Is this an accurate method to showing how the correct Decision Altitude/Height for an approach has been determined?
This is USA information. The summary: determine the obstacle clearance surfaces, add the required obstacle clearance buffers to those surfaces, adjust DA for glide slope angle and aircraft speed if not already above the minimum due to obstacle clearance. The procedures are all calculated in true altitude, not indicated altitude. Aircraft that fly IFR in the USA are required to have adjustable precision altimeters based on the ISA atmosphere and barometric altimeter based approaches must have a local weather station that provides the altimeter setting for that airport. The difference in DA based on temperature is not considered significant, however there are low temperature limits placed on baro-vnav approaches due to effects on glide path [not DA].
A typical DA in the USA is determined without altimeter temperature adjustments because a DA is only used with positive vertical course guidance, a three degree slope is the same at any temperature. There may be be a fixed decision-altitude adjustment calculated when a remote weather source must be used, based on potential difference in pressure. There may also be a low temperature limit in some cases for procedures that allow uncompensated baro-vnav systems because this equipment can change the glide path angle.
While there were some old manual calculation standards that could be simplified into the answer you are looking for, the modern method is calculated by computers using rather complex algorithms with multiple intersecting surfaces and measurement-uncertainty adjustments as well as large databases of terrain, obstacles, and local winds. FAA order 8260.3D contains most of the approach design structure, it is 509 pages, but even with all of that in several places it simply references the use of software, an example quote &quot;Increase ROC values by the amount specified by the software.&quot; See 8260.3D page 198, 202-203,(cat1 final obstacle surfaces and DA) and appendix C(precipitous terrain adjustments) for some of the formulas.
This is completed with a detailed in flight inspection of the procedure using specialized aircraft to carefully map the navigation signals and controlling obstacles. The FAA also performs this service for many other countries and performs regular flight checks of existing procedures, nav-aids, and airways on a regular schedule. Some basic procedure/airway design requirements can be altered if a flight inspection determines the deviation is safe in that specific case.
As for the core components, they check obstacle clearance of the final approach segment, and recently they also compute the vertical guidance surface.(the part of final between DA and threshold. Note the 34:1 clearance symbol added to new FAA plates, it is related to VGS. Jeppeson omits this piece.) If this requires an increased glide slope angle to meet required clearances the DA may be raised for the faster category aircraft. Then the missed segment is calculated and checked for obstacles, if needed the DA is raised again so that the missed segment has required clearances. The missed segment includes an inertia allowance below DA for aircraft that fail to react until they are at DA,(this is a buffer, not intended for normal use.) this inertia is also why higher speed aircraft are given a higher DA. The difference in height between the navigation equipment in the cockpit, or antenna placement, and the wheels of the aircraft-class expected at that airport is considered for the area between DA and threshold.(A 747 will have its wheels about 30 feet lower than a cessna 172 while following the same glide path.)