Roll helix angle=&; (radians) 
where 
p=rate of roll, radians per second 
6=wing span, ft. 
V=airplane flight velocity, ft. per sec. 
and, one radian=S7.3 degrees 
pb Generally, the maximum values of rVobtained 
by control in roll are approximately 0.1 to 0.07. 
The helix angle of roll, $i, is, actually a com- 
mon denominator of rolling performance. 
The deflection of the lateral control surfaces 
creates the differential lift and the rolling 
moment to accelerate the airplane in roll. The 
roll rate increases until an equal and opposite 
moment is created by the resistance to rolling 
motion or “damping in roll.” The second 
illustration of figure 4.29 defines the source 
of the damping in roll. When the airplane 
is given a rolling velocity to the right, the 
downgoing wing experiences an increase in 
angle of attack due to the helix angle of roll. 
Of course, the upgoing wing experiences a 
decrease in angle of attack. In flight at angles 
of attack less than that for maximum lift, the 
downgoing wing experiences an increase in 
lift and the upgoing wing experiences a de- 
crease in lift and a rolling moment is developed 
which opposes the rolling motion. Thus, the 
steady state rolling motion occurs when the 
damping moment equals the control moment. 
The response of the airplane to aileron deflec- 
tion is shown by the time history diagram of 
figure 4.29. When the airplane is restrained 
so that pure rolling motion is obtained, the 
initial response to an aileron deflection is a 
steady increase in roll rate. As the roll rate 
increases so does the damping moment and the 
roll acceleration decreases. Finally, the 
damping moment approaches the control mo- 
ment and a steady state roll rate is achieved. 
NAVWEPS 00-6OT-60 
STABILITY AND CONTROL 
If the airplane is unrestrained and sideslip is 
allowed, the affect of the directional stability 
and dihedral effect can be appreciated. The 
conventional airplane will develop adverse 
yawing moments due to aileron deflection and 
rolling motio6. Adverse yaw tends to produce 
yawing displacements and sideslip but this is 
resisted by the directional stability of the air- 
plane. If adverse yaw produces sideslip, di- 
hedral effect creates a rolling moment opposing 
the roll and tends to reduce the roll rate. The 
typical transient motions (A) and (B) of the 
time history diagram of figure 4.29 show that 
high directional stability with low dihedral 
effect is the preferable combination. Such a 
combination provides an airplane which has 
no extreme requirement of coordinating aileron 
and rudder in order to achieve satisfactory 
rolling performance. While the coupled mo- 
tion of the airplane in roll is important, 
further discussion of lateral control will be 
directed to pure uncoupled rolling performance. 
ROLLING PERFORMANCE. The required 
rolling performance of an airplane is generally 
specified as certain necessary values of the roll 1 
helix angle, &I$ However, in certain condi- 
tions of flight, it may be more appropriate to 
specify minimum times for the airplane to 
accelerate through a given angle of roll. 
Usually, the maximum value of 2% should be 
on the order of 0.10. Of course, fighters and 
attack airplanes have a more specific require- 
ment for high rolling performance and 0.09 
Pb may be considered a minimum necessary 2v. 
Patrol, transport, and bomberairplaneshaveless 
requirement for high rolling performance and a 
Pb 2-V of 0.07 may be adequate for these types. 
The ailerons or spoilers must be powerful 
Pb enough to provide the required rV’ While 
the size and effectiveness of the lateral control 
devices is important, consideration must be 
301 
Revised January 1965