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#!/usr/bin/nickle -f
/*
* 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).
*/
const real GRAVITATIONAL_ACCELERATION = -9.80665;
const real AIR_GAS_CONSTANT = 287.053;
const int NUMBER_OF_LAYERS = 7;
const real MAXIMUM_ALTITUDE = 84852;
const real MINIMUM_PRESSURE = 0.3734;
const real LAYER0_BASE_TEMPERATURE = 288.15;
const real LAYER0_BASE_PRESSURE = 101325;
/* lapse rate and base altitude for each layer in the atmosphere */
const real[NUMBER_OF_LAYERS] lapse_rate = {
-0.0065, 0.0, 0.001, 0.0028, 0.0, -0.0028, -0.002
};
const int[NUMBER_OF_LAYERS] 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 */
real altitude_to_pressure(real altitude) {
real base_temperature = LAYER0_BASE_TEMPERATURE;
real base_pressure = LAYER0_BASE_PRESSURE;
real pressure;
real base; /* base for function to determine pressure */
real exponent; /* exponent for function to determine pressure */
int layer_number; /* identifies layer in the atmosphere */
int 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 */
real pressure_to_altitude(real pressure) {
real next_base_temperature = LAYER0_BASE_TEMPERATURE;
real next_base_pressure = LAYER0_BASE_PRESSURE;
real altitude;
real base_pressure;
real base_temperature;
real base; /* base for function to determine base pressure of next layer */
real exponent; /* exponent for function to determine base pressure
of next layer */
real 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;
}
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