An aeroplane rolls at \( 0.6 \ \mathrm{rad/s} \) with a semi-span of \( 14 \ \mathrm{m} \) at \( 70 \ \mathrm{m/s} \). Its helix angle is
Answer: A
The helix angle is \( pb/2V = 0.6 \times 14/70 = 0.12 \) radians. Certification requirements are written in terms of this non-dimensional group rather than roll rate, because it captures roll capability independently of size and speed.
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A rolling moment derivative with sideslip is \( -0.09 \) per radian. At 6 degrees of sideslip the coefficient produced is approximately
Answer: B
Correct answer: Minus 0.0094
The derivative is per radian, so the sideslip must be converted before multiplying:
\[ 6^\circ = 6 \times \frac{\pi}{180} = 0.1047\ \mathrm{rad} \]
\[ C_l = -0.09 \times 0.1047 = -0.0094 \]
The distractor −0.54 uses degrees directly, which overstates the result by a factor of 57.3 - the commonest error with these derivatives, and one worth guarding against by checking the units of the coefficient before any arithmetic. The negative sign confirms a restoring moment.
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A wing has 5 degrees of geometric dihedral and its sweep contributes the equivalent of a further 4. The effective dihedral is
Answer: C
Correct answer: 9 degrees
Effective dihedral is the sum of all the contributions to the dihedral effect, expressed as the geometric dihedral angle that would produce the same rolling moment:
\[ 5 + 4 = 9\ \text{degrees} \]
Sweep, wing position and the fin's side force above the rolling axis all contribute alongside the geometric angle. That is why a designer works in effective dihedral rather than in the angle visible on the drawing - and why a swept, high-mounted wing may need anhedral to bring the total back to what is wanted.
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An aeroplane rolls 60 degrees in 2.5 seconds. Its average roll rate is
Answer: D
Correct answer: 24 degrees per second
Average roll rate is the bank angle achieved divided by the time taken:
\[ p = \frac{60}{2.5} = 24\ \mathrm{deg/s} \]
The distractor 150 multiplies instead of dividing, and 0.42 inverts the ratio. Note that this is an average over the manoeuvre: the true rate starts at zero, builds as the roll accelerates, and settles at a steady value where the aileron's moment is balanced by roll damping - so the peak rate exceeds the average.
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A wing of \( 30 \ \mathrm{m} \) span rolls at 24 degrees per second at \( 80 \ \mathrm{m/s} \). The helix angle is approximately
Answer: A
Correct answer: 0.079
The helix angle is the non-dimensional roll rate \( pb/2V \), and the rate must be in radians per second:
\[ p = 24 \times \frac{\pi}{180} = 0.419\ \mathrm{rad/s} \]
\[ \frac{pb}{2V} = \frac{0.419 \times 30}{2 \times 80} = \frac{12.57}{160} = 0.079 \]
It is called the helix angle because it is the angle of the spiral path a wing tip traces through the air. Values around 0.07 to 0.09 are typical requirements for a transport, which makes it the standard measure of roll performance across aeroplanes of different size.
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Anhedral of 3 degrees is applied to a wing whose sweep contributes 7 degrees of effective dihedral. The net effect from these two is
Answer: B
Correct answer: 4 degrees of effective dihedral
Anhedral is negative dihedral, so the two contributions subtract:
\[ -3 + 7 = +4\ \text{degrees} \]
The result is a net stabilising effect, but a smaller one than sweep alone would give - which is exactly why the anhedral was applied. A swept wing's dihedral effect grows with lift coefficient and can become excessive at low speed, giving a poorly damped Dutch roll, and drooping the wing is the standard way of trimming it back.
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Differential ailerons deflect 20 degrees up and 14 degrees down. The differential ratio is approximately
Answer: C
Correct answer: 1.43 to 1
The differential ratio is the up travel divided by the down travel:
\[ \frac{20}{14} = 1.43 \]
The distractor 0.70 inverts it and 34 adds the two deflections. Ratios in this range are usual: enough to cut the drag differential appreciably, but not so much that the down-going aileron's contribution to roll is thrown away. The rigging is set in the linkage geometry, so the ratio is fixed and does not vary with deflection.
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A roll rate requirement of 0.09 helix angle at \( 90 \ \mathrm{m/s} \) on a \( 34 \ \mathrm{m} \) span demands a roll rate of
Answer: D
Rearranging gives \( p = 0.09 \times 90/17 \approx 0.476 \) radians per second, about 27 degrees per second. Larger aeroplanes need lower roll rates to meet the same helix angle, which is why the requirement is framed that way.
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Sideslip of 8 degrees requires 5 degrees of aileron to hold. The ratio of aileron to sideslip is
Answer: A
Dividing gives \( 5/8 = 0.625 \) degrees of aileron per degree of sideslip. This ratio is a direct flight test measure of the dihedral effect, since it is the aileron needed to resist the rolling moment sideslip produces.
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A high wing contributes the equivalent of 4 degrees of dihedral and the geometry adds 1 more. A low wing version of the same design would lose the interference benefit and need
Answer: B
Correct answer: About 5 degrees of geometric dihedral
The high wing version has 5 degrees of effective dihedral in total - 4 from fuselage interference and 1 from the geometry.
A low wing version loses the interference contribution entirely, so the geometric angle must supply the whole 5 degrees if the same effective dihedral is to be reached. The reasoning explains a visible feature of light aircraft: low wing types show a pronounced dihedral angle while high wing types often appear nearly flat, both arriving at similar handling.
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