A straight line from sea-level climb to the absolute ceiling
The linear model is ROC(h) = ROC0 (1 − h/habs). Set ROC equal to the service residual ROCsvc (100 ft/min unless you change it) and the service ceiling is hsvc = habs (1 − ROCsvc/ROC0). A sea-level 1,200 ft/min and a 12,000-foot absolute ceiling therefore have an 11,000-foot service ceiling, and 600 ft/min left at 6,000 feet. If you have climb rates at two density altitudes instead, the page fits the same straight line.
Real climb performance is not exactly linear, and it depends on weight, configuration, and temperature in ways a two-point fit cannot see. A POH climb chart always wins. For the density altitude you are actually departing from, use the density-altitude calculator; for a gradient in feet per nautical mile, use climb gradient.
Sources
- FAA Pilot’s Handbook of Aeronautical Knowledge, service, absolute, and cruise ceilings; rate of climb versus altitude.
- Linear ROC-versus-altitude model as used in performance textbooks (e.g. Anderson, Introduction to Flight; Phillips, Mechanics of Flight).
Frequently asked questions
Why is the default service residual 100 ft/min?
That is the usual light-airplane definition of service ceiling. Some jet or special-performance manuals use a different residual; type the number your book uses.
Can I use indicated altitude instead of density altitude?
The model is in density altitude. Using indicated or pressure altitude on a non-standard day will misplace the ceiling.
What if climb increases with altitude in my two points?
The page will not fit that pair. A service-ceiling line has to slope down.