CLIMB performance

During climbing flight, the airplane gains potential energy by virtue of elevation. This increase in potential energy during a climb is provided by one, or a combination, of two means-, (1) expenditure of propulsive energy above that required to maintain level flight or

(2) expenditure of airplane kinetic energy, i. e., loss of velocity by a zoom. Zooming for alti­tude is a transient process of trading kinetic energy for potential energy and is of considera­ble importance for airplane configurations which can operate at very high levels of kinetic energy. However, the major portions of climb performance for most airplanes is a near steady process in which additional propulsive energy is converted into potential energy. The funda­mental parts of airplane climb performance in­volve a flight condition where the airplane is in equilibrium but not at constant altitude.

The forces acting on the airplane during a climb are shown by the illustration of figure

2.21. When the airplane is in steady flight with moderate angle of climb, the vertical component of lift is very nearly the same as the actual lift. Such climbing flight would exist with the lift very nearly equal to the weight. The net thrust of the powerplant may be in­clined relative to the flight path but this effect will be neglected for the sake of simplicity. Note that the weight of the aircraft is vertical but a component of weight will act aft along the flight path.

If it is assumed that the aircraft is in a steady climb with essentially small inclination of the flight path, the summation of forces along the flight path resolves to the following:

Forces forward=Forces aft

T__ n і tj/ _: –

x УУ ЫН У

where

T= thrust available, lbs.

D=drag, lbs.

W= weight, lbs.

у = flight path inclination or angle of climb, degrees (“gamma’

This basic relationship neglects some of the factors which may be of importance for air­planes of very high climb performance. For example, a more detailed consideration would account for the inclination of thrust from the flight path, lift not equal to weight, subse­quent change of induced drag, etc. However, this basic relationship will define the principal factors affecting climb performance. With this relationship established by the condition of equilibrium, the following relationship exists to express the trigonometric sine of the climb angle, y:

This relationship simply states that, for a given weight airplane, the angle of climb (7) depends on the difference between thrust and drag (T— D), or excess thrust. Of course, when the excess thrust is zero (T— D=0 or Т-D’), the inclination of the flight path is zero and the airplane is in steady, level flight. When the thrust is greater than the drag, the excess thrust will allow a climb angle depend­ing on the value of excess thrust. Also, when the thrust is less than the drag, the deficiency of thrust will allow an angle of descent.

The most immediate interest in the climb angle performance involves obstacle clearance. The maximum angle of climb would occur where there exists the greatest difference be­tween thrust available and thrust required, i. e., maximum (T—Z>). Figure 2.21 illustrates the climb angle performance with the curves of thrust available and thrust required versus velocity. The thrust required, or drag, curve is assumed to be representative of some typical airplane configuration which could be powered by either a turbojet or propeller type power – plant. The thrust available curves included are for a characteristic propeller powerplant and jet powerplant operating at maximum output.

The thrust curves for the representative pro­peller aircraft show the typical propeller thrust which is high at low velocities and decreases with an increase in velocity. For the pro­peller powered airplane, the maximum excess thrust and angle of climb will occur at some speed just above the stall speed. Thus, if it is necessary to clear an obstacle after takeoff, the propeller powered airplane will attain maximum angle of climb at an airspeed con­veniently close to—if not at—the takeoff speed.

The thrust curves for the representative jet aircraft show the typical turbojet thrust which is very nearly constant with speed. If the thrust available is essentially constant with speed, the maximum excess thrust and angle of climb will occur where the thrust required

and*

e*8)

near the speed for (Z,/jD)met. There is no direct relationship which establishes this situation since the variation of propeller efficiency is the principal factor accounting for the variation of power available with velocity. In an ideal sense, if the propeller efficiency were constant, maximum rate of climb would occur at the speed for minimum power required. How­ever, in the actual case, the propeller efficiency of the ordinary airplane will produce lower power available at low velocity and cause the maximum rate of climb to occur at a speed greater than that for minimum power required.

The power curves for the representative jet aircraft show the near linear variation of power available with velocity. The maximum rate of climb for the typical jet airplane will occur at some speed much higher than that for max­imum rate of climb of the equivalent propeller powered airplane. In part, this is accounted for by the continued increase in power – avail­able with speed. Note that a 50 percent in­increase in thrust by use of an afterburner may cause an increase in rate of climb of approxi­mately 100 percent.

The climb performance of an airplane is affected by many various factors. The con­ditions of maximum climb angle or climb rate occur at specific speeds and variations in spe’ed will produce variations in climb performance. Generally, there is sufficient latitude that small variations in speed from the optimum do not produce large changes in climb performance and certain operational items may require speeds slightly different from the optimum. Of course, climb performance would be most critical at high weight, high altitude, or dur­ing malfunction of a powerplant. Then, opti­mum climb speeds are necessary. A change in airplane weight produces a twofold effect on climb performance. First, the weight, W, appears directly in denominator of the equa­tions for both climb angle and climb rate. In addition, a change in weight will alter the drag and power required. Generally, an in­crease in weight will reduce the maximum rate

of climb but the airplane must be operated at some increase of speed to achieve the smaller peak climb rate (unless the airplane is compres­sibility limited).

The effect of altitude on climb performance is illustrated by the composite graphs of figure

2.22. Generally, an increase in altitude will increase the power required and decrease the power available. Hence, the climb perform­ance of an airplane is expected to be greatly affected by altitude. The composite chart of climb performance depicts the variation with altitude of the speeds for maximum rate of climb, maximum angle of climb, and maximum and minimum level flight airspeeds. As alti­tude is increased, these various speeds finally converge at the absolute ceiling of the airplane. At the absolute ceiling, there is no excess of power or thrust and only one speed will allow steady level flight. The variation of rate of climb and maximum level flight speed with altitude for the typical propeller powered air­plane give evidence of the effect of supercharg­ing. Distinct aberrations in these curves take place at the supercharger critical altitudes and blower shift points. The curve of time to climb is the result of summing up the incre­ments of time spent climbing through incre­ments of altitude. Note that approach to the absolute ceiling produces tremendous increase in the time curve.

Specific reference points are established by these composite curves of climb performance. Of course, the absolute ceiling of the airplane produces zero rate of climb. The service ceiling is specified as the altitude which produces a rate of climb of 100 fpm. The altitude which produces a rate of climb of 500 fpm is termed the combat ceiling. Usually, these specific refer­ence points are provided for the airplane at the combat configuration or a specific design configuration.

The composite curves of climb performance for the typical turbojet airplane are shown in figure 2.22. One particular point to note is the more rapid decay of climb performance

ABSOLUTEJ CEILING

with altitude above the tropopause. This is due in great part to the more rapid decay of engine thrust in the stratosphere.

During a power off descent the deficiency of thrust and power define the angle of descent and rate of descent. Two particular points are of interest during a power off descent: minimum angle of descent and minimum rate of descent, The minimum angle of descent would provide maximum glide distance through the air. Since no thrust is available from the power plant, minimum angle of descent would be obtained at (LjD’)vua. At (L/D’)max the deficiency of thrust is a minimum and, as shown by figure 2.22, the greatest proportion between velocity and power required is ob­tained. The minimum rate of descent in power off flight is obtained at the angle of attack and airspeed which produce minimum power required. For airplanes of moderate aspect ratio, the speed for minimum rate of descent is approximately 75 percent of the speed for minimum angle of descent