The acceleration of the airplane at any 
instant during takeoff roll is a function of the 
net accelerating force and the airplane mass. 
From Newton’s second law of motion: 
or 
where 
a=acceleration,~fr. per set 
Fn- net accelerating force, 
W=weight, lbs. 
g? gravitational accelerat 
=32.17 ft. per sec.* 
M= mass, slugb 
= WE 
The riet aicelerating fdrce on ‘the airplane, 
F,, is the net of thiust, T, drag, D, and rolling 
friction, F. Thus, the acceleration -at any 
instant during takeoff roll is: 
a=&T-D-F) 
Figure 2.32 illustrates the typical variation of 
the various fbrces acting on the aircraft 
throughout the takeoff roll: If ‘it is assumed 
that the aircraft is at essentially constant 
angle of attack during takeoff roll, CL and Co 
are constant and the forces of lift and drag 
vary as the square of the speed. For the case 
of uniformly accelerated motion, distance 
along the takeoff roll is proportional also to 
the square bf the velocity hence velocity 
squared and distance can be used almost synon- 
omously. Thus, lift and drag will vary lint 
arly with dyriamic pressure (4) or P from 
the point of beginning takeoff roll. As the 
rolling friction coefficient -is esscnti&y un- 
affected by velocity, the rolling ftiction will 
vary as the normal force on the wheels. At 
zero velocity, the normal force on the wheels 
is equal to the airplane weight but, at takeoff 
velocity, the lift is equal to the weight and 
the normal force is zero. Hence, rolling fric- 
tion decreases linearly with 4 or Vz from the 
beginning of takeoff roll and reaches zero at 
the point of takeoff. 
NAVWEPS 00-801-80 
AIRPLANE PERFORMANCE 
The total retarding for& on the aircraft is 
the sum of drag and rolling friction (D+F) 
and, for the majority of configurations, this 
sum is nearly Constant or changes only slightly 
during the takeoff roll. The net accelerating 
force is then the difference between the power- 
plant thrust and the total retarding force, 
Fn=T-D-F 
The variation of the net accelerating force 
throughout the takeoff roll is shown in figure 
2.32. The typical propeller airplane demon- 
strates a net accelerating force which decreases 
with velocity and the resulting acceleration is 
initially high but decreases throughout the 
takeoff roll. The typical jet airplane demon- 
strates a net accelerating force which is essen- 
tially constant throughout the takeoff roll. 
As a result, the takeoff performance of the 
typical turbojet airpiane will compare closely 
with the case for uniformly accelerated motion. 
The pilot technique required to achieve peak 
acceleration throughout takeoff roll can vary 
considerably between airplane configurations. 
In some instances, maximum acceleration will 
be obtained by allowing the airplane to remain 
in the three-point attitude throughout the roll 
until the airplane simply reaches lift-equal-to- 
weight and flies off the ground. Other air- 
planes may require the three-point attitude 
until the takeoff speed is reached then rotation 
to the takeoff angle of attack to become air- 
borne. Still other configurations may require 
partial or complete rotation to the takeoff 
angle of attack prior to reaching the takeoff 
speed. In this case, the procedure may be 
necessary to provide a smaller retarding force 
(D+F) to achieve peak acceleration. When- 
ever any form of pitch rotation is necessary the 
pilot must provide the proper angle of attack 
since an excessive angle of attack will cause 
excessive drag and hinder (or possibly pre- 
clude) a successful takeoff. Also, irisufficient 
rotation may provide added rolling resistance 
or require that the airplane accelerate to some 
excessive speed prior to becoming airborne. 
185 
Revised January 1965