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To see the effect of the tailplane on the trim of our example helicopter, let us take
α T0 = 12°, VT = 0.1, aT = 3.5, and let the distance of the tailplane below the hub be
1.25 m (= 0.156R). For the appropriate values of the downwash angle ε, we use the
charts below, Figs 4.9 and 4.10, taken from Reference 2, which summarise the results
of Heyson and Katzoff referred to in Chapter 3. As described there, the downwash
pattern behind the rotor consists of two distinct trailing vortices. The mean downwash
angle ε0, based on the mean induced velocity, is used to define the axis of reference
for longitudinal and normal position coordinates ξ and ζ (positive aft and downwards
from the rotor hub, and non-dimensionalised on R) of which the downwash, vi, is a
function. Vertical downwash distributions are provided for two positions aft of the
rotor hub.
Taking the case μ = 0.3, as before, we have
ε 0 = vi0 /V = λi /Vˆ ≈ λ i /μ
= 0.024 = 1.38°
and ξ = lT = 1.2
Referring to Fig. 4.8, the vertical displacement of the trailing vortices at the nondimensional
distance ξ = 1.2 behind the rotor is 1.2(ε0 – αD)R = 1.2(0.024 + 0.134) R
= 0.19R below the rotor plane. Since the distance of the tailplane below the rotor is
0.142R (having taken account of the small angle a1 – B1), the tailplane is 0.048R
above the ζ axis. Using the ξ = 1.07 case in Fig. 4.9 as being the closest to the desired
ξ = 1.2, with ζ = + 0.048, we find vi /vi0 = 1.8. Thus, the downwash angle at the
tailplane is 1.8 × 1.38° = 2.48°.
3
1
vi
/vi0
–0.3 –0.2 –0.1 0 0.1 0.2 0.3
ζ
ξ = 1.07
Fig. 4.9 Vertical distribution of induced velocity at ξ = 1.07 behind rotor
Trim and performance in axial and forward flight 125
From the data given previously, we find that αD + αT – ε = 1.85 0 ° and kT = 1.32,
so that, from eqn 4.15,
B1 – a1 = – 0.19°
whereas, without the tailplane,
B1 – a1 = 0.36°
Figure 4.11 shows the effect of the given tailplane on the longitudinal trim. The
full line shows the previously calculated tailplane case with the c.g. on the shaft and
with e = 0.04, as shown in Fig. 4.5. The two broken lines show the cyclic pitch to trim
for two tailplane settings of 12° and 15°. At low speeds the large downwash angle
causes the tailplane incidence to be negative and the consequent download requires
a small forward application of the stick to trim, relative to the tailless case. At higher
speeds the downwash angle increases, the tailplane incidence tends to become positive
and a backward stick movement is required. At still higher speeds the increasingly
nose down attitude acquired by the fuselage causes the tailplane incidence to reduce
again, and the slope of the trim curve rapidly increases. For a fixed tailplane the trend
indicated in Fig. 4.11 is quite general.
4.2.3 Lateral control to trim
One of the forces contributing to the lateral trim of the helicopter is the tailrotor
thrust Tt. Assuming that the tailrotor thrust moment is the only moment balancing the
main rotor torque, we have
Tt = Q/ltR
vi
/vi0
ξ = 2.07
–0.3 –0.2 –0.1 0 0.1 0.2 0.3
ζ
2
1
Fig. 4.10 Vertical distribution of induced velocity at ξ = 2.07 behind rotor
10°
8°
6°
4°
2°
0 0.1 0.2 0.3
B1
μ
No tail, f = 0, e = 0.04
Fig. 4.11 Effect of tailplane on longitudinal control to trim
α T0 = 15°
α T0 = 12°
126 Bramwell’s Helicopter Dynamics
where ltR is the distance of the tailrotor from the c.g. of the helicopter. Calculation of
the torque coefficient at μ = 0.3 from eqn 3.67 gives
qc = 0.00632 or Q = 25800 Nm
If the tailarm is 11 m, the tailrotor thrust is
Tt = 2340 N
From the parameters already calculated, and from eqn 3.53 we find
b1 = 2.24°
For the lateral cyclic pitch to trim, eqn 1.53 can be written in non-dimensional
form as
A b
w f T W t h
t h Cm
1 1
c 1 t c t
c
= – –
+ ( / )
+ s
(4.16)
and the lateral tilt φ of the fuselage is
φ = –b1 – A1 – Tt/W (4.17)
If we take f1 = 0, i.e. no lateral displacement of the c.g., and ht = 0.2, we find
A1 = –3.34° and φ = –1.98°
The lateral trim quantities b1, A1, and φ are shown in Fig. 4.12.
Although there may be a contribution from the fin and fuselage, it will be supposed,
　
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