Maximum Flight Altitude, Absolute and Service Ceilings

The RC information can be used to estimate the flight altitude that can be reached by an airplane. Again, we use the Messerschmitt fighter as an example. Clearly, the RC decreases with altitude so that the maximum achievable altitude or absolute ceiling, corresponds to the condition at which no further RC is available—that is, the altitude for which there remains no excess power. Such a flight condition is of little use because there is no margin left for maneuvering. For example, if an aircraft is required to execute a simple turn under this flight condition, it would descend because of insufficient thrust for level flight. It would stall if the stall speed happens to be at or near the speed for maximum RC at this altitude. Part of the lift then would be required to produce the turn, and no power would be available to adjust the speed to increase the vertical component of lift needed to balance the weight. Thus, we define the service ceiling, which represents a practical maximum altitude with some excess power remaining for minimal maneuvering capability. The service ceiling is usually defined as that altitude at which the maximum RC drops to 100 ft/min.

If we again neglect the effect of altitude on power available, we can estimate this altitude for an aircraft like the Bf-109G. First, we solve for the power required for the stated RC by using Eq. 9.20:

RC = 100 = TV – DV = 550(0.88 • 1,200 – PR)

W 6,700 ‘

This indicates that for this flight condition, the power required is:

PR = 162.2 horsepower.

Notice the handling of the units in this calculation; it is necessary to convert from horsepower to ft-lbf/sec. The simplest procedure is to vary the density until the required condition is met. Directly solving equations for the density is difficult algebraically. To make a realistic calculation, it is necessary to account for the degradation of power available as the altitude increases. Because we do not have the Daimler-Benz power-available curves, we can only make educated guesses. The simplest possibility is that the power available drops off in direct proportion to the ratio of the density to the sea-level density. A more common assumption is that it drops off as the square root of this ratio, as does the power required. Both cases are displayed in Fig. 9.7, which is a plot of maximum RC versus density. The service ceilings for the cases are 34,500 ft. for the linear dependence on density and 46,500 for the square-root density dependence of the power available. The published service ceiling for the Bf-109G is 37,900 ft., so a reasonable estimate was achieved without knowledge of the exact power-available curves for this aircraft.