NAVWEPS 00-801-80 
AIRPLANE PERFORMANCE 
the distance varies directly as the square of the 
velocity and inversely as the acceleration. 
As an example of this relationship, assume 
that during takeoff an airplane is, accelerated 
uniformly from zero velocity to a takeoff 
velocity of 150 knots (253.5 ft. per sec.) with 
an acceleration of 6.434 ft. per sec.* (or, 0.2g, 
since g=32.17 ft. per sec.*). The takeoff 
distance would be: 
= (253.5)* 
(2)(6.434) 
=5,ooo ft. 
If the acceleration during takeoff were reduced 
10 percent, the takeoff distance would increase 
11.1 percent; if the takeoff velocity were 
increased 10 percent, the takeoff distance 
would increase 21 percent. These relation- 
ships point to the fact that proper accounting 
must be made of altitude, temperature, gross 
weight, wind, etc. because any item affecting 
acceleration or takeoff velocity will have a 
definite effect on takeoff distance. 
If an airplane were to land at a velocity of 
150 knots and be decelerated uniformly to a 
stop with the same acceleration of 0.2g, the 
landing stop distance would be 5,000 ft. 
However, the case is not necessarily that an 
aircraft may have identical takeoff and landing 
performance but the principle illustrated is that 
distance is a function of velocity and accelera- 
tion. As before, a 10 percent lower accelera- 
tion increases stop distance Il.1 percent, and a 
10 percent higher landing speed increases 
landing distance 21 percent. 
The general relationship of velocity, accel- 
eration, and distance for uniformly accelerated 
motion is illustrated by figure 2.31. In this 
illustration., acceleration distance is shown as 
a function of velocity for various values of 
acceleration. 
TAKEOFF PERFORMANCE. The mini- 
mum takeoff distance is of primary interest in 
the operation of any aircraft because it defines 
the runway requirements. The minimum take- 
off distance is obtained by takeoff at some 
minimum safe velocity which allows sufficient 
margin above stall and provides satisfactory 
control and initial rate of climb. Generally, 
the takeoff speed is some fixed percentage of 
the stall speed or minimum control speed for 
the airplane in the takeoff configuration. As 
such, the takeoff will be accomplished at some 
particular value of lift coefficient and angle of 
attack. Depending on the airplane character- 
istics, the takeoff speed will be anywhere from 
1.05 to 1.25 times the stall speed or minimum 
control speed. If the takeoff speed is specified 
as 1.10 times the stall speed, the takeoff lift 
coefficient is 82.6 percent of CL- and the angle 
of attack and lift coeticient for takeoff are 
fixed values independent of weight, altitude, 
wind, etc. Hence, an angle of attack indicator 
can be a valuable aid during takeoff. 
To obtain minimum takeoff distance at the 
specified takeoff velocity, the forces which act 
on the aircraft must provide the maximum 
acceleration during the takeoff roll. The 
various forces acting on the aircraft may or 
may not be at the control of the pilot and 
various techniques may be necessary in certain 
airplanes to maintain takeoff acceleration at 
the highest value. 
Figure 2.32 illustrates the various forces 
which act on the aircraft during takeoff roll. 
The powerplant thrust is the principal force to 
provide the acceleration and, for minimum 
takeoff ,distance, the output thrust should be 
at a maximum. Lift and drag are produced as 
soon as the airplane has speed and the values 
of lift and drag depend on the angle of attack 
and dynamic .pressure. Rolling friction results 
when there is a normal force on the wheels 
and the friction force is the product of the 
normal force and the coefficient of rolling 
friction. The normal force pressing the wheels 
against the runway surface is the net of weight 
and lift while the rolling friction coefficient is 
a function of the tire type and runway surface 
texture.