IN VELOCITY AND ACCELERATION DIAGRAMS 303 
to this and equal to V*/r. Hence the total acceleration of A in the 
direction AC is equal to V?/r+V?/l. Referring to Fig. 473, it follows 
in the same way that the acceleration of A in the direction CA is equal 
2 2 
to V?/r—V?/l. Hence f= va(- + 7) = Ya + *) = “(a +) where 7 is 
the ratio of the length of the connecting-rod to the length of the crank ; 
the plus sign applies to the outer and the minus sign to the inner end 
of the stroke. For example, if V = 10 feet per second, r= 10 inches, and 
2 
1=50 inches, f= W a (1 + > = 144 feet per second per second at the 
~ 50. 
outer end, and 96 feet per second per second at the inner end of the stroke. 
263. Piston Acceleration Diagrams.—Having shown how the piston 
acceleration may be determined at any point of the stroke, the results for 
a number of points may be plotted, and acceleration curves obtained 
corresponding to the piston velocity curves described in Art. 260. Fig. 
474 shows the various piston acceleration curves for the case where the 
length of the connecting-rod is 2} times the length of the crank. 
Fig. 474. 
264. Piston Acceleration Scale.—It was shown in Art. 261 that 
BK - AB= BD? (Fig. 471), and when the piston is at the outer end 
of its stroke (Fig. 472) this becomes BL- AB = BC? or B =a Now 
2 
OL BOE, therstors OL = BC+ PC = Bo(1 + a) is Bo(1 + +}. 
AB A n 
But it was shown in Art. 262 that the piston acceleration at the outer 
end of the stroke is equal to 
2 . 2 2 
¥ 1++)=s. Hence #'CL=y, po(1+?)="(1+4) or no=". 
r n n) or n r 
Therefore the scale on which CL ‘will measure the acceleration of 
2 
the piston is one on which a length equal to BC represents ha , the 
radial acceleration of the crank pin. For example, if BC on the drawing 
measures 2} inches (on a full size scale), and if V =10°5 feet per second, 
72 “52 
and r= 9 inches = 0°75 foot, then =aa5 147 feet per second per 
second, and the acceleration scale is such that 1 inch represents 
147 + 2°5=58°8 feet per second per second, or 100 feet per second per 
second is represented by 100+58*3=1°7 inches. ~ 
