#!/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 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; } real feet_to_meters(real feet) { return feet * (12 * 2.54 / 100); } real meters_to_feet(real meters) { return meters / (12 * 2.54 / 100); } /* * Values for our MP3H6115A pressure sensor * * From the data sheet: * * Pressure range: 15-115 kPa * Voltage at 115kPa: 2.82 * Output scale: 27mV/kPa * * * 27 mV/kPa * 2047 / 3300 counts/mV = 16.75 counts/kPa * 2.82V * 2047 / 3.3 counts/V = 1749 counts/115 kPa */ real counts_per_kPa = 27 * 2047 / 3300; real counts_at_101_3kPa = 1674; real fraction_to_kPa(real fraction) { return (fraction + 0.095) / 0.009; } real count_to_kPa(real count) = fraction_to_kPa(count / 2047); typedef struct { real m, b; int m_i, b_i; } line_t; line_t best_fit(real[] values, int first, int last) { real sum_x = 0, sum_x2 = 0, sum_y = 0, sum_xy = 0; int n = last - first + 1; real m, b; int m_i, b_i; for (int i = first; i <= last; i++) { sum_x += i; sum_x2 += i**2; sum_y += values[i]; sum_xy += values[i] * i; } m = (n*sum_xy - sum_y*sum_x) / (n*sum_x2 - sum_x**2); b = sum_y/n - m*(sum_x/n); return (line_t) { m = m, b = b }; } real count_to_altitude(real count) { return pressure_to_altitude(count_to_kPa(count) * 1000); } real fraction_to_altitude(real frac) = pressure_to_altitude(fraction_to_kPa(frac) * 1000); int num_samples = 1024; real[num_samples] alt = { [n] = fraction_to_altitude(n/(num_samples - 1)) }; int num_part = 128; int seg_len = num_samples / num_part; line_t [dim(alt) / seg_len] fit = { [n] = best_fit(alt, n * seg_len, n * seg_len + seg_len - 1) }; int[num_samples/seg_len + 1] alt_part; alt_part[0] = floor (fit[0].b + 0.5); alt_part[dim(fit)] = floor(fit[dim(fit)-1].m * dim(fit) * seg_len + fit[dim(fit)-1].b + 0.5); for (int i = 0; i < dim(fit) - 1; i++) { real here, there; here = fit[i].m * (i+1) * seg_len + fit[i].b; there = fit[i+1].m * (i+1) * seg_len + fit[i+1].b; alt_part[i+1] = floor ((here + there) / 2 + 0.5); } real count_to_fit_altitude(int count) { int sub = count // seg_len; int off = count % seg_len; line_t l = fit[sub]; real r_v; real i_v; r_v = count * l.m + l.b; i_v = (alt_part[sub] * (seg_len - off) + alt_part[sub+1] * off) / seg_len; return i_v; } real max_error = 0; int max_error_count = 0; real total_error = 0; for (int count = 0; count < num_samples; count++) { real kPa = fraction_to_kPa(count / (num_samples - 1)); real meters = pressure_to_altitude(kPa * 1000); real meters_approx = count_to_fit_altitude(count); real error = abs(meters - meters_approx); total_error += error; if (error > max_error) { max_error = error; max_error_count = count; } # printf (" %7d, /* %6.2g kPa %5d count approx %d */\n", # floor (meters + 0.5), kPa, count, floor(count_to_fit_altitude(count) + 0.5)); } printf ("/*max error %f at %7.3f%%. Average error %f*/\n", max_error, max_error_count / (num_samples - 1) * 100, total_error / num_samples); printf ("#define NALT %d\n", dim(alt_part)); printf ("#define ALT_FRAC_BITS %d\n", floor (log2(32768/(dim(alt_part)-1)) + 0.1)); for (int i = 0; i < dim(alt_part); i++) { real fraction = i / (dim(alt_part) - 1); real kPa = fraction_to_kPa(fraction); printf ("%9d, /* %6.2f kPa %7.3f%% */\n", alt_part[i], kPa, fraction * 100); }