Stress Analysis and Design of a 155Mm Projectile Shell to Be Used in Firefighting

Stress analysis and design of a 155mm projectile shell to be used in ﬁreﬁghting

Lu´ısReis Moitinho de Almeida [email protected]

Instituto Superior T´ecnico,Lisboa, Portugal March 2016

Abstract The objective of the Firend project is the development of a firefighting projectile to be launched from a Howitzer. This Thesis has two major purposes: (1) identify and understand the main parameters affecting the behaviour of a firefighting 155 mm projectile; (2) make a proposal of a design for this projectile. Stress analyses were made in ABAQUS for the movement of the projectile inside the Howitzer. With a solid payload - material inside the projectile - there was almost no bending at the walls and the stresses were mainly located at the base. The implementation of a conical shaped base (boat tail) reduced the stresses. With liquid payload, the hydrostatic pressures caused the appearance of high stresses. This problem was solved by introducing a boat tail and assuming the side walls of the projectile are not able to move radially inside the Howitzer. The factors influencing the flight stability of the projectile were studied and it was decided to reduce m the initial size of the projectile. The final version presented assumed a muzzle velocity of vf = 150 /s and the materials chosen were: Polycarbonate - good resistance to high temperatures; Polylactide - biodegradable and compostable material. In the prototyping stage the manufacturing process was decided to be Thermoforming because of the low costs associated with it and the ease in creating modifications to the mold. With the results from this Thesis it was concluded that the Firend Projectile is a firefighting method with economic, strategic and environmental potential to succeed.

Keywords: Fireﬁghting projectile, Stresses in projectiles, Internal Ballistics, Projectile Design.

1. Introduction Humanity has always been dependent on the many resources provided by forests around the world in order to breath clean air and collect food and raw materials that provide heating and essential feed- stock for multiple industries. The forest area in Portugal has grown more than five times its size in the last one and a half centuries, from 7% in 1870 to 35,4% in 2010. Nevertheless, between 1995 and 2010 there was a loss in total forest area of about 0,3% [1] per year mainly due to forest fires, growing urban areas and diseases. Portugal has been the country inside Europe with the highest proportion of burned forest area to total forest area in the last four decades [1]. The causes are mainly man related and between 1990 and 2012 more than 2.5 million ha of forest burned. In 2003, one dramatic year for the Portuguese forests, 20 people died and 8% of the total area of forest stands was destroyed due to fires [3]. The repeated oc- Figure 1: Burned areas in Portugal between 1994 currence of fires every year, sometimes in the same and 2014 [2].

1 The Firend Project began in 2005 and has been target of many studies regarding the format and size of the projectile, the flight stability, the method of detonation of the fuse and the influence of different propellants are some of the main topics addressed. 2. Interior Ballistics Overview To understand the stresses observed in the projectile, here are presented the main parameters that influence the behaviour of a typical projectile while it is inside the tube - Internal Ballistics. 2.1. Internal Ballistics During this phase, the projectile is inserted at the Figure 2: Render of a possible final Firend rear of the Howitzer - Breech - into the tube with Projectile. only two zones in direct contact with it: the Bour- relet at the beginning of the nose and the Rotating region in just a matter of few years difference - Fig- Band located after the tappered base - Boat Tail. ure 2 - has transformed part of the landscape into Once the ignition of the propellant is initiated, the bushes areas, where the vegetation is rather short increase of the pressure inside the powder cham- and dry, increasing the probability of more fires to ber pushes the projectile forward and the rotating appear. band is engraved onto the rifling of the tube, follow- There are mainly three factors with a strong in- ing the lands and grooves, thus acquiring rotation fluence on the fire behaviour: composition of the that is transmitted to the whole projectile [6]. combustible, meteorological conditions and topog- Figures 3 and 4 are two schemes of the main ele- raphy [4]. If this factors are all propitious for fire ments of ballistics: projectile and tube. spreading the results are devastating and it can be a very dangerous and difficult mission to successfully fight the fire. The use of a projectile to help fighting forest fires - Firend Projectile - was first idealized in 2005 and the idea is still up today. It may handle different quantities of liquid fire retardant depending on the mechanical characteristics and the requirements imposed, and is going to be launched from Portuguese Army Howitzers, in batteries of 6. In comparison to the typical aerial firefighting methods used nowadays - helicopters and planes such as the Canadair -, and considering a projectile made of a polymeric material, the Firend Pro- jectile has got potential to become a much more economical alternative, specially when considering the industrial production in large batch sizes. The cost per liter of a 70cm projectile is approximately 0.30AC and for the Canadair CL-215 this value in- Figure 3: Scheme of a typical high calibre shell [7]. creases up to 1.40AC [5]. Also, the liquid pulveriza- tion that can be achieved with the detonation of the projectile ’s fuse while it is in the air is proba- bly much better that the one observed in the aerial discharges from firefighting helicopters and planes, making this alternative more efficient, specially in scenarios of fires in bushes areas, where the fire in- tensity is smaller. Figure 4: Scheme of a typical howitzer tube [6]. The usage of the Firend Projectile may be not limited for forest fires. The safe working distance to When the rate of gases produced by the com- the fire front provided by the launch from Howitzers bustion of the propellant is lower than the rate at makes it also a good alternative for fighting fires in which the volume behind the projectile grows, the industrial buildings and oil platforms. pressure begins to drop.

2 Figure 5: Drawing of the shell of the projectile in millimeters.

2.2. Howitzer M114 A1 155mm/23 Characteristics In both cases, a zero velocity boundary condi- • Calibre - 155mm; tion is created at the rotating band and bourrelet. The front mass inside the half sphere in the front • Bore Length - 23 Calibres = 23 × 155 = of the projectile is connected to the inner wall of 3.565mm; the projectile by a Tie Constraint that prevents the • Twist Rate - Length required to complete 360o movement of both surfaces in relation to each other in the longitudinal direction of the Bore - 25 in every direction. Between the payload and the Calibres = 25 × 155 = 3.875mm. projectile, the contact characteristics depend on the type of payload and the load applied. 2.3. Projectile The initial configuration assumed for the projectile 2.5. Loads are given bellow, where the front mass located at The much lower weight of the Firend Projectile - the half sphere of the front of the projectile has the less than 15 kg against the 45 kg of a normal shell - same density of the payload. and the fact that this new projectile is to be thrown at much lower velocities to shorter ranges are the • Dimensions - Figure 5: main reasons for the cutback in the peak pressure – Calibre - 155mm; in relation to the common projectiles. The pressure profile is an important factor that – Length - 700mm; influences the behaviour of the projectile inside the – Thickness - 5mm; Howitzer. Three types of profile were defined for a m – Length of the Rotating Band - 50mm; projectile exiting the muzzle at vf = 240 /s: Con- stant Pressure, Linear Pressure Variation and Ex- – Length of the Bourrelet - 20mm; ponential Pressure Variation. • Densities: • Constant Pressure: – Projectile - 1500kg/m3; – Interior and front mass - 1000kg/m3 p(x) = 5.814 × 106 Pa (1)

With these characteristics the projectile has a total mass of 13.58 kg. • Linear Pressure Variation x 2.4. Boundary Conditions p(x) = 1.163 × 107 1 − (2) 3.565 In ABAQUS analyses it was necessary to define several boundary conditions. For the solid payload scenario it is possible to • Exponential Pressure Variation use an axisymmetric configuration while consider- p(x) = P axe1−ax (3) ing just the base pressure. In this case, ABAQUS 0 automatically imposes a zero velocity boundary Here, f is a friction factor related to the pres- condition in the direction perpendicular to the sym- a sure that is still acting on the projectile at the metry axis along the edges laying on it. end of the tube and a is a variable that controls For all the other scenarios, including liquid pay- the position of the pressure peak. load and when there is a torque applied, it must be used a 3-dimensional model and a cylindrical coor- The value for a that requires the least amount dinate system is created to facilitate the identifica- of pressure applied at the base - P0 = 13.5 MPa −1 5 tion of the stress components. - is a ≈ 1.4 m ≈ L .

3 Figure 6: Base Pressure proﬁles.

Figure 6 shows a plot of the various pressures firing of a projectile and in problems with Fluid profiles addressed without considering the friction Structure Interactions (FSI). factor, that is why the minimum value of pressure The main parameters defined in ABAQUS that correspond to a different value of the variable a. are relevant to the analyses are related to mesh re- The main parameters affecting the shape of the finement, interactions between different parts and pressure curve related to the propellant are: Explicit Environment parameters such as the Stable Time Increment (STI) - the shortest time required • Chemical composition and geometry of the pro- for a stress wave to cross an element of the assembly pellant; - and the mass scaling used to increase the STI [9]. • Rate of burning of the propellant; 3.2. Solid Payload • Ignition characteristics; To get the stresses distribution when there is a solid • Charge weight. payload in the projectile, analyses were made keeping constant all the parameters and changing indi- The tube of the Howitzer only has a length of vidually others such as: 23 calibers = 3.565m, thus once the projectile exists the Howitzer it has completed 92% of a rotation. • Pressure profile; Assuming a muzzle velocity of 240 m/s, the spin of the projectile at the beginning of the phase of • Thickness; external ballistics is ω = MuzzleV elocity × 60 = T wistRate • Front mass; 3716 rpm = 389 rad/s [8]. This spin was transferred to the projectile by a • Boat tail. Kinematic Coupling Constraint between the rotating band and a reference point at the axis of sym- For better identification of the origin of the metry. It was defined a rotating velocity profile ge- stresses, the first analyses were run with the pres- ometrically identical to the axial velocity profile. sure at the base or the torque at the rotating band, 3. Stress Analysis never both at the same time. Getting the Firend projectile to work depends on The results for the base pressure analyses showed its capacity to bear the different stresses imposed, that the solid payload case is very advantageous specially when it is inside the barrel - Internal Bal- since there is almost no bending of the walls of the listics. The pressure and torque are going to have projectile, thus resulting in a maximum stress al- different effects on the projectile depending on its ways smaller than 1.5 times the value of the pressure thickness, material, type of payload and geometry. applied at the base, which for a muzzle velocity of m vf = 240 /s corresponds to σVM ≈ 16.5 MPa. Fig- 3.1. ABAQUS ure 7 shows a plot of the stress evolution at the in- The software used to make the finite element analy- ner wall of the projectile, from the center of the base sis was ABAQUS, which allows working in the Ex- until the top. The thickness of the walls is 5mm. plicit environment for dynamic events such as the The dashed horizontal line is the pressure applied

4 Figure 7: Stress distribution along the inner wall of the projectile at the maximum pressure time step: 12 ms - 11 MPa. and the vertical lines separate the different parts of the projectile - base, side wall from the base until the rotating bang, rotating band, side wall from the rotating band until the beginning of the nose and nose. The presence of a boat tail proved to be a good option to decrease the stresses observed at the base because of the introduction of pressure to the side walls that resulted in a reduction of the small bending present in this zone. For the rotation of the projectile, after the cre- ation of a 3-dimensional model, it was first studied the amount of friction coefficient required to trans- fer the rotation of the rotating band to the solid payload - about f = 0.8. The resultant stresses are approximately three times less of the ones observed Figure 8: Stress distribution for a 1 cm thick for the base pressure and have a maximum above projectile with a liquid payload in the moment of the rotating band. maximum pressure applied at the base - Pmax = 1.06 MPa. 3.3. Liquid Payload The other possibility for the projectile’s payload is to the volume inside the projectile. The zone of the having a liquid that attacks the fire in the form Eulerian mesh that is not occupied by the Prede- of droplets after the detonation. This seems to be fined Field is void. This analysis is named CEL - the most plausible situation for the final projectile Coupled Eulerian-Lagrangian. in terms of effectiveness in extinguishing the fire The refinement and the adequate properties def- but carries with it some additional complications re- inition of the projectile’s and Eulerian’s mesh are lated to the computational analysis and the stresses important to ensure that there is no water leakage observed at the walls of the projectile. through the walls. It is advised to have an Eule- ABAQUS/Explicit has a powerful tool for rian mesh more refined than the projectile’s mesh analysing this type of problems. Fluid Structure so it is necessary to have a very large number of Interaction (FSI) can only be performed on 3- elements for the Eulerian part, making the compu- dimensional parts and it requires a lot of computational cost of the analysis increase. To get results tational power to obtain good results. For the faster the thickness of the walls was increased sig- ABAQUS/Explicit to make the FSI calculations, a nificantly for most of the CEL analyses made in this Lagrangian Part must be defined - the projectile - section. and an Eulerian Part that is bigger than the pro- When considering only the base pressure and no jectile is filled up using a Predefined Field at the torque, the analysis can be made with only one sec- Initial Step with a Volume Fraction of Liquid equal tion of the projectile. This section may be any frac-

5 attack between its longitudinal axis and the direction of the flight path. When the CP is located in front of the CG an overturning moment is generated that tries to tumble the projectile and destabilize it - Figure 10. It is the gyroscopic effect caused by the spinning of the projectile that contradicts this moment and keeps the projectile stable [10]. There are several parameters affecting the stability of a projectile: Spin Rate, Weight, Calibre, Velocity, Length and Aerodynamic Efficiency. Due to the subsonic velocity of the Firend Projectile, the drag forces are going to be low. The Gyroscopic Stability Factor, Sg, - Equation 4 - is a way to determine how stable a projectile is during its flight and to know if it is possible to sta- bilize it by spinning. If the bullet is stable when Figure 9: Maximum stress distribution for a boat leaving the Howitzer, it is going to be stable until tail angle of 15◦ and a liquid payload in a projectile the end of the flight because the longitudinal veloc- with 1 cm thickness and a maximum base pressure ity decreases faster than the spin rate [11]. of 10.6 MPa. 2 Ix ω.d 2.Ix Sg = 5 (4) Iy V ρπd CMα tion of the whole projectile. It is only necessary to In order to have a gyroscopically (or statically) create a boundary condition that prevents move- stable flight, it is necessary to have the condition ment perpendicular to both free section surfaces. Sg > 1 fulfilled. The coefficient CMα is called the Figure 8 shows the von Mises stress result ob- Overturning Moment Coefficient Derivative and is tained for the base pressure analysis in a projec- related to the distance between the CP and the CG - tile containing water, with no boat tail and walls static margin [10] -, decreasing for smaller distances. of 1cm. The hydrostatic behaviour of the water creates a high internal pressure at the bottom side walls of the projectile that result in stresses more than 8 times the pressure applied at the base. The presence of the boat tail helps reducing this stresses by adding a pressure at the side walls bellow the rotating band - Figure 9. The rotation of a projectile with a liquid payload is an important aspect to be considered. At the end of the Howitzer, the liquid inside the projectile is not rotating at the same speed as the shell and this is going to bring additional complications to the stability of the flight. It is necessary to add interior fins to the projectile in order to make the water gain the desired rotation.

4. Stability Figure 10: Projectile’s main characteristics during For a successful mechanical design of the Firend External Ballistics. Projectile it is also mandatory to ensure the ﬂight

stability and accuracy. The Dynamic Stability Factor - Sd - represents The stabilization of a projectile can be achieved the capacity of the projectile to damp out the angle with fins or by spinning it while inside the bar- of yaw during the flight phase. If dynamic stability rel. The spin stabilization is the one chosen for the is not achieved, the yaw angle may increase until Firend Projectile due to the characteristics of the the flight is no longer stable [11]. Howitzer. Several calculations were performed in order to The main factor about the stabilization of projec- understand how stable the Firend Projectile can tiles is the distance between the Centre of Pressure be, depending on its materials characteristics, the (CP ) and the Center of Gravity (CG). In the phase length of the projectile or the placement of a mass of external ballistics, a projectile adopts an angle of on the front.

6 Figure 11: Drawing of the ﬁnal projectile’s shell. Dimensions: millimetres.

It was made an approximation for the location of projectiles in the future. the centre of pressure in order to calculate the CMα The downside of PLA is its low Maximum Ser- in the diﬀerent conﬁgurations vice Temperature (45◦C to 55◦C - data from CES For a rigid projectile with 70 cm, one could Edupack Software) because of the high tempera- only achieve Sg > 1 for material densities above tures that will occur inside the Howitzer during ρ = 3720 kg/m3. This result shows that a 0.7 m the launch and before it due to the accumulated projectile with no mass added on the front is going heat caused by the previous launches. The alterna- to be unstable since both the projectile, made of a tive chosen for the base of the projectile, where the polymer, and the payload will have a much lower highest temperatures will be reached, is to use PC density than required. (polycarbonate) due to its good mechanical charac- Keeping a constant density of ρ = 1000 Kg/m3 teristics and capacity to handle high temperatures. and changing the length of the projectile, it was calculated a length of L = 0.45 m as the boundary between a stable and an unstable projectile, i.e. Sg = 1. For a 70 cm projectile with a density of ρ = 1000 Kg/m3 it would be necessary to have a front mass with ρ = 11470 Kg/m3. If the length decreases to 50 cm, the density of this mass also needs to be less - ρ = 2803 Kg/m3.

5. Final Design 5.1. Material For this final projectile it was decided that the extinguishing substance would be a liquid with characteristics identical to water. The material chosen for the shell needs to be able to handle the high stresses observed at the walls. This is the most important parameter right after ensuring it is non-flammable. The decision of using a polymer was made because these materials are usually inexpensive when produced in high quantities and are also lighter than Figure 12: Exploded view of the projectile. the metallic alternatives used for common projectiles, making them easier to handle. Looking at the environmental impact of the pro- 5.2. Design jectile, one specific polymer is at the top of the list The final design of the projectile has some signifi- - PLA (Polylactide). The fact that this polymer cant changes in relation to the initial geometry of is 100% biodegradable and 100% compostable, be- the projectile used for the stress analyses, mainly sides its good mechanical characteristics are good due to the necessity of creating a projectile with indicators for choosing it. Even though it is impor- thin walls that demanded the application of lower tant to ensure the biodegradability, it is the fact pressure values at the base, but also because the that PLA is compostable that makes the difference projectile needs to be stable. and may allow it to be used in forest fire fighting The projectile proposed is mainly made of PLA

7 Figure 13: Stress evolution for the simplified version of the projectile. except at the base and boat tail walls, where PC is friction that could result in an unsuccessful launch used. The technical drawing is shown in Figure 11. if they were thinner. The projectile is made of 5 parts plus the fins in The friction mentioned also means that the ap- order to simplify the process of manufacturing. The plied pressure should in fact increase in order to get assembly is represented by an exploded view of the the same muzzle velocity due to energy losses in the projectile in Figure 12. tube. With the present safety factor the projectile could bear this increase. 5.3. Pressure Profile With the design described, the weight of the pro- 5.5. Stability jectile is distributed in the following way: The stability of the projectile is easily achieved due to its lower length than the original projectile. With the data provided by ABAQUS/Explicit, it was cal- • Mass - mT OT AL = 8.0 kg culated a gyroscopic stability of Sg = 1.22. • Shell - m = 0.8 kg SHELL 5.6. Manufacturing It was considered that the Thermoforming process • Water - mW AT ER = 5.9 kg is the most suited alternative for the projectile be-

• Front mass - mF RONT MASS = 1.3 kg; cause besides the molds used are rather cheap and easy to modify, it is also a good process for proto- To calculate the pressure profile it was decided typing. m to have a muzzle velocity of vf = 150 /s and a = In a further stage of the project, an injection 1.4 m−1, moving the location of the peak pressure - molding process could also mean an improvement Pmax = 2.561 MPa - to 20% of the tube length. in terms of quality and thus a possible reduction of the walls thickness and consequently of the unit 5.4. Stresses price of the projectile. The usage of PC instead of PLA at the base of the projectile not only brings an improvement in terms 6. Conclusions of heat resistance, but also in terms of stresses. Fig- The study of the stresses during the phase of inter- ure 13 shows the plot of the von Mises stress evolu- nal ballistics of the Firend Projectile was the main tion at the inner and outer wall of the projectile at focus of this Thesis. It was defined as a final ob- the time step of maximum pressure applied at the jective the proposal of a stable projectile made of base. a polymeric material with the minimum thickness Looking at the previous plot, it should be possible possible. to use even less thickness since both materials Yield Two types of payload were analysed: solid and Strength is about 65 MPa, giving a safety factor liquid. For the first one, the walls of the projectile of more than 2 at the base and more than 16 at suffered small bending and it was possible to de- the side walls and top of the projectile considering crease the thickness keeping low von Mises stresses. only the base pressure. Despite this, due to the For the liquid payload the results showed much fact that the outer surface of the projectile is going higher stresses when compared to the solid case due to contact the tube of the projectile, it is may be to the hydrostatic behaviour of liquids. With the a good option to protect the side walls from this introduction of the boat-tail and allowing the outer

8 walls of the projectile to contact the internal sur- sultados preliminares. [pdf], 34pp, Instituto face of the Howitzer tube, there was a significant da Conserva¸cãoda Natureza e das Florestas, decrease in the stresses. 2013. Lisbon. Regarding the final projectile it was decided to modify the dimensions and muzzle velocity in order [4] Alexandre Vaz Correia, Cristina Gabriel, Mari- to decrease the base pressure, making it possible to ana Carvalho, and Maria da Concei¸cãoCola¸co. get acceptable stresses without compromising the Floresta, muito mais que árvores, chapter 4. gyroscopic stability and using a thickness of 4 mm. Floresta em perigo, pages 39–43. [pdf], 132pp, It was made a short study about the variants of Autoridade Florestal Nacional, 2009. polymer likely to be used and the ways of manu- [5] Lu´ısFaria, 2015. private communication. facturing the projectile. Two polymers were chosen: Polylactide - PLA - Biodegradable and com- [6] US Army. Fm 6-40/mcwp 3-16.19 tactics, tech- postable material; Polycarbonate - PC - High values niques, and procedures for field artillery man- of maximum service temperature and good mechan- ual cannon gunnery (field manual). US Army, ical characteristics. Oct, 1999. The manufacturing process selection was based on the necessity of performing many changes in the [7] US Army. Manual 6-50, tactics, techniques and prototyping phase. Thermoforming presents low procedures for the field artillery cannon bat- prices and flexibility for small geometry changes. tery. US Army, Dec, 1996. With this work it can be seen that the Firend [8] Donald E Carlucci and Sidney S Jacobson. Bal- Projectile is a very promising economic and envi- listics: theory and design of guns and ammu- ronmental alternative, which is important for the nition. CRC Press, 2013. future acceptance of this technology in real firefighting situations. [9] Dassault Systemes Simulia. Abaqus 6.12 doc- umentation. Providence, Rhode Island, US, 6.1. Future Work 2012. The Firend project requires the work from different areas in order to become a reality in the future. It [10] A Elsaadany and Yi Wen-jun. Accurate trajec- is necessary to make specific studies and analyses tory prediction for typical artillery projectile. for the following topics, even though most of them In Control Conference (CCC), 2014 33rd Chi- were briefly referred in this Thesis. nese, pages 6368–6374. IEEE, 2014. It will be necessary to study the dynamic stability, the contact between the projectile and the [11] Nennstiel Ruprecht. How do bullets fly? tube, the evolution of temperatures during succes- Nennstiel Ruprecht, 2006. sive launches, the working principle and manufacturing of the fuse, the fins responsible for accelerat- ing the liquid and the assembly process. All this knowledge must be tested and results compared. Only then it will be possible to see how close the calculations are to reality. A working version of the Firend Projectile can be successfully achieved, but after that there is still a need for understanding how much social impact and acceptance will have its usage in real forest fires. This impact is even more important than the economic because of all the ethical and political dis- cussion it may bring. References [1] JoãoSantos Pereira. O Futuro da Floresta em Portugal. Funda¸cãoFrancisco Manuel dos San- tos, January 2014. [2] JoséS. Uva. A ocupa¸cãoflorestal do solo em portugal continental. Technical report, ICNF, June 2015. [3] ICNF. IFN6 - Areas´ dos usos do solo e das espéciesflorestais de Portugal continental. Re-