Schmidt-Appleman-Criterion (SAC)
This file:	https://purl.org/aero/SAC
				Magnus-Equation
a_w	611.2	Pa
b_w	17.62
c_w	243.12	°C
a_i	611.2	Pa
b_i	22.46
c_i	272.62	°C
				https://de.wikipedia.org/wiki/Sättigungsdampfdruck#Berechnung_des_Sättigungsdampfdrucks_von_Wasser_über_die_Magnus-Formel
				https://en.wikipedia.org/wiki/Vapour_pressure_of_water					contains also alternative equations
t	-43.936	°C		No contrail above this temperatur
E_w'	1.354	Pa/°C
E_w' - G	7.65692E-07	Pa/°C		<= drive to Zero with the Solver (settings on the right)					= a_w*b_w*c_w*EXP(b_w*t/(c_w+t))/(c_w+t)^2-G
E_w	12.54	Pa							= a_w*EXP(b_w*t/(c_w+t))
E_i	8.17	Pa							= a_i*EXP(b_i*t/(c_i+t))
L	1.9812E-03	°C/ft
t_0	15.0	°C
k_a	6.8756E-06	1/ft		Constants of the ISA, Scholz
k_b	4.8063E-05	1/ft
k_exp	5.25588
H_T	36089	ft
p_0	101315	Pa
p_T	22632	Pa
H	40000	ft		Input of the flight altitude
p	18754	Pa		Pressure from the ISA, Scholz					= WENN(H<H_T;p_0*(1-k_a*H)^k_exp;p_T*EXP(-k_b*(H-H_T)))
			Kerosine:
EI_H2O	1.25		1.25	Data for the fuel
c_p	1004	J/(kgK)	1004
eps	0.622		0.622				GIERENS, Klaus, et al.,2008. A Review of Various Strategies for Contrail Avoidance. In: OASC, vol.2, pp. 1-7.
Q	4.30E+07	J/kg	4.30E+07				https://doi.org/10.2174/1874282300802010001
eta	0.35		0.35
G	1.354	Pa/°C		= EI_H2O*p*c_p/(eps*Q*(1-eta))
t_Schumann	-43.47	°C		= -46+9,43*LN(G-0,053)+0,72*(LN(G-0,053))^2				Approximate equation from Schumann 1996 (https://elib.dlr.de/32128), Schumann 2000 (https://elib.dlr.de/9281)
t_Scholz	-43.86			= a_SLZ*LN(G)^2+b_SLZ*LN(G)+c_SLZ				See on Tab "t_SAC". Parameters are similar to those from Schumann.
G0	72.0	Pa		= E_w-G*t
f(t)	12.54	Pa		= G*t+G0
f(t)=E_w(t) ?	true			Check of calculation must be "true"!
t	E_w	E_i	G*t+G0	phi = E_i/E_w
-60	1.901	1.080	-9.21	56.8%
-59	2.158	1.236	-7.86	57.3%
-58	2.447	1.413	-6.50	57.7%
-57	2.771	1.613	-5.15	58.2%
-56	3.134	1.839	-3.79	58.7%
-55	3.539	2.094	-2.44	59.2%
-54	3.992	2.381	-1.09	59.7%
-53	4.497	2.705	0.27	60.2%
-52	5.060	3.070	1.62	60.7%
-51	5.686	3.479	2.98	61.2%
-50	6.382	3.939	4.33	61.7%
-49	7.155	4.455	5.68	62.3%
-48	8.011	5.032	7.04	62.8%
-47	8.960	5.678	8.39	63.4%
-46	10.010	6.401	9.74	63.9%
-45	11.171	7.208	11.10	64.5%
-44	12.452	8.108	12.45	65.1%
-43	13.865	9.111	13.81	65.7%
-42	15.423	10.227	15.16	66.3%
-41	17.137	11.469	16.51	66.9%
-40	19.021	12.850	17.87	67.6%
-39	21.092	14.382	19.22	68.2%
-38	23.364	16.082	20.57	68.8%
-37	25.855	17.966	21.93	69.5%
-36	28.584	20.051	23.28	70.1%
-35	31.571	22.358	24.64	70.8%
-34	34.836	24.908	25.99	71.5%
-33	38.403	27.723	27.34	72.2%
-32	42.297	30.830	28.70	72.9%
-31	46.543	34.254	30.05	73.6%
-30	51.169	38.025	31.41	74.3%
-29	56.205	42.175	32.76	75.0%
-28	61.683	46.739	34.11	75.8%
-27	67.636	51.753	35.47	76.5%
-26	74.102	57.258	36.82	77.3%
-25	81.117	63.297	38.17	78.0%
Minimum Relative Humidity for Persistent Contrails
according to Gierens (2008)
exact:	RH_min = E_i(t) / E_w(t)
approx.:	RH_min = RH_a*t + RH_b
	RH_a	6.059E-03	1/°C
	RH_b	0.92261
	This according to:
	GIERENS, Klaus, et al.,2008. A Review of Various Strategies for Contrail Avoidance. In: OASC, vol.2, pp. 1-7.
	https://doi.org/10.2174/1874282300802010001
Checking the Influence of the Altitude of the Tropopause on Pressure
p(H, H_T)	hPa	p_0 =	1013.15	hPa
H	ft		20000	25000	30000	35000	36089	40000	45000	50000	55000	60000	65000	70000		title of legend
H_T	ft	20000	466	366	288	226	215	178	140	110	87	68	54	42		H_T = 20000 ft
		36089	466	376	301	238	226	188	147	116	91	72	56	44		H_T = 36089 ft
		50000	466	376	301	238	226	187	145	111	87	68	54	42		H_T = 50000 ft
		70000	466	376	301	238	226	187	145	111	83	62	45	32		H_T = 70000 ft
Result:
The influence of the altitude of the tropopause, H_T on the pressure is small!
Further approach:
The SAC and SAD is calculated with a standard H_T = 36089 ft,
even if later the SAD is evaluated for the temperatures of various other H_T.