Atmospheric Model

The atmosphere hands the integrator exactly two numbers. One is how dense the air is, which scales the drag the projectile feels. The other is how fast sound travels through it, which defines the Mach number that the drag curve is indexed by. Everything in this chapter exists to produce those two numbers correctly from whatever a shooter actually knows about the weather.

The standard atmosphere as a backbone

The backbone is the International Standard Atmosphere, a reference model of how the air behaves: temperature falls steadily as altitude climbs, pressure follows from the temperature, and density follows from pressure and temperature together. It is a definition rather than a measurement, which is exactly its value here. It means lob has a defensible atmosphere even when the shooter supplies no weather data at all, and it means that any real measurement can be treated as a correction away from a known starting point.

The model has one structural wrinkle worth knowing. The steady temperature fall applies only up to the tropopause. Above it the atmosphere stops cooling with height and becomes isothermal, so pressure there follows an exponential law instead. Without the branch, a very high shot would be handed a temperature the atmosphere cannot have. lob branches on the tropopause rather than extrapolating the linear lapse past it.

Making the best of imperfect inputs

Weather data arrives wrong in ways that are specific and fixable, and each correction handles one of them.

A pressure reading is almost never taken at the shooter's altitude. It comes from a weather station, a barometer indoors, or a phone app, each reporting the pressure where it is. lob shifts the reading barometrically to the firing site, so a pressure taken a thousand feet below the shooter describes the air the bullet actually leaves. If you supply that barometer altitude, the shift is exact; if you do not, lob assumes the barometer was at the firing site.

Temperature has the same problem with the same fix. A reading comes from wherever the thermometer sat, and lob lapses it to the firing site.

Then there is what was not measured at all. No temperature means the standard sea-level value, lapsed down to the firing site. No pressure means the standard sea-level value, propagated up to the firing-site altitude barometrically. No firing-site altitude means sea level. No humidity means dry air.

The design intent is worth stating plainly, because it is unusual: lob never refuses to produce a solution for lack of environmental data. Every missing input has a standard-atmosphere substitute, and every present-but-wrong input gets corrected into place. The alternative, an error demanding a fuller weather report, pushes the cost of a partial answer onto the caller, and the whole design is arranged to avoid that. The same philosophy that lets a builder take a bare ballistic coefficient also lets the atmosphere be half-specified.

Humidity

Humidity does two things to the air, in opposite directions. It makes the air slightly less dense than dry air at the same temperature and pressure, and it makes the air slightly faster at carrying sound. Drag and Mach both shift as a result, so both corrections apply.

Both corrections are driven by the saturation vapor pressure at the measured temperature, which is what says how much water vapor the air can be holding. Getting that quantity normally means a lookup table of measurements. lob uses a published closed-form approximation instead, chosen specifically so that a library which otherwise carries no data files does not need to ship one.

The humidity corrections themselves are linear, valid across the range of humidity where the effect matters at all. Beyond the extremes the model is not trying to be right; a shooter measuring near-saturation conditions in absolute humidity is outside what this correction represents.

From atmosphere to solver

Density and speed of sound are computed once, when the context is built, and then carried by the context for the rest of the solve.

Density does not enter the solver as density. It is converted into the drag coefficient that scales the drag curve, which is why the drag model never has to know about air pressure, temperature, or humidity. Speed of sound divides projectile speed to produce the Mach number the drag curve is evaluated at.

For the per-step variant described in the point-mass model, one further quantity is precomputed: a lapse coefficient. It lets the solver project how far the projectile has climbed onto the standard lapse rate, and derive from that how much thinner and faster the air has become at the projectile's current altitude, without redoing the atmospheric model at every step.

Limitations