For this aircraft, you are given the following parameters:
l(wing)=34.9m, l(tail)-67.8m, S=437 m^2, S_H=93 m^2, C_=8.25m, a=4.8/rad , a_t=5.2/rad.
Furthermore we will assume that the downwash angle is equal to 10% of the angle of attack of the wing. Given that the centre of gravity of this A340-600 is situated 39.2 metres from the nose, find the static margin (in metres) of this A340.
The static margin of an aircraft is the distance between the center of gravity (CG) and the neutral point (NP), expressed as a percentage of the mean aerodynamic chord (MAC) length.
To calculate the static margin, we need to find the MAC length first.
MAC = (2/3) * C [where C is the mean aerodynamic chord]
Given:
l(wing) = 34.9m
C_ = 8.25m
The mean aerodynamic chord can be calculated as:
C = (2/3) * C_
C = (2/3) * 8.25m = 5.5m
Now, we need to find the neutral point (NP).
Neutral point (NP) = l(tail) - (S_H/S) * MAC
Given:
l(tail) = 67.8m
S_H = 93m^2
S = 437m^2
MAC = 5.5m
NP = 67.8m - (93m^2 / 437m^2) * 5.5m
NP = 67.8m - (0.2128) * 5.5m
NP = 67.8m - 1.1692m
NP = 66.6308m
Finally, we can calculate the static margin (SM) as:
SM = CG - NP
Given:
CG = 39.2m
NP = 66.6308m
SM = 39.2m - 66.6308m
SM = -27.4308m
Therefore, the static margin of this A340-600 aircraft is -27.4308 meters.
To find the static margin of the A340-600, we need to first calculate the aerodynamic center (AC) and the neutral point (NP), and then compute the static margin using the formula:
Static Margin (SM) = AC - NP
To calculate the AC, we can use the formula:
AC = (l(wing) * S + l(tail) * S_H) / (S + S_H)
Substituting in the given values:
AC = (34.9m * 437m^2 + 67.8m * 93m^2) / (437m^2 + 93m^2)
AC = (15,251.3m^3 + 6,288.6m^3) / 530m^2
AC = 30,537.9m^3 / 530m^2
AC = 57.7m
Next, to calculate the NP, we can use the formula:
NP = (C_ - a_t * l(tail)) / (1 - (a * S_H) / (a_t * S))
Substituting in the given values:
NP = (8.25m - 5.2/rad * 67.8m) / (1 - (4.8/rad * 93m^2) / (5.2/rad * 437m^2))
NP = (8.25m - 351.36m) / (1 - (434.4/rad * m^2) / (2402.4/rad * m^2))
NP = (-343.11m) / (1 - 0.18)
NP = -343.11m / 0.82
NP = -418.90m
Finally, we can compute the static margin (SM) using the formula:
SM = AC - NP
SM = 57.7m - (-418.90m)
SM = 476.6m
Therefore, the static margin of this A340-600 is 476.6 meters.
To find the static margin of the A340-600 aircraft, we need to calculate the distance between the center of gravity (CG) and the neutral point (NP). The static margin is defined as the distance between the CG and the NP.
First, let's find the NP using the given parameters:
1. Calculate the tail moment arm (l_t) by subtracting the wing length (l_wing) from the tail length (l_tail):
l_t = l_tail - l_wing
l_t = 67.8m - 34.9m
l_t = 32.9m
2. Calculate the ratio of the tail area (S_H) and the wing area (S), known as V:
V = S_H / S
V = 93m^2 / 437m^2
V = 0.213
3. Calculate the coefficient moment for the wing (C_m) using the given formula:
C_m = a * (l_t / C_)
C_m = 4.8 / rad * (32.9m / 8.25m)
C_m = 19.2
4. Calculate the coefficient moment for the tail (C_mt) using the given formula:
C_mt = a_t * (l_t / C_)
C_mt = 5.2 / rad * (32.9m / 8.25m)
C_mt = 20.8
5. Calculate the neutral point (NP) using the formula:
NP = (C_m * S + C_mt * V * S) / (C_m + C_mt * V)
NP = (19.2 * 437m^2 + 20.8 * 0.213 * 437m^2) / (19.2 + 20.8 * 0.213)
NP = 8361.636 / 23.248
NP ≈ 359.51m
Now that we have the NP, we can find the static margin:
Static Margin = CG - NP
Static Margin = 39.2m - 359.51m
Static Margin ≈ -320.31m
The static margin of this A340-600 aircraft is approximately -320.31 meters.