VARIATIONS OF THRUST REQUIRED AND POWER REQUIRED

The curves of thrust required and power required versus velocity provide the basis for comprehensive analysis of all the major items of airplane performance. The changes in the drag and power curves with variations of air­plane gross weight, configuration, and altitude furnish insight for the variation of range, endurance, climb performance, etc., with these same items.

The effect of a change in weight on the thrust and power required is illustrated by figure 2.2.

I The primary effect of a weight change is a change in the induced drag and induced power required at any given speed. Thus, the great­est changes in the curves of thrust and power required will take place in the range of low speed flight where the induced effects pre­dominate. The changes in thrust and power required in the range of high speed flight are relatively slight because parasite effects pre­dominate at high speed. The induced effects at high speed are relatively small and changes in these items produce a small effect on the total thrust or power required.

In addition to the general effect on the in­duced drag and power required at particular speeds, a change in weight will require that the airplane operate at different airspeeds to main­tain conditions of a specific lift coefficient and angle of attack. If the airplane is in steady flight at a particular CL, the airpseed required for this CL will vary with weight in the fol­lowing manner:

vrVWt

where

Vi — speed corresponding to a specific CL and weight, Wx

V2= speed corresponding to the same CL
but a different weight, W%

For the example airplane of figure 2.2, a change of gross weight from 15,000 to 22,500 lbs. re­quires that the airplane operate at speeds which are 22.5 percent greater to maintain a specific lift coefficient. For example, if the 15,000-lb. airplane operates at 160 knots for QL/D’)mai, the speed for (_L/D’)maI at 22,500 lbs. is:
—196 knots

The same situation exists with respect to the curves of power required where a change in weight requires a change of speed to maintain flight at a particular CL. For example, if the 15,000-lb. airplane achieves minimum power required at 122 knots, an increase in weight to 22,500 lbs. increases the speed for minimum power required to 149 knots.

Qf course, the thrust and power required at specific lift coefficients are altered by changes in weight. At a specific CL, any change in weight causes a like change in thrust required, e. g., a 50-percent increase in weight causes a 50-per­cent increase in thrust required at the same CL. The effect of a weight change on the power re­quired at a specific CL is a bit more complex be­cause a change in speed accompanies the change

THRUST

REQUIRED

(LBS)

POWER

REQUIRED

in drag and there is a two-fold effect. A 50- percent increase in weight produces an increase of 83.8 percent in the power required to main­tain a specific CL. This is the result of a 50- percent increase in thrust required coupled with a 22.5-percent increase in speed. The effect of a weight change on thrust required, power re­quired, and airspeed at specific angles of attack and lift coefficients provides an important basis for various techniques of cruise and endurance conditions of flight.

I Figure 2.3 illustrates the effect on the curves of thrust and power required of a change in the equivalent parasite area,/, of the configuration. Since parasite drag predominates in the region of high flight speed, a change in /will produce the greatest change in thrust and power re­quired at high speed. Since parasite drag is relatively small in the region of low speed flight, a change in / will produce relatively small changes in thrust and power required at low speeds. The principal effect of a change in equivalent parasite area of the configuration is to change the parasite drag at any given air­speed.

The curves of figure 2.3 depict the changes in the curves of thrust and power required due to a 50 percent increase in equivalent parasite area of the configuration. The minimum total drag is increased by an increase in / and the (L(D)mox is reduced. Also, the increase in / will increase the CL for (L/D)^ and require a reduction in speed at the new, but decreased, (LjD^ma. The point of minimum power re­quired occurs at a lower airspeed and the value of the minimum power required is increased slightly. Generally, the effect on the mini­mum power required is slight because the para­site drag is only 25 percent of the total at this specific condition of flight.

An increase in the equivalent parasite area of an airplane may be brought about by the deflection of flaps, extension of landing gear, extension of speed brakes, addition of external stores, etc. In such instances a decrease in the airplane efficiency factor, e, may accompany

an increase in / to account for the additional changes in parasite drag which may vary with

CL.

A change in altitude can produce signifi­cant changes in the curves of thrust and power required. The effects of altitude on these curves provide a great part of the explanation of the effect of altitude on range and endurance. Figure 2.4 illustrates the effect of a change in altitude on the curves of thrust and power re­quired for a specific airplane configuration and gross weight. As long as compressibility effects are negligible, the principal effect of increased altitude on the curve of thrust re­quired is that specific aerodynamic conditions occur at higher true airspeeds. For example, the subject airplane at sea level has a minimum drag of 1,250 lbs. at 160 knots. The same airplane would incur the same drag at altitude if operated at the same equivalent airspeed of 160 knots. However, the equivalent airspeed of 160 knots at 22,000 ft. altitude would produce a true airspeed of 227 knots. Thus, an in­crease in altitude will cause the curve of thrust required to flatten out and move to the direc­tion of higher velocity. Note that altitude alone will not alter the value of minimum drag.

The effect of altitude on the curve of power required can best be considered from the effect on true airspeed to achieve a specific aero­dynamic condition. The sea level power re­quired curve of figure 2.4 indicates that occurs at 160 knots and requires 615 h. p. If this same airplane is operated at (L/D^wa at an altitude of 22,000 ft., the same drag is incurred at a higher velocity and re­quires a higher power. The increase in ve­locity to 227 knots accounts for the increase in power required to 872 h. p. Actually, the various points on the curve of power required can be considered affected in this same fashion. At specific lift coefficients and angles of attack, a change in altitude will alter the true airspeed particular to these points and cause a change in power required because of the change in true airspeed. An increase in altitude will

POWER

REQUIRED

(HP)

THRUST

REQUIRED

(LBS)

POWER

REQUIRED

(HP.)

cause the power required curve to flatten out and move to higher velocities and powers required.

The curves of thrust and power required and their variation with weight, altitude, and con­figuration are the basis of all phases of airplane performance. These curves define the require­ments of the airplane and must be considered with the power and thrust available from the powerplants to provide detailed study of the various items of airplane performance.