THE FORM OF AN AIRPLANE LOOP 
211 
the r.p.m. are 1400, and the speed of flight 70 miles per hour. 
For higher speeds, with the same r.p.m., the thrust is less. Near 
point 5.92 the engine was cut off and not turned on again until 
near point 10.83. The centrifugal force and the tangential accel- 
eration at each point were obtained by a method of graphic 
differentiation, as follows. First, with dividers the length of the 
curve was determined, and platted as a function of the time. 
ds 
Then for the various points the linear velocities — were found 
dt 
from the slopes of the tangent to the curve at these points. Next 
these velocities were platted as functions of the time, and the 
1 - , . , dv d^s . . 
slopes of this latter curve, — , or —o at these various points 
dt dr 
yielded the tangential accelerations. These were sometimes pos- 
itive, and sometimes negative. The centrifugal force was de- 
termined from Wv^/gr, where r the radius of curvature was de- 
termined graphically from the original curve. The tangential 
force was determined from W/g(dv/dt) , and lastly the air pres- 
sure vector was determined as the difference between the vector 
for the tangential acceleration and the resultant vector of weight, 
centrifugal force, and engine thrust. On the curve (Fig. 44) are 
drawn to scale the air pressure vectors in solid lines, and the vector 
resultant of weight, centrifugal force, and engine thrust as dotted 
lines. The resultant of these two at each point represents the 
tangential accelerating force on the airplane. The details of these 
various forces are given in table I. 
