Sorry for the late reply to several queries. Don’t forget that the True Altitude correction applies only to the 7,500 ft column of air between the Reference Station and the aircraft.
.1. ISA Temperature at 10,000 ft = 15 – 10 X 1.9812 = -4.812°C
.2. ISA Deviation at 10,000 ft = OAT – ISA = –20 – - 4.812 = ISA – 15.188
.3. ISA Temperature at 2,5000 ft = 15 – 5 X 1.9812 = +10.047°C
.4. ISA Temperature of Mean column of air above Reference Station = (-4.812+10.047) / 2 = + 2.6175°C + 273.15 = 275.7675°A(K)
.5. Actual Temperature of Mean column of air above Reference Station = 275.7675°A – 15.188 = 260.5795°A(K)
.6. True Altitude above Reference Station = 7,500 ft X 260.5795 / 275.7675 = 7086.9 ft
.7. True Altitude Above Sea Level = 2500 + 7086.9 = 9586.9 ft
If you consider that the QNH of 29.62” EQUALLY affects the Station Pressure Height and the Aircraft Pressure Height (to 2,780 and 10,280 ft respectively) it makes a VERY slight difference to the calculation. If this is considered, the True Altitude above the station becomes 7086.1 ft (9586.1 ft AMSL), an error of a mere 0.8 feet.
Regards,
Old Smokey