256 
ZAHM. 
Knowing, then, the friction at the same speed on five dif¬ 
ferent boards, there remained to determine the law of its 
variation with length of surface. To that end, the values in 
' t - 
a. 
--—- J 
ca 
LU 
C u 
7 1111 - J 
--( 
r-— j 
-- 
_ 
& 
CD 
-j 
FEET 
Fig. 5. —Relation between Length and Unit Friction at 10 Feet per Second. 
table III were plotted on logarithmic cross-section paper, as 
shown in figure 5. The result is a straight line whose 
equation is of the form, 
f=al, -°- 07 
whence F = fl = al * 93 . . . . (y), 
in which f is the average friction in pounds per square foot 
and l is the length of surface in feet. At one foot per second 
the coefficient is 0.00000778; hence at any speed, v feet a 
second, the average friction per square foot is 
f= 0.00000778 l -°- 07 v 1 ’ 85 . . . 0 = ft. sec.), 
f= 0.0000158 l ~ 0 - 07 v l * 85 . . . . 0 = mi. hr.). 
Assuming the two laws thus far derived to be true for the 
planes and wind speeds employed, we may readily express 
the total friction on a plane of any length from 2 to 16 feet, 
moving at any speed from 5 to 40 feet a second. Thus, by 
the last equation, the total friction F on a surface 1 foot wide 
and 1 foot long is 
F — fl — 0.00000778 l * 93 v 1>85 . . . (v = ft. sec.). 
F = 0.0000158 l * 93 v 1,65 . . . . (v == mi. hr.). 
Of course this value of F must be doubled for a material 
plane of length l and width one foot, since a material plane 
has two sides. 
In order to facilitate the computation of skin-friction in 
