part is already inside normal gravity, and it is on by default. It is small: in one test it moves the landing point of a 3 km parachute descent 0.37 m east. See Gravity.

COTS motor

A commercial off-the-shelf motor: a solid rocket motor bought from a manufacturer, single-use or as a reload for a reusable case. hpr-sim covers only these for now, and bundles 32 of their thrust curves, listed under The bundled motors. See Solid motors and Start here.

Covariance

How two quantities vary together: positive when both tend to be high together, negative when one tends to be high while the other is low, zero when neither says anything about the other. For distances on the ground it is in square meters (m²). A spread of points on the ground has three numbers: the variance east (the square of the standard deviation), the variance north, and their covariance. Together they give the shape and the turn of a landing ellipse. See Monte Carlo dispersion.

Crate

A Rust package: the unit that Rust code is built, versioned and shared in. hpr-sim is split into crates, such as hpr-core for the maths and the Earth and hpr-sim for the flight, so a program takes only the ones it needs. See The API reference.

CRS (coordinate reference system)

The definition that turns a file’s coordinates into places on Earth: an ellipsoid and its datum (where the ellipsoid sits), and either latitude and longitude or a map projection such as UTM. Most have an EPSG code. hpr’s elevation-file reader takes latitude and longitude on a datum within a few meters of WGS 84. See A launch site’s elevation.

Decision record (ADR)

A short record of a significant choice, the alternatives considered and why one was picked, labelled like ADR-011 (the rigid-body flight decision). All of them are in the decision log. See Decisions and the roadmap.

Declination (magnetic)

The angle from true north to the north a compass shows, positive when magnetic north lies east of true north. A compass bearing becomes a true one by adding it: at Spaceport America in 2026 it is about +7.75°. hpr computes it from the World Magnetic Model. See The magnetic field.

DEM (digital elevation model)

A grid of ground heights, one per cell, such as the US Geological Survey’s (USGS) 1-arc-second map of the United States, whose cells are about 30 m across. Most are published as GeoTIFF files. See A launch site’s elevation.

Deployment

The moment a recovery device, such as a parachute, comes out to its full line length (line stretch) and starts to fill. In hpr it follows the device’s trigger (apogee, a height above the ground, a time, or a motor’s ejection delay) after a set lag. The flight’s first deployment switches the rocket to the descent, as a point mass. See Recovery.

Descent rate

How fast a rocket falls under its recovery device, in m/s. Once drag balances weight it settles at the equilibrium descent speed v_e = √(2 m g / (ρ C_D S)), with m the mass, g gravity, ρ the air density and C_D S the drag area. A 1.1 kg rocket under a 1 m flat canopy with C_D 0.8, in air of 1.225 kg/m³, falls at 5.294 m/s. See Recovery.

Design file

A rocket design saved as text, so it can be kept, shared and read back. hpr’s own is the .hpr design format: one JSON document with a versioned header, the rocket, its motor configurations, recovery and stored simulations. A .hprz is the same document in a zip archive, with other files beside it, such as flight logs. hpr sim flies both, and hpr convert writes them from a .ork. The rocket inside it is the JSON of hpr’s Rocket type, which hpr sim also reads on its own: each key is a Rust field’s name, with its unit in the name (length_m), and a mounted motor is written out in full, thrust curve included. The format is version 0.2, a draft until hpr’s first release; an older document is migrated when it is read, but keep the source file too. See Your own rocket.

Digest

OpenRocket’s fingerprint (a hash) of a motor’s thrust-curve data. A .ork file records it for each motor, and OpenRocket uses it to find that curve in the motor database it ships. hpr uses it to find a curve the file embeds, or one a caller supplies. Two different motors can, rarely, share a digest. See the .ork format.

Dispersion

The uncertainty given to one input of a Monte Carlo run, as a standard deviation: how far the rocket’s mass, its motor’s impulse or the wind’s speed may differ from the plan from one flight to the next. See Monte Carlo dispersion.

Dormand–Prince and RK4

Two ways of stepping the equations of motion through time. Dormand–Prince 5(4), also called DOPRI5, makes two estimates on each step and shrinks or grows the step to keep their difference under a tolerance; it is hpr’s default. RK4, the classic fourth-order Runge–Kutta method, takes steps of a fixed size. See Time integration.

Drag area

A recovery device’s drag coefficient times the area that coefficient is measured on, C_D S, in m². The drag force is the dynamic pressure times it. hpr takes it directly (RocketPy’s cd_s) or from a canopy’s diameter and its coefficient on the nominal area, and adds up the drag areas of every open device. See Recovery.

Drag coefficient

Drag divided by dynamic pressure and an area: a number without units that says how draggy a shape is. For the rocket, C_D0 is the coefficient at zero angle of attack on the reference area, built up from skin friction, pressure, base and fin terms, or read from a table instead. For a parachute, Knacke’s C_D0 is on the canopy’s nominal area, a different convention. See Aerodynamics and Recovery.

Drag crisis

A sudden fall in a blunt body’s drag coefficient over a narrow range of Reynolds number, as the flow along its surface turns turbulent and stays attached further round. For a cylinder lying across the flow it comes at a Reynolds number of a few hundred thousand. For streamers, Carruthers and Filippone report a sudden drop near 7.2e5, which they put down to a change in how the streamer oscillates. hpr’s recovery models include none. See Recovery.

Drift

How far the wind carries a rocket sideways while it descends, in meters. In the comparison with RocketPy it is the horizontal distance from where the descent starts to the landing point, with an east and a north part. In still air a small drift remains from the Coriolis acceleration: 0.19 m for Valetudo’s descent. See Recovery.

Drogue and main

The two parachutes of a dual-deployment recovery. The small drogue opens at or near apogee, so the rocket falls fast but steadily; the large main opens lower down for a slow landing, and in hpr it can release (cut away) the drogue once it is fully open. RocketPy’s Calisto example flies a drogue of 1.0 m² drag area and a 10 m² main that opens at 800 m. See Recovery.

Dynamic pressure

The pressure of the oncoming air due to its motion, q = ½ ρ V², with ρ the air density and V the airspeed, in pascals (Pa). Every aerodynamic force is q times a reference area times a coefficient, so forces grow with the square of airspeed. Near apogee, where the rocket is slow, q is small. See Frames and Rigid-body flight.

ECEF (Earth-centered, Earth-fixed)

The x, y, z frame that turns with the Earth. Its origin is the Earth’s center of mass, +Z points along the rotation axis to the north pole, +X through the prime meridian at the equator, and +Y to 90° E. hpr converts between it and latitude, longitude and height on the WGS 84 ellipsoid. See Frames and Geodesy.

Effective exhaust velocity

A motor’s thrust divided by its propellant mass flow, c = F/ṁ, in m/s. hpr holds it constant through the burn, c = I/m_p (total impulse over propellant mass), so propellant burns in proportion to the impulse delivered. It also refuses a motor whose c falls outside 200 to 5,000 m/s, which catches a propellant mass given in the wrong unit, such as grams for kilograms; ThrustCurve.org’s catalog has a median of 1,867 m/s. See Solid motors.

Ejection

A piece of the airframe leaving the rest on a trigger, at a joint you choose rather than only at a stage boundary: a nose cone pushed off its airframe, a body section, or a payload carried inside. Each piece then comes down on its own under its own recovery device. Pieces tied together by a shock cord fly as one, so they are not an ejection. Compare separation, which parts the rocket at a stage boundary. In hobby use “ejection” often means the charge firing; in hpr that is a recovery device’s trigger (see ejection delay), and the charge’s push on the pieces can be given to the ejection as an impulse in newton-seconds. See Recovery: ejected pieces.

Ejection delay

The time from a motor’s burnout to its ejection charge, in seconds. Motor files list the delays available; P means plugged, with no ejection charge, and hpr reads a 0 as “zero or plugged” rather than as ejection at burnout, because most files mean plugged. A .ork design says none for plugged, so its 0 is a charge at burnout (.ork files). A recovery device can use a motor’s delay as its trigger. See Solid motors and Recovery.

Elementary effect

In Morris’s screening, the change in a result when one input steps part of its range with the others held, scaled to the input’s whole range. The mean of their sizes, μ*, ranks the inputs. See Sensitivity analysis.

Ellipsoidal height

Height above the WGS 84 ellipsoid, measured along the ellipsoid’s normal, in meters. It is hpr’s internal height, and it is not height above sea level: the two differ by up to about 100 m. See Frames.

EPSG code

A number naming a CRS, a datum or a unit in the EPSG Geodetic Parameter Dataset, which most mapping software shares: 4326 is latitude and longitude on WGS 84, 4269 on NAD83, 5703 heights above NAVD88 in meters, 9001 the meter. See A launch site’s elevation.

ERA5

The European Centre for Medium-Range Weather Forecasts’ reanalysis of the whole Earth’s weather, every hour since 1940 on a grid a quarter of a degree apart, from the Copernicus Climate Data Store. Its pressure-level files give the temperature, wind and geopotential height at each pressure level. See ERA5 weather files.

Event

A moment the simulator locates exactly and records, such as liftoff, rail exit, burnout, apogee and ground hit, and in recovery a trigger, a deployment, a release or a separation. The integrator finds each as the zero of a function of the state, adding at most about 2e-12 s of error to the solution’s own, and stops there so the flight can change phase. See Time integration and events and Rigid-body flight.

Example rockets

The rockets hpr is compared on. Calisto, Valetudo, NDRT 2020, Prometheus, Juno III, Cavour and Bella Lui come from RocketPy’s own examples; their designs, as hpr reads them, are in the repository’s validation/designs/ folder. The Recruiter and Barrowman’s other rockets are worked examples from his papers, with their printed values in barrowman-worked-examples.json. See Accuracy.

Fillet

A fin fillet: the rounded glue joint along a fin’s root, filling the corner between the fin and the body tube on each side. Its face is a circle of the fillet’s radius. hpr weighs fillets as OpenRocket does, as a prism of that corner’s section along the root chord, in their own material. The aerodynamics leaves them out. See Mass properties.

Fineness ratio

A nose cone’s length divided by its base diameter. A 3:1 tangent ogive has a fineness ratio of 3, which the pages also write as “fineness 3”. For a shoulder, a transition that widens toward the tail, the drag pages use its length over its rise in diameter, so a conical shoulder has the fineness of the cone with the same surface angle. See Aerodynamics.

Flare

A transition that widens toward the aft end, the opposite of a boattail: a conical skirt at the tail, or the step up onto a wider aft section. Its normal-force slope is positive, so it moves the center of pressure aft, which is why one is sometimes added for stability. Faster than sound, hpr marches a conical flare through the shock-expansion method while the shock at its corner stays attached, and reads a steeper one as a flare of the same radii drawn out to that angle. What that is worth against the one measured flare in the sources is What a marched flare is worth; how the model works is A flare through the method. Where the march itself stops, which is not where that shock detaches, is in Where a flare’s march stops. A flare shallow enough that its element is reduced is read by the older generalized method instead: A near-flat flare.

Flow separation

Air leaving a surface it can’t follow, such as the aft end of a steep boattail, and leaving a slow, recirculating region behind it. There the pressure is about the base’s, not what the attached flow would give. hpr blends a boattail’s drag toward that value between 16° and 30°, where measured boattails separate. Not the same as a separation of stages or recovery bodies. See Boattails faster than sound.

Flight log

The record an altimeter or flight computer writes during a flight: a row per sample, each with its time and what the logger measured then, such as its altitude. Its format is the logger maker’s. hpr analyze reads one and prints what it says, with no design file (Reading a flight log).

Flutter

A fin shaking itself apart: above a certain speed, the air’s push twists the fin, the twist changes the push, and the fin’s bending and twisting feed each other instead of dying out. How fast that happens depends on the fin’s outline and thickness, its shear modulus and the air. hpr screens for it with NACA TN 4197’s criterion. See Fin flutter.

Forebody

Everything of a rocket but its flat aft end, the base: the nose, the body tube, the fins and any boattail. A wind-tunnel model sits on a sting that disturbs the air behind its base, so tunnel reports often give the forebody’s drag alone, as NASA’s Arcas Robin reports do, and hpr is compared with them on its drag without the base drag. See Aerodynamics.

Forecast run (cycle)

One start of a weather model: it begins from the weather observed at one hour, the run’s cycle, and steps forward. Each forecast hour is the forecast for that many hours after the cycle. NOAA’s GFS starts a run every 6 hours and its RAP every hour. See NOAA forecasts: GFS and RAP.

Gate and target

Two ways a validation result is held to a bound. A gate fails the test suite when a number falls outside it, so a change that breaks agreement cannot merge. A target is the same kind of bound, but a miss is only reported, with its explanation in the case file, and never fails the suite: it is used where neither side of the comparison is known to be right, as for hpr’s own drag against the drag RocketPy’s examples ship. Either way the report is committed, so any number that moves shows up in review. See Accuracy. Separately from both, the accuracy census fails CI when any number it counts moves, whether or not it is inside its gate or target.

Geodesic

The shortest path between two places on the WGS 84 ellipsoid: the true distance between them over ground that curves. Its length is the distance, and its direction where it leaves is the bearing to the second place. hpr’s flight output still measures the landing on a flat map round the pad. See Geodesy.

Geodetic latitude

Latitude as maps and GPS give it: the angle between the equator’s plane and the WGS 84 ellipsoid’s normal through the point, positive north. Gravity depends on it: at the surface it runs from 9.780 m/s² at the equator to 9.832 m/s² at the poles. See Frames and Gravity.

Geopotential height

A height measured by the work done lifting a unit of mass against gravity, divided by standard gravity g₀ = 9.80665 m/s², in geopotential meters. Weather data give heights this way. Where gravity is stronger than g₀, a geopotential meter is a little shorter than a meter; hpr turns it into height above sea level with the site’s own gravity. See Atmosphere and ERA5 weather files.

GeoTIFF

A TIFF image whose tags say where on Earth its pixels lie (the OGC GeoTIFF Standard 1.1). In a DEM each pixel is a height. See A launch site’s elevation.

GRIB2

GRIdded Binary, edition 2: the World Meteorological Organization’s binary format for weather on a grid (WMO-No. 306, code FM 92). A file is a run of messages, each holding one variable on one level over the grid, with the values packed as whole numbers and a formula to turn them back. See NOAA forecasts: GFS and RAP.

Grid point

A place where a weather model gives its values. Between grid points hpr blends the four around a site, weighting each more as the site nears it (bilinear interpolation). See NOAA forecasts: GFS and RAP.

Height above sea level (MSL)

Height above mean sea level, as field elevations and soundings give it. hpr queries the atmosphere and the wind with it, and gets it from ellipsoidal height by subtracting the geoid undulation N, the height of sea level above the ellipsoid (up to about 100 m). hpr has no geoid model, so a flight takes N at the site as an input. See Atmosphere and Frames.

Hypsometric equation

How thick a layer of air is between two pressures: the geopotential thickness is (R_d T̄_v / g₀) ln(p_bottom / p_top), with p_bottom and p_top the pressures at its bottom and top, R_d dry air’s gas constant (287.05 J/(kg·K)), g₀ standard gravity and T̄_v the layer’s mean virtual temperature (WMO-No. 8, the Guide to Instruments and Methods of Observation, eqs. 12.17 and 12.18). Warm air makes a thicker layer. hpr checks each row of a weather-balloon sounding against it; see Weather-balloon soundings.

Impulse class

The letter that ranks a motor by its total impulse, also called its motor class. Class C covers 5.01 to 10.0 N·s, each letter after it doubles the top of the range, and the upper limits are inclusive. See Solid motors.

Inflation and filling time

How a parachute opens: from deployment, its drag area grows over the filling time t_f to its full value. hpr can open it at once (RocketPy’s model), over a fixed time, or over Knacke’s t_f = n D₀/v, with n the canopy’s fill constant, D₀ its nominal diameter and v the airspeed. hpr leaves out the drag’s overshoot as a canopy fills, and opening at once it ignores how a light rocket slows while the canopy fills, so the opening load it reports is no safe bound either way. See Recovery.

Internal momentum

The momentum of the propellant and gas moving inside a burning motor. A thrust curve measured on a test stand already includes its effect. hpr’s equations of motion, like RocketPy’s, add it again, so it is counted twice; hpr keeps it that way so the two codes can be compared like for like. On Valetudo it adds 21 N to the push at liftoff and changes the burnout speed by at most 0.05 m/s. See Rigid-body flight.

Jet damping

The damping of a rocket’s turning by its own exhaust: gas leaving the nozzle carries away some of the rocket’s rotation. hpr includes it through RocketPy’s equations of motion, so it acts only while a motor burns. See Rigid-body flight.

Lambert conformal projection

A map made by wrapping a cone around the Earth, touching it along one latitude, and unrolling it flat. It keeps shapes true locally, so weather models over the mid-latitudes use it for their grids. Its “up” points true north along one line of longitude only, so winds given along the map must be turned to east and north. See NOAA forecasts: GFS and RAP.

Landing ellipse

An ellipse on the ground drawn around the landings of a Monte Carlo run so that it holds a chosen share of them, its level: a 95% ellipse holds about 19 landings in 20. It is centered on their mean, its axes lie along the directions the landings spread most and least, and its size comes from the normal distribution. It is used to judge how likely a rocket is to come down inside a field. See Monte Carlo dispersion.

Launch frame (ENU)

The frame fixed at the launch pad, which the flight’s position and velocity are kept in: x_L east, y_L north and z_L up along the ellipsoid’s normal at the pad, hence East-North-Up (ENU). It turns with the Earth, so the equations add the Coriolis acceleration. It is a flat plane, so z_L is not altitude: 10 km from the pad the plane is 7.8 m above the ellipsoid. See Frames.

Liftoff

The moment the rocket starts to move up the rail: the push up the rail, mostly the thrust, first beats the weight’s pull down it and the rail’s friction. The motor ignites a little earlier, at time zero. If the motors burn out first, the flight ends on the pad. See Rigid-body flight.

Loft lesson

A mistake found in Loft, the project that came before hpr-sim, such as Loft lesson L15 (a shoulder’s drag as its length goes to zero). A test here guards against each one, or will once its milestone ships. See Start here and Lessons from Loft.

Lip

A short flare at the very base of a rocket, rising from the end of a boattail or a step down: the Arcas Robin wind-tunnel models end in one, and a motor retainer ring is another. Sitting in the wake of what narrows ahead of it, a lip sees slow, turned air, so hpr takes its drag away there and gives it no normal force faster than sound. See Aerodynamics.

Mach cone

Faster than sound, a disturbance, such as a fin’s tip, can only affect the air downstream of it inside a cone that opens backward at the Mach angle, atan(1/√(M² − 1)): 30° at Mach 2. hpr halves the fin’s lift inside the cone from each tip. See Aerodynamics.

Mach number

Airspeed divided by the local speed of sound, which the atmosphere gives from the air’s temperature. hpr’s normal force and drag both cover Mach 0 to 5, and a flight that reaches Mach 5 stops with an error. Both were checked against a wind tunnel from Mach 0.6 to 4.63, where the drag reads high at most speeds; the drag was also checked at Mach 0.3 against other programs’ curves. See Aerodynamics and Aerodynamics.

Mean aerodynamic chord (MAC)

An average of a fin’s chords (its lengths along the airflow, root to tip), weighted so that the long chords count more: c̄ = (1/A)∫c² dy over the span, A being one fin’s area. hpr puts each fin set’s center of pressure a quarter of the way back along it up to Mach 0.8, and moves it aft from there to the center of the load supersonic linear theory gives. See Aerodynamics.

Metric

One number a validation case compares between hpr and its reference, such as the descent time or the drift to the north. Each metric has its own tolerance, also called its gate. See Accuracy.

MIL-HDBK-762

Design of Aerodynamically Stabilized Free Rockets, a 1990 U.S. Army handbook for designing unguided rockets, and a U.S. Government work. hpr takes its fin-count factor from it, and compares its drag with the handbook’s worked example, a rocket whose drag it calculates term by term from Mach 0.5 to 3.2. That is a calculation by the handbook’s methods, not a measurement. See Aerodynamics.

Milestone

A step of the roadmap, the ordered plan of work, labelled like M1.8 (transonic and supersonic aerodynamics). The pages link a milestone where they say what it will add. See Decisions and the roadmap.

Monte Carlo

Flying the same rocket many times, each time with its uncertain inputs drawn at random, to see how far the results spread: the apogee, the landing. Named after the casino, for the random draws. See Monte Carlo dispersion.

Motor designation

A motor’s name, such as F32 or L1150R: the impulse class letter, then the average thrust in newtons. Makers add their own codes around it, such as a propellant letter (the R of L1150R), the total impulse in N·s in front (411I175) or a delay after a dash. A RASP .eng file’s name field is meant to hold only the class and average thrust, but often holds the full designation. See RASP .eng files.

netCDF

A file format for gridded data, such as weather over a map at several heights and times, from Unidata. hpr reads its two classic kinds; the newer netCDF-4 kind is HDF5 inside and is converted first. See ERA5 weather files.

Newtonian theory

A simple rule for the pressure on the front of a body in fast flow: the air hits the surface and loses the speed it had toward it, so the pressure rises with the square of the sine of the angle between the surface and the wind, C_p = C_p,max sin²δ. C_p,max is the pressure coefficient at the nose’s stagnation point, where the air comes to rest behind a normal shock. It suits the steep, blunt front of a body better than its shallow sides. hpr uses it on the cap of a blunt or vertical nose tip faster than sound, ahead of the shock-expansion method. See Aerodynamics.

NFPA 1125

The US National Fire Protection Association’s code for making model and high-power rocket motors. ThrustCurve.org measures a motor’s burn time by its rule: from the moment the thrust first reaches 5% of its peak to the moment it last falls to 5%. hpr does the same. See Solid motors.

Nominal area

A parachute canopy’s reference area, S₀ = π D₀²/4, from its nominal diameter D₀; it includes the vent and every other opening. Knacke’s canopy drag coefficients, which hpr uses, are on this area: 0.75 to 0.80 for a flat circular canopy, whose middle, 0.775, is hpr’s default. RocketPy’s default parachute coefficient of 1.4 is on a different area, so the two can’t be compared directly. See Recovery.

Normal distribution

The bell-shaped spread of a quantity that is the sum of many small, independent effects, described by its mean and its standard deviation. A standard normal number has mean 0 and standard deviation 1; hpr’s Monte Carlo runs scatter each uncertain input by a standard deviation times such a number. Not to be confused with the normal force. See Monte Carlo dispersion.

Normal force

The sideways aerodynamic force on a rocket flying at an angle of attack, square to its axis and in the plane of the airflow. It acts at the center of pressure, and its coefficient C_N is positive in the direction the crossing air pushes the body. It is what makes a stable rocket weathercock. See Aerodynamics and Frames.

Normal gravity

The gravity of a smooth, spinning model Earth: the pull of the WGS 84 ellipsoid plus the centrifugal effect of the Earth’s rotation, which changes with latitude and height. By default hpr applies the full normal-gravity vector at the rocket’s position, leaving out the real Earth’s local anomalies, typically within ±1e-4 of it. The standard gravity 9.80665 m/s² is a unit convention, not a model of local gravity. See Gravity.

Normal-force slope

How fast the normal force coefficient grows with angle of attack at small angles, C_Nα, per radian. Each nose, transition and fin set has its own, and the rocket’s is their sum; a pointed nose cone’s is 2. The center of pressure is the components’ positions averaged with these slopes as weights. See Aerodynamics.

NSGA-II

The non-dominated sorting genetic algorithm II, K. Deb and co-authors’ optimization method for several goals at once. It breeds a population of designs, sorts parents and children into fronts by which designs beat which, and keeps the best half, spread out along the front. It finds a Pareto front rather than one design. See Trade-offs.

Octave band

A range of frequencies, or of wavelengths, whose top is twice its bottom. The turbulence test splits the gust spectrum into octave bands and checks each against the Dryden formula. See Turbulence.

Opening load

The peak force a parachute puts on the rocket as it opens. Knacke writes it as F = (C_D S) q C_x X1: the steady drag at the dynamic pressure q at line stretch, times C_x for the canopy’s overshoot when the load doesn’t slow (1.7 for a flat circular canopy), times X1 for how much the rocket slows while the canopy fills. hpr leaves out the overshoot. With a filling time it already includes the slowing, so X1 must not be applied on top; a canopy that opens at once has none. So the opening load it reports is no safe bound either way: don’t size recovery hardware from it. See Recovery.

OpenRocket

A widely used open-source rocket design and simulation program. hpr may run it as an external program to compare results, but never reads or copies its source code, whose license (GPL) is incompatible with hpr’s. The comparison with it is M2.2, the OpenRocket milestone: its mass comparison is done (M2.2a), and flights come in M2.2d.

Optimization

Searching for the design that makes a chosen number as small (or as large) as it can be: the squared miss from a target apogee, say. hpr’s optimizer is CMA-ES. See Optimization.

Oracle

An independent program run to produce reference values for hpr’s tests. Usually it is another simulator: RocketPy 1.13.0, and OpenRocket 24.12, so far for mass, flights, and the reading of .ork design files and .orc parts catalogs. Scripts that evaluate a published formula in high precision, ThrustCurve.org’s own statistics code, and GDAL (through rasterio) for elevation files, serve as oracles too; all of them live under validation/oracles/. See Recovery and the list of simulator oracles.

Override

A measured mass, center of mass or inertia that replaces the value hpr computes, for one part, a part with everything attached to it, or a whole stage. Motors are never covered by one. See The design tree.

A part or a stage can also state its own drag coefficient, in place of the drag its shape gives, as OpenRocket’s Override tab does. See A part’s stated drag coefficient.

Aerodynamic override tables are separate: another program’s drag, or its normal force and center of pressure, flown in place of hpr’s own. See Aerodynamics.

Parallel stage

A stage strapped beside the rocket instead of stacked behind it, such as a set of boosters around a sustainer: copies placed around a body tube, like pods, that burn with the core and drop at a separation of their own. OpenRocket calls it a parallel stage or booster set. See The design tree: Parallel stages and Staging: Boosters beside the core.

Parallel-axis theorem

The rule for moving a moment of inertia from an axis through a part’s own center of mass to a parallel axis: add the part’s mass times the square of the perpendicular distance between the two axes. A part on the rocket’s center line adds nothing to the roll inertia this way, only to pitch and yaw. hpr uses its tensor form to add up the inertias of a rocket’s parts. See Mass properties.

Pareto front

The designs that trade two or more goals off against each other: no design on the front can improve one goal without giving up some of another. A design dominates another when it is no worse in any goal and better in at least one; the front is the designs nothing dominates. Higher apogee against a larger stability margin is one such trade-off. See Trade-offs.

Parquet data page

A Parquet file stores a table column by column, and each column in pieces called data pages, each with a small header saying how many values it holds and how they are stored. A reader decodes a page at a time. hpr-sim’s pages hold up to 1024 numbers of 8 bytes each: 8 KiB, the page size the format’s specification recommends. See Exporting a flight.

Percentile

The value below which a given share of a sample falls: the 5th percentile of 200 apogees is the height that about 10 of them didn’t reach. The 50th is the median. hpr computes them by linear interpolation between the sorted values (Hyndman and Fan’s definition 7, as R and NumPy do). See Monte Carlo dispersion.

Pod

A body mounted beside the airframe rather than on its axis: a side pod, or an outboard pod that holds a motor. hpr repeats one pod, and everything in it, evenly around the axis, turning each copy with its pod as a fin set’s fins turn, and weighs each copy where it sits, so the pods’ inertia is mostly the parallel-axis term. Each pod’s parts fly with their own normal force and drag, once per pod, without the pods’ and the body’s effect on each other’s flow (aerodynamics: Pods). See Pods.

Power-on and power-off drag

Drag while a motor burns, and while the rocket coasts. Under power, hpr subtracts the burning motors’ cross-section from the base area, as Niskanen does (a rule no measurement has checked; see base drag), and a drag table can carry separate power-on and power-off curves. A flight uses power-on drag while any motor burns. OpenRocket 24.12 keeps the whole base under power; with_full_base_drag_under_power flies its rule, for comparisons with OpenRocket. See Aerodynamics.

Prandtl–Meyer expansion

What happens to a flow faster than sound when its path turns away from itself, as around the shoulder of a boattail: it speeds up and its pressure falls, by an amount that depends only on the Mach number and the angle turned (the Prandtl–Meyer function). hpr uses the pressure after such a turn as the upper limit of a boattail’s wave drag. See Boattails faster than sound.

Probe design

A small design made only to ask an oracle one question, such as “what radius does OpenRocket give four tubes written auto?”. It is usually a single body tube carrying the one part being asked about. A probe can be a small file of another kind too: the parts catalog probes are small .orc files, most with one part. hpr’s probe designs for OpenRocket are written by scripts under validation/oracles/openrocket/, and OpenRocket’s answers are committed under validation/fixtures/ork/, where tests hold hpr to them. See .ork design files for one set of them.

Product of inertia

An off-diagonal term of the inertia tensor, such as I_yz = −∫ y z dm. It is zero when the mass is balanced about the axes, as in a rocket that is symmetric about its center line, and not zero when mass sits off the axis on one side, like a single side pod. Its sign follows the positive convention in Mass properties. A rocket with products of inertia turns a little about one axis when pushed about another.

Property test

A test that checks a rule on many randomly generated inputs rather than a few chosen ones, such as that every interpolation table passes exactly through its own points. hpr writes them with the proptest library. See Interpolation tables.

QUADPACK

A library of routines for computing integrals numerically, published by Piessens and others in 1983 and in the public domain. hpr’s adaptive quadrature uses its 15-point Gauss–Kronrod rule, without its extrapolation. See Adaptive quadrature.

Rail exit and rail-exit velocity

Rail exit is the moment the rocket leaves the launch rail and starts to fly free; the rail-exit velocity is its speed then. hpr keeps the rocket guided until the aft edge of its aft-most rail button or launch lug passes the top of the rail (RocketPy stops at the forward button), and it leaves with no rotation, since tip-off is not modeled. The slower the exit in a crosswind, the larger the angle of attack just after it, where hpr’s models are least trustworthy. See Rigid-body flight.

Radiosonde

The instrument package a weather balloon carries: it measures pressure, temperature and humidity on the way up, and its drift, tracked by GPS, gives the wind. About 800 stations release one at 00 and 12 UTC each day. What it records is a sounding. See Weather-balloon soundings.

RASAero II

A rocket aerodynamics and flight program. Several of RocketPy’s example rockets carry drag curves labelled as RASAero’s, though only Calisto’s traces to an export. hpr’s drag is compared with those curves from Mach 0.1 to 2.0, with the fin shapes and surface finish guessed, because the curves don’t record them. See Aerodynamics. hpr can also fly the normal force and center of pressure from RASAero II’s exported table (The normal force from RASAero II).

RASP and RockSim files

The two thrust-curve file formats ThrustCurve.org serves. A RASP .eng file is plain text, named after RASP, the rocket simulation program it comes from; a RockSim .rse file is XML, from the RockSim simulator. hpr reads and writes both, and converts one to the other with hpr convert. See Solid motors.

Reanalysis

A record of past weather made by running a weather model over the past, held at each step to the observations of the time (weather balloons, aircraft, satellites, ground stations). It gives the weather everywhere, not just where it was measured. ERA5 is one. See ERA5 weather files.

Reference area

The area every aerodynamic coefficient of the rocket is divided by, A_ref = π d²/4. By default d is the largest body diameter; it can be set to the nose’s base diameter or to a given value, and a drag table with its own reference diameter is rescaled to the rocket’s. A drag model of your own is not (Models of your own). Coefficients from two programs compare only on the same reference area. See The design tree.

Reference value and fixture

A reference value is a number hpr’s result is checked against: a value printed in a source, a worked example, a closed-form answer or an oracle’s output. A fixture is a committed file under validation/fixtures/ holding reference values and where they came from, written by a generator under validation/oracles/ or transcribed from print. Tests read fixtures and never write them: a reference changes only when its generator runs again. See the validation harness.

Relative and absolute difference

Two ways to say how far a result is from its reference. An absolute difference carries a unit, such as 2e-8 m. A relative difference is the gap as a fraction of the reference value, so 2e-14 relative means two parts in a hundred million million, and a percentage is a relative difference in hundredths. hpr’s pages mark relative differences with the word relative or a percent sign. See Accuracy.

Reynolds number

The ratio of the air’s inertia to its viscosity over a length, R = V L/ν (often written Re), without units, with V the airspeed, L a length and ν the air’s kinematic viscosity. For skin friction hpr takes L as the whole rocket, nose tip to the aft end of the last body component, and treats the flow as fully turbulent. See Aerodynamics.

RocketPy

An open-source (MIT) rocket flight simulator written in Python, and hpr’s main partner for code-to-code comparisons. hpr runs RocketPy 1.13.0, pinned to one commit, to produce its reference values. See Checking a claim.

Roll damping and roll forcing

Roll forcing is the twist that canted fins put on a rocket about its own axis: each fin pushes sideways off the axis. Roll damping is the air’s resistance to the spin: a rolling fin moves sideways through the air and is pushed back. They balance at a steady roll rate that grows with the airspeed. See Roll: forcing and damping.

Roughness length

The height above the ground at which the logarithmic wind law’s wind falls to zero, written z₀. Rougher ground has a larger one: 0.03 m for open flat terrain with grass, and 0.001–0.01 m for mown grass. hpr’s LogLawWind takes it as roughness_length_m. See Wind.

Running median

A filter that replaces each sample of a series with the median of the samples around it: the middle value once they are sorted. A short spike, fewer samples wide than half the window, is outvoted by its neighbours and disappears, while a steady climb or fall passes through unchanged. hpr reads a flight log’s altitude after a 0.3 s running median, which removes the pressure pulse of an ejection charge (Flight-log readings).

Same-drag and predicted mode

Two ways of comparing hpr’s whole flights with another simulator’s. In same-drag mode both codes fly one drag coefficient that the comparison declares, so a difference comes from the equations of motion, the motor or the air, not the drag. In predicted mode hpr works out its own aerodynamics from the rocket’s shape, and the other code flies the drag its example ships (from RASAero, OpenRocket or the team). A difference is then mostly the two drags. Neither drag is known to be right, so those results are held to a target, not a gate. See Accuracy and Accuracy.

Scientific notation

Writing a very small or very large number as a power of ten, the way programs print it. The number after the e says how many places the decimal point moves, to the left when it is negative: 1e-12 is a millionth of a millionth, and 1e6 is a million. 2²⁰ is 2 multiplied by itself 20 times, about a million. See Accuracy.

Seed

A number that starts a random-number generator. The same seed gives the same sequence of numbers, so a run that uses random numbers, such as turbulence or a Monte Carlo run, repeats exactly on the same platform (operating system and processor). The program that runs it chooses the seed. On another platform each random draw can differ in its last binary digit, and over a whole flight such differences can grow. See Turbulence.

Sensitivity analysis

Finding which uncertain inputs move a result most, so you know which to measure carefully and which don’t matter. hpr has Morris’s screening, which ranks inputs from a few runs each through their elementary effects, and Sobol’ indices, which share out the result’s variance. See Sensitivity analysis.

Separation

A stack coming apart for recovery. At its trigger hpr splits the rocket into bodies (body 0 keeps the nose), and each descends on its own under its own recovery devices, which it must have. It adds no impulse, and the aft part’s motors must have burned out. When the forward part still has a motor to burn, it flies on as a sustainer and only the aft part descends. A part leaving at any other joint is an ejection. See Recovery and Staging.

Shear modulus

How hard a material resists being twisted or sheared, G, in pascals (Pa): the shear stress over the shear strain it causes. Aluminium’s is about 26 GPa, birch plywood’s 0.75 GPa. A fin twists in its own plane, so its flutter speed needs the shear modulus in that plane. See Fin flutter.

Shoulder

The sleeve at the end of a nose cone or transition that slides into the next body tube. It counts toward the rocket’s mass, but it is inside the body, so it adds no aerodynamic force. The drag buildup also uses the word for a transition that widens toward the tail, whose pressure drag is counted like a nose’s. See Aerodynamics.

SI units

The International System of Units: meters, kilograms and seconds, and units built from them, such as newtons for force and pascals for pressure. hpr works in SI throughout, with angles in radians. Degrees appear only where values come in or go out, as in Geodetic::from_degrees. In the code, a quantity’s name ends in its unit, such as mass_kg or vertical_speed_m_s. See Frames.

Slender-body theory

A way to work out the air’s forces on a long, thin body from how fast its cross-section grows along its length. It gives a nose as wide as the reference a normal-force slope of 2 per radian whatever its shape, a transition 2ΔA/A_ref, and a plain tube nothing, at any Mach number. Barrowman’s method uses it for every body part. hpr uses it below Mach 1.2, and at every speed for bodies the shock-expansion method can’t take (steps; a widening shape that isn’t a cone, isn’t flush with the part ahead of it, or rides in a boattail’s wake; a nose too blunt for its cap); NASA’s wind tunnel shows a real body lifting more past Mach 3. See Aerodynamics.

Sobol’ index

The share of a result’s variance that one uncertain input causes: alone (its first-order index), or alone and together with the others (its total index). Named after I. M. Sobol’, who defined them. See Sensitivity analysis.

Sounding

A measured or forecast profile of the air against height: pressure, temperature and wind, and sometimes humidity, as from a weather balloon (a radiosonde) or a forecast service. hpr can fly one in place of the standard atmosphere, which carries on above its top level. Flights above a few kilometers need one, because an offset to the standard for field conditions holds all the way up. See Atmosphere.

Specific impulse

Impulse per unit weight of propellant, I_sp = I/(m_p g₀), in seconds, with g₀ = 9.80665 m/s²: the effective exhaust velocity divided by g₀. RockSim .rse files carry it as Isp; hpr works with the exhaust velocity instead. See Solid motors and RockSim .rse files.

Stability margin

How far the center of pressure lies behind the center of gravity, usually in calibres. A positive margin turns the rocket’s nose back into the oncoming air when it is disturbed, which in a crosswind is not quite its flight path (weathercocking). It changes through a flight as propellant burns and speed changes. hpr gives it from the rail exit to apogee or the first deployment, with the air along the axis, at Mach 0 (the static margin) and at the flight’s Mach number (the flight margin), and gives none where the parts’ normal forces all but cancel. A rocket with a fin set of one or two fins has a different margin for each direction the air crosses it, and hpr gives the least. See Flight metrics.

Stage

A section of a rocket’s stack in the design tree, listed forward to aft. A separation splits the rocket at the boundary between two stages, so a rocket that stays in one piece needs only one stage. Each motor lights at its own time, so stages can fire in sequence. See The design tree and Staging.

Stall

The pages use the word in two ways. In aerodynamics it is the loss of lift at a large angle of attack; hpr models none, so it overstates forces at large angles. In the flight engine it is the rocket’s speed along the rail falling to zero, which ends a flight as StalledOnRail when it happens after burnout. See Aerodynamics and Rigid-body flight.

Standard atmosphere

An agreed model of the air’s temperature, pressure and density against height. hpr uses the 1976 U.S. Standard Atmosphere from −5 to 86 km (288.15 K and 101,325 Pa at sea level). It can be offset to match conditions at the field, or replaced by a sounding. See Atmosphere.

Standard deviation

How widely a set of numbers spreads about its mean: the square root of the mean squared difference from the mean (dividing by one less than the count, for a sample). For a normal distribution about two values in three lie within one standard deviation of the mean, and 95% within two. See Monte Carlo dispersion.

Standard error

The scatter expected by chance in an average taken from a random sample; it shrinks as the sample grows. hpr’s turbulence test requires each band’s average to lie within 4 standard errors of the Dryden formula. See Turbulence.

Station

A position along the rocket, in meters aft of the nose tip, the way design files give positions. Station s is z_B = −s in the body frame. See The design tree.

Sting

The rod that holds a wind-tunnel model from behind, entering its base. It changes the air pressure on the base, so a tunnel can’t measure a free-flying rocket’s base drag, only the forebody’s. See Aerodynamics.

Stiff problem

A problem in which some motion is so fast, and so strongly damped, that a method such as Dormand–Prince has to take tiny steps to stay stable. hpr doesn’t detect stiffness: the run stops with an error when its steps get too small or too many. See Time integration.

Stop time

A time the integrator steps to exactly rather than across, because the equations change there: thrust-curve points, burnouts, deployments and the end of a canopy’s filling. A Runge–Kutta step across such a jump loses most of its accuracy. See Time integration and events.

Streamer

A long strip of fabric used instead of a parachute to slow a rocket’s fall. Its drag is taken on its one-side area, length times width. hpr’s default model reads 9% fast on the one flat streamer in Kidwell’s drop tests, and models no pleats, so it predicts a faster descent for a pleated one. See Recovery.

Supersonic linear theory

The small-angle theory of thin surfaces faster than sound: a flat plate at an angle α feels a pressure proportional to α/√(M² − 1), the same all along its chord. hpr uses it for fins from the speed where it holds (about Mach 1.2 or later, set by each fin’s sweep and shape). See Aerodynamics.

Surface layer

The air nearest the ground, where friction with the ground sets how fast the wind grows with height. hpr’s power-law and log-law winds describe it, but keep growing above it, so winds aloft should come from a table of levels. See Wind.

Sustainer

The forward part of a staged rocket, with the nose, that flies on after the booster is dropped and lights its own motor. In hpr a separation whose forward part still has a motor to burn makes it a sustainer, flown in six degrees of freedom with its own shape and mass. See Staging.

Tangent cone

The cone that touches a body along one short element of it: the same half-angle, with its apex on the axis. hpr’s supersonic body method works element by element, and each element’s pressure relaxes toward the pressure on its own tangent cone, looked up in tables that stop at 30°. A cylinder’s tangent cone is the free stream. See Bodies faster than sound.

Tangent ogive

A nose cone whose sides are a circular arc that meets the body tube without a kink: its slope is zero at the base. A 3:1 tangent ogive is three times as long as its base is wide, a fineness ratio of 3. hpr models it as the secant ogive whose arc radius equals the tangent radius. See Shapes.

Thrust curve

A motor’s thrust against time since ignition: (time, thrust) points joined by straight lines, read from a RASP .eng or RockSim .rse file. hpr starts it from zero thrust at ignition, takes the thrust as zero from the last point on, and treats two points at the same time as a sudden step. See Solid motors.

ThrustCurve.org

A public database of motor thrust curves and data. hpr bundles 32 of its curves, and runs its statistics code to check its own. A file downloaded from it can be read and flown (A motor from a file); the library can search it and download a motor’s files itself (Matching motors to ThrustCurve.org), and hpr sim and hpr motors fetch fetch a motor the bundled catalog lacks into hpr’s cache (Motors from ThrustCurve.org). See Solid motors.

Tip-off

The unwanted turn a rocket picks up as it is let go. Leaving a launch rail, it pivots about its last guide; the recovery page uses the word for a separation too. hpr models neither: a rocket leaves the rail with no rotation, a separated body starts with no spin of its own, and no milestone plans either yet. See Rigid-body flight and Recovery.

Tolerance

How far a result may be from its reference and still pass, such as the 3% every parachute-descent number is held to. Each test and each validation case states its own, next to the reason for its size. The integrator’s rtol and atol are tolerances in a second sense: how much error each adaptive time step may make. See the validation report and Time integration and events.

Total impulse

A motor’s total push, the area under its thrust curve, I = ∫ F dt, in newton-seconds (N·s). It sets the impulse class. hpr integrates the straight-line curve exactly. See Solid motors.

Transonic and supersonic

Flight near the speed of sound (transonic) and above it (supersonic), where shock waves change the drag and the lift. Since M1.8a hpr carries the normal force and center of pressure through both, to Mach 5: supersonic linear theory for the fins, joined to the subsonic method between Mach 0.8 and the speed where that theory holds. Since M1.8b1 (drag through Mach 1) its drag goes to Mach 5 too: Niskanen’s semi-empirical method, with the wave drag of noses and shoulders from closed forms and from Stoney’s 1961 NASA measurements. See Aerodynamics and Aerodynamics.

Tube fin

A short open tube glued along the airframe in place of a flat fin. A tube fin set is a ring of them around the body. hpr weighs each tube as a hollow cylinder beside the body. A .ork file can leave the tubes’ radius to OpenRocket. With three tubes or more, OpenRocket makes them just wide enough to touch the body and each other; one or two take the body’s radius. hpr reads that radius as OpenRocket does. The aerodynamics flies each tube as a ring wing, below Mach 0.8 (M2.2e9). See .ork design files, Mass properties and Aerodynamics.

Tumble recovery

Recovery with nothing deployed: the body falls broadside, tumbling, and its own drag slows it. hpr takes its drag area from the OpenRocket technical documentation’s fit to the fin and side-profile areas, which comes out −10% to +19% off that source’s own drop tests. hpr doesn’t decide by itself when a body tumbles: you give the tumble a trigger. See Recovery.

Turbulence (Dryden)

Random gusts on top of the steady wind. hpr models them with the Dryden spectra of MIL-F-8785C, a military aircraft specification, from a seeded generator that repeats bit for bit for the same seed on one platform. No flight uses turbulence yet, none is planned (issue #39), and Dryden is unvalidated for rockets. See Turbulence.

Validation case

One comparison the validation suite runs: what to fly, which numbers (metrics) to compare, each with its own tolerance, and against which reference values. cargo xtask validate runs every case and writes the committed validation report, with every number and its verdict. See the validation harness.

Verification and validation

Verification checks that the code does what its model says, against closed-form answers, printed tables and worked examples. Validation checks that the model matches the real world. hpr ranks its evidence in four kinds, named as on Accuracy: analytic (exact answers), published source (printed tables and worked examples), another code (code-to-code comparison), and real flights. See Accuracy.

Variance

The square of the standard deviation: the mean squared distance of a quantity from its mean. Unlike standard deviations, the variances that independent causes contribute add up, which is why Sobol’ indices share out the variance. See Sensitivity analysis.

Vertical datum

The surface heights are measured from. NAVD88, the North American Vertical Datum of 1988, and EGM2008, a worldwide model of the geoid, are both within a meter or two of the geoid (NAVD88, set by levelling, is about half a meter off and tilted about a meter coast to coast: NGS), so hpr takes heights above them as heights above sea level; an ellipsoidal height is measured from the ellipsoid instead. See A launch site’s elevation.

Virtual temperature

The temperature dry air would need to have the density of a humid parcel at the same pressure: T_v = T / (1 − (e/p)(1 − M_v/M₀)), with e the water vapour’s pressure and M_v/M₀ ≈ 0.622 the ratio of the molar masses of water and dry air (WMO-No. 8, eq. 12.18). Water vapour is lighter than air, so T_v is a little above T: about 1.6% at 30 °C, saturation and sea-level pressure. See Atmosphere.

Wave drag

The drag from the shock waves that form on a rocket at and above the speed of sound. Air meeting a nose, a shoulder that widens or a fin’s leading edge passes through a shock, which raises the pressure pushing back on the surface. Behind a boattail the opposite happens: the air expands around it, its pressure falls, and that pulls back on the boattail. It is much of the steep rise in drag near Mach 1. hpr has no separate term for it: it is part of the pressure drag of each nose, shoulder and step, which Niskanen’s 2009 method carries through Mach 1, and of each boattail (Boattails faster than sound). For fins, hpr uses a blunt leading edge’s formula, which reads far high for thin, sharp fins (Drag limits). See Aerodynamics.

Weathercocking

A stable rocket turning into the wind it feels. Off the rail in a crosswind, the airflow meets the rocket partly from the side, and the normal force, acting behind the center of gravity, swings the nose toward it, so the rocket climbs upwind. In hpr’s test, a 5 m/s wind from the west puts Valetudo’s apogee 86 m upwind. See Rigid-body flight.

WGS 84

The World Geodetic System 1984: the model of the Earth’s shape and gravity that GPS uses. Its ellipsoid has an equatorial radius a = 6378137.0 m and a flattening 1/f = 298.257223563. hpr’s latitudes, heights and normal gravity are all on it. See Geodesy.

Wind direction

hpr gives the wind’s direction the meteorological way: where it blows from, clockwise from true north, so a wind from the west (3π/2 rad, 270°) blows toward the east. RocketPy’s wind heading is where it blows toward, 180° from this. The wind itself is the air’s velocity in the launch frame’s east and north axes. See Wind.

World Magnetic Model (WMM)

The model of the Earth’s main magnetic field that NOAA and the British Geological Survey publish every five years, used by GPS receivers and phones to give compass headings. hpr bundles WMM2025, valid from 2025.0 to 2030.0, and gives the field’s strength, dip and declination anywhere in that time. See The magnetic field.