Improve OTU calculations

Implement the protocol in Erik Baker's document
"Oxygen Toxicity Calculations". This code uses a
third-order polynomial approximation of Baker's
equation 2. Provision is made for
PSCR and CCR dive logs and dive plans. In the
case of dive logs, the values of o2 sensors are
used if there are data from such sensors. For CCR
only the data from the first O2 sensor is used even if
there are more than one sensor. This is a potential
weakness, but this function is probably NOT the
place to calculate mean o2 values accross all sensors
and to emulate voting logic to reject info from
aberrant sensors.

Signed-off-by: willemferguson <willemferguson@zoology.up.ac.za>
Signed-off-by: Robert C. Helling <helling@atdotde.de>

CHANGELOG.md

@@ -1,3 +1,5 @@
+- Dive: Perform more accurate OTU calculations, and include
+  OTU calculations for rebreather dives [#1851 & #1865].
 - Mobile: add initial copy-paste support
 - Desktop: translate trip date
 ---

core/divelist.c

@@ -159,27 +159,52 @@ static int active_o2(const struct dive *dive, const struct divecomputer *dc, dur
 	return get_o2(gas);
 }
 
-/* calculate OTU for a dive - this only takes the first divecomputer into account */
+/* Calculate OTU for a dive - this only takes the first divecomputer into account.
+   Implement the protocol in Erik Baker's document "Oxygen Toxicity Calculations". This code
+   implements a third-order continuous approximation of Baker's Eq. 2 and enables OTU
+   calculation for rebreathers. Baker obtained his information from:
+   Comroe Jr. JH et al. (1945)  Oxygen toxicity. J. Am. Med. Assoc. 128,710-717
+   Clark JM & CJ Lambertsen (1970) Pulmonary oxygen tolerance in man and derivation of pulmonary
+      oxygen tolerance curves. Inst. env. Med. Report 1-70, University of Pennsylvania, Philadelphia, USA. */
 static int calculate_otu(const struct dive *dive)
 {
 	int i;
 	double otu = 0.0;
 	const struct divecomputer *dc = &dive->dc;
-
 	for (i = 1; i < dc->samples; i++) {
 		int t;
-		int po2;
+		int po2i, po2f;
+		double pm;
 		struct sample *sample = dc->sample + i;
 		struct sample *psample = sample - 1;
 		t = sample->time.seconds - psample->time.seconds;
-		if (sample->setpoint.mbar) {
+		if (sample->o2sensor[0].mbar) {			// if dive computer has o2 sensor(s) (CCR & PSCR) ..
-			po2 = sample->setpoint.mbar;
+			po2i = psample->o2sensor[0].mbar;
+			po2f = sample->o2sensor[0].mbar;	// ... use data from the first o2 sensor
 		} else {
-			int o2 = active_o2(dive, dc, psample->time);
+			if (dc->divemode == CCR) {
-			po2 = lrint(o2 * depth_to_atm(sample->depth.mm, dive));
+				po2i = psample->setpoint.mbar;		// if CCR has no o2 sensors then use setpoint
+				po2f = sample->setpoint.mbar;
+			} else {						// For OC and rebreather without o2 sensor/setpoint
+				int o2 = active_o2(dive, dc, psample->time);	// 	... calculate po2 from depth and FiO2.
+				po2i = lrint(o2 * depth_to_atm(psample->depth.mm, dive));	// (initial) po2 at start of segment
+				po2f = lrint(o2 * depth_to_atm(sample->depth.mm, dive));	// (final) po2 at end of segment
+			}
+		}
+		if ((po2i > 500) || (po2f > 500)) {			// If PO2 in segment is above 500 mbar then calculate otu
+			if (po2i <= 500) {				// For descent segment with po2i <= 500 mbar ..
+				t = t * (po2f - 500) / (po2f - po2i);	// .. only consider part with PO2 > 500 mbar
+				po2i = 501;				// Mostly important for the dive planner with long segments
+			} else {
+				if (po2f <= 500){
+					t = t * (po2i - 500) / (po2i - po2f);	// For ascent segment with po2f <= 500 mbar ..
+					po2f = 501;				// .. only consider part with PO2 > 500 mbar
+				}
+			}
+			pm = (po2f + po2i)/1000.0 - 1.0;
+			// This is a 3rd order continuous approximation of Baker's eq. 2, therefore Baker's eq. 1 is not used:
+			otu += t / 60.0 * pow(pm, 5.0/6.0) * (1.0 - 5.0 * (po2f - po2i) * (po2f - po2i) / 216000000.0 / (pm * pm));
 		}
-		if (po2 >= 500)
-			otu += pow((po2 - 500) / 1000.0, 0.83) * t / 30.0;
 	}
 	return lrint(otu);
 }