ASSIGNMENT 5: CG
The structures group consists of the following components:
- wing
- horizontal tail /canard
- vertical tail
- fuselage
- landing gear - main and nose/tail wheel
- nacelle, engine pod and air intake
The propulsion group consists of the following components:
- engine as installed
- reduction gear
- cooling provisions
- engine controls
- fuel system and tanks
The equipment group consists of the following items:
- flight controls
- auxiliary power unit (APU)
- instruments
- hydraulic, pneumatic, electrical, armament, air conditioning, anti-icing
- avionics
- furnishings in passenger airplanes
The useful load consists of:
(i) Crew
(ii) Fuel
(iii) Oil
(iv) Payload – passengers, crew, luggage
Approximate group weights method:
Wing:
S = 30 m2
b = 15 m
bsemi = (15/2) – (1.5/2) = 6.75m
cR = 2.857m
cT = 1.1428 m
Fuselage width = 1.5m
mac = 1.0339 m
S(exposed)wing = 30 – (2.857x1.5) = 25.7145m2
From the table, the weight of the wing is,
Wwing = 25.7145x 49 = 1260.0105 kg
Wwing / W0 = 9.5%
From the table, c.g of the wing is at 40% of mac
Hence, the location of the c.g. of wing from the leading edge of the root chord is, 0.4x1.0339 =
.41356m
Horizontal tail:
btail = 4.449m
Stail = 6.6m2
cR ,h.tail = 2.28 m
cT, htail = .6846m
mac, htail = 1.625m
S(exposed)tail = 5.12m2
From the table,
Weight of Horizontal tail = 27 x 5.12= 138 kg
Wht / W0 = 1.04%
From the table, c.g of the h.tail is at 40% of mac.
Hence, the location of the c.g. of h.tail from the leading edge of the root chord of h.tail is, 0.4 x
1.625= 0.65m
Vertical tail:
The contribution of dorsal fin to the weight of v.tail is ignored at this stage of preliminary design.
Sv.tail = 2.178m2
From the table,
Weight of vertical tail = 2.178 x 27= 58.806kg
Hence, the location of c.g of engine from L.E of the wing is,
= -2.5 + (0.4 x 3) = -1.3 m i.e., 1.3 m ahead of the L.E of root chord of wing.
Landing gear:
From the table, the weight of the nose wheel plus the main landing gear is 4.3% of W0. i.e.,
0.043 x 84907 = 3651 kg
Out of this total weight, the nose wheel and main wheel account for 15% and 85% respectively.
Hence, nose wheel weighs 0.15 x 3651 = 547.65 kg
And the main wheels weigh 0.85 x 3651 = 3103.35 kg.
With regard to the locations of the c.g.’s of nose wheel and main wheels, it is recalled that the
nose wheel and main wheels share respectively 10 % and 90 % of the airplane weight.
Wheel base is 17.17 m.
Hence, the c.g. of the nose wheel is 0.9 x 17.17 = 15.45 m ahead of the c.g. of the airplane.
The c.g. of the main wheels, as a group, is:
= 0.1 x 17.17 = 1.717 m behind the c.g. of the airplane. 80
Fuselage:
An approximate estimation of fuselage wetted area is,
= 0.75 x perimeter of fuselage x length of fuselage
= 0.75 x π x 3.76 x 42
= 372.1 m2
(Wfuse + Wsyst)/ W0 = (Wempty/W0) – [(Ww/W0) + (Wht/W0) + (Wvt/W0) + (We/W0) +
(Wlg/W0)]
(Wfuse + Wsyst)/ W0 = 0.5375 – (0.068 + 0.00887 + 0.0084 + 0.1162 + 0.043)
(Wfuse + Wsyst) = 0.2932 x 84907 = 24894.73 kg
From the table, the c.g of fuselage and systems is, 0.45 x length of fuselage
= 0.45 x 42 =18.9 m from the nose of the fuselage.
Wing location and c.g. of the airplane:
The wing is chosen such that the c.g. of the entire airplane with the gross weight is at 25% of the
mean aerodynamic chord of the wing.
The distance of the leading edge of the root chord of the wing from the nose of the fuselage is
denoted by xlew. The 25% of the mean aerodynamic chord (mac) of wing is 1.5 m behind xlew.
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Hence, the chosen location of the c.g. of the entire airplane is at (xlew + 1.5) m from the nose
of fuselage.
The location of wing from nose of airplane is,
45696.89(xlew + 1.5) = 20800.9xlew + 512964.34
xlew = 17.85 m
Hence, the c.g. of the airplane is at 17.85 + 1.5 = 19.3 m from nose of fuselage.
Since, c.g lies at a.c of wing, aerodynamic centre also lies at 19.3 m from nose of fuselage.
