ao-tools/lib: Add atmosphere model

Converts between pressure and altitude

Signed-off-by: Keith Packard <keithp@keithp.com>

3 files changed, 201 insertions, 0 deletions

diff --git a/ao-tools/lib/Makefile.am b/ao-tools/lib/Makefile.am
index de6c1946..47f9d30c 100644
--- a/ao-tools/lib/Makefile.am
+++ b/ao-tools/lib/Makefile.am
@@ -40,6 +40,8 @@ libao_tools_a_SOURCES = \
 	chbevl.c \
 	mconf.h \
 	cephes.h \
+	ao-atmosphere.c \
+	ao-atmosphere.h \
 	ao-hex.c \
 	ao-hex.h \
 	ao-editaltos.c \
diff --git a/ao-tools/lib/ao-atmosphere.c b/ao-tools/lib/ao-atmosphere.c
new file mode 100644
index 00000000..f11ca7f6
--- /dev/null
+++ b/ao-tools/lib/ao-atmosphere.c
@@ -0,0 +1,175 @@
+/*
+ * Copyright © 2019 Keith Packard <keithp@keithp.com>
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ */
+
+#include <math.h>
+#include "ao-atmosphere.h"
+
+#define GRAVITY 9.80665
+
+/*
+ * Pressure Sensor Model, version 1.1
+ *
+ * written by Holly Grimes
+ *
+ * Uses the International Standard Atmosphere as described in
+ *   "A Quick Derivation relating altitude to air pressure" (version 1.03)
+ *    from the Portland State Aerospace Society, except that the atmosphere
+ *    is divided into layers with each layer having a different lapse rate.
+ *
+ * Lapse rate data for each layer was obtained from Wikipedia on Sept. 1, 2007
+ *    at site <http://en.wikipedia.org/wiki/International_Standard_Atmosphere
+ *
+ * Height measurements use the local tangent plane.  The postive z-direction is up.
+ *
+ * All measurements are given in SI units (Kelvin, Pascal, meter, meters/second^2).
+ *   The lapse rate is given in Kelvin/meter, the gas constant for air is given
+ *   in Joules/(kilogram-Kelvin).
+ */
+
+#define GRAVITATIONAL_ACCELERATION	(-GRAVITY)
+#define AIR_GAS_CONSTANT		287.053
+#define NUMBER_OF_LAYERS		7
+#define MAXIMUM_ALTITUDE		84852.0
+#define MINIMUM_PRESSURE		0.3734
+#define LAYER0_BASE_TEMPERATURE		288.15
+#define LAYER0_BASE_PRESSURE		101325
+
+	/* lapse rate and base altitude for each layer in the atmosphere */
+static const double lapse_rate[] = {
+	-0.0065, 0.0, 0.001, 0.0028, 0.0, -0.0028, -0.002
+};
+
+static const double base_altitude[] = {
+	0, 11000, 20000, 32000, 47000, 51000, 71000
+};
+
+/* outputs atmospheric pressure associated with the given altitude.
+ * altitudes are measured with respect to the mean sea level
+ */
+double
+ao_altitude_to_pressure(double altitude)
+{
+	double base_temperature = LAYER0_BASE_TEMPERATURE;
+	double base_pressure = LAYER0_BASE_PRESSURE;
+
+	double pressure;
+	double base; /* base for function to determine pressure */
+	double exponent; /* exponent for function to determine pressure */
+	int layer_number; /* identifies layer in the atmosphere */
+	double delta_z; /* difference between two altitudes */
+
+	if (altitude > MAXIMUM_ALTITUDE) /* FIX ME: use sensor data to improve model */
+		return 0;
+
+	/* calculate the base temperature and pressure for the atmospheric layer
+	   associated with the inputted altitude */
+	for(layer_number = 0; layer_number < NUMBER_OF_LAYERS - 1 && altitude > base_altitude[layer_number + 1]; layer_number++) {
+		delta_z = base_altitude[layer_number + 1] - base_altitude[layer_number];
+		if (lapse_rate[layer_number] == 0.0) {
+			exponent = GRAVITATIONAL_ACCELERATION * delta_z
+				/ AIR_GAS_CONSTANT / base_temperature;
+			base_pressure *= exp(exponent);
+		}
+		else {
+			base = (lapse_rate[layer_number] * delta_z / base_temperature) + 1.0;
+			exponent = GRAVITATIONAL_ACCELERATION /
+				(AIR_GAS_CONSTANT * lapse_rate[layer_number]);
+			base_pressure *= pow(base, exponent);
+		}
+		base_temperature += delta_z * lapse_rate[layer_number];
+	}
+
+	/* calculate the pressure at the inputted altitude */
+	delta_z = altitude - base_altitude[layer_number];
+	if (lapse_rate[layer_number] == 0.0) {
+		exponent = GRAVITATIONAL_ACCELERATION * delta_z
+			/ AIR_GAS_CONSTANT / base_temperature;
+		pressure = base_pressure * exp(exponent);
+	}
+	else {
+		base = (lapse_rate[layer_number] * delta_z / base_temperature) + 1.0;
+		exponent = GRAVITATIONAL_ACCELERATION /
+			(AIR_GAS_CONSTANT * lapse_rate[layer_number]);
+		pressure = base_pressure * pow(base, exponent);
+	}
+
+	return pressure;
+}
+
+
+/* outputs the altitude associated with the given pressure. the altitude
+   returned is measured with respect to the mean sea level */
+double
+ao_pressure_to_altitude(double pressure)
+{
+
+	double next_base_temperature = LAYER0_BASE_TEMPERATURE;
+	double next_base_pressure = LAYER0_BASE_PRESSURE;
+
+	double altitude;
+	double base_pressure;
+	double base_temperature;
+	double base; /* base for function to determine base pressure of next layer */
+	double exponent; /* exponent for function to determine base pressure
+			    of next layer */
+	double coefficient;
+	int layer_number; /* identifies layer in the atmosphere */
+	int delta_z; /* difference between two altitudes */
+
+	if (pressure < 0)  /* illegal pressure */
+		return -1;
+	if (pressure < MINIMUM_PRESSURE) /* FIX ME: use sensor data to improve model */
+		return MAXIMUM_ALTITUDE;
+
+	/* calculate the base temperature and pressure for the atmospheric layer
+	   associated with the inputted pressure. */
+	layer_number = -1;
+	do {
+		layer_number++;
+		base_pressure = next_base_pressure;
+		base_temperature = next_base_temperature;
+		delta_z = base_altitude[layer_number + 1] - base_altitude[layer_number];
+		if (lapse_rate[layer_number] == 0.0) {
+			exponent = GRAVITATIONAL_ACCELERATION * delta_z
+				/ AIR_GAS_CONSTANT / base_temperature;
+			next_base_pressure *= exp(exponent);
+		}
+		else {
+			base = (lapse_rate[layer_number] * delta_z / base_temperature) + 1.0;
+			exponent = GRAVITATIONAL_ACCELERATION /
+				(AIR_GAS_CONSTANT * lapse_rate[layer_number]);
+			next_base_pressure *= pow(base, exponent);
+		}
+		next_base_temperature += delta_z * lapse_rate[layer_number];
+	}
+	while(layer_number < NUMBER_OF_LAYERS - 1 && pressure < next_base_pressure);
+
+	/* calculate the altitude associated with the inputted pressure */
+	if (lapse_rate[layer_number] == 0.0) {
+		coefficient = (AIR_GAS_CONSTANT / GRAVITATIONAL_ACCELERATION)
+			* base_temperature;
+		altitude = base_altitude[layer_number]
+			+ coefficient * log(pressure / base_pressure);
+	}
+	else {
+		base = pressure / base_pressure;
+		exponent = AIR_GAS_CONSTANT * lapse_rate[layer_number]
+			/ GRAVITATIONAL_ACCELERATION;
+		coefficient = base_temperature / lapse_rate[layer_number];
+		altitude = base_altitude[layer_number]
+			+ coefficient * (pow(base, exponent) - 1);
+	}
+
+	return altitude;
+}
diff --git a/ao-tools/lib/ao-atmosphere.h b/ao-tools/lib/ao-atmosphere.h
new file mode 100644
index 00000000..0a24cb02
--- /dev/null
+++ b/ao-tools/lib/ao-atmosphere.h
@@ -0,0 +1,24 @@
+/*
+ * Copyright © 2019 Keith Packard <keithp@keithp.com>
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * General Public License for more details.
+ */
+
+#ifndef _AO_ATMOSPHERE_H_
+#define _AO_ATMOSPHERE_H_
+
+double
+ao_altitude_to_pressure(double altitude);
+
+double
+ao_pressure_to_altitude(double pressure);
+
+#endif /* _AO_ATMOSPHERE_H_ */