Horsepower For Climbing. Up to the present we have only considered horizontal flight. The power available for climbing is the difference between the power required to maintain horizontal flight at any speed, and the actual horsepower that can be delivered by the propeller. Thus, if the actual power delivered by a motor through the propeller is 85 horsepower, and the power required for horizontal flight at that speed is 45, then we have: 85–45= 40 horsepower available for climbing. Since the difference between the driving power and the power required for horizontal flight is less at extremely low and high speeds, it is evident that we will have a minimum climbing reserve at the high and low speeds. Consulting the power curve for the Bleriot monoplane, we see that the power required at 56 feet per second is 40 horsepower, and at 85 feet per second it is 38 horsepower. At the low speed we have a climbing reserve of 44–40 = 4 H. P., and at the higher speed 44–38 = 6 H. P. The maximum available horsepower "AV" is 44 horsepower. The minimum horizontal power required is found at 63 feet per second, the climbing reserve at this point being 44–28 = 16 horsepower. At 55 feet per second, and at 90, we would not be able to climb, as we would only have sufficient power to maintain horizontal flight.
If W = total weight of aeroplane, c = climbing speed, and H = horsepower reserve for climbing, then the climbing speed with a constant air density will be expressed by: c = 33000H/W. Assuming that the weight of the Bleriot monoplane is 800 pounds, and that we are to climb at the speed of the greatest power reserve (16 horsepower), our rate of climb is:
c = 33000H/w = 33000 x 16/800 = 660 feet per minute. It should be understood that this is the velocity at the beginning of the climb. After prolonged climbing the rate falls off because of diminishing power and increasing speed. Much depends upon the engine performance at the higher altitudes, so that the reserve power for climb usually diminishes as the machine rises, and hence the rate of climb diminishes in proportion.
The following table taken from actual flying tests will show how the rate of climb decreases with the altitude. These machines were equipped with 150 H. P. Hispano-Suisa motors. It will be noted that the S. P. A. D. and the Bleriot hold their rate of climb constant up to 7800 feet altitude, which is a feat that is undoubtedly performed by varying the compression of the engine.
Besides increasing the power, the rate of climb can also be increased by decreasing the weight of the aeroplane.
Maximum Altitude. The maximum altitude to which a machine can ascend is known as its "Ceiling." This again depends on both the aeroplane and the motor, but principally on the latter. It has been noted that machines having the greatest rate of climb also have the greatest ceiling. Thus the ceiling of a fast climbing scout is higher than that of a larger and slower machine. Based on this principle, a writer in "Flight" has developed the following equation for ceiling, which, of course, assumes a uniform decrease in density. Let H = maximum altitude, h = the altitude at any time t after the start of the climb, and a = the altitude after a time equal to twice the time t, then:
H = h / (2 - a/h)
Approximate values of h and a may be had
from the following table, which are the results of a test on a certain aeroplane: