$1$ An aerofoil $-$ or wing $-$ having a $C_{\text{L}\text{m}\text{a}\text{x}}$ of $1\mathrm{.}3$ is to carry a person of mass $70kg$ at a relative wind speed of $10\frac{m}{s},$ rather like for a hang glider.

Calculate the span of the aerofoil if the chord is to be $1m.$ Ignore end effects i$.$e$.$ assume the wing behaves as a two$-$dimensional aerofoil $-$ and initially ignore the mass of the aerofoil. Assume ISA sea$-$level conditions apply.

If the mass of the wing is $2kg$ per metre of span calculate the span required.

$8\mathrm{.}6m,11\mathrm{.}4m$

$2$ If the drag coefficient of the aerofoil in Question $1$ is $0\mathrm{.}05$ and the drag coefficient of the person is $0\mathrm{.}8$ calculate

a$)$ the drag force at $10\frac{m}{s}$

b$)$ angle of descent when the propulsive force is provided entirely by gravity. $($Assume angle of descent is small.$)$

Note, the drag coefficient for the aerofoil is defined in terms of its plan surface area, and the drag coefficient for the person is defined in terms of the frontal area. Assume the latter is $0\mathrm{.}3mx1\mathrm{.}5m,$ and that the span is $11\mathrm{.}4m.$

$57\mathrm{.}0(N),3\mathrm{.}6$

$3$ The simple aircraft representation illustrated in the figure below is such that the chord and span of the tail plane are each $1/4$ those of the wing. The distance between the aerodynamic centres is $5c,$ where $c,$ is the wing chord.

Ignoring end effects and any effect of one aerofoil on the other, calculate the position at which the lift forces act, aft of the wing a$.$c$..$ Assume the aerofoil profiles are symmetrical in cross section, the lift curve slopes are equal and the incidence, $,$ is small.

$5\frac{c}{17}$