THE INFLUENCE OF MASS PARAMETERS OF THE BODY ON ACTIVE SAFETY OF A FIRE ENGINE IN TERMS OF THE SELECTION OF CHASSIS

The position of the centre of masses affects the distribution of wheel loads and, at the same time, the stability of the vehicle in drive on bends as well as the course (intensity and efficiency) of braking. For fire engines heading for the site of emergency, these are important properties regarding performance. The paper presents a simplified factor analysis of the influence of the centre of masses position in special vehicles with fire fighting bodywork on the characteristics of steering, lateral stability and braking forces. A relation between the transfer function and the driving speed has been presented and the influence of the distance between the centre of masses from the rear axle of the vehicle on its steerability has been analysed. With the examples of given vehicles, it has been shown to what extent the mentioned indices and parameters can be changed after equipping a standard truck chassis with our bodywork system. The information contained herein may be useful for the construction departments of specialized vehicle bodywork manufacturers.


Introduction
As we know, most of special cars, including fire engines (fire trucks), are built on standard truck chassis.Chassis manufacturers provide a number of construction and operating parameters that should not change or should fall within acceptable ranges after fitting a specialized body.Changes of such parameters could have an adverse impact on safety.Assessment of the degree of influence of individual parameters requires a factor analysis that should be carried out at the design stage.
The position of the centre of masses affects the distribution of wheel loads and, at the same time, the stability of the vehicle in drive on bends as well as the course (intensity and efficiency) of braking.The position of the centre of masses influences also the value of the moment of inertia in relation to the axes of the coordinate system associated with the vehicle (this point is the beginning of the system) [14].The moment of inertia in relation to the x-axis (J x ) affects the transverse tilt (fast drive on bends, passing by and overtaking), the moment in relation to the y axis (J y ), the longitudinal tilt (rapid braking or acceleration) and the moment in relation to the z axis (J z ) -for safe drive on bends and maneuvering without slipping.For fire engines heading for the site of emergency, these are important properties regarding performance.
The issues related to Safety are comprehensively covered in the PN-EN 1846 standard [12] drawn up for such vehicles, Chapter 4 of the document includes table 1, containing the list of situations hazardous for the safety of vehicles.However, passive safety was taken into account in most cases, while the active safety of the vehicle -only to a certain extent.
The cited standard also contains a number of recommendations and procedures enabling experimental verification of the safety of constructed vehicles.
Among the standards of other countries, NFPA 414 [8], concerning a certain variety of fire engines constructed for airports ought to be mentioned.The standard covers active safety issues in chap.4, 5 and 6.These chapters describe the stability and drivability test procedures (e.g.test procedure in steady state conditions on circular track, lane double change and others).Application of these requirements to all fire engines is recommended.

Simplified factor analysis of the impact of the bodywork fitted to standard chassis on steering, stability and braking process of the vehicle
The structure of specialized bodywork is shaped at the stage of construction of this assembly.In addition to external dimensions, the arrangement of water and extinguishing tanks is planned, as well as the location of other elements of the emergency equipment.As a result, a bodywork is obtained with a specified position of the centre of masses and moments of inertia of the system connected with the body.With the appropriate (optimal) arrangement of the above-mentioned elements, basic stability and drivability characteristics mentioned in the previous chapter, should not change significantly.However, this requires careful observation and analysis of the scope and extent of such changes.
This chapter analyses the influence of the bodywork structure parameters on the stability of the vehicle's curvilinear motion and on selected braking indices.

Influence on the vehicle steering characteristics
After the specialized bodywork has been mounted, the centre of masses in the vehicle is shifted towards the rear axle.Fig. 1 presents an auxiliary drawing for determination of the centre of masses.Technical documentations of chassis manufacturers include chassis mass m p , wheelbase L and the distance L 2p from the centre of masses to the rear axle.Therefore, the reaction of total loads on the roadway of Z p front axle and Z t rear axle can be calculated as follows: Technical documentations of chassis manufacturers include chassis mass mp, wheelbase L and the distan from the centre of masses to the rear axle.Therefore, the reaction of total loads on the roadway of Zp fron and Zt rear axle can be calculated as follows: where L2p is the distance from the centre of chassis mass to the rear axle.
The L2 distance of the centre of masses in the vehicle, after the specialized bodywork has been moun different: where ∆Zp is the incremented value of the total reaction of roadway to the front axle loads, after the speci bodywork has been mounted, W = Wp + Wn, the mass of the ready vehicle.
Incremented values of vertical reactions of a roadway to total axle loads; ∆Zp, ∆Zt, caused by fitti bodywork to the chassis, shall be as follows: One of the indices for the evaluation of the vehicle performance in a given curvilinear motion is the ra the deviation speed (dψ/dt)) to the average turning angle of wheels δk, (the transfer function) (dψ/dt)/δ, The said transfer function can be expressed by the formula, where the average turning angle of the whee defined by the turning angle of the steering wheel δH and the kinematic steering ratio is: (derivation; see, e. where m=mp+mn is the permissible total vehicle mass (chassis mass mp + body mass mn) determined by the c manufacturer, v is the speed and Cα1, Cα2, are the replacement coefficients of resistance to drifting of the fro rear axles, respectively.These coefficients depend on the mass load per a given axle and on replacemen angles of α1 front axle and α2 rear axle.
where L 2p is the distance from the centre of chassis mass to the rear axle.
The L 2 distance of the centre of masses in the vehicle, after the specialized bodywork has been mounted, is different: General drawing of the vehicle for the analysis of the influence of the parameters taken into conside in chapter 2. Technical documentations of chassis manufacturers include chassis mass mp, wheelbase L and the distan from the centre of masses to the rear axle.Therefore, the reaction of total loads on the roadway of Zp fron and Zt rear axle can be calculated as follows: where L2p is the distance from the centre of chassis mass to the rear axle.
The L2 distance of the centre of masses in the vehicle, after the specialized bodywork has been moun different: where ∆Zp is the incremented value of the total reaction of roadway to the front axle loads, after the speci bodywork has been mounted, W = Wp + Wn, the mass of the ready vehicle.
Incremented values of vertical reactions of a roadway to total axle loads; ∆Zp, ∆Zt, caused by fitti bodywork to the chassis, shall be as follows: One of the indices for the evaluation of the vehicle performance in a given curvilinear motion is the ra the deviation speed (dψ/dt)) to the average turning angle of wheels δk, (the transfer function) (dψ/dt)/δ, The said transfer function can be expressed by the formula, where the average turning angle of the whee defined by the turning angle of the steering wheel δH and the kinematic steering ratio is: (derivation; see, e. where m=mp+mn is the permissible total vehicle mass (chassis mass mp + body mass mn) determined by the c manufacturer, v is the speed and Cα1, Cα2, are the replacement coefficients of resistance to drifting of the fro rear axles, respectively.These coefficients depend on the mass load per a given axle and on replacemen angles of α1 front axle and α2 rear axle.
where ΔZ p is the incremented value of the total reaction of roadway to the front axle loads, after the specialized bodywork has been mounted, W = W p + W n , the mass of the ready vehicle.
Incremented values of vertical reactions of a roadway to total axle loads; ΔZ p , ΔZ t , caused by fitting the bodywork to the chassis, shall be as follows: General drawing of the vehicle for the analysis of the influence of the parameters taken into conside in chapter 2. Technical documentations of chassis manufacturers include chassis mass mp, wheelbase L and the distan from the centre of masses to the rear axle.Therefore, the reaction of total loads on the roadway of Zp fron and Zt rear axle can be calculated as follows: where L2p is the distance from the centre of chassis mass to the rear axle.
The L2 distance of the centre of masses in the vehicle, after the specialized bodywork has been moun different: where ∆Zp is the incremented value of the total reaction of roadway to the front axle loads, after the speci bodywork has been mounted, W = Wp + Wn, the mass of the ready vehicle.
Incremented values of vertical reactions of a roadway to total axle loads; ∆Zp, ∆Zt, caused by fitti bodywork to the chassis, shall be as follows: One of the indices for the evaluation of the vehicle performance in a given curvilinear motion is the ra the deviation speed (dψ/dt)) to the average turning angle of wheels δk, (the transfer function) (dψ/dt)/δ, The said transfer function can be expressed by the formula, where the average turning angle of the whee defined by the turning angle of the steering wheel δH and the kinematic steering ratio is: (derivation; see, e. where m=mp+mn is the permissible total vehicle mass (chassis mass mp + body mass mn) determined by the c manufacturer, v is the speed and Cα1, Cα2, are the replacement coefficients of resistance to drifting of the fro rear axles, respectively.These coefficients depend on the mass load per a given axle and on replacemen angles of α1 front axle and α2 rear axle.
One of the indices for the evaluation of the vehicle performance in a given curvilinear motion is the ratio of the deviation speed (dψ/dt)) to the average turning angle of wheels δ k , (the transfer function) (dψ/dt)/δ.
The said transfer function can be expressed by the formula, where the average turning angle of the wheels δ is defined by the turning angle of the steering wheel δ H and the kinematic steering ratio i s : (derivation; see, e.g.[2,6,7]), Fig 1.General drawing of the vehicle for the analysis of the influence of the parameters taken into conside in chapter 2. Technical documentations of chassis manufacturers include chassis mass mp, wheelbase L and the distan from the centre of masses to the rear axle.Therefore, the reaction of total loads on the roadway of Zp fron and Zt rear axle can be calculated as follows: where L2p is the distance from the centre of chassis mass to the rear axle.
The L2 distance of the centre of masses in the vehicle, after the specialized bodywork has been moun different: where ∆Zp is the incremented value of the total reaction of roadway to the front axle loads, after the speci bodywork has been mounted, W = Wp + Wn, the mass of the ready vehicle.
Incremented values of vertical reactions of a roadway to total axle loads; ∆Zp, ∆Zt, caused by fitti bodywork to the chassis, shall be as follows: One of the indices for the evaluation of the vehicle performance in a given curvilinear motion is the ra the deviation speed (dψ/dt)) to the average turning angle of wheels δk, (the transfer function) (dψ/dt)/δ, The said transfer function can be expressed by the formula, where the average turning angle of the whee defined by the turning angle of the steering wheel δH and the kinematic steering ratio is: (derivation; see, e. where m=mp+mn is the permissible total vehicle mass (chassis mass mp + body mass mn) determined by the c manufacturer, v is the speed and Cα1, Cα2, are the replacement coefficients of resistance to drifting of the fro rear axles, respectively.These coefficients depend on the mass load per a given axle and on replacemen angles of α1 front axle and α2 rear axle.
where m=m p +m n is the permissible total vehicle mass (chassis mass mp + body mass mn) determined by the chassis manufacturer, v is the speed and C α1 , C α2 , are the replacement coefficients of resistance to drifting of the front and rear axles, respectively.These coefficients depend on the mass load per a given axle and on replacement drift angles of α 1 front axle and α 2 rear axle.
The drift angles depend also on the inflation pressure of the tyres.Air pressure in tyres is one of the crucial factors affecting the resistance to drifting.In use, this pressure is adjustable within specific ranges (e.g. when the vehicle load changes), which at the same time affects tyre drifting [6].Further information can be found in this book.
For the TMeasy tyre model [17] used in simulation tests very often, the influence of inflation pressure on vertical, longitudinal and lateral stiffness of tyres (that is on coefficients C α1 , C α2 ) was assumed as a linear value.
L, m are defined in the interrelation (6).In accordance with the theory presented in [9], it can be assumed that the C α1 and C α2 coefficients shall not change significantly if inflation pressures of tyres are adjusted when the axle loads change as a result of the L 2 change.Corresponding diagrams showing the interrelation between tyre drift resistance coefficient and the inflation pressure can be found in specialist literature (e.g.[6]).
With the defined average wheel turning angle δ k (that is, for the defined turning angle of the steering wheel δ H , (because δ k =δ H /i s ) and driving speed v, when L 2 increases -that is when the centre of masses is shifted forward, the transfer function decreases, so the ψ deviation angle decreases at the same time.This affects understeering, which increases in this case.When L 2 decreases, understeering decreases at the same time.Trucks are characterised by low understeering, so shifting L 2 backwards is unfavourable, because it can cause oversteering of the vehicle.3), which is considered a motion instability (on a bend, with a fixed steering wheel turning angle, the vehicle automatically narrows the turn, which results in moving the vehicle to the opposite traffic lane).
For a speed of 15m/s (54 km/h), the dependence [(dψ/dt)/δ H ] is L for different distances between the centre of mass and the rear axle, L 2 , decreased by 0.1 and 0.2 m was determined.The results are shown in Fig. 3.
Reduction of L 2 causes approaching to the state of oversteering.At the speed of 80 km/h, the car shifts to oversteering for L 2 =1,25 m.
Road tests for this car showed a change in the characteristics, from slight understeering to oversteering, at lateral acceleration of ca.3,5 m/s 2 .
For a speed of 80 km/h, this can occur on a curve of the road with a radius of ca.140 m.

Influence on lateral stability (roll over)
n important element of the factor analysis is determination of the value of lateral acceleration while driving ends, at which the lateral stability is lost, beginning with one of the inner wheels loosing contact with the way when turning.Fig. 3 shows a fire engine in a transverse tilt to the right, in driving around a circular track.angle of transverse tilt for this car has reached the value of 6 o .n the work [1], the relationship between lateral acceleration and structural parameters of the body and the cle is determined.A simplified model corresponding to the rear axle which, as known, can go into a skid as a t of relieving (and, in extreme cases, of detachment) of an inner wheel while driving on a bend, and make the cle roll over, was analysed therein. he model adopted in the above-mentioned work is described by the following equation: he homogeneous equation is as follows: e: Jx -is the moment of inertia of the body in relation to the axis of the tilt.K-Wsh3 -is a substitute tilt stiffness e suspension, C -is a coefficient of tilt damping in the suspension.Fy force appears suddenly after entering end causing tilting and further consequences -rolling over of the vehicle after the limit is crossed.For the e-mentioned work, it is assumed that the sprung mass is much greater than the unsprung mass.

Influence on lateral stability (roll over)
An important element of the factor analysis is determination of the value of lateral acceleration while driving on bends, at which the lateral stability is lost, beginning with one of the inner wheels loosing contact with the roadway when turning.Fig. 3 shows a fire engine in a transverse tilt to the right, in driving around a circular track.The angle of transverse tilt for this car has reached the value of 6°.
In the work [1], [3] and [5] the relationship between lateral acceleration and structural parameters of the body and the vehicle is determined.A simplified model corresponding to the rear axle which, as known, can go into a skid as a result of relieving (and, in extreme cases, of detachment) of an inner wheel while driving on a bend, and make the vehicle roll over, was analysed therein.
The model adopted in the above-mentioned work [1] is described by the following equation: which results in moving the vehicle to the opposite traffic lane).
For a speed of 15m/s (54 km/h), the dependence [(dψ/dt)/δH] is L for different distances between the mass and the rear axle, L2, decreased by 0.1 and 0.2 m was determined.The results are shown in Fig. 3.
Reduction of L2 causes approaching to the state of oversteering.At the speed of 80 km/h, the ca oversteering for L2=1,25 m.Road tests for this car showed a change in the characteristics, from slight understeering to oversteering, acceleration of ca.3,5 m/s 2 .For a speed of 80 km/h, this can occur on a curve of the road with a radius of ca.140 m.

Influence on lateral stability (roll over)
An important element of the factor analysis is determination of the value of lateral acceleration whi on bends, at which the lateral stability is lost, beginning with one of the inner wheels loosing contac roadway when turning.Fig. 3 shows a fire engine in a transverse tilt to the right, in driving around a circu The angle of transverse tilt for this car has reached the value of 6 o .
In the work [1], the relationship between lateral acceleration and structural parameters of the bod vehicle is determined.A simplified model corresponding to the rear axle which, as known, can go into a result of relieving (and, in extreme cases, of detachment) of an inner wheel while driving on a bend, and vehicle roll over, was analysed therein.
The model adopted in the above-mentioned work is described by the following equation: The homogeneous equation is as follows: where: Jx -is the moment of inertia of the body in relation to the axis of the tilt.K-Wsh3 -is a substitute til of the suspension, C -is a coefficient of tilt damping in the suspension.Fy force appears suddenly afte the bend causing tilting and further consequences -rolling over of the vehicle after the limit is crosse above-mentioned work, it is assumed that the sprung mass is much greater than the unsprung mass.
For a speed of 15m/s (54 km/h), the dependence [(dψ/dt)/δH] is L for different distances between the mass and the rear axle, L2, decreased by 0.1 and 0.2 m was determined.The results are shown in Fig. 3.
Reduction of L2 causes approaching to the state of oversteering.At the speed of 80 km/h, the ca oversteering for L2=1,25 m.Road tests for this car showed a change in the characteristics, from slight understeering to oversteering, acceleration of ca.3,5 m/s 2 .For a speed of 80 km/h, this can occur on a curve of the road with a radius of ca.140 m.

Influence on lateral stability (roll over)
An important element of the factor analysis is determination of the value of lateral acceleration whi on bends, at which the lateral stability is lost, beginning with one of the inner wheels loosing contac roadway when turning.Fig. 3 shows a fire engine in a transverse tilt to the right, in driving around a circu The angle of transverse tilt for this car has reached the value of 6 o .
In the work [1], the relationship between lateral acceleration and structural parameters of the bod vehicle is determined.A simplified model corresponding to the rear axle which, as known, can go into a result of relieving (and, in extreme cases, of detachment) of an inner wheel while driving on a bend, and vehicle roll over, was analysed therein.
The model adopted in the above-mentioned work is described by the following equation: The homogeneous equation is as follows: where: Jx -is the moment of inertia of the body in relation to the axis of the tilt.K-Wsh3 -is a substitute til of the suspension, C -is a coefficient of tilt damping in the suspension.Fy force appears suddenly afte the bend causing tilting and further consequences -rolling over of the vehicle after the limit is crosse above-mentioned work, it is assumed that the sprung mass is much greater than the unsprung mass.
where: J x -is the moment of inertia of the body in relation to the axis of the tilt.K-W s h 3 -is a substitute tilt stiffness of the suspension, C -is a coefficient of tilt damping in the suspension.F y force appears suddenly after entering the bend causing tilting and further consequences -rolling over of the vehicle after the limit is crossed.For the above-mentioned work, it is assumed that the sprung mass is much greater than the unsprung mass.The relation a y =f(q 1 , q 2 ,…,q n ) presented in work [1] is the implicit function, in the following form : The The relation ay=f(q1, q2,…,qn) presented in work [1] is the implicit function, in the following form : where: B, h1, h2, h3, are the values marked in fig.4, η={(dMx/dα)/dFy/dα)}the coefficient describing interaction of a tyre with the roadway; representing the shift of the point of application of the roadway no reaction to the outer wheel while tu αwheel drift angle, Mx -tilting point, Fy=Fy,w+Fy,z -the total of all lateral forces on wheels, b -shift of the c of masses towards the external curvature of the t ζ -dimensionless damping coefficient in the suspension, The moment of inertia Jx is included in ζ determined by the formula: As it follows from formula (10), with specified C, K, the ζ coefficient included in the (8) formula depend Jx and the height of the h3 sprung mass centre.These values are developed during the bodywork constru process.In the (9) formula, B is constant.It can also be assumed that h1 is constant, because changes in tyre deflectio slight.Moreover, the h2 distance characterizing the distance from the tilt axis to the plane that runs throug front and rear axes is very small: h2<<h3 and for the [1] work h2=0 was assumed.

Example 2
where: B, h 1 , h 2 , h 3 , are the values marked in fig.4, η={(dM x /dα)/dF y /dα)} -the coefficient describing the interaction of a tyre with the roadway; representing the shift of the point of application of the roadway normal reaction to the outer wheel while turning α -wheel drift angle, M x -tilting point, F y =F y,w +F y,z -the total of all lateral forces on wheels, b -shift of the centre of masses towards the external curvature of the track, ζ -dimensionless damping coefficient in the suspension, The moment of inertia J x is included in ζ determined by the formula: The Archives of Automotive Engineering -Archiwum Motoryzacji Vol.82, No. 4, 2018 Fig. 4. View of the car during a fixed ride around a circular track, turn to the right.(on the basis of [1]) The relation ay=f(q1, q2,…,qn) presented in work [1] is the implicit function, in the following form : where: B, h1, h2, h3, are the values marked in fig.4, η={(dMx/dα)/dFy/dα)}the coefficient describing interaction of a tyre with the roadway; representing the shift of the point of application of the roadway no reaction to the outer wheel while tu αwheel drift angle, Mx -tilting point, Fy=Fy,w+Fy,z -the total of all lateral forces on wheels, b -shift of the c of masses towards the external curvature of the t ζ -dimensionless damping coefficient in the suspension, The moment of inertia Jx is included in ζ determined by the formula: As it follows from formula (10), with specified C, K, the ζ coefficient included in the (8) formula depend Jx and the height of the h3 sprung mass centre.These values are developed during the bodywork constru process.In the (9) formula, B is constant.It can also be assumed that h1 is constant, because changes in tyre deflectio slight.Moreover, the h2 distance characterizing the distance from the tilt axis to the plane that runs throug front and rear axes is very small: h2<<h3 and for the [1] work h2=0 was assumed.
As it follows from formula (10), with specified C, K, the ζ coefficient included in the (8) formula depends on J x and the height of the h 3 sprung mass centre.These values are developed during the bodywork construction process.
In the (9) formula, B is constant.It can also be assumed that h 1 is constant, because changes in tyre deflection are slight.Moreover, the h 2 distance characterizing the distance from the tilt axis to the plane that runs through the front and rear axes is very small: h 2 <<h 3 and for the [1] work h 2 =0 was assumed.

Example 2
Because of the lack of own data, the set of data provided in [1] was used for a car with a permissible total weight ≈ 22700 kg.
Other data is given below (see Fig.For the ζ =0.2 dimensionless damping coefficient, J x =19669 kg m 2 and the K=1113895 Nm, and C=493410 rad kg m 2 s -1 the transverse vibration equation coefficients in the equation were determined.For this set of data, a y /g, according to equation (9), is: a y /g = 0.28 If the h 3 height of the centre of masses increases by 0.05m, the J x moment of inertia will increase by ∆J x =577 kgm 2 (i.e. by 3%).Then, the natural frequency of tilting vibration ω n =6.2801 rad/s (that is, it increases slightly), and dimensionless damping coefficient ζ= 0.194 (it decreases minimally), which gives, as a result, a y /g = 0.276.As it can be seen, the increase is minimal.
For a y /g = 0.28 at the speed of 80 km/h, the loss of contact of the outer rear wheel when turning will take place on a 180 m radius curve, and at the speed of 50 km/h -on a 70 m radius curve.Fire engine must often turn curves with such radii on their way to emergency sites.
Passing by and overtaking should also be mentioned here, for which double lane change attempts are adequate.In the specialist standard [4], the required speed is not less than 40 km/h.For a y /g =0.8 the radius of the curve can therefore be 45 m.If the total length of the vehicle is 10 m, then the radius on the lane change attempt section on the lane change attempt track (track dimensions -see the above-mentioned norm) is about 70 m, and therefore the speed at the verge of the wheel detachment from the ground cannot exceed 50 km/h.

Influence over braking forces
The influence of the position of the height of the centre of masses on braking will be analysed on the basis of the formulas taken from [11,13].
Total normal wheel reactions: Z p , Z t depend on mass distribution on the axle and on the height of the centre of masses above the roadway.If the car brakes on a road slope with an angle with inclination α d (unfavourable case), the normal reactions on the axles are determined by the following formulas: y on a 180 m radius curve, and at the speed of 50 km/h -on a 70 m radius curve.Fire engine must often turn c with such radii on their way to emergency sites.
Passing by and overtaking should also be mentioned here, for which double lane change attempts are ade In the specialist standard [4], the required speed is not less than 40 km/h.For ay/g =0.8 the radius of the curv therefore be 45 m.If the total length of the vehicle is 10m, then the radius on the lane change attempt sect the lane change attempt track (track dimensions -see the above-mentioned norm) is about 70 m, and therefo speed at the verge of the wheel detachment from the ground cannot exceed 50 km/h.

Influence over braking forces
The influence of the position of the height of the centre of masses on braking will be analysed on the ba the formulas taken from [6,8].
Total normal wheel reactions: Zp , Zt depend on mass distribution on the axle and on the height of the cen masses above the roadway.If the car brakes on a road with an angle with inclination αd (unfavourable case), the normal reactions on the axles are determined following formulas: The analysis of the braking process defines κ=Hp/Ht) -the braking force distribution coefficient, where Hp braking force on the wheels of the front axle, Ht -total braking force on the wheels of the rear axle.Design in the formula (11): h-the height of the centre of masses above the roadway; ah/g=z -braking intensity.The total, required braking force on the wheels at a given intensity is determined by the formula: Braking force of the front wheels should be: ) Braking force of the rear wheels: Example 3 A fire truck (see: example 1) with total mass m=11320 kg, weight distribution on the front / rear axles: 4250 kg, (L1=2.45m,L 2 =1.48m), wheelbase L=3.93 m.The height of the centre of masses above the roadwa 2.36m.It has been assumed that braking takes place on a horizontal road.Changes of normal reactions and the required braking forces on individual axles, after changing the di of L2 and h, are presented in table 2. In the calculations according to formulas (8), the braking effic z=(ay/g)=0.5 was assumed.The analysis of the braking process defines κ=H p /H t ) -the braking force distribution coefficient, where H p -total braking force on the wheels of the front axle, H t -total braking force on the wheels of the rear axle.Designations in the formula (11): h -the height of the centre of masses above the roadway; a h /g=z -braking intensity.
The total, required braking force on the wheels at a given intensity is determined by the formula: and dimensionless damping coefficient ζ= 0.194 (it decreases minimally), which gives, as a result, ay/g = As it can be seen, the increase is minimal.
For ay/g = 0.28 at the speed of 80 km/h, the loss of contact of the outer rear wheel when turning will take on a 180 m radius curve, and at the speed of 50 km/h -on a 70 m radius curve.Fire engine must often turn c with such radii on their way to emergency sites.
Passing by and overtaking should also be mentioned here, for which double lane change attempts are ade In the specialist standard [4], the required speed is not less than 40 km/h.For ay/g =0.8 the radius of the curv therefore be 45 m.If the total length of the vehicle is 10m, then the radius on the lane change attempt sect the lane change attempt track (track dimensions -see the above-mentioned norm) is about 70 m, and therefo speed at the verge of the wheel detachment from the ground cannot exceed 50 km/h.

Influence over braking forces
The influence of the position of the height of the centre of masses on braking will be analysed on the ba the formulas taken from [6,8].
Total normal wheel reactions: Zp , Zt depend on mass distribution on the axle and on the height of the cen masses above the roadway.If the car brakes on a road with an angle with inclination αd (unfavourable case), the normal reactions on the axles are determined following formulas: The analysis of the braking process defines κ=Hp/Ht) -the braking force distribution coefficient, where Hp braking force on the wheels of the front axle, Ht -total braking force on the wheels of the rear axle.Design in the formula (11): h-the height of the centre of masses above the roadway; ah/g=z -braking intensity.The total, required braking force on the wheels at a given intensity is determined by the formula: Braking force of the front wheels should be: A fire truck (see: example 1) with total mass m=11320 kg, weight distribution on the front / rear axles: 4250 kg, (L1=2.45m,L 2 =1.48m), wheelbase L=3.93 m.The height of the centre of masses above the roadwa 2.36m.It has been assumed that braking takes place on a horizontal road.Changes of normal reactions and the required braking forces on individual axles, after changing the di of L2 and h, are presented in table 2. In the calculations according to formulas (8), the braking effic z=(ay/g)=0.5 was assumed.Braking force of the front wheels should be: Braking force of the rear wheels: Example 3 A fire truck (see: example 1) with total mass m=11320 kg, weight distribution on the front / rear axles: 4250/7070 kg, (L 1 =2.45m,L 2 =1.48m), wheelbase L=3.93 m.The height of the centre of masses above the roadway: h= 2.36m.It has been assumed that braking takes place on a horizontal road.
Changes of normal reactions and the required braking forces on individual axles, after changing the distance of L 2 and h, are presented in table 2. In the calculations according to formulas (8), the braking efficiency z=(a y /g)=0.5 was assumed.As it follows from the data provided in table 2, the centre of masses shifted backwards causes the greatest increment in the required braking force of the rear axle wheels.This increase can be compensated by the correction of the braking forces.

Summary
The analysis carried out in the above-mentioned work allows to see the range of changes of significant characteristics of the vehicle motion resulting from the construction of the fire truck bodywork.This is facilitated by the results of calculations carried out in chapter 2 for specific vehicles, according to the formulas derived in the publications of other Authors ( [1], [4], [10], [14]).
The work can be helpful for construction departments of special vehicle manufacturers with van bodywork characterized by high position of the centre of masses.

Fig 1 .
Fig 1.General drawing of the vehicle for the analysis of the influence of the parameters taken into consideration in chapter 2

Fig 1 .
Fig 1.General drawing of the vehicle for the analysis of the influence of the parameters taken into conside in chapter 2. Technical documentations of chassis manufacturers include chassis mass mp, wheelbase L and the distan from the centre of masses to the rear axle.Therefore, the reaction of total loads on the roadway of Zp fron and Zt rear axle can be calculated as follows:

Fig. 2
Fig. 2 shows general diagram of relation between the transfer function {(dψ/dt)/δ k } and driving speed v.

Fig. 3
Fig. 3 The influence of shifting the L 2 distance between the centre of masses from the rear axle of the actual vehicle over its steerability, at the speed of 15 m/s (54 km/h) and 22.22 m/s (80 km/h)

3 v
of 15m/s (54 km/h), the dependence [(dψ/dt)/δH] is L for different distances between the centre of and the rear axle, L2, decreased by 0.1 and 0.2 m was determined.The results are shown in Fig.3.eduction of L2 causes approaching to the state of oversteering.At the speed of 80 km/h, the car shifts to steering for L2=1,25 m.tests for this car showed a change in the characteristics, from slight understeering to oversteering, at lateral leration of ca.3,5 m/s 2 .speed of 80 km/h, this can occur on a curve of the road with a radius of ca.140 m.e 1 Figures to fig.

Fig. 4 .
Fig. 4. View of the car during a fixed ride around a circular track, turn to the right.(on the basis of [1])

Table 1 .
Figures to fig.

Table 1
Figures to fig.3

Table 2
Change of normal reactions and braking forces on individual axles after the mass distribution param have been changed.

Table 2
Change of normal reactions and braking forces on individual axles after the mass distribution param have been changed.

Table 2 .
Change of normal reactions and braking forces on individual axles after the mass distribution parameters have been changed Basic values for the reaction: Z po , Z to , and L 2 as well as h *