During takeoff, it is necessary to monitor the performance of the airplane and evaluate the acceleration to insure that the airplane will

achieve the takeoff speed in the specified dis­tance. If it is apparent that the airplane is not accelerating normally or that the airplane or powerplant is not functioning properly, a decision must be made to refuse or continue takeoff. If the decision to refuse takeoff is made early in the takeoff roll, no problem exists because the airplane has not gained much speed and a large portion of runway distance is unused. However, at speeds near the takeoff speed, the airplane has used a large portion of the takeoff distance and the distance required to stop is appreciable. The problem which exists is to define the highest speed attained during takeoff acceleration from which the airplane may be decelerated to a stop on the runway length remaining, i. e., the “refusal speed.’’

The refusal speed will be a function of take­off performance, stopping performance, and the length of available runway. The ideal situation would be to have a runway length which exceeds the total distance required to accelerate to the takeoff speed then decelerate from the takeoff speed. In this case, the refusal speed would exceed the takeoff speed and there would be little concern for the case of refused takeoff. While this may be the case for some instances, the usual case is that the runway length is less than the “accelerate – stop’’ distance and the refusal speed is less than the takeoff speed. A graphical representation of the refused takeoff condition is illustrated in figure 6.12 by a plot of velocity versus dis­tance. At the beginning of the runway, the airplane starts accelerating and the variation of velocity and distance is defined by the takeoff acceleration profile. The deceleration profile describes the variation of velocity with distance where the airplane is brought to a stop at the end of the runway. The inter­section of the acceleration and deceleration profiles then defines the refusal speed and the refusal distance along the runway. Of course, an allowance must be made for the time spent at the refusal speed as the power is reduced and braking action is initiated.

During takeoff, the airplane could be accel­erated to any speed up to the refusal speed, then decelerated to a stop on the runway remaining. Once past the refusal speed, the airplane cannot be brought to a stop on the runway remaining and the airplane is com­mitted to an unsafe stop. If takeoff is refused when above the refusal speed, the only hope is for assistance from the arresting gear, run­way barrier, or an extensive overrun at the end of the runway. This fact points to the need for planning of the takeoff and the require­ment to monitor the takeoff acceleration.

If the refusal speed data are not available, the following equations may be used to ap­proximate the refusal speed and distance:


VT = refusal speed Tr = refusal distance

and for the appropriate takeoff configuration,

Vt0= takeoff speed

St0= takeoff distance

VL= landing speed

Ті. = landing distance

Ra = runway length available

These approximate relationships do not ac­count for the time spent at the refusal point and must not be used in lieu of accurate handbook data.

In the case of the single-engine airplane, the pilot must monitor the takeoff performance to recognize malfunctions or lack of adequate ac­celeration prior to reaching the refusal speed. Obviously, it is to advantage to recognize the

possibility of a refused takeoff before exceed­ing the refusal speed. To this end, the pilot must carefully evaluate airplane and power – plant performance and judge the acceleration of the airplane by the use of “line speeds." The accelerated motion of the airplane during takeoff roll will define certain relationships be­tween velocity and distance when the acceler­ation of the airplane is normal. By comparison of predicted and actual speeds at various points along the runway, the pilot can evaluate the acceleration and assess the takeoff perform­ance.

An example of an acceleration profile is shown by the second illustration of figure 6.12, where the variation of velocity and distance is defined for the case of uniformly accelerated motion, i. e., constant acceleration. While the case of uniformly accelerated motion does not correspond exactly to the takeoff performance of all airplanes, it is sufficiently applicable to illustrate the principle of line speeds and ac­celeration checks. If the takeoff acceleration of the airplane were constant, the airplane would develop specific percentages of the take­off speed at specific percentages of the takeoff distance. Representative values from figure 6.12 are as follows:

Percent (if takeoff

Patent of takeoff

Patent of takeoff



















As an example of this uniformly accelerated motion, the airplane upon reaching the half­way point of takeoff roll would have spent 70.7 percent of the total takeoff time and ac­celerated to 70.7 percent of the takeoff speed. If the airplane has not reached a specific speed at a specific distance, it is obvious that the ac­celeration is below the predicted value and the airplane surely will not achieve the takeoff speed in the specified takeoff distance. There­fore, properly computed line speeds at various points along the runway will allow the pilot to monitor the takeoff performance and recog­nize a deficiency of acceleration. Of course, a deficiency of acceleration must be recognized prior to reaching some point along the runway where takeoff cannot be safely achieved or refused.

The fundamental principles of refusal speeds and line speeds are applicable equally well to single-engine and multiengine airplanes. How­ever, in the case of the multiengine airplane additional consideration must be given to the decision to continue or refuse takeoff when engine failure occurs during the takeoff roll. If failure of one engine occurs prior to reaching the’refusal speed, takeoff should be discon­tinued and the airplane brought to a stop on the remaining runway. If failure of one engine occurs after exceeding the refusal speed, the airplane is committed to continue takeoff with the remaining engines operative or an unsafe refused takeoff. In some cases, the remaining runway may not be sufficient to allow acceler­ation to the takeoff speed and the airplane can neither takeoff or stop on the runway remain­ing. To facilitate consideration of this prob­lem, several specific definitions are necessary.

(1) Takeoff and initial climb speed: A speed,

usually a fixed percentage above the stall speed, at which the airplane will become airborne and best clear obstacles immediately after takeoff. For a particular airplane in the takeoff con­figuration, this speed (in BAS or CAS) is a function of gross weight but in no circumstances should it be less than the minimum directional control speed for the critical asymmetrical power condition. Generally, the takeoff and initial climb speed is referred to as the ‘ V2” speed. •

(2) Critical engine failure speed: A speed

achieved during the takeoff roll at which fail­ure of one engine will require the same distance to continue accelerating with the operative en­gines to accomplish safe takeoff or refuse takeoff and decelerate to a stop utilizing the airplane brakes. At critical engine failure


speed, the distance necessary to continue take­off with one engine inoperative is equal to the stopping distance. The critical engine failure speed is generally referred to as the "Fj” speed and it is a function of the same factors which determine the takeoff performance, e. g., density altitude, gross weight, temperature, humidity, etc.

(3) Critical field length: The runway length necessary to accelerate with all engines opera­tive to the critical engine failure speed (У0 then continue accelerating to the takeoff and initial climb speed (Fs) with one engine inoperative and achieve safe takeoff or refuse takeoff. By this definition, critical field length describes the minimum length of run­way necessary for safe operation of the multi­engine airplane. Obviously, the critical field length is a function of the same factors affect­ing the takeoff distance of the airplane.

The conditions of Vu and critical field length are illustrated by figure 6.13. The first illustration of figure 6.13 depicts the case where the runway length is equal to the critical field length. In this case, the airplane could accelerate to Fj with all engines opera­tive then either continue takeoff safely with one engine inoperative or refuse takeoff and decelerate to a stop on the remaining runway. For this condition, an engine failure occurring at less than Vt speed dictates that takeoff must be refused because inadequate distance remains to effect a safe takeoff at V3 speed. However, at or below Vi speed, adequate distance re­mains to bring the airplane to a stop. If engine failure occurs at some speed greater than Vt speed, takeoff should be continued because adequate distance remains to accelerate to Fs speed and effect a safe takeoff with one engine inoperative. If engine failure occurs beyond Vi speed, inadequate distance remains to brake the airplane to a stop on the runway.

The second illustration of figure 6.13 depicts the case where the runway length is less than the critical field length. In this case, the term of “Ft” speed is not applicable because of inadequate distance and the refusal speed is less than the minimum speed necessary to continue a safe takeoff with one engine inoper­ative. If engine failure occurs below refusal speed, the takeoff must be refused and adequate distance remains to effect a stop on the runway. If engine failure occurs above refusal speed but below the minimum speed necessary to continue takeoff with one engine inoperative, an accident is inevitable. Within this range of speeds, the airplane cannot effect a safe takeoff at Fa with one engine inoperative or a safe stop on the remaining runway. For this reason, the pilot must properly plan the takeoff and insure that the runway available is equal to or greater than the critical field length. If the runway available is less than the critical field length, there must be sufficient justification for the particular operation be­cause of the hazardous consequences of engine failure between the refusal speed and the minimum speed necessary to continue takeoff with one engine inoperative. Otherwise, the gross weight of the airplane should be reduced in attempt to decrease the critical field length to equal the available runway.


From the standpoint of public relations and the maintaining of friendly public support for Naval Aviation, great care must be taken to prevent sonic booms in populated areas. While the ordinary sonic boom does not carry any potential of physical damage, the disturb­ance must be avoided because of the undesirable annoyance and apprehension. As supersonic flight becomes more commonplace and an ordinary consequence of flying operations, the prevention of sonic booms in populated areas becomes a difficult and perplexing job.

When the airplane is in supersonic flight, the local pressure and velocity changes on the airplane surfaces are coincident with the formation of shock waves. The pressure jump through the shock waves in the immediate vicinity of the airplane surfaces is determined

by the local flow changes at these surfaces. Of course, the strength of the shock waves and the pressure jump through the wave decreases rapidly with distance away from the airplane. While the pressure jump through the shock wave decreases with distance away from the surface, it does not disappear com­pletely and a measurable—but very small— pressure will exist at a considerable distance from the airplane.

Sound is transmitted through the air as a series of very weak pressure waves. In the ordinary range of audible frequencies, the threshold of audibility for intensity of sound is for pressure waves with an approximate R. M.S. value of pressure as low as 0.0000002 psf. Within this same range of frequencies, the threshold of feeling for intensity of sound is for pressure values with an approximate R. M.S. value of pressure of 0.2 to 0,5 psf. Continuous sound at the threshold of feeling is of the intensity to cause painful hearing. Thus, the shock waves generated by an air­plane in supersonic flight are capable of creat­ing audible sound and, in the extreme case, can be of a magnitude to cause considerable dis­turbance. Pressure jumps of 0.02 to 0.3 psf have been recorded during the passage of an airplane in supersonic flight. As a result, the sonic "booms” are the pressure waves generated by the shock waves formed on the airplane in supersonic flight.

The source of sonic booms is illustrated by figure 6.14. When the airplane is in level supersonic flight, a pattern of shock waves is developed which is much dependent on the configuration and flight Mach number of the airplane. At a considerable distance from the airplane, these shock waves tend to combine along two common fronts and extend away from the airplane in a sort of conical surface. The waves decrease in strength with distance away from the airplane but the pressure jump remains of an audible intensity for a consider­able distance from the airplane. If the w-ave extends to the ground or water surface, it will be reflected and attenuated to some extent depending on the character of the reflecting surface. Of course, if this attached wave form is carried across a populated area at the surface, th: population will experience the pressure waves as a sonic boom.

The intensity of the boom will depend on many different factors. The characteristics of the airplane generating the shock waves will be of some importance since a large, high drag, high gross weight airplane in flight at high Mach number will be transferring a greater energy to the air mass. Flight altitude will have an important bearing on boom intensity since at high altitude the pressure jump across a given wave form is much less. In addition, at high altitude a greater distance exists be­tween the generating source of the pressure disturbance and the ground level and the strength of the wave will have a greater dis­tance in which to decay. The ordinary vari­ation of temperature and density plus the natural turbulence of atmosphere will tend to reflect or dissipate the shock wave generated at high altitude. However, in a stable, quies­cent atmosphere, the pressure wave from the airplane in high supersonic flight at high alti­tude may be of an audible magnitude at lateral distances as great as 10 to 30 miles. Thus, supersonic flight over or adjacent to populated areas will produce a sonic boom.

Actually, it is not necessary for an airplane to fly supersonic over or adjacent to a popu­lated area to create a sonic boom. This possibility is shown by the second illustration of figure 6.14 where an airplane decelerates to subsonic from a supersonic dive. As the air­plane slows to subsonic from supersonic speed, the airplane will release the leading bow and tail waves which formed as the airplane accel­erated from subsonic to supersonic speed. The release of these shock waves is analogous to the case where a surface ship slows to below the wave propagation speed and releases the bow wave which then travels out ahead of

the ship. When the airplane slows to sub­sonic, the shock wave travels out ahead of the airplane in a form which is somewhat spheri­cal. Because there are density variations through the shock wave, the shock wave moving ahead of the airplane can cause aber­rations in light waves and it may appear, to the pilot as if a large sheet of clear cellulose or plastic were in front of the airplane. In addition, the density variation and initial shape of the wave leaving the airplane may cause reflection of sunlight which would appear as a sudden, brilliant “flash” to the pilot.

Of course, the wave released by decelerating to subsonic speed can travel out ahead of the airplane and traverse a populated area to cause a sonic boom. The initial direction of the released wave will be the flight path of the airplane at the instant it decelerates to sub­sonic speed. To be sure, the released wave should not be aimed in the direction of a popu­lated area, even if a considerable distance away. There are instances where a released wave has been of an audible magnitude as far as 30 to 40 miles ahead of the point of release. The released pressure wave will be of greatest intensity when created by a large, high drag configuration at low altitude. Since the wave intensity decreases rapidly with distance away from the source, the boom will be of strongest audibility near the point of release.

It should become apparent that sonic booms are a byproduct of supersonic aviation and, with supersonic flight becoming more common­place, the problem is more perplexing. The potential of sonic booms is mostly of the audible nature and nuisance of the disturbance. The damage potential of the ordinary sonic boom is quite small and the principal effects are confined to structures which are extremely brittle, low strength, and have characteristic high residual stresses. In other words, only the extremes of pressure waves generated by airplanes in flight could possibly cause cracked plaster and window glass. Such materials are quite prone to sharp dynamic stresses and, when superimposed on the high residual stresses common to the products and building construction, slight but insignificant damage may result. Actually, the most objectionable feature of the sonic boom is the audibility and the anxiety or apprehension caused by the sharp, loud noise which resembles a blast.

The pressure jump through the shock waves in the immediate vicinity of the airplane is much greater than those common to the audible “booms” at ground level. Thus, airplanes in close formation at supersonic speeds may encounter considerable interference between airplanes. In addition, to eliminate even the most remote possibility of structural damage, a high speed airplane should not make a supersonic pass close to a large air­plane which may have low limit load factor and be prone to be easily disturbed or damaged by a strong pressure wave.

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