2 * Copyright © 2019 Keith Packard <keithp@keithp.com>
4 * This program is free software; you can redistribute it and/or modify
5 * it under the terms of the GNU General Public License as published by
6 * the Free Software Foundation, either version 2 of the License, or
7 * (at your option) any later version.
9 * This program is distributed in the hope that it will be useful, but
10 * WITHOUT ANY WARRANTY; without even the implied warranty of
11 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
12 * General Public License for more details.
16 #include "ao-atmosphere.h"
18 #define GRAVITY 9.80665
21 * Pressure Sensor Model, version 1.1
23 * written by Holly Grimes
25 * Uses the International Standard Atmosphere as described in
26 * "A Quick Derivation relating altitude to air pressure" (version 1.03)
27 * from the Portland State Aerospace Society, except that the atmosphere
28 * is divided into layers with each layer having a different lapse rate.
30 * Lapse rate data for each layer was obtained from Wikipedia on Sept. 1, 2007
31 * at site <http://en.wikipedia.org/wiki/International_Standard_Atmosphere
33 * Height measurements use the local tangent plane. The postive z-direction is up.
35 * All measurements are given in SI units (Kelvin, Pascal, meter, meters/second^2).
36 * The lapse rate is given in Kelvin/meter, the gas constant for air is given
37 * in Joules/(kilogram-Kelvin).
40 #define GRAVITATIONAL_ACCELERATION (-GRAVITY)
41 #define AIR_GAS_CONSTANT 287.053
42 #define NUMBER_OF_LAYERS 7
43 #define MAXIMUM_ALTITUDE 84852.0
44 #define MINIMUM_PRESSURE 0.3734
45 #define LAYER0_BASE_TEMPERATURE 288.15
46 #define LAYER0_BASE_PRESSURE 101325
48 /* lapse rate and base altitude for each layer in the atmosphere */
49 static const double lapse_rate[] = {
50 -0.0065, 0.0, 0.001, 0.0028, 0.0, -0.0028, -0.002
53 static const double base_altitude[] = {
54 0, 11000, 20000, 32000, 47000, 51000, 71000
57 /* outputs atmospheric pressure associated with the given altitude.
58 * altitudes are measured with respect to the mean sea level
61 ao_altitude_to_pressure(double altitude)
63 double base_temperature = LAYER0_BASE_TEMPERATURE;
64 double base_pressure = LAYER0_BASE_PRESSURE;
67 double base; /* base for function to determine pressure */
68 double exponent; /* exponent for function to determine pressure */
69 int layer_number; /* identifies layer in the atmosphere */
70 double delta_z; /* difference between two altitudes */
72 if (altitude > MAXIMUM_ALTITUDE) /* FIX ME: use sensor data to improve model */
75 /* calculate the base temperature and pressure for the atmospheric layer
76 associated with the inputted altitude */
77 for(layer_number = 0; layer_number < NUMBER_OF_LAYERS - 1 && altitude > base_altitude[layer_number + 1]; layer_number++) {
78 delta_z = base_altitude[layer_number + 1] - base_altitude[layer_number];
79 if (lapse_rate[layer_number] == 0.0) {
80 exponent = GRAVITATIONAL_ACCELERATION * delta_z
81 / AIR_GAS_CONSTANT / base_temperature;
82 base_pressure *= exp(exponent);
85 base = (lapse_rate[layer_number] * delta_z / base_temperature) + 1.0;
86 exponent = GRAVITATIONAL_ACCELERATION /
87 (AIR_GAS_CONSTANT * lapse_rate[layer_number]);
88 base_pressure *= pow(base, exponent);
90 base_temperature += delta_z * lapse_rate[layer_number];
93 /* calculate the pressure at the inputted altitude */
94 delta_z = altitude - base_altitude[layer_number];
95 if (lapse_rate[layer_number] == 0.0) {
96 exponent = GRAVITATIONAL_ACCELERATION * delta_z
97 / AIR_GAS_CONSTANT / base_temperature;
98 pressure = base_pressure * exp(exponent);
101 base = (lapse_rate[layer_number] * delta_z / base_temperature) + 1.0;
102 exponent = GRAVITATIONAL_ACCELERATION /
103 (AIR_GAS_CONSTANT * lapse_rate[layer_number]);
104 pressure = base_pressure * pow(base, exponent);
111 /* outputs the altitude associated with the given pressure. the altitude
112 returned is measured with respect to the mean sea level */
114 ao_pressure_to_altitude(double pressure)
117 double next_base_temperature = LAYER0_BASE_TEMPERATURE;
118 double next_base_pressure = LAYER0_BASE_PRESSURE;
121 double base_pressure;
122 double base_temperature;
123 double base; /* base for function to determine base pressure of next layer */
124 double exponent; /* exponent for function to determine base pressure
127 int layer_number; /* identifies layer in the atmosphere */
128 int delta_z; /* difference between two altitudes */
130 if (pressure < 0) /* illegal pressure */
132 if (pressure < MINIMUM_PRESSURE) /* FIX ME: use sensor data to improve model */
133 return MAXIMUM_ALTITUDE;
135 /* calculate the base temperature and pressure for the atmospheric layer
136 associated with the inputted pressure. */
140 base_pressure = next_base_pressure;
141 base_temperature = next_base_temperature;
142 delta_z = base_altitude[layer_number + 1] - base_altitude[layer_number];
143 if (lapse_rate[layer_number] == 0.0) {
144 exponent = GRAVITATIONAL_ACCELERATION * delta_z
145 / AIR_GAS_CONSTANT / base_temperature;
146 next_base_pressure *= exp(exponent);
149 base = (lapse_rate[layer_number] * delta_z / base_temperature) + 1.0;
150 exponent = GRAVITATIONAL_ACCELERATION /
151 (AIR_GAS_CONSTANT * lapse_rate[layer_number]);
152 next_base_pressure *= pow(base, exponent);
154 next_base_temperature += delta_z * lapse_rate[layer_number];
156 while(layer_number < NUMBER_OF_LAYERS - 1 && pressure < next_base_pressure);
158 /* calculate the altitude associated with the inputted pressure */
159 if (lapse_rate[layer_number] == 0.0) {
160 coefficient = (AIR_GAS_CONSTANT / GRAVITATIONAL_ACCELERATION)
162 altitude = base_altitude[layer_number]
163 + coefficient * log(pressure / base_pressure);
166 base = pressure / base_pressure;
167 exponent = AIR_GAS_CONSTANT * lapse_rate[layer_number]
168 / GRAVITATIONAL_ACCELERATION;
169 coefficient = base_temperature / lapse_rate[layer_number];
170 altitude = base_altitude[layer_number]
171 + coefficient * (pow(base, exponent) - 1);