Altimeter error across a pressure and temperature gradient: Christchurch to Queenstown
At 0900 NZST you plan a VFR flight in a Cessna 172 from Christchurch (NZCH, elevation 123 ft) to Queenstown (NZQN, elevation 1,171 ft), tracking via the Rakaia Gorge and Lindis Pass at 9,500 ft AMSL. Your sole altimeter is set to the Christchurch ATIS QNH of 1,002 hPa. A colleague who landed at Queenstown 20 minutes ago reports that airfield's QNH as 995 hPa. There is no area QNH for the mountain zone that you can obtain in the cockpit, and you have no datalink. The forecast temperature at 9,500 ft is -15 C; the freezing level is 7,000 ft. For the Lindis Pass sector your personal minimum terrain clearance is 1,000 ft, and the highest ground on your track is 7,500 ft. Winds are light. Christchurch surface temperature is 4 C. You are not instrument rated and the aircraft has no oxygen.
1. Estimate your true altitude over the Lindis Pass with the altimeter reading 9,500 ft on the Christchurch QNH, and state whether the planned profile meets your clearance requirement.
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Two corrections apply and they act in the same direction.
Pressure. Queenstown is 7 hPa lower. Near sea level 1 hPa is about 30 ft, but at 9,500 ft the air is roughly three-quarters of sea-level density, so 1 hPa is about 40 ft. Correction is about 7 x 40, roughly 280 ft. Flying from higher to lower pressure with a fixed subscale makes the altimeter over-read, so true altitude is about 280 ft below indicated.
Temperature. ISA at 9,500 ft is 15 - (2 x 9.5) = -4 C. The forecast -15 C is 11 C colder than ISA. Correction is about 9,500 x 11/273, roughly 380 ft, and cold air again puts true altitude below indicated.
Total. 280 + 380 = about 660 ft, so true altitude is roughly 8,840 ft. Required is 7,500 ft terrain plus 1,000 ft, i.e. 8,500 ft. The margin is only about 340 ft, which is smaller than the altimeter and static-system tolerance plus the uncertainty in the pressure assumption, with no terrain warning on board. The profile does not meet your own minimum. Options are to plan higher (10,500 ft is within the no-oxygen band) or to take the lower valley route with visual terrain reference. Cold-temperature corrections must also be applied to any MSA or circling minima you use.
2. How should you manage the altimeter setting en route, given that the true QNH changes along the track?
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New Zealand uses QNH below the transition altitude of 13,000 ft, and MetService publishes area QNH for defined zones so aircraft can reset when crossing a zone boundary. You cannot obtain the area QNH here, so you must reason about which error is tolerable rather than guess.
The key asymmetry: with a fixed indicated altitude, a lower QNH setting makes the altimeter read higher and a higher setting makes it read lower. In terrain an under-reading altimeter is conservative and an over-reading one is not. If you reset from 1,002 to 995 hPa at the boundary and held 9,500 ft indicated, your true altitude would drop by another 280 ft on top of the temperature error, which is exactly the wrong direction.
Therefore keep the highest credible QNH set (1,002 hPa here), treat the indicated altitude as an upper bound on true altitude, and add a terrain buffer or cross-check against GPS and visual reference. Never use a lower QNH from a remote station as a reason to descend. If area QNH were available, reset at the boundary but add the difference to your planned altitude instead of holding the same indicated figure. Set the destination QNH only when visual with the ground and clear of terrain.