Forces and moments acting on the aircraft. Synthesis of regulators for controlling the longitudinal control channel of a small aircraft
The following forces act on an aircraft during takeoff:
1) thrust force of the propulsion system Р; at the beginning of the takeoff, its value is maximum, and then, as the speed increases, it gradually decreases; for aircraft with piston engines, the decrease in takeoff thrust is more significant than for aircraft with turbojet engines;
2) aircraft weight force Q ; unchanged in size, directed downward;
3) lifting force Y; at the beginning of the takeoff it is equal to zero, and at the end of the takeoff, during takeoff, it reaches the value of the weight of the aircraft;
4) drag force Q ; increases with the takeoff from zero to a certain value (depending on the angle of attack, speed, flight altitude);
5) normal ground reaction force N; at the beginning of the takeoff, it is equal to the weight of the aircraft, and as the speed increases and lift increases, it decreases to zero at liftoff;
6) friction force of pneumatics on the ground F; depends on the coefficient of friction of the wheels on the ground and on the force N.
F=N ×f
Rice. 1. Forces acting on the aircraft during takeoff.
The total aerodynamic force
P-X a -(F 1 + F 2) - accelerating force that tells the aircraft to accelerate on the run
m is the mass of the aircraft
g - free fall acceleration
Y a - lifting force
F 1 +F 2 - friction force on the front and rear supports of the aircraft, respectively. F 1 is taken as 10% of F 2
i X= movement acceleration.
(2.2)
It follows from the equation that an unbalanced force acts in the direction of motion, equal to the difference of forces
R - (Q+F) (2.3)
and causing acceleration. The increase in takeoff speed will be the faster, the greater the magnitude of this unbalanced force.
The friction force of the wheels on the ground is
F=f × N=f(G-Y) (2.4)
It can be seen from the formula that the friction force at the end of the run vanishes, since at separation G=U.
In real conditions, the average acceleration strongly depends on the value of the coefficient of friction, which varies depending on the condition of the runway.
Table 1 shows the values of the friction coefficient for various runways.
Table 1. Friction coefficients for various runways.
3. Takeoff run
The length of the takeoff is the distance traveled by the aircraft from the start to the point of separation from the ground. The length of the takeoff is one of the main characteristics of the aircraft, which determines the required size of the runway.
Considering the takeoff run of an aircraft as a uniformly accelerated movement with acceleration it can be noted that the length of the takeoff depends mainly on the takeoff speed and the magnitude of the average acceleration on the takeoff run.
Let us find out the influence of various operational and design factors on the length of the aircraft takeoff run.
1) The influence of the magnitude of the thrust force of the power plant. With an increase in the traction force P, the accelerating force increases P-(Q+F), as a result, the acceleration increases and the aircraft picks up speed faster (on a shorter distance), equal to the speed separation. This is due to the use of one or another mode of engine operation. As a rule, takeoff is carried out in takeoff mode, i.e., the mode of maximum thrust (power). An increase in thrust by 25% (due to switching to takeoff or afterburner mode) reduces the takeoff run from hard ground by 20 - 25%. To reduce the length of the takeoff run on some types of aircraft during takeoff, starting accelerators are used, which are engines of the LRE type or powder rockets. They short-term (within 10 - 15 seconds) create an additional significant thrust and thereby reduce the length and time of the run. The take-off speed of aircraft with turbojet engines does not depend on the mode of operation of jet engines, and for aircraft with piston engines (and turboprops) it can decrease due to the increasing efficiency of blowing the bearing surfaces with a jet from propellers, as a result of which C UMAX increases.
2) The effect of takeoff weight on the takeoff run is twofold. Increasing it increases the liftoff speed (greater lift is needed) and acceleration decreases (the aircraft becomes more inert and the drag increases slightly). Both increase the run length.
3) The influence of the state of the surface of the airfield is associated with the presence of the friction force of the wheels on the surface of the runway. With loose, soft soil, the friction force increases, and the accelerating force [R - (Q + R)] decreases, resulting in a decrease in acceleration, and the length of the takeoff increases. The force of friction expressed by the coefficient of friction f, depends on the load on the wheels and the condition of the airfield surface.
The lower the coefficient of friction, the lower the friction force F, and the accelerating force increases, which shortens the takeoff run. Therefore, the use of paved runways is one of the ways to reduce the takeoff run.
4) Influence of wing mechanization. Before takeoff, most modern aircraft extend the flaps (or flaps) to the takeoff position to increase the aircraft's maximum lift coefficient.
In this case, the lifting force necessary for separation occurs at a lower speed. To achieve a lower speed, a shorter takeoff run is also required.
5) Influence of wind direction and speed. The speed at which the necessary lift is generated is the speed of the aircraft relative to the air mass. In a headwind, the liftoff speed is the sum of the aircraft's ground speed and the wind speed. w.
Therefore, it is advantageous to take a run against the wind, since in this case the air speed relative to the aircraft will be greater than the speed of the aircraft relative to the ground. And the break will happen sooner.
When taking off with the wind, the take-off run increases due to the fact that airspeed aircraft in this case is equal to the difference between ground speed and wind speed. Therefore, in order to reduce the length of the takeoff run of the aircraft, the start is broken in such a way that the takeoff is made against the wind.
6) Influence of air pressure and temperature. The separation speed and thrust force of the propulsion system depend on the pressure and temperature of the atmospheric air. With a decrease in pressure, the takeoff speed increases, and the thrust force decreases, which leads to an increase in the takeoff run. With an increase in the outside air temperature, the take-off run increases, as the take-off speed increases and the thrust force decreases. This is due to the decrease in mass density p with increasing temperature. For aircraft with turbojet engines, it can be approximately considered that with a temperature deviation of 1 °, the take-off run changes by 1%.
7) The influence of wind on the takeoff of an aircraft. The takeoff of an aircraft is usually carried out against the wind, as a headwind shortens the takeoff run and takeoff distance and makes it easier to control the aircraft.
The take-off speed of the Yak-55 aircraft is Votr = 100 km/h, and the Yak-52 aircraft = 120 km/h. This means that the wings of the aircraft will be blown by the oncoming flow at the corresponding speeds, at these speeds the lift force will balance the weight of the aircraft, which is currently lifted off the ground.
Consider the takeoff of an aircraft with a headwind U=36 km/h. This means that when the plane is at the start, it is already blown by the oncoming air flow at a speed of 36 km/h. Since for the aircraft to take off from the ground, the speed Votr = 100 km / h (Yak-55) and Votr = 120 km / h (Yak-52) is required, then, consequently, there is not enough speed for the Yak-55 aircraft, equal to the difference (100 -36=64 km/h), for Yak-52-(120-36=84 km/h). Thus, when taking off against the wind, the aircraft will take off already at the moment when its speed relative to the ground will be 64 km/h for the Yak-55 aircraft and 84 km/h for the Yak 52.
When taking off with a tailwind, the picture will be reversed. When the aircraft reaches a speed of 36 km / h relative to the ground, then relative to the air flow, its speed will be equal to zero (V=0). And since the takeoff requires the speed Votr = 100 km/h (Yak-52) and Votr = 120 km/h (Yak-55), the aircraft must increase its speed, and therefore its speed relative to the ground will be equal to (100+36= 136 km/h) for the Yak-55 and (120+36=156 km/h) for the Yak-52.
The takeoff run length formula, taking into account the tailwind or headwind, will look like
(3.1)
where the minus sign indicates that the takeoff is against the wind.
As can be seen from the problem, the length of the run upwind is less than downwind. The length of other stages of the takeoff distance during takeoff against the wind also reduces the ground speed of the aircraft, and in the second it increases.
When taking off against the wind, the aircraft is better controlled than when there is no wind, since at the very beginning of the run it is blown by an oncoming air stream.
When taking off with the wind, on the contrary, at the beginning of the takeoff run, the aircraft does not obey the rudders, since the oncoming flow begins to blow only some time after the start of the takeoff (when the speed of the aircraft on the ground becomes equal to or greater than the wind speed). In addition, a tailwind weakens the effect of blowing the rudders with a jet from propeller until the aircraft's speed increases sufficiently. This circumstance, and mainly the increase in the length of the takeoff, leads to the unsuitability of taking off into the wind, and sometimes dangerous. Therefore, takeoff must be carried out against the wind, especially if the wind is strong.
SYSTEM OF FORCES AND EQUATIONS OF MOTION IN THE PROCESS OF DESCENT OF THE AIRCRAFT. AIRCRAFT PLANNING
The rectilinear and uniform motion of an aircraft along an inclined downward trajectory is called scheduling or steady decline.
The angle formed by the planning path and the horizon line is called planning angle sq.
The reduction can be made both in the presence of traction, and in its absence.
Gliding is a special case of aircraft descent, in which the aircraft descends with the engine turned off or the engine running at low speed, with thrust practically equal to zero. Aircraft planning is carried out in order to reduce the flight altitude and to fly to the landing site.
For gliders, gliding is the primary mode of flight. Gliding with angles pl exceeding 30 ° is called a dive.
During gliding, the aircraft's weight force G and the total aerodynamic force R act on the aircraft. Since the aircraft moves along a downward inclined trajectory, the forces act as follows fig. 9.
1. The weight force G is directed vertically downwards and is decomposed into two components: in the direction perpendicular to the trajectory of motion - 
, and in the direction of the aircraft - 
.
2. The total aerodynamic force R is decomposed into:
The lifting force Y, which balances the force G 1, which ensures the straightness of the movement;
The force of drag, balancing the force G 2, which ensures the constancy of the speed along the trajectory.
Since gliding is considered as a plane translational steady motion of the aircraft, the lines of action of all forces acting on the aircraft intersect at its center of gravity.
Since when planning the aircraft moves in a straight line and uniformly, all forces must be mutually balanced, and the aircraft in this case will move by inertia.
In order for the movement of the aircraft to be rectilinear, a balance of forces acting perpendicular to the trajectory of movement is necessary.
The condition for straightness of motion is the equality of forces Y and G 1
(14)
Rice. 9. Diagram of the forces acting on the aircraft during gliding
In order for the aircraft to move uniformly, the forces acting along the trajectory must be mutually balanced. The condition for the uniformity of motion is the equality of the forces G 2 and Q
(15)
Consequently, in the absence of thrust, the equations of motion of the center of gravity of the aircraft during planning will have the form
(16)
These two equations are closely related, and if one of them is violated, the other is also violated.
The resultant of the forces Y and Q, i.e., the total aerodynamic force R, is always directed upward during gliding and is equal to the flight weight of the aircraft.
From the equations of motion during planning, the following conclusions can be drawn:
1. The lifting force in gliding is less than in level flight at the same angle of attack, since it balances only part of the weight force G 1 . With an increase in the planning angle, the component of the weight force G 1 decreases, therefore, the lifting force Y must also decrease.
2. The component of the weight force G 2 plays the role of thrust during planning. If the planning angle increases, then the force G 2 also increases, which causes an increase in the speed of movement along the trajectory, and this in turn will cause an increase in the drag force Q, which will balance G 2, and the movement will again become uniform.
The aircraft moves in the air under the influence of aerodynamic forces, engine thrust and gravity. The movement of an aircraft on Earth occurs under the action of these forces, as well as the reaction forces of the Earth and friction forces.
The engine thrust P usually lies in the plane of symmetry XOY of the aircraft and makes up some known angle φα with the positive direction of the OX axis.
Using the matrix of direction cosines between the axes of the coupled and trajectory coordinate systems, we obtain the projections of engine thrust on the axes of the trajectory system in the following form:
Рхя - р cos (a - f fr) cos р;
Ru k \u003d P)
