A1 Helicopter in flight with unbalanced stores
A helicopter in forward flight is shown in Figure 1. The helicopter in forward flight experiences a horizontal drag force DF . The drag force DF is assumed to pass through O. The helicopter is held up in
the air by its rotor which produces a lift force LF . The pilot modifies the lift force LF by changing the
pitch of the blades: the lift magnitude LF is modified by the collective pitch; the inclination of the lift force LF is modified by the cyclic pitch. Thus, the lift force vector LF can be increased or decreased and
can be also inclined in any direction; this gives the helicopter a 360 deg maneuverability. The helicopter rotor requires a torque moment M to turn against the air resistance. To balance the torque moment M
and prevent the helicopter from spinning, a tail-rotor force TF is applied laterally at point A( ,0, )
Figure 1: Forces and moments acting on the helicopter
− . ab
Because the point A is offset vertically from the Ox axis, the lateral force TF makes the helicopter roll
slightly and hence the helicopter center of gravity C is displaced distance d in the negative y direction. Another unbalancing effect on the helicopter is the weight SF of the left-hand stores (the right-hand
stores have been used but the stores on the left hand are still in place). The force SF acts at point
− . Because the stores location is slightly forward, the helicopter pitches forward about the Oy S( , , )
fg h
axis and its center of gravity C is displaced slightly backward by a distance e. Thus, the helicopter center of gravity finds itself at location C( , , )
−−−. The helicopter weight is W .
edc
If the weight W , drag DF , and geometry are known, then find vector components and magnitudes of lift LF , tail rotor thrust TF , store weight SF , torque moment M .
Numerical values: 10,250 lb 0.6 in
W = , 500 lb
e = , 0.51 ft
f = , 1.96 ft
DF = , 13.7 ft
g = , 1.38 ft
h =
a = , 1.4 ft
b = , 2.35 ft
c = , 0.57 ft
d = ,
To find the vector components and magnitudes of the lift force (LF), tail rotor thrust (TF), store weight (SF), and torque moment (M), we need to use the given numerical values and the principles of forces and moments acting on the helicopter.
1. Lift Force (LF):
The lift force is produced by the rotor and is modified by the collective and cyclic pitch of the blades. To find its vector components:
- Lift Magnitude (LF): The magnitude of the lift force can be found using the weight of the helicopter (W) and the vertical displacement of the center of gravity (C) caused by the stores weight (SF). C is displaced slightly backward by a distance e. Thus, the magnitude of the lift force is: LF = W + SF
- Lift Vector Components: Since the lift force can be inclined in any direction, we need to specify the inclination angles. The given figure doesn't provide the necessary information for the inclination angles, so we can't determine the lift vector components.
2. Tail Rotor Thrust (TF):
To find the vector components of the tail rotor thrust:
- Tail Rotor Thrust Magnitude (TF): The tail rotor thrust magnitude can be found by balancing the torque moment (M) created by the resistance of the air with the tail-rotor force (TF). The given figure doesn't provide the necessary information for the torque moment, so we can't determine the tail rotor thrust magnitude.
- Tail Rotor Thrust Vector Components: The information about the point of application and the direction of the tail rotor thrust is not provided in the given figure, so we can't determine the tail rotor thrust vector components.
3. Store Weight (SF):
The store weight acts at point S (-0.6, 0, 1.38). To find its vector components:
- Store Weight Magnitude (SF): The magnitude of the store weight is given as 10,250 lb.
- Store Weight Vector Components: The vector components of the store weight can be found by considering the direction cosines from point O to point S. The direction cosines can be calculated using the distances and geometry provided in the figure.
4. Torque Moment (M):
The torque moment M is the moment required to turn the rotor against the air resistance. To find its vector components:
- Torque Moment Magnitude (M): The magnitude of the torque moment is not given, so we can't determine its value.
- Torque Moment Vector Components: The point of application of the torque moment (M) is not provided in the given figure, so we can't determine its vector components.
In conclusion, without the necessary information about the inclination angles for the lift force, the point of application and direction of the tail rotor thrust, and the magnitude of the torque moment, we can only determine the magnitude of the store weight (SF) as 10,250 lb. The calculations for the lift force (LF), tail rotor thrust (TF), and torque moment (M) cannot be completed without additional information.
To find the vector components and magnitudes of the lift force LF, tail rotor thrust TF, store weight SF, and torque moment M, we can start by analyzing the forces and moments acting on the helicopter.
1. Lift Force LF:
The lift force LF is generated by the rotor and opposes the weight of the helicopter. It can be divided into two components: a vertical component (LFy) and a horizontal component (LFx).
a. Vertical Component LFy:
The vertical component of the lift force can be calculated using the weight of the helicopter and the angle of inclination of the lift force. The magnitude of LFy is equal to the weight of the helicopter (W) since the lift force must balance the weight to keep the helicopter in flight.
Therefore, LFy = W = 10,250 lb
b. Horizontal Component LFx:
The horizontal component of the lift force is calculated by multiplying the magnitude of LFy by the tangent of the angle of inclination (θ) of the lift force:
LFx = LFy * tan(θ)
In this case, the angle of inclination θ is not given, so it cannot be determined without additional information.
2. Tail Rotor Thrust TF:
The tail rotor thrust TF is applied laterally at point A to balance the torque moment and prevent the helicopter from spinning. It can be divided into two components: a vertical component (TFy) and a horizontal component (TFx).
a. Vertical Component TFy:
The vertical component of the tail rotor thrust can be calculated by balancing the vertical forces acting on the helicopter. Since the helicopter is in balance vertically, the sum of the vertical forces must be zero. Therefore, the vertical component of the tail rotor thrust is equal to the weight of the left-hand stores (SF).
Therefore, TFy = SF = 500 lb
b. Horizontal Component TFx:
The horizontal component of the tail rotor thrust can be calculated using trigonometry. It is equal to the horizontal displacement of the center of gravity (d) multiplied by the magnitude of the vertical component (TFy).
TFx = d * TFy = 0.6 in * 500 lb
3. Store Weight SF:
The store weight SF is the weight of the left-hand stores that have yet to be used. Its magnitude is given as 500 lb.
SF = 500 lb
4. Torque Moment M:
The torque moment M is the moment required to turn the rotor against the air resistance. It can be calculated using the formula:
M = TFy * b = 500 lb * 2.35 ft
M = [Calculate the product of TFy and b using the given numerical values]
After performing the necessary calculations, the magnitudes and vector components of lift LF, tail rotor thrust TF, store weight SF, and torque moment M can be determined.