In this sense, an angle of attack indicator is 
especially useful for night or instrument takeoff 
conditions as well as. the ordinary day VFR 
takeoff conditions. Acceleration errors of the 
attitude gyro usually preclude accurate pitch 
rotation under these conditions. 
FACTORS AFFECTING TAKEOFF PER- 
FORMANCE. In addition to the important 
factors of proper technique, many other vari- 
ables affect the takeoff performance of an air- 
plane. Any item which alters the takeoff 
velocity or acceleration during takeoff roll will 
affect the takeoff distance. In order to evalu- 
ate the effect of the many variables, the prin- 
cipal relationships of uniformly accelerated 
motion,will be assumed and consideration will 
be given to those effects due to any nonuni- 
formity of acceleration during the process of 
takeoff. Generally, in the case of uniformly 
accelerated motion, distance varies directly 
with the square of the takeoff velocity and in- 
versely as the takeoff acceleration. 
where 
S= distance 
V= velocity, 
a= acceleration 
;’ con&&‘(I) applies to some known takeoff 
distance, Si, which was common to 
some original takeoff velocity, Vi, and 
acceleration, ai. 
condition (2) applies to some new takeoff 
distance, Sa, which is the result of some 
different value of takeoff velocity, Vs, or 
acceleration, aa. 
With xhis basic relationship, the effect of the 
many variables on takeoff ‘distance can be 
approximated. 
The effect of gross weight on takeoff distance is 
large and proper consideration of this item 
must be made in predicting takeoff distance. 
Increased gross weight can be considered to 
produce a threefold effect on takeoff perform- 
ance: (1) increased takeoff velocity, (2) greater 
NAVWEPS 00401-80 
AIRPLANE PERFORMANCE 
mass to accelerate, and (3) increased retarding 
force (D+F). If the gross weight increases, 
a greater speed is necessary to produce the 
greater lift to get the airplane airborne at the 
takeoff lift coefficient. The relationship of 
takeoff speed and gross weight would be as 
follows: 
where 
VI= takeoff velocity corresponding to 
some original weight, Wi 
V2= takeoff velocity corresponding to 
some different weight, W, 
Thus, a given airplane in the takeoff configura- 
tion at a given gross weight will have a specific 
takeoff speed (EAS or CAS) which is invariant 
with altitude, temperature, wind, etc. because 
a certain value of 4 is necessary to provide lift 
equal to weight at the takeoff CL. As an ex- 
ample of the effect of a change in gross weight 
a 21 percent increase in takeoff weight will 
require a 10 percent increase in takeoff speed to 
support the greater weight. 
A change in gross weight will change the 
net accelerating force, Fn, and change the 
mass, M, which is being accelerated. If the 
airplane has a relatively high thrust-to-weight 
ratio, the change in the net accelerating force 
is slight and the principal effect on accelera- 
tion is due to the change in mass. 
To evaluate the effect of gross weight on 
takeoff distance, the following relationship 
are used : 
the effect of weight on takeoff velocity is 
if the change in net accelerating force~is 
neglected, the effect of weight on accelera- 
tion is 
187