Abstract

The propulsion may become sine shape to 520kN i.e. 52tons with time to 4s, meantime it will increase with increasing inclination to 13º in one blade of helicopter. The high rotation firstly and then heavy blade mass and radius has been turned and arrived in. The speed of propulsion may be sine shape to maximum 3km/s with increasing time to 2s at inclination q=13º and n=600r/m &power R=17m in one blade of helicopter. The minimum propulsion speed arrives in 0.5km/s at the time moment 1s with inclination q=3º under the same conditions. The propulsion force may decrease from 800N to 400N as the rotational radius R increases from 2m to 12m with angle f= 8º at defined rotation speed n=300r/m and power P=2,566kW in one blade of helicopter. As the rotation speed attains 1,600r/m and radius becomes 17m the propulsion acceleration may reach 100m/s2 under blade gravity to be 110kg and total gravity to be 220tons. On the contrary, it attains 6m/s2 at the rotation speed 400r/m under the same conditions that may save materials.

Keywords: Propulsion modelling; One blade; propulsion force; rotation; time; helicopter; inclination q; angle f; radius R; Propulsion acceleration

Introduction

The helicopter is prevail in modern society because it has rapid flight than other usual vehicle. It accommodates more people to proceed transportation task in large helicopter. For example the injured one and substantial is needed rapidly arrangement. It can wield its effect in modern war due to its swiftness and mobile. It has attacking capacity in large scope. So it is investigated for the purpose of this utility. The propulsion of helicopter is studied to search its effect on speed which is important simulation. It is known that the speed will decline the propulsion. So the high rotation will be searched further because of its result of high speed. The propulsion determines the speed directly. For the sake of the helicopter security the loaded blades force has been searched widely in papers on current. In this paper the propulsion force has been investigated with rotation speed and time and discussed in details. Meanwhile, because of the function of heavy load in it the attack ability with many missiles weapon may be possible in war. On the other hand it will be affected by load so it is determined by a certain load. To promote the load it will be designed big for example the blade radius length and quantities and other like angle f and rotation speed & inclination. So as to incline the load and speed it is investigated three directions in this paper i.e. rotation, angle f and radius. Through comparing with each other the advantage is searched in this study to further investigation later. On the other side, the speed of helicopter is also important one for us to search further in this paper because it is significant property to evaluate its function. Speed is a key factor to complete its task rapidly so here the detail situation is discussion to model its function. Through the acceleration the propulsion force may be solved, so the circular acceleration is the key that is deduced with modelling in detail in this paper. Overall, the propulsion and speed of helicopter is important factor so its effect is needed to search in detail. The turn is concluded in total according to this model. In this paper the acceleration is computed in terms of theory dynamics to use this research. It is supposed that five blades exist in. The lift force is second factor to consider because of its neglect role. The speed is a factor to model for finding the relation of them. It is to promote the property of helicopter through modelling is our destination finally [1-28].

Modelling and Equation

In the schematic graph as Figure (a &b) 1 O is blade centre; q is inclination, º; FL is lift force, N; Fn is normal force, N; Ft is rotational force, N; Fp is propulsion force, N; Mc is the mass centre, kg. The model equation has been deduced as below. It is known that the plane is vertical to the Figure 1(b) plane. Figure 2 shows the relationship between the propulsion force and rotational one in rotational plane of blades.

  • Propulsion and Lift force
  • Force in rotational plane

Figure 1: The schematic of propulsion force in a blade of helicopter.

Figure 2: The schematic of force and speed blade of helicopter.

Mass center Mc’s orbit equation is

(1)

Here it has

(2)

It has been derived, it is

(3)

It has been secondly derived, it has

(3)

Since

(4)

It has

(5)

Here  (6) and  (7)

(8)

(9)

(10)

So it has

(11)

And    (12)

It has    (13)

Here r is the radius of blade, m; n is the rotation, r/m; am is center of mass in blade, m/s2; q is inclination, º; f  is angle a+b, º; vp is the speed of helicopter，m/s2; t is the time, s; m is the mass, Kg; t is the time, s; M is helicopter mass; ap is the propulsion acceleration, m/s2

Discussions

The relationship between propulsion and time is investigated as below with different parameters. Three conditions of inclinationq, angle f and blade radius R as corresponding parameters to compute for helicopter’s blade. It gains three groups of value to estimate theses. In this paper all the relational parameters have been calculated on the helicopter blades. It is tried out that finding intrinsic relationships happens in helicopter flight in order to simulate the data to change conditions. The propulsion force and time is searched here according to different inclination q, angle f & blade radius in helicopter while the forceˎ speed and time is in research of the rotation of blade and radius of helicopter with inclinations. The main task has grasped the force and propulsion speed with the time. The other parameters like blade inclination qˎ angle fˎ blade radius r & rotation speed n are used to proceed as well. The detail discussions are shown as below.

  • R=9.7m; n=600r/m
  1. b) R=10.7m; n=500r/m

Figure 3: The relationship of various propulsion and time with various rotation speed n=500r/m~600r/m and radius R=9.7m~10.7m & blade gravity M=380kG in one blade of helicopter.

In Figure 3(a &b) the propulsion may become sine shape to 520kN i.e. 52tons with time to 4s, meantime it will increase with increasing inclination to 13º in one blade of helicopter. So total force may be 260tons that is biggest one in this paper. The parameters of condition has attained at 1s and 3s with inclination q=13º and one blade gravity M=390kG & rotation speed n=500r/m in helicopter. The periodic time has been as 3.4s and 4s respectively as seen in Figure 3(a &b).

(a)          R=17m; n=600r/m

 

  1. b) R=21m; n=700r/m
  2. c) R=37m; n=800r/m

(d)          R=47m; n=1,000r/m

Figure 4: The relationship of various propulsion speed and time with defined rotation speed n=600r/m, 700r/m, 800r/m &1000r/m and radius R=17m, 21m, 37m &47m in one blade of helicopter.

As seen in Figure 4(a) the speed of propulsion may be sine shape to maximum 3km/s with increasing time to 2s at inclination q=13º and n=600r/m &power R=17m in one blade of helicopter. The minimum propulsion speed arrives in 0.5km/s at the time moment 1s with inclination q=3º under the same conditions as above. Figure 4(b) shows that the propulsion force may attain 4km/s and 10km/s at the time 0.8s and 2.1s with radius 21m and rotation speed 700r/m. The speed difference between adjacent inclinations attains 1km/s at their change 3º. As the inclination increases the propulsion speed may increase as well. They correspond with the theory very well. Since the rotation speed arrives in higher the periodic time may decrease from 1.6s to 1.4s in Figure 4(a &b). Figure 5(c &e) shows that the status of parameters may change. In other words, the propulsion speed with time increases from 8km/sˎ 12km/s to 20km/s under different blade radius from 37m, 47m to 47m and rotation speed 800r/m to 1,500r/m in helicopter of one blade respectively.

  • n=600r/m

 

(b)          N=700r/m

 

 

Figure 5: The relationship of propulsion and rotation with various angle f= 5º, 8º, 15º &20º with defined rotation speed n=600r/m~700r/m and power P=2,566kW in one blade of helicopter.

  • R=9.7m; n=800r/m
  • R=9m; n=780r/m

Figure 6: The relationship of propulsion speed and time with various angle q= 4º, 7º, 10º &13º with defined rotation speed n=780r/m~800r/m and radius R=9m~9.7m in blade of helicopter.

Figure 5 shows that the propulsion force and blade radius length with the angle f is exhibited. It is seen that the propulsion force may decrease from 800N to 400N as the rotational radius R increases from 2m to 12m with angle f= 8º at defined rotation speed n=300r/m and power P=2,566kW in one blade of helicopter. With increasing the angle f the propulsion force will increase as well, which fits to the dynamics well. The detail data has been as below. It may become 1.3kNˎ 1kNˎ 500N & 300N as the angle is f= 5º, 8º, 15º &20º at radius R=8m. At the least one the prolusion force may become 1,5tons totally with five blades of f= 5º in one helicopter. On the contrary, the maximum propulsion force may attain 6.5tons with f= 20º in one helicopter. As the radius increases from 600r/m to 700r/m the force may decrease from 0.8kN to 0.7kN at the radius 5m with rotation speed from 600r/m to 700r/m under the same power respectively. In Figure 6(a &b) the propulsion speed may increase from 500m/s to 450m/s with increasing time to 0.11s at R from 9.7m to 9m and n from 800r/m to 780r/m respectively. It decreases from 500m/s to 100m/s as the time attains 0.11s at the same conditions. Meanwhile, the adjacent inclination difference may arrive in 100m/s in both of the conditions. The speed will attain the minimum 140m/s i.e. 504km/h at the inclination 4º and time 0.11s as shown in Figure 6(b). That speed may be used in the actual highest one in helicopter flight.

  1. R=9.7m; n=800r/m
  2. R=9.2m; n=850r/m
  • R=17m; n=900r/m
  1. R=17m; n=1,600r/m
  2. R=17m; n=1,200r/m

(e)   R=17m; n=1,200r/m

(f)    R=17m; n=800r/m

  1. R=17m; n=400r/m

Figure 7: The relationship of propulsion acceleration and time with various angle q= 4º, 7º, 10º &13º with defined rotation speed n=400r/m~1,500r/m and radius R=9.2m~17m in blade of helicopter (helicopter gravity 22tons &blade 110kg).

Figure 7(a &b) shows that the propulsion acceleration becomes sine shap periodically with time in one blade at the parameters condition of total helicopter gravity 22tons and blade gravity 110kg. It may reach the biggest one with 15m/s2 in Figure 7(a). The value will increase to 17.5m/s2 in Figure 7(b) because of increasing rotation speed. The period time reduces from 2.5s to 2s respectively. In Figure 7(g) the propulsion acceleration reaches 6m/s2 as time to be 4s, 6s, 9s & 11s with radius to be 17m and rotation speed to be 400r/m. Figure 7(c~g) shows the propulsion acceleration with various rotation up to 1,600r/m and the same blade radius 17m under the same conditions. Here, the maximum acceleration may reach 100m/s2 with blade radius 17m and rotation speed 1,600r/m under the conditions as shown in Figure 7(d). As the rotation speed increases the acceleration may become shorter periodically. With increasing the inclination it will reach bigger. That corresponds with theory very well. The bigger the parameters is the higher acceleration may be attained correspondingly. Overall, the propulsion force and speed has been searched in this study. The propulsion force and speed may maintain sine shape with the time. Meantime when the blade radius increases the propulsion force can maintain certain reducing curve. Its cause for reducing propulsion force whose dynamics can produce the force has resulted by non-dynamics but component.

Conclusions

The propulsion speed with time increases from 8km/sˎ 12km/s to 20km/s under different blade radius from 37m, 47m to 47m and rotation speed 800r/m to 1,500r/m in helicopter of one blade respectively. The propulsion may become sine shape to 520kN i.e. 52tons with time to 4s, meantime it will increase with increasing inclination to 13º in one blade of helicopter. The high rotation firstly and then heavy blade mass and radius has been turned and arrived in. The speed of propulsion may be sine shape to maximum 3km/s with increasing time to 2s at inclination q=13º and n=600r/m &power R=17m in one blade of helicopter. The minimum propulsion speed arrives in 0.5km/s at the time moment 1s with inclination q=3º under the same conditions. The propulsion force may decrease from 800N to 400N as the rotational radius R increases from 2m to 12m with angle f= 8º at defined rotation speed n=300r/m and power P=2,566kW in one blade of helicopter. As the rotation speed attains 1,600r/m and radius becomes 17m the propulsion acceleration may reach 100m/s2 under blade gravity to be 110kg and total gravity to be 220tons. On the contrary, it attains 6m/s2 at the rotation speed 400r/m under the same conditions that may save more materials.

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