OTH 93 398
COMPUTER SIMULATION
OF THE PERFORMANCE OF
LIFEJACKETS -
A Feasibililty Study
Prepared by
Frazer-Nash Consultancy Limited
Shelsley House, Randalls Way
Leatherhead
Surrey KT22 7TX
London: HMSO
© Crown copyright 1993
Applications for reproduction should be made to HMSO: First published 1993
ISBN 0-11-882176-8
This report is published by the Health and Safety Executive as part of a series of reports of work which has been supported by funds formerly provided by the Department of Energy and lately by the Executive. Neither the Executive, the Deparment nor the contractors concerned assume any liability for the reports nor do they necessarily reflect the views or policy of the Executive or the Department.
Results, including detailed evaluation and, where relevant, recommendations stemming from their reearch projects are published in the OTH series of reports.
Background information and data arising from these research projects are published in the OTI series of reports.
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CONTENTS 12 Simulation of Trials 5.2 12 Lifejacket models 5.1 12 INITIAL SIMULATIONS BASED ON TRIALS
5. 10 Results 4.4 9 Test Procedure 4.3 9 Lifejackets 4.2 9 Test Facility 4.1 9 SELF-RIGHTING TRIALS 4. 7 Results 3.3 7 Description 3.2 7 Introduction 3.1 7 DYNAMAN DEMONSTRATION SIMULATION
3.
5 Summary of Simulation Features
2.7 4 Test Case 2.6 4 Sea Conditions 2.5 3 Drag 2.4 3 Buoyancy 2.3 2 The Forces on Bodies in Water
2.2
2 The DYNAMAN Technique
2.1
2 THE SIMULATION CONCEPT
2. 1 INTRODUCTION 1.
iii
SUMMARY
PAGE
21 Results of Revised Simulations
9.2 21 Model Changes 9.1 21 REVISED SIMULATIONS 9. 19 BUOYANCY AND DENSITY MEASUREMENT
8.
17 Simulation Improvements
7.4
17 Inherently Buoyant Lifejacket
7.3 16 Inflatable Lifejacket 7.2 16 Righting Mode 7.1 16 DISCUSSION 7. 15 Inherently Buoyant Lifejacket
6.2
15 Inflatable Lifejacket
6.1
15 COMPARISON BETWEEN TRIALS AND INITIAL
SIMULATIONS 6.
13 Results
SUMMARY
This report describes work carried out by Frazer-Nash Consultancy Limited (FNC) on behalf of the Offshore Safety Division of the Health and Safety Executive (HSE) under agreement number E/5B/CON/8387/2804.
The objective of the work has been to demonstrate the feasibility of using the DYNAMAN computer simulation technique, developed by FNC, to study the performance of lifejackets.
The effects of buoyancy and drag have been implemented in DYNAMAN to allow lifejacket behaviour to be modelled. In addition, the ability to model simulated wave conditions has been included. These features have been quantitatively validated with simple test cases.
A series of in-water trials has been carried out at the Institute of Naval Medicine (INM) with a marine manikin to obtain data on the self-righting characteristics of the manikin wearing two types of lifejacket. Computer simulations of the trials have been generated to validate the modelling technique. These initial simulations highlighted the need for accurate buoyancy and density data. Further, detailed measurements of the buoyancy and density properties for the marine manikin and lifejackets were therefore made at INM. These data were used in revised simulations aimed at achieving a closer match between the trials and simulations. The simulations have shown that the DYNAMAN technique can be used to model the self-righting behaviour of lifejackets. Very good correlation can be achieved between trials and computer simulations provided that the weight and buoyancy distribution in DYNAMAN himself and in his lifejacket are correctly modelled. Applications of the technique have been identified as:
w gaining an understanding of the principles of buoyancy aid behaviour, in particular in the case of complex systems such as lifejacket/survival suit combinations;
w use as a design tool for screening designs at an early stage, reducing the need for expensive prototyping;
w use as a means of assessing the suitability of a particular aid to meet specific performance requirements;
w use as part of an approval process, either to help define physical tests or to assess designs in conditions where physical testing is inappropriate.
1.
INTRODUCTION
This report describes work carried out by Frazer-Nash Consultancy Ltd (FNC) on behalf of the Offshore Safety Division of the Health and Safety Executive (HSE) under agreement number E/5B/CON/8387/2804.
The purpose of the work has been to demonstrate the feasibility of using the DYNAMAN computer simulation technique, developed by FNC, to study the performance of lifejackets. Computer simulation could have a number attractions:
w For many applications the cost of computer simulations is lower than that of corresponding physical tests.
w The timescales for simulations are often shorter which can be very important in bringing new products rapidly to the market place or identifying possible problems during the design process.
w Sometimes a simulation can actually give more understanding of underlying mechanisms than a physical test since a correct
representation of the fundamental physics of a problem is an integral part of any simulation.
w For studying lifejacket performance, computer simulation would avoid the ethical and safety issues associated with the use of human subjects in physical testing.
The work has been carried out in a number of stages as follows:
w The effects of buoyancy and drag forces were implemented in DYNA3D. The implementation was validated with a simple test case.
w A demonstration simulation was carried out in which DYNAMAN was used to simulate the behaviour of a man wearing a typical lifejacket in simulated wave conditions. The purpose of this stage was to demonstrate the feasibility of using the DYNAMAN technique to model behaviour in a moving sea.
w A series of self-righting trials was carried out at the Institute of Naval Medicine (INM) using a marine manikin and two types of lifejacket; a typical inherently buoyant jacket and a typical inflatable jacket. These trials provided self-righting data against which the DYNAMAN technique could be validated.
w DYNAMAN simulations of the self-righting trials were carried out. One simulation was run for each lifejacket. The results of the simulations were compared with the trials. Assessment of the results highlighted the need for more accurate buoyancy data for the manikin and lifejackets.
w As a result of the previous stage, detailed measurements were made at INM of the density and volume of each part of the marine manikin and the two lifejackets. This allowed the buoyancy of the manikin and lifejackets to be determined.
w The computer simulations were re-run with revised input data based on the measurements made at INM. The results of the revised simulations were compared with the self-righting trial data.
Section 2 describes the theoretical basis of the simulation technique and the implementation of buoyancy and drag forces to allow lifejacket behaviour to be modelled. A validation test case is also presented in this section. Section 3 describes the demonstration simulation. In Section 4, the self-righting trials carried out at INM are described. In Section 5 the initial computer simulations based on the trials are described and the results presented. Comparisons between the trials and simulations are drawn in Section 6 and discussed further in Section 7. The measurements made to determine the buoyancy of manikin and lifejackets are described in Section 8. In Section 9 the revised computer simulations are described. The results are compared with the self-righting trials in Section 10.
Conclusions from the work, recommendations for further work and applications of the technique are summarised in Section 11.
2.
THE SIMULATION CONCEPT
2.1 THE DYNAMAN TECHNIQUE
The DYNAMAN technique was developed by FNC for modelling the dynamic behaviour of human, or surrogate dummies, under a range of different loadings. DYNAMAN is based on the finite element analysis code DYNA3D (Reference 1). DYNA3D has been written specifically for modelling transient events where there are large material or geometric non-linearities. FNC has already successfully used DYNAMAN in work carried out for the HSE Railway Inspectorate (Reference 2). In particular, the model helped to explain injury patterns in the Cannon Street rail crash.
Figure 1 shows a typical DYNAMAN model of the type used to assess rail crash injuries. The dimensions of any part of the body can be adjusted to suit the requirements of the particular simulation and mass and inertia properties of each part can be individually assigned. The limbs are joined together so that each joint is free to bend (as would be the case with a human) but rotations are limited to a realistic extent.
In a typical DYNAMAN analysis, the model is adjusted to the required position and a dynamic loading is then applied. The load may be applied either direct to DYNAMAN (such as in a blast loading scenario) or to the structure modelled around him (such as in a rail crash). DYNAMAN predicts the resulting motion of the person including any impact between the person and his surrounding. From the results of a simulation it is possible to make an assessment of likely injuries, examine the effect of adding padding or restraints, etc.
In this project, DYNAMAN has been used to model the dynamic behaviour of unconscious people or surrogate dummies wearing buoyancy aids in water. The results that are of particular interest in this application include the general motion of DYNAMAN, the relative position of the airways to the water surface, and the time taken for the body to right from a face down position. These are important indicators of the relative performance of different buoyancy aid designs.
2.2 THE FORCES ON BODIES IN WATER
In order to model the behaviour of bodies in water, the forces acting on them must be correctly applied. The form include:
w buoyancy
w drag
w gravity
w surface tension
The first three of these forces are believed to be the most significant ones for the analysis of lifejacket self-righting performance. It was agreed with the HSE that only these effects would be considered in this work programme.
The ability to apply gravitational forces is a standard feature of DYNAMAN. However, it has been necessary to include the effects of buoyancy and drag to allow lifejacket performance to be modelled. The theory used and its implementation in DYNAMAN is described in the next two sections.
2.3 BUOYANCY
When a body is fully or partially immersed in a fluid the fluid exerts a pressure on it as shown in Figure 3. If the pressure were uniform over the entire surface there would be no resultant force on the object. However, where pressure varies (for example, with depth) there will be a net resultant force on the object. This force is known as the buoyancy force.
On any small area, A, on the surface of an object, the buoyancy force, which acts normal to the surface of the object, is given by;
Eqn 1
F
buoy=
ρ
waterg
∆
hA
Where
ρ
water = density of waterg = gravitational acceleration
∆
h = depth of the centre of the area, A, below the water surface. In DYNAMAN this buoyancy force is implemented by applying a pressure Pbuoy toeach small segment of the man or lifejacket which is below the surface of the water. Pbuoy is given by;
Eqn 2
P
buoy=
ρ
waterg
∆
h
2.4 DRAG
The conventional theory of hydrodynamics assumes that the total drag force acting on an object moving relative to surrounding water is given by;
Eqn 3
F
drag= ½
ρ
wateru
2C
DA
a reference area of the object (often the presented area of the object). =
A
drag coefficient =
CD
velocity of the object relative to the water = u density of water =
ρ
WhereCD is an empirically determined factor dependent (among other things) on the shape
of the object. Typical values of CD for some simple shapes are given below:
1 Long cylinder 1.2 Sphere 2 Flat plate CD Shape
In DYNAMAN it is assumed that the total drag force is due to high pressure on parts of the object's surface which are moving into the fluid and low pressure on parts of the object's surface moving away from the fluid as shown in Figure 4. Surfaces moving into the flow are given an increased pressure given by
Eqn 4
P
drag= ½
ρ
waterU
2and surfaces moving away from the fluid are given a reduced pressure given by
Eqn 5
P
drag= ½
ρ
waterU
2(1 - C
p)
The total drag force on the whole object is then given by Equation 3.
For objects partly immersed in the water, drag forces act only on the wetted surface. Although wind loading is not being considered here, the form acting due to the wind could be calculated in a similar way and applied to those surfaces not in the water.
2.5 SEA CONDITIONS
To investigate the behaviour of buoyancy aids in rough sea conditions an idealised sinusoidal motion of the sea surface has been included in the DYNAMAN model. The height of the water surface is given by
Eqn 6
h = h
o+ h
avsin w (v
xt + x)
time =t
x position =x
wave velocity =v
x wave frequency =w
wave amplitude =h
avmean depth of sea =
h
0In addition to the plane wave travelling on the sea surface, currents in the plane of the sea can also be included in the model. Other, possibly more realistic, sea surface shapes could be incorporated into the model at a later date.
For visualisation purposes a sheet of shell elements has been used to represent the sea surface.
2.6 TEST CASE 2.6.1 Description
A simple test case has been used to demonstrate and validate the features which have been added to DYNAMAN. The test model consists of a low density ball (relative density 0.5) which is released a distance below the surface of the water. The water surface has a sinusoidal shape. The model is shown in Figure 5.
2.6.2 Expected Behaviour
The expected behaviour of the ball in this model is that it should initially accelerate upwards towards the water surface due to buoyancy. At some stage the drag force plus the gravitational force will balance the buoyancy force and the ball should reach a terminal velocity. The ball should then rise at the terminal velocity until it reaches the water surface. When it reaches the surface the ball should oscillate slightly and then take up a periodic motion with the same frequency as the surface wave. Since its relative density is 0.5, approximately half of the ball should be visible on the surface of the water as it oscillates.
The expected terminal velocity, u, occurs when:
Drag force + Gravitational force = Buoyancy force ie
Eqn 7
½
ρ
wateru
t2C
DA +
ρ
bodyg v =
ρ
waterg v
gravitational acceleration =
g
radius of ball =r
density =ρ
volume of the ball = 4/3
Π
r3 =V
plan area of the ball =
Π
r
2= A terminal velocity =
u
t whereEquation 7 can be rearranged to give;
Eqn 8
=
u
t 4 3(qw ate r−qbo dy)r g 1 2qw a terCDIn the test case 1.2 = CD 5 mm =
r
500 kg/m3 =ρ
body 1000 kg/m3 =Ρ
waterIn this case, from Equation 8, the predicted terminal velocity is 233 mm/s.
The equations of motion of the ball can be solved numerically to give the expected variation of vertical velocity with time.
2.6.3 Results
Figure 6 compares the velocity history of the ball obtained from the simulation with the expected behaviour. It can be seen that the correct temporal variation is obtained and the terminal velocity is 233 mm/s as expected.
The vertical motion history of the ball is shown in Figure 7. It can be sew that, after a small oscillation in the first cycle, the ball settles down to a smooth, roughly sinusoidal motion as expected. The position the ball takes on the surface of the water is shown in Figure 8. As expected half the volume is out of the water.
This test case validates the implementation of the buoyancy and drag laws and the sinusoidal sea surface described in Sections 2.3, 2.4 and 2.5.
2.7 SUMMARY OF SIMULATION FEATURES
With the features described above successfully implemented in DYNAMAN, the simulation technique now has the ability to model the following features:
w Properties of each segment of the person - dimensions
- inertial properties - effective drag coefficient
w Properties of the lifejacket - shape
- weight
- method of attachment - effective drag coefficient
- surface motion (Sinusoidal motion. Amplitude, speed and frequency are specified by the user)
- current (constant in the horizontal plane)
Post-processing allows both the person and the water surface to be displayed pictorially. In addition, the displacement, velocity and acceleration of any point on DYNAMAN or the lifejacket may be plotted as a function of time.
3.
DYNAMAN DEMONSTRATION SIMULATION
3.1 INTRODUCTION
As a demonstration simulation, the behaviour of a 'person' wearing a typical lifejacket in simulated waves has been modelled using DYNAMAN. For the demonstration DYNAMAN is configured to behave in a similar manner to a marine manikin representing an unconscious person. The lifejacket used in the simulations is not representative of any particular design but has a representative volume.
3.2 DESCRIPTION
Figure 9 shows the initial configuration of the demonstration model. Note that two views of the model are shown, one from above and one from below the water surface. The model consists of three main parts:
w The “man”,
w The lifejacket
w The water
The standard DYNAMAN torso consists of three sections; the thorax, the abdomen and the pelvis which can all move relative to each other. However, to represent more closely the stiffness a marine manikin these sections of DYNAMAN have been joined together so that they move as one part.
The density data used for DYNAMAN was taken from Reference 3 which gives densities of the parts of an actual human body. Using these figures the overall relative density of the body is very close to 1.0. The relative density of the lifejacket is very much lower (about 0.02). The overall relative density of the body and lifejacket combined is about 0.8.
For the purpose of this simulation a simple representation of a lifejacket was generated to demonstrate qualitatively the body behaviour when supported by a buoyancy aid. Thus the model has a rather square appearance compared with a real lifejacket.
Some lifejackets hold the head quite snugly when fitted to prevent the head moving relative to the lifejacket. In the simulation, the head and neck are not allowed to move at all relative to the lifejacket. The removed degrees of freedom can easily be reintroduced for other lifejacket designs. The lifejacket is attached to DYNAMAN by springs which represent the tapes which would be used to tie a jacket on.
The wave conditions chosen for the test represent a swell of 600 mm peak to trough, and a period of 4 seconds.
In the simulation DYNAMAN is initially lying on his back. The initial position chosen for DYNAMAN is such that the mass of water displaced by DYNAMAN and the jacket is close to the mass of DYNAMAN to minimise the time taken for the model to reach a realistic floating position.
3.3 RESULTS
Figures 9 to 13 show the motion of DYNAMAN and the water surface at intervals of 1.0 second for a total of 9 seconds. Figure 14 shows the motion history of DYNAMAN's nose during the analysis. The following features of the motion should be noted from Figures 9 to 14:
w From the initial position DYNAMAN rises out of the water. This indicates that in the initial position the buoyancy forces exceed the gravitational forces.
w As the first wave passes over DYNAMAN the legs and pelvis drop relative to the torso. This happens for two reasons: firstly because the large buoyancy force lifts the lifejacket and thorax causing rotation at the hips, and secondly because the legs and pelvis are slightly denser than water and so tend to drop anyway. The arms drop for similar reasons.
w From the initial straight position the joints of the model bend and DYNAMAN takes a very realistic relaxed position in the water.
w As the waves pass DYNAMAN rises and falls in the water. The postures assumed by DYNAMAN are the same at each point in successive waves.
w As the water surface rises so the sea covers more of the lifejacket. Similarly, as the water falls so the jacket rides higher in the water.
w Figure 14 gives an indication of DYNAMAN's motion during the analysis. The X-displacement history shows that DYNAMAN moves backwards and forwards as he slides down the wave surfaces. Overall he moves in the direction of travel of the wave. The Y-displacement history shows very little lateral movement. The Z-displacement history shows that, after the first half cycle,
DYNAMAN assumes a cyclic vertical motion in phase with the wave.
Discussions with experts at INM confirmed that the motion of DYNAMAN in this simulation is representative of the types of motion which would be expected of unconscious subjects in wave conditions.
4.
SELF-RIGHTING TRIALS
A series of in-water trials were carried out at INM using a marine manikin to obtain data on the self righting characteristics of a manikin wearing two types of lifejacket. The self-righting trials were conducted by INM staff. The trials were observed by FNC.
The trials and the results of the trials are discussed in this section. Initial DYNAMAN simulations of the trials are presented in Section 5.
4.1 TEST FACILITY
The INM testing facility consists of a large water tank with lifting equipment to aid handling of the manikin. Underwater video cameras were positioned in the tank so that video recordings could be made of the trials from both the head of the manikin and side on to the manikin.
The manikin was manually positioned in the water for the tests by an INM member of staff from inside the water tank.
4.2 LIFEJACKETS
Two lifejackets were used for the trials. The first was a typical inflatable jacket and the second a typical inherently buoyant jacket.
4.2.1 Inflatable Lifejacket
This is a single piece jacket which is put on in the uninflated state and inflated when needed by means of a gas discharge or the wearer blowing it up. The majority of the buoyancy aid is worn at the front although a collar around the back of the neck fits snugly and can support the head when in the water. The jacket is secured to the body with a single waist strap.
4.2.2 Inherently Buoyant Jacket
The inherently buoyant jacket consisted of a series of nylon bags filled with buoyant material. A large section forms the front, a slightly smaller on the back, and two very small sections act as epaulettes holding the front and back together.
The jacket is secured by long tapes which pass through loops on the front and back sections of the jacket. The tapes are finally tied across the front of the jacket.
It was found that the jacket could be fastened in a number of ways so that the positioning on the body is variable. The jacket does not make contact with the head and therefore offers no support to the head.
4.3 TEST PROCEDURE
The manikin was unclothed for the trials and a 4 litre lung was fitted into the chest representing the full lung capacity of a man.
A series of trials was carried out with each of the lifejackets. The lifejackets were fitted to the manikin out of the water and tied on as tightly as possible at the beginning of each series of trials.
The conventional test procedure for determining lifejacket righting times involves holding the jacketed manikin or person face down in the water with legs and arms straight and in line with the torso and then letting go once settled. It was found difficult for only one person holding the manikin to achieve this starting position in the water so a different initial position was adopted for the purpose of these trials. The manikin was held face downward with the arms and legs dropped down so that it was lying on top of the lifejacket. It is felt that this may be a more severe test of the jacket's self righting ability.
The manikin was held still in the initial position described above. Once the water had settled, the manikin was let go.
Several trials were carried out with each of the lifejackets and videoed for later analysis.
4.4 RESULTS
4.4.1 The General Behaviour of the Marine Manikin
The manikin used in the trials is intended to represent an unconscious person. The neck is very flexible allowing the head to move in all directions but other joints are fairly stiff. In particular, it was found that in certain positions the joints (particularly the shoulder) could lock-up. When wearing a lifejacket in the water the manikin took up a relaxed position on its back. The torso lay at an angle of about 30° to the water surface with the arms lying close to the torso in the same attitude. The legs bent at the knees and hips with the thighs adopting almost a sitting position.
4.4.2 Righting Modes
Throughout the trials two different modes of self righting could be identified. In one, the hips drop, the jacket rises and the man manikin tries to sit up (the “sit-up” mode). In the other, the shoulders rotate about a head-hip axis as the lifejacket rises out of the water to one side of the body and the manikin rolls over (the “roll-over” mode). Figure 15 illustrates the two modes. In reality any particular righting motion includes a combination of both modes. However, one is usually dominant.
A typical response of the manikin in the trials was as follows:
w When released the hips were seen to drop (sit up mode).
w One shoulder rose up out of the water as the body rotated about the head to hip axis (roll over mode).
w The body turned through 90° about the hip to hip axis and 90° about the head to hip axis.
w Once righted the manikin took up the position described in Section 4.4.1.
4.4.3 Self Righting Time
The determination of a self righting time is somewhat subjective since it is difficult to define precisely a starting and finishing point. This was made particularly difficult because each trial produced slightly different body motions.
The most workable definition of the self righting time was found to be from the time when the hips began to drop until the time when the lifejacket was furthest out of the water with the head fully visible.
From this definition, typical righting times from the trials are summarised in Table 1. Note that, there was considerable scatter in the results for each jacket even though the initial conditions were nominally the same in each case.
Table 1
Trial Self Righting Times
3.6 3.5
2.4 Inherently Buoyant Life Jacket
2 2 1.9 Inflatable lifejacket Trial 3 Trial 2 Trial 1
Righting Time (sec) Jacket
4.4.4 Lifejacket Position
During each of the trials the lifejackets were seen to move around on the manikin. To some extent this movement would be restricted in a real situation by clothing since friction form would be generated between the fabric straps and clothing. The inflatable lifejacket remained in position somewhat better than the inherently buoyant lifejacket and also held the head more firmly.
4.4.5 Position of Airways
With the equipment available it was not possible to measure the relative position of the water surface and the airways on the manikin accurately enough to determine an airway motion history.
5.
INITIAL SIMULATIONS BASED ON TRIALS
5.1 LIFEJACKET MODELS
In order to simulate the self righting trials, DYNAMAN models of the manikin wearing the two life jackets were required. These models were generated as discussed below.
It should be noted that in this stage of the work the two simulations were set up with prior knowledge of the manikin's initial position and with access to the jackets themselves. However, the results presented in this section are from the first iteration of each simulation. That is, no tuning or modification of the models was carried out at this stage to make the simulation fit the trials better.
5.1.1 Inflatable Lifejacket
The inflatable lifejacket consists of two layers of material which are sealed at the edges and blown up with gas. The inflated shape of the jacket is difficult to measure and is difficult to generate as a finite element mesh. For this reason the jacket geometry for the simulation was generated by mimicking the inflation process. The jacket material was modelled with shell elements connected around the periphery and a pressure was applied to their inside surfaces. The resultant shape of the jacket is shown on DYNAMAN in Figure 16. It was found that this method produced a realistic jacket shape.
The positioning of the jacket on the body was determined by examining its fit on a real person. The jacket fits snugly around the neck such that an attachment here is not necessary. The lower part of the jacket is pulled into the body by two straps fixed to a belt. These have been modelled in DYNAMAN by stiff spring elements between the jacket and abdomen. Very little movement is therefore allowed between the jacket and DYNAMAN. The density of the elements forming the jacket has been chosen such that the overall mass of the jacket in the model is the same as the real jacket.
The real lifejacket holds the head reasonably securely. In the simulation the head is assumed to be held completely by the jacket.
5.1.2 Inherently Buoyant Lifejacket
The inherently buoyant lifejacket consists of a series of nylon bags filled with buoyant material. It comprises two large rectangular sections, one of which forms the front of the jacket, the other sits behind the head. These pieces are joined by two buoyant epaulettes.
A model of this jacket has been generated as shown in Figure 17. Its positioning on DYNAMAN was determined by examining a person wearing the jacket. In practice the jacket could be tied to the body in a number of ways and the relative motion between the wearer and jacket will be dependent on the ability of the wearer to fasten it tightly. In the simulation, motion has been prevented between the jacket and thorax to simulate the case where the jacket is attached very securely. In contrast to
the inflatable lifejacket, the inherently buoyant jacket does not hold the head at all. In the simulation the head is therefore allowed to move freely.
The density of the jacket was chosen so that the model mass is equal to the actual mass of the jacket.
5.2 SIMULATION OF TRIALS
A DYNAMAN simulation was generated and run for each of the life jackets representing as closely as possible the trial conditions.
From the video of the trials a typical starting position was determined for DYNAMAN, as shown in Figure 18. DYNAMAN is face down in the water with arms and legs hanging down. The relative positions of parts of the body and the water surface were taken from sketches made from the video.
In the simulation, some simplifying assumptions were made as follows:
w The water was assumed to be stationary although in practice some disturbance was unavoidable,
w The relative motion of the lifejacket and DYNAMAN was restricted as discussed in Section 5.1,
w A drag coefficient of 1.0 was assumed for all parts of the model. DYNAMAN was allowed to move freely from the initial position from time zero. The total simulation time was 8 seconds in each case.
5.3 RESULTS
The results of the simulations which were used to make a comparison between the trials and the computer simulations are the general motion of the body and the righting time as defined in Section 4.4.3. These are presented for each lifejacket in the following sections.
5.3.1 Inflatable Lifejacket
The motion of DYNAMAN in this simulation is shown in Figures 19 and 20. To aid with determining the self righting time, the vertical position of a point on the centre of the life jacket is plotted in Figure 21. To show airway motion, the vertical position of DYNAMAN's nose is plotted in Figure 22.
The following points should be noted:
w Self righting occurs in one smooth movement. Initially the model starts to turn in a “roll-over” mode (Section 4.4.2). However, the hips quickly drop and righting continues in a “sit-up” mode.
w From examination of Figures 19 - 22, it is estimated that righting begins at about 0.5 seconds and is complete by about 3.5 seconds giving a self righting time of about 3 seconds.
w At the end of the simulation (8 seconds) the model has reached an equilibrium position. The body lies at about 45° to the horizontal with the arms dropped vertically and the legs in line with the torso. The body has turned through just over 90° about a vertical axis. The airway ends up about 100 mm above the water surface.
5.3.2 Inherently Buoyant Lifejacket
The motion of DYNAMAN wearing this jacket is shown in Figure 23 and 24. To aid determination of the self righting time the vertical motion of the centre of the lifejacket is shown in Figure 25. The height of the nose above water is shown in Figure 26.
The following points should be noted:
w The model takes some time to begin to right. Righting occurs mainly in the “roll-over” mode although towards the end the hips do drop into a “sit-up” mode. The head moves around considerably during the simulation.
w It is estimated that righting begins at about 2.25 seconds and is completed at about 7.5 seconds giving a righting time of about 5.25 seconds. There is a noticeable pause from about 4.5 seconds to 5.5 seconds where the manikin has rolled to about 90° and remains at that angle.
w At the end of the simulation (8 seconds) the model has not yet reached equilibrium. It is believed that, given a longer simulation time, the model would end face up in a similar position to the final state in the inflatable lifejacket simulation but with the head to one side. The airway reaches a maximum height of 175 mm above the water surface but is clearly moving down again at the end of the simulation.
6.
COMPARISON BETWEEN TRIALS AND INITIAL
SIMULATIONS
Comparison between the trials results described in Section 4 and the initial simulations described in Section 5 shows that the simulation of the inflatable lifejacket agrees quite well with the trial. However, the simulation of the inherently buoyant lifejacket agrees less well.
The following sections compare the trials and simulations for each jacket in turn.
6.1 INFLATABLE LIFEJACKET
The following comparisons can be made:
w In both the trial and the simulation, the jacket succeeded in self righting.
w Righting occurred in a single, smooth movement dominated by the sit-up mode in both the trial and the simulation. However, there was also some roll-over mode apparent. This was more noticeable in the simulation than in the trial.
w In the trial, self righting was estimated to take about 2 seconds. In the simulation, self righting took longer, about 3 seconds.
w The final positions were very similar. However, in the simulation the arms hung more vertically and the legs were spread apart.
w In the trial, some movement of the jacket relative to the manikin occurred. In particular, the belt holding the jacket slid up the manikin's torso. In the simulation this could not occur.
6.2 INHERENTLY BUOYANT LIFEJACKET
The following comparisons can be made:
w In both the trial and the simulation, the jacket succeeded in self righting.
w In the trial, the manikin righted in a smooth movement dominated by the sit-up mode with a small roll-over component. However, in the simulation the reverse was true. The greater part of the motion was in the roll-over mode and was by no way continuous (see Section 5.3.2). Only at the end of the simulation, where righting was almost complete, did the model begin to sit-up.
w The trial and simulation give significantly different righting times (2.4 -3.6 seconds in the trial and 5.25 seconds in the simulation).
final position would be similar to that seen in the trial with the head rolled to one side and the torso tilted with one shoulder lower in the water than the other. As with the inflatable lifejacket the inherently buoyant lifejacket simulation would probably give the arms more vertical than in the trial and the legs spread further apart.
w In the trial the inherently buoyant jacket moved around a great deal on the manikin. In particular, the jacket had a noticeable tendency to slip sideways on the manikin and also to ride up towards the head. In the simulation the position of the jacket relative to the torso was fixed and no relative movement occurred.
7.
DISCUSSION
It would appear that the inflatable lifejacket simulation agreed much more closely with the trials than did the inherently buoyant lifejacket simulation in that the overall motion of the model and the righting time were closer to those observed in the trial. In the inherently buoyant lifejacket simulation righting was much slower than was observed in the trials.
As noted in Section 5.1, the results presented here represent the first iteration of both models. The following sections discuss the factors which influence righting and then consider in detail changes which could be made to the simulations to improve the results.
7.1 RIGHTING MODE
The “sit-up” and “roll-over” righting modes can be explained in terms of the principal forces acting on the lifejacket and the body as it rights.
The forces acting are the downward force due to the weight of the body acting at the centre of gravity (typically somewhere in the abdomen), and the upward buoyancy force acting at the centre of buoyancy (typically near the centre of the lifejacket). These forces are shown pictorially in Figure 27.
The side-on view in Figure 27 shows how the forces act to cause the sit-up mode. The lines of action of the gravitational and buoyancy forces are separated by a distance ‘x’ which gives rise to a turning moment about a lateral axis.
The head on view in Figure 27 shows how the forces act to cause the roll-over mode. The fines of action of the gravitational and buoyancy forces are separated by a distance ‘y’ which gives rise to a turning moment about a head-to-hip axis.
Clearly both of those moments will be dependent on the magnitude of the gravitational and buoyancy forces. An increase in either will increase the turning moment and speed up self-righting.
Which of the two modes is dominant will depend on the relative magnitude of the distances ‘x’ and ‘y’ and the rotational inertia of the body about the two axes. In general, as ‘x’ increases (ie the centre of buoyancy moves away from the centre of gravity) the sit up component of the righting mode will become more significant, and as ‘y’ increases the more significant will be the rolling component of the righting mode.
In a self-righting trial the righting motion will be a complex combination of roll-over and sit up modes. Although the size of the gravitational force will be constant, the C of G will move as the body bends. In addition, the centre of buoyancy and the size of the buoyancy force will change constantly as the volume of water displaced changes as parts of the body and lifejacket move in and out of the water. Thus x and y and the magnitude of the buoyancy force will change throughout the righting process.
7.2 INFLATABLE LIFEJACKET
The overall righting motion for the inflatable lifejacket simulation was close to that seen in the trials. However, righting was a bit slow to start. In the trials the first observed movement of the manikin was the hips dropping (see Section 4.4.2). There was a noticeable delay in the hips dropping in the simulation which suggests that the centre of gravity of the body may have been too close to the head of DYNAMAN or the centre of buoyancy may have been too close to the hips of DYNAMAN.
In addition the righting time in the simulation was 1½ times longer than observed in the trials. This implies that the turning moment was too small or the resistance to motion eg inertia, drag too high.
The discrepancy in the positions of the centre of gravity or the centre of buoyancy and the size of the forces could be due to some combination of the following:
w The mass of DYNAMAN may have been different to the manikin such that the gravitational force was incorrect.
w The density distribution of DYNAMAN may have been different to that in the marine manikin so that DYNAMAN's centre of gravity was nearer the head than in the manikin which would reduce the turning moment.
w The model of the lifejacket may have been smaller than in reality. This would mean that the buoyancy force and turning moment provided by the jacket was too small.
w The lifejacket may have been incorrectly positioned on DYNAMAN. If it were too low down the chest the centre of buoyancy would be brought closer to the centre of gravity thus reducing the sit-up moment. Although the jacket was free to move away from DYNAMAN on springs representing tapes holding the jacket, it was not free to slide up the chest. In the trials this was seen to happen on the manikin as the chest strap slid over the smooth surface of the manikin.
w The drag forces acting on the body could have been larger than in reality. However, results of the simulation showed that these forces are small in comparison to the buoyancy forces and probably have a less significant effect on righting time and mode.
The other difference between the inflatable lifejacket simulation and the trials was the final position of the bodies. In the simulation, DYNAMAN's arms dropped vertically in the water and the legs were splayed and relaxed. The arms and legs of the manikin however, remained in line and close to the body. The difference in the position arises because the joints of DYNAMAN have less resistance to rotation and do not “lock up” as the manikin's tended to in some positions. This increased freedom allows hips to rotate, legs to spread, shoulders to relax and arms to drop.
7.3 INHERENTLY BUOYANT LIFEJACKET
The righting time of DYNAMAN in the inherently buoyant lifejacket simulation was clearly greater than measured in the trials with the marine manikin.
The possible reasons for the differences between the trials and simulation are as for the inflatable jacket, ie different density distribution, undersize jacket (possibly of a slightly different shape) and jacket attachment.
However, with this jacket when the body has rolled through 90° it appears to pause in the rolling mode (Figures 28 and 29). This pause occurs when the back of the jacket enters the water so that buoyancy forces act each side of the centre of gravity giving a stable system which is reluctant to continue to roll. This feature could have arisen because of an incorrect distribution of buoyancy between the front and back of the jacket in the simulation.
At the end of the 8 second simulation DYNAMAN had not reached a stable position. However, the final position would be much the same as that achieved in the inflatable lifejacket simulation with one exception. Because the head rolls to one side in the inherently buoyant lifejacket simulation the body floats with one shoulder further in the water than the other. This occurred in the trials also. A likely difference between the final positions in the simulation and trial would be the position of the arms and legs due to the greater flexibility of DYNAMAN as discussed in 7.2.
7.4 SIMULATION IMPROVEMENTS
From the preceding discussion it is evident that the prediction of correct righting motion and times will require some improvement in the initial simulations.
Aspects of the simulation which could be varied include:
w Provision of more accurate density data for the marine manikin and lifejackets. This would enable the correct magnitude of the
gravitational force to be calculated.
w Provision of more accurate volume data for the marine manikin and lifejacket. This would provide the correct buoyancy forces.
w Revision of lifejacket position on the body.
w Introduction of some movement in the water which may provide additional turning moments.
w Modification of the drag coefficient used to determine the fluid resistance to body motion.
Of these possible modifications, the first three were considered likely to have the greatest effect on the behaviour of DYNAMAN. As a result, it was agreed with HSE that further measurements would be made on the real manikin and lifejackets to allow more accurate simulations to be generated. Section 8 describes the
measurements which were made while Section 9 describes revised simulations which incorporate the new data.
8.
BUOYANCY AND DENSITY MEASUREMENT
As discussed in Section 7.4, a series of measurements were made at INM after the initial simulations had been carried out to determine the volume and density of each major component of the marine manikin and lifejackets used in the self-righting trials reported in Section 4.
The volume and density were determined by weighing each component in air and then in water. In the case of buoyant components (ie density less than water) sink weights were used in the measurements. The volume and density were calculated as follows:
Eqn 9
Weight in air (W
A) -
ρ
cg V
c+ W
sAEqn 10
Weight in water (W
w) =
ρ
cg V
c-
ρ
wg V
cW +W
swweight of sink weight in water. =
W
swweight of sink weight in air =
W
s volume of component =V
c gravity =g
density of water =ρ
w density of component =ρ
c Where From (9) and (10)q
c= qw 1− 1Ww− −Wsw WA −WsA andV
c= WAq−cgWsAThe marine manikin was disassembled into the following components for measurement;
w 4 litre lung
w thigh
w upper arm
w lower arm and hand
w head and torso (without lung)
w pelvis and abdomen.
The measured values for these component parts and the two lifejackets are compared in Table 2 with the values used in the initial simulations. Note that the inherently buoyant jacket is composed of three sections, the front, the back and the shoulder epaulettes as shown in Figure 17.
It can be seen from Table 2 that the densities of the individual parts and overall density of DYNAMAN used in the initial simulations were slightly lower than the values measured or the marine manikin. The table also shows that the volume of the body parts used in the initial simulation were larger than measured.
In addition, the lifejacket densities were larger and volumes significantly smaller in the initial simulations compared with the measured values.
In summary, the table shows that DYNAMAN was more buoyant and the jackets less buoyant in the initial simulation compared with the values for the marine manikin and lifejackets measured at INM.
Table 2
Density and Buoyancy Measurements
68.6 1.05
78.5 0.99
Total with 4 litre lung
24.4 0.09
19.7 0.1
Inherently Buoyant lifejacket
17.9 0.04 14.1 0.07 Inflatable lifejacket 40.4 1.03 47.9 0.95
Head and torso
2.6 1.09
1.9 1.07
Lower arm and hard
1.9 1.11 2.2 1.07 Upper arm 4.5 1.08 5.1 1.04
Shin and foot
5.7 1.06 6.1 1.04 Thigh 4.5 0.05 4 0.05 4 litre lung Volume (litres) Relative Density Volume (litres) Relative Density Measured Values Initial Simulations Component
9.
REVISED SIMULATIONS
The two simulations presented in Section 5 were refined using the measured data presented in Section 8.
Modifications were made to the volume and density of DYNAMAN to more closely represent the marine manikin. The volume of the lifejackets was also revised. The specific changes and the results of the revised simulations are presented in this section.
9.1 MODEL CHANGES
9.1.1 DYNAMAN
The value of density and volume given in Table 2 were used to adjust the size and density of the individual components of DYNAMAN. The changes resulted in a 7.8% decrease in total mass of DYNAMAN. The centre of gravity of the revised DYNAMAN moved away from the head towards the feet by 36 mm.
The volume changes gave a 12.8% reduction in DYNAMAN volume and hence an equivalent decrease in the buoyancy force. The change in volume is greater than the change in mass since the marine manikin was found to be slightly denser overall than the DYNAMAN used in the initial simulations.
9.1.2 Lifejackets
As shown in Section 8, the volume measurements made of the lifejackets showed that the models used in the initial simulations were both about 25% too small. This difference will have a significant effect on the turning moment generated by the jackets.
The revised shape of the inflatable jacket is shown in Figure 28. The shape was generated by inflating the jacket within the simulation as described in Section 5, using a higher inflation pressure than in the initial simulation to achieve the required increase in volume.
The revised shape and position of the inherently buoyant lifejacket is shown in Figure 34. This jacket is modelled as a solid as described in Section 5. The dimensions of the front, back and epaulettes were adjusted to achieve the required volume.
In the initial simulations the position of the jackets was determined from the observed position taken when the manikin was out of the water as described in Section 5. In the revised simulation, the jackets have been repositioned to represent the position taken when the manikin is in the water. The revised inflatable lifejacket simulation has the jacket further away from the chest as can be seen by comparing Figure 28 with Figure 16. In the revised inherently buoyant jacket simulation the jacket is positioned higher up DYNAMAN's chest as can be seen by comparing Figures 29 and 17.
9.2 RESULTS OF REVISED SIMULATIONS
The results of the simulations which were used to make a comparison between the trials and computer simulations are the general motion of the body and the righting time as defined in Section 4.4.3. These are presented for each lifejacket in the following sections.
9.2.1 Inflatable Lifejacket
The motion of DYNAMAN in this simulation is shown in Figures 30 and 31. To aid with determining the self-righting time, the vertical position of a point on the centre of the lifejacket is plotted in Figure 32. To show airway motion, the vertical position of DYNAMAN's nose is plotted in Figure 33.
The following points should be noted and compared with the behaviour described in Section 5.3.1 for the initial simulation:
Self-righting occurs in one smooth movement. The hips drop quickly and DYNAMAN rights in predominantly the 'sit-up' mode.
From the figures it is estimated that righting begins as soon as the simulation starts and is completed in about 1.6 seconds.
Within 4 seconds DYNAMAN has reached an equilibrium position. The body lies at about 60° to the horizontal with the arms dropped vertically and legs in line with the torso. The body has turned through about 60° about a vertical axis. The airway ends up about 180 mm above the water surface.
9.2.2 Inherently Buoyant Lifejacket
The motion of DYNAMAN in this simulation is shown in Figures 34 and 35. To aid with determining the self-righting time the vertical position of a point on the centre of the lifejacket is plotted in Figure 36. To show airway motion, the vertical position of DYNAMAN's nose is plotted in Figure 37.
The following points should be noted and compared with the behaviour described in Section 5.3.2 for the initial simulation:
w Self-righting occurs in one smooth movement. Righting occurs mainly in the ‘roll’-over mode although the hips drop more quickly than in the initial simulation. The head moves around considerably during the simulation.
w It is estimated from Figure 41 that righting begins at about 0.5 seconds and is complete by about 3 seconds giving a righting time of about 2.5 seconds. There is a short pause in the righting at about 1.5 - 2.0 seconds.
w Within about 6 seconds, DYNAMAN has reached equilibrium. The body lies at about 45° to the horizontal with the arm and legs dropped vertically. The body has turned through just over 90° about
a vertical axis. The airway ends up about 250 mm above the water surface.
10.
COMPARISON OF TRIALS WITH INITIAL AND REVISED
SIMULATIONS
A comparison between the trials and initial simulations is made in Section 6. It was found that the initial simulations were slow to right (the inherently buoyant simulation being particularly slow). The simulations were revised to improve buoyancy and density properties as described in Section 8.
The following sections compare the trials with the revised simulations and highlight improvements over the initial simulations.
10.1 INFLATABLE LIFEJACKET
The following comparisons can be made:
w In both the trials and revised simulation the jacket succeeded in self-righting.
w In the trial, self-righting was estimated to take 2 seconds. In the initial simulation self-righting took longer, about 3 seconds. However, in the revised simulation the self-righting time was only 1.6 seconds. This significant decrease in righting time was due to the increase in turning moment resulting from the increase in buoyancy force and the increased separation between the centres of gravity and buoyancy due to changes in DYNAMAN's mass distribution and repositioning of the larger lifejacket.
w Righting occurred in a single, smooth movement in both simulations. In the initial simulation this was dominated by the roll-over mode. However, in the revised simulation it was dominated by the sit-up mode. The reason for this is that in the revised simulation the jacket is positioned significantly further away from DYNAMAN's chest. As explained in Section 6, this increases the turning moment about the shoulder to shoulder axis compared to that about a head to hip axis and hence increases the ‘Sit-up’ mode in the righting action.
w In the trials, the equilibrium position of the manikin in the water was to lie at about 45° to the horizontal with the arms in line with and beside the torso. The legs were bent with the knees at about 90° to the thighs which were slightly raised relative to the fine of the torso. The knees stayed together.
In the initial simulation the torso was seen to take up a similar equilibrium position, however the limbs were spread and relaxed due to differing joint constraints between DYNAMAN and the manikin. In the revised simulation, DYNAMAN lay at about 60° to the horizontal with limbs in the same relaxed position. The increase in the angle of the body to the horizontal occurred due to the increased angle between the jacket and DYNAMAN in the revised
w In the trial some movement of the jacket relative to the manikin occurred. In both simulations such movement could not occur.
10.2 INHERENTLY BUOYANT LIFEJACKET
The following comparisons can be made:
w In both the trial and the simulations, the jacket succeeded in self-righting.
w The righting time in the trial was 2.4 - 3.6 seconds and in the initial simulation was 5.25 seconds. However, the righting time was reduced to 2.5 seconds in the revised simulation. As with the inflatable lifejacket, this reduction in righting time was due to the increased turning moment brought about by the revisions made to the DYNAMAN
w In the trial, the manikin righted in an apparently smooth movement. However, in the initial simulation righting was by no means
continuous. The body was seen to stay on its side for several seconds before righting was completed.
In the revised simulation the right motion was much improved in that it occurred in a smoother movement although a small delay still occurred when the body was on its side.
w The equilibrium position of the manikin in the trials wearing the inherently buoyant jacket was similar to its position when wearing the inflatable jacket described in Section 10.1.
In the initial simulation, DYNAMAN did not reach equilibrium after 8 seconds. In the revised simulation, equilibrium was reached about 6 seconds into the simulation. As for the inflatable jacket simulation the body lay at about 45° to the horizontal with relaxed limbs laying almost vertically. The relaxed final position of the limbs indicate the increased joint flexibility in DYNAMAN compared to a manikin.
w In the trial the jacket moved around a great deal on the manikin. In particular, the jacket had a noticeable tendency to slip sideways and move up towards the head. In both the initial and revised simulation this motion was prevented.
10.3 SUMMARY
The revised simulations have given much better righting times then the initial simulations. The results are summarised in Table 3. The inflatable jacket rights a little faster than measured (1.6 seconds as opposed to 2 seconds) and the inherently buoyant jacket rights within the range of observed time (2.5 seconds in the revised simulation as opposed to 2.4 to 3.6 seconds measured).
Table 3 Self-Righting Times 2.5 sees 1.6 secs Revised Simulation 5.25 secs 3.00 secs Initial Simulation 2.4 - 3.6 secs 1.9 - 2.00 secs Trial Inherently Buoyant Inflatable Jacket
The reduction in righting time is a direct consequence of the increase in buoyancy of the jackets and the adjustment in density and volume of DYNAMAN.
The predicted righting modes differ between the initial and revised simulations but it was apparent from the trials that a range of modes can occur and the one which occurs is very much dependent on the initial position of the lifejacket. This point is demonstrated most clearly by the change from roll-over to sit-up mode observed with the inflatable jacket in the initial and revised simulation.
11.
CONCLUSIONS, RECOMMENDATIONS AND
APPLICATIONS OF THE TECHNIQUE
11.1 CONCLUSIONS
The work carried out in this project has demonstrated that the DYNAMAN technique can be used to investigate the behaviour of humans and manikins wearing buoyancy aide.
The effects of buoyancy and drag have been implemented in DYNAMAN for this particular modelling application. The validation test cases give quantitatively correct behaviour when compared with analytical results. Good results have also been obtained in a demonstration simulation of a lifejacket wearer in simulated waves. A series of trials were carried out at INM with a marine manikin to obtain data on the self righting characteristics of two lifejackets. Initial DYNAMAN simulations were then carried out based on these trials and the results compared with the trial data. The simulations were not specially tuned to obtain better agreement after the first iteration.
The initial simulations produced slower righting times than measured in the trials. Several reasons for this were identified. The most significant cause of the different was felt to be inaccurate volume and mass distributions in the simulation. Measurements were made at INM to obtain data for the manikin and lifejacket. The computer simulations were revised to incorporate this data. Righting times in the revised simulations were then much closer to those measured.
The computer simulations showed that self righting in still water can be modelled with the DYNAMAN technique. The results demonstrated that good correlation can be achieved between trials and simulation provided that the distributions of weight and buoyancy are correct. A major contributor to the buoyancy is (of course) the lifejacket.
11.2 RECOMMENDATIONS
The current work programme has contributed, significantly to the understanding of lifejacket behaviour. Further benefit would be gained from extra work. In particular, further work is recommended in the following areas:
w Investigate further the mechanisms of self righting, including: - simulate people, not manikins
- simulate clothed subjects
- investigate behaviour in real sea conditions
- simulate survival suits and suit-jacket combinations - simulate buoyancy aids which inflate in the water.
Some of this investigation could use DYNAMAN as it stands. Other aspects may require development of the simulation technique.
w Investigate the sensitivity of the righting behaviour to, - lifejacket attachments
- person size and shape - lifejacket size and shape - other factors.
This investigation should be carried out by generating and analysing further DYNAMAN models.
11.3 APPLICATIONS OF THE TECHNIQUE
Ultimately the technique could have four main arm of application:
w As a research tool to understand more about the principles of lifejacket behaviour and the way that different types of design would work. This could be particularly valuable in the case of lifejackets for very specialist applications or for looking at more complex systems such as lifejacket/survival suit combinations;
w The technique could help the lifejacket manufacturer to develop new products quicker and more cheaply. It could, for example, allow him to try out new designs on the computer without having to go to the expense of prototyping and physical testing until he has some confidence in the design;
w DYNAMAN could help the lifejacket user - especially those users with very specific performance requirements - to ensure that they chose a product which will do exactly what they want it to do;
w The technique could be used as part of an approval process either to help define appropriate physical tests or to allow a new design to be assessed for conditions which would not be practical to test.
12.
REFERENCES
1. “DYNA3D User's Manual (Non-Linear Dynamic Analysis of Structures in Three Dimensions)” J.O. Hallquist, D J Benson, Lawrence Livermore National Laboratory.
2. “Dynamic Modelling of Occupant Motion - Final Report”. FNC 731/2475R Frazer-Nash Consultancy report to HSE Railway Inspectorate.
3. “Properties of Body Segments based on Size and Weigh” American Journal of Anatomy, 1967.