EXPERIMENTAL AERODYNAMICS.
§ 245
∴
13
2
n
+
(
.875
−
17
2
n
)
×
17
2
13
2
=
1.26
{\displaystyle 13^{2}\ n+{\frac {(.875-17^{2}n)\times 17^{2}}{13^{2}}}=1.26}
∴
169
n
−
494
n
=
1.26
−
1.495
{\displaystyle 169\ n-494\ n=1.26-1.495}
or,
325
n
=
.235
{\displaystyle 325\ n=.235}
n
=
.000724
{\displaystyle n=.000724}
or,
x
=
.000724
V
2
grams.
{\displaystyle x=.000724\ V^{2}\ {\mbox{grams.}}}
or, in poundals per square foot
000724
×
144
16
×
32.2
453.6
=
.000461
{\displaystyle 000724\times {\frac {144}{16}}\times {\frac {32.2}{453.6}}=.000461}
ξ
=
.000461
.7
×
.078
−
.0015
{\displaystyle \xi ={\frac {.000461}{.7\times .078}}-.0015}
=
.0085
−
.0015
=
.007
{\displaystyle =.0085-.0015=.007}
the deduction .0015 being made, as in the last example, for ballast resistance.
Determination of constant
c
.
{\displaystyle c.}
W
=
A
P
β
=
A
c
β
P
90
{\displaystyle W=A\ P_{\beta }=A\ c\ \beta \ P_{90}}
=
A
c
β
C
ρ
V
2
{\displaystyle =A\ c\ \beta \ C\ \rho \ V^{2}}
or,
β
=
W
A
c
C
ρ
V
2
=
1.26
{\displaystyle \beta ={\frac {W}{A\ c\ C\ \rho \ V^{2}}}=1.26}
but,
y
=
W
β
{\displaystyle y=W\ \beta \quad }
∴
y
=
W
2
A
c
C
ρ
V
2
{\displaystyle \quad y={\frac {W^{2}}{A\ c\ C\ \rho \ V^{2}}}}
and,
y
=
m
V
2
{\displaystyle y={\frac {m}{V^{2}}}}
∴
m
=
W
2
A
c
C
ρ
{\displaystyle m={\frac {W^{2}}{A\ c\ C\ \rho }}}
or,
c
=
W
2
A
m
×
.0546
{\displaystyle c={\frac {W^{2}}{A\ m\times .0546}}}
all quantities in absolute units.
Thus, for the determination of
c
{\displaystyle c}
m
{\displaystyle m}
A
{\displaystyle A}
W
{\displaystyle W}
Example .—Planes 1 and 2.
Flight data as given.
By (5)
m
=
15
2
(
.84
−
15
2
n
)
{\displaystyle m=15^{2}\ (.84-15^{2}\ n)}
where
n
=
.000532
{\displaystyle n=.000532}
