Empennage Sizing Questions and Answers

Answer: A

Correct answer: \( V_H = S_H l_H / (S \bar{c}) \)

The horizontal tail volume coefficient is

\[ V_H = \frac{S_H\,l_H}{S\,\bar{c}} \]

It is dimensionless because the numerator is an area times a length and the denominator is the wing area times a length. The mean aerodynamic chord is the right reference because the tail's business is pitching moments, and pitching moments are non-dimensionalised on \( \bar{c} \). Area ratio alone ignores the arm, which matters as much as the area; the arm alone ignores the area.

Answer: B

Correct answer: The wing span

The vertical tail volume coefficient is

\[ V_V = \frac{S_V\,l_V}{S\,b} \]

The span is used because the vertical tail produces yawing and rolling moments, and those are conventionally referred to the span, just as pitching moments are referred to the mean aerodynamic chord. Using the same reference for the horizontal and vertical coefficients would make them non-comparable with published values, and it is the difference in reference length that explains why \( V_V \) is typically an order of magnitude smaller than \( V_H \).

Answer: C

Correct answer: The wing and tail aerodynamic centres

The tail arm is the distance between the wing's aerodynamic centre and the tail's, since it is about those points that the moments are taken.

Using the geometric extremities of the aircraft instead would give a longer figure with no aerodynamic meaning. In preliminary design the arm is often approximated from the quarter-chord points of the two surfaces, which is close enough for subsonic estimation. The distinction matters because tail volume is linear in the arm, so a mismeasured arm mis-sizes the surface directly.

Answer: D

Correct answer: Halved

The tail volume coefficient is proportional to the product \( S_H l_H \), so holding it constant means that product is fixed:

\[ S_H \propto \frac{1}{l_H} \]

Doubling the arm therefore halves the area required. This is the fundamental trade in empennage sizing, and it is not free either way: a longer arm means more rear fuselage structure and weight, while a larger area means more wetted area and drag. The optimum depends on the fuselage the aircraft has anyway, which is why long-fuselage aircraft carry proportionately small tails.

Answer: A

Correct answer: A negative slope

Static stability requires a restoring moment. If a disturbance raises the angle of attack, the aircraft must generate a nose-down moment to bring it back, which means

\[ \frac{dC_m}{d\alpha} < 0 \]

A positive slope would amplify the disturbance and a zero slope would leave the aircraft neutrally stable, with no tendency to return. The condition is equivalent to the centre of gravity lying forward of the neutral point, and the distance between them - the static margin - measures how negative the slope is.

Answer: B

Correct answer: The neutral point and the centre of gravity

The static margin is

\[ K_n = \frac{x_{np} - x_{cg}}{\bar{c}} \]

expressed as a fraction of the mean aerodynamic chord. It is positive, and the aircraft statically stable, when the centre of gravity lies forward of the neutral point.

The neutral point is a property of the aerodynamic configuration; the centre of gravity moves with loading. So the aft centre of gravity limit is set by the minimum margin the design requires, typically around 5 per cent for a transport, and the fourth option confuses that limit with the margin itself.

Answer: C

Correct answer: Aft

The neutral point is the centre of gravity position at which the aircraft is neutrally stable, and a larger tail contributes a larger stabilising moment per degree of angle of attack, which moves it aft.

The practical value of that is a wider centre of gravity range: with the neutral point further back, the aft loading limit moves back with it, and a transport gains loading flexibility. The cost is tail area, weight and drag, which is the trade every empennage sizing exercise resolves. A canard sits ahead of the centre of gravity and moves the neutral point forward.

Answer: D

One engine out at low speed produces the largest asymmetric yawing moment the aircraft will ever meet, and the fin and rudder must balance it with enough left over to manoeuvre. The certified minimum control speed follows directly from that balance.

Answer: A

Correct answer: The elevator

The elevator is hinged to the trailing edge of the tailplane and changes the tail's lift, producing a pitching moment about the centre of gravity.

The rudder controls yaw from the fin, and the ailerons control roll from the wing. A flap is a high-lift device rather than a control. Two variants are worth knowing: an all-moving tailplane, or stabilator, dispenses with a separate elevator and pivots as a whole, and a V-tail's ruddervators combine the elevator and rudder functions in one pair of surfaces.

Answer: B

Pivoting the whole surface gives far more pitch authority per degree, which is why it appears on fast aircraft where a trailing-edge elevator would lose effectiveness. Its power is also why it needs an anti-servo tab to restore feel.