NAVWEPS 00401-80 
APPLICATION OF AERODYNAlvllCS 
TO SPECIFIC PROBLEMS OF FLYING 
achieve the takeoff speed in the specified dis- 
tance. 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 take- 
off 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 dis- 
tance. 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 inter- 
section 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 accel- 
erated 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 com- 
mitted to an unsafe stop. If takeoff is refused 
when above the refusal speed, the only hope 
is for assistance from the arresting gear, run- 
way barrier, or an extensive overrun at the 
end of the runway. This fact points to the 
need for planning of the takeoff and the require- 
ment to monitor the takeoff acceleration. 
If the refusal speed data are not available, 
the following equations may be used to ap- 
proximate the refusal speed and distance: 
where 
V,= refusal speed 
S,= refusal distance 
and for the appropriate takeoff configuration, 
V,*= takeoff speed 
S,,= takeoff distance 
V,= landing speed 
J,=landing distance 
R. = runway length available 
These approximate relationships do not ac- 
count 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 ac- 
celeration prior to reaching the refusal speed. 
Obviously, it is to advantage to recognize rhe 
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