The influence of the reactive force in the repression pipe on the reactions in the cinematic couples

Nicolae Ştefan Trache,

Fire Officers Faculty, Police Academy „Alexandru Ioan Cuza”)

  1. Introduction

The rapid growth in technology and the progress made in mechanic engineering, now allow the design of high-performance equipment with a high degree of incorporated “intelligence”.

The distinctive results (especially geometric) obtained by the current articulated mechanisms mounted on fire trucks (they can reach a height of up to 90m) could not have been obtained without a thorough theoretical approach with an insight on the details regarding cinematic and dynamic processes and without carrying out detailed experimental research to allow the investigation of the increasingly complex phenomena that accompany their operation

Such trucks (height operating platforms, concrete pumps) have initially been used for construction purposes (exterior finishing, pumping concrete at heights). Using these ideas, companies such as Pierce and Schwing designed fire trucks mounted with articulated mechanisms, which are successfully used by firemen to extinguish fires.

One of the basic requirements an articulated mechanism fire truck must meet today is obtaining higher intervention performances (reaching higher, greater stability when using high pressure and large output – when the equipment is at the peak height, shortening the intervention time by quickly extending the equipment and detecting the source of the fire using video cameras), while maintaining low weight, size and costs.

Satisfying more and more restrictive demands and the diverse conditions under which fire trucks must function (narrow spaces between buildings, avoiding obstacles, the impossibility of repression when working at heights) are the main factors that have imposed studying articulated mechanisms to [1], [2]:

  • modernize these mechanisms by proposing a type of fire truck with articulated arms that can use the extinguishing substance stream to reach farther and ensure sufficient protection for the equipment;
  • reduce the extinguishing substance consumption and fuel consumption by reducing the intervention time;
  • reduce the risk of accidents by having an unmanned repression pipe or by increasing the distance between the operator and the fire;

2. Determining the reactive force in the repression pipe

2.1.Theoretically determining the reactive force in the repression pipe

In the first stage, using a program from the Swedish company “CONJET”, a theoretical determination of the reactive force in the repression pipe with a 1’ jet was made. The results are shown in table 1 [3],[4].

2.2 Experimentally determining the reactive force using unadditived water as a repression agent

The measurements were made using unadditived water as a repression agent, varying the work pressure between 6-15 bar.

With a certain degree of error the pressure was varied using a 0.5 bar pace. By directly measuring the pressure with a dynamometer the following values were obtained for the reactive force, values presented in table 2.

The graph showing the variation of the reactive force using experimental data versus the theoretically determined values for the repression force is presented in figure 1.

Fig. 1 – Graph reprezenting the variation with pressure of the reactive force in the repression pipe

3. Determining the reactions in the cinematic couples

The mechanism proposed for study is mounted on a 4R type fire truck

For the cinetostatic study only the gravity force and the reactive force in the repression pipe (Fr) (figure 2) will be taken into account. These forces will be reduced to the articulation in point D. The reduction equations are shown in 1.

Fig.2 -Fire truck sketch depicting forces

The inertial forces were neglected being very small compared to the other forces created by the weight of the arms and the acting cylinders.

The cinematic sketch necessary to make the calculations is presented in figure 3, in which the gravity forces are also shown.

In the cinematic sketch, the O1D arm has a rotation movement around the horizontal axis passing through O1 with an angular speed of ω1. The hydraulic cylinder 1’s body has an absolute rotation movement around a horizontal axis passing through B with an angular speed of ω2, and its shaft has a rotation movement relative to the O1D arm, around a horizontal axis passing through A, with an angular speed of ω3. [5]

Fig.3-Cinematic sketch

For the calculus we will consider the position immediately following the start of the hydraulic cylinder (position O1D), position that makes an angle of φ1 with the initial position (horizontal).

Considering ω1 as constant and known, we can impose a movement rule for the O1D element. In the next calculations we have considered a movement rule such as

where: φ0 – the angle made by the O1D0 element in the initial position and the O1B element, considered fixed; considered known.

After isolating all the elements and drawing all the forces that influence them, by writing the equilibrium equations we can determine the reactions in the cinematic couples as follows:

in which the angle ξ is known (the angle made by the fixed base O1B and the horizontal). In this case, we find:

The following values can be proposed for the parameters that intervene in the above equations, values close to the ones the concrete pump Z36 by Putzmeister has:





L1=8,74m – the length of the first element (“arm”)

L2=7,70m – the length of the second element;

L3=7,71m – the length of the third element;

L4=7,54m –the length of the fourth element;

m1=1815kg – the weight of the first;

m2=1600kg – the weight of the second element;

m3=1395kg – the weight of the third element;

m2=1125kg – the weight of the fourth element;

mcil.2=360kg – the weight of the acting cylinder 2;

mcil.3=219kg – the weight of the acting cylinder 3;

mcil.4=180kg – the weight of the acting cylinder 4;

Imposing: τ=30° – repression angle close to Freeman’s repression angle;

For the reactive force we choose a value of Fr=1418,538N experimentally determined in the case of unadditived water at a pressure of 15 bars.

Replacing these values in (3) the values for the variation of the reactions in the cinematic couples are obtained and graphically shown in figure 4.

Fig.4-Variation of reactions

By using a special software (such as Working Model 2D – by Working Model inc. – world leader in motion simulation software) we can obtain values for the reactions’ variation


[1]TRACHE ŞT. – Tipologii de mecanisme utilizate la autospecialele de pompieri, Bucureşti, 2006;

[2]FIRE AND RESCUE – Fire and Rescue,pg. 43, May 1999;

[3]FIRE ENGINEERING – Fire Engineering, Pg. 21, Apr. 2002;

[5]FIREFFIGHTING IN CANADA – Fireffighting in Canada, Pg. 35, Sept. 2003;

[6]THOT-TAŞCĂU M. – Elemente de inginerie mecanică. Introducere în cinematica şi dinamoca roboţilor, vol. I, II, DRĂGULESCU D. Timişoara, 1993.

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