210 
IOWA ACADEMY OF SCIENCE Voi.. XXVII, 1920 
P/ er A 
Fig. 43 
Equations (1) to (8) are sufficient to determine X, Y, and 
Z. Equation (9) is a valuable check equation for the latter 
quantity. 
The original plate measurements, corrections, etc., that were em- 
ployed to obtain the X, Y, and Z of the loop will not be given here. 
In the actual determination there was a wind blowing transversely 
to the loop, which carried the airplane out of a plane. By ap- 
propriate methods the wind was determined, and the path of the 
plane reduced relative to the air. Lastly the F-co~ordinate was 
eliminated by rotating the plane of the loop into the X~Z plane. 
In figure 44 is drawn the resultant loop referred to the X-Z 
plane. The distances are in feet. The numbers beside the various 
points of the curve represent the time in seconds from the be- 
ginning, arbitrarily chosen at a given point as zero. The loop is 
executed from right to left. 
Forces Involved in Looping. At any given point in the loop 
there are the following forces to consider: the weight of the 
airplane (taken as 2000 lbs.), the centrifugal force, the engine 
thrust, the air lift on the wings, and the resultant of all these, 
yielding tangential acceleration in the path of the plane. Any 
other forces, such as parasite resistance, are merged into the 
above forces. The weight vector is simply obtained by drawing 
a fixed vector downward at each point to a scale representing 
2000 pounds. The engine thrust is taken as 450 pounds when 
