Agricultural and Biosystems Engineering Publications Agricultural and Biosystems Engineering
2019
Extraction Force Prediction for Male Entrapment Victims with Different Body Types Submerged below the Grain Surface
Charles V. Schwab Iowa State University, [email protected]
Lauren E. Schwab Iowa State University, [email protected]
Pamela J. Schwab Civil Software Design LLC
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Abstract One contributor to agriculture‘s high death rate is confined space fatalities caused yb entrapment in grain. Over 1,000 grain-related fatalities have been documented by researchers in 43 states, and states with the largest grain storage capacities have been shown to experience a proportionally larger number of suffocation fatalities. Several researchers have measured extraction forces in specific conditions, but a reference standard is needed for estimating the extraction forces for grain suffocation victims in common conditions. A prediction model for estimating extraction forces was developed using the principle of boundary shear, an approximation of human surface area, and a commonly accepted equation for lateral granular pressure. This research reintroduces the prediction model for extraction forces and explores several sensitivity analyses of the input variables. It also updates the anthropometric data used in the model calculations and produces extraction force estimates for adult male victims with different body shapes submerged below the grain surface. Results from the prediction model are presented graphically for common input variables, various entrapment depths, and adult male body shapes.
Keywords Farm safety, Grain suffocation, Prediction model, Rescue, Safety
Disciplines Agriculture | Bioresource and Agricultural Engineering | Civil and Environmental Engineering
Comments This article is published as Schwab, Charles V., Lauren E. Schwab, and Pamela J. Schwab. "Extraction Force Prediction for Male Entrapment Victims with Different Body Types Submerged below the Grain Surface." Journal of Agricultural Safety and Health 25, no. 2 (2019): 77-90. DOI: 10.13031/jash.13155. Posted with permission.
This article is available at Iowa State University Digital Repository: https://lib.dr.iastate.edu/abe_eng_pubs/1113 Extraction Force Prediction for Male Entrapment Victims with Different Body Types Submerged below the Grain Surface
C. V. Schwab, L. E. Schwab, P. J. Schwab
ABSTRACT. One contributor to agriculture’s high death rate is confined space fatalities caused by entrapment in grain. Over 1,000 grain-related fatalities have been documented by researchers in 43 states, and states with the largest grain storage capacities have been shown to experience a proportionally larger number of suffocation fatalities. Several re- searchers have measured extraction forces in specific conditions, but a reference standard is needed for estimating the extraction forces for grain suffocation victims in common con- ditions. A prediction model for estimating extraction forces was developed using the prin- ciple of boundary shear, an approximation of human surface area, and a commonly ac- cepted equation for lateral granular pressure. This research reintroduces the prediction model for extraction forces and explores several sensitivity analyses of the input variables. It also updates the anthropometric data used in the model calculations and produces ex- traction force estimates for adult male victims with different body shapes submerged below the grain surface. Results from the prediction model are presented graphically for common input variables, various entrapment depths, and adult male body shapes. Keywords. Farm safety, Grain suffocation, Prediction model, Rescue, Safety.
he U.S. agricultural workforce does not have the largest number of hours worked for an industry in the U.S., but it receives the distinction as the deadliest industry, with a T worker fatality rate of 22.6 deaths per 100,000 workers (NSC, 2017). This death rate is more than seven times the all-industry average death rate of 3.0 deaths per 100,000 work- ers. The industry with the largest number of hours worked is educational and health services (41,469 million h), which has 8.5 times more hours worked than agriculture (4,859 million h) and a death rate of 0.5 deaths per 100,000 workers. Some other industries with larger num- bers of hours worked than agriculture, such as transportation/warehousing, construction, and manufacturing, are viewed as dangerous by the general public but typically have lower death rates than agriculture: 12.8, 9.8, and 2.0 deaths per 100,000 workers, respectively. One contributor to agriculture’s high death rate is confined space fatalities caused by en- trapment in grain. This confined space hazard has been acknowledged by educators for dec-
Submitted for review in October 2018 as manuscript number JASH 13155; approved for publication by the Ergonomics, Safety, & Health Community of ASABE in February 2019. The authors are Charles V. Schwab, Professor, Department of Agricultural and Biosystems Engineering, and Lauren E. Schwab, Lecturer, Department of Civil, Construction and Environmental Engineering, Iowa State University, Ames, Iowa; Pamela J. Schwab, Director, Civil Software Design LLC, Ames, Iowa. Corresponding author: Charles V. Schwab, 3335 Elings Hall, Iowa State University, Ames, IA 50011; phone: 515-294-4131; e-mail: [email protected].
Journal of Agricultural Safety and Health 25(2): 77-90 © 2019 ASABE ISSN 1074-7583 https://doi.org/10.13031/jash.13155 77 ades (Loewer and Loewer, 1974; NRAES, 1986; Schwab et al., 1997; Collins, 2005; Iowa FACE, 2011; CASHRE, 2016). More than 1,000 grain-related fatalities were documented in 43 states from 1964 to 2016 (Issa et al., 2016). Issa et al. (2016) demonstrated that states with a large number of farms with on-site grain storage (i.e., Iowa, Illinois, Indiana, Nebraska, and Wisconsin) experienced a proportionally larger number of suffocation fatalities. Beyond reporting the numbers of grain suffocations and the circumstances responsible for these tragic outcomes, it is important to understand the physical conditions during an entrapment. Mathematically modeling the extraction forces for an entrapment victim as- sists safety researchers in identifying the variables that influence the extraction forces and establishing the base assumptions and parameters that are significant for extraction force prediction. A model allows exploration of innovations for rescue and the ability to under- stand new or different entrapment conditions that could be encountered. A model, along with experimental results, strengthens the general understanding of extraction forces. Schwab (1982) measured extraction forces for different test mannequins using two grains, three flow rates, and two flow conditions. Measured extraction forces for a 75 kg (165 lb) adult mannequin ranged from 4,230 to 9,212 N (951 to 2071 lbf). This research is the source of a common informational graphic that shows the extraction force by depth submerged in grain for a 75 kg (165 lb) victim, as shown in figure 1. Other researchers have measured extraction forces for different types of entrapment conditions. Roberts et al. (2015) measured the difference between extraction forces with and without a grain rescue tube around an entrapped victim. The extraction force increased if no grain was removed from inside the grain rescue tube compared to not using a grain
Figure 1. Informational graphic of extraction forces for submerged victims (source: Schwab et al., 1997).
78 Journal of Agricultural Safety and Health rescue tube. When grain was removed from inside the grain rescue tube, the extraction force was less. Issa and Field (2017) measured the extraction forces of a victim pulled from various angles and found that sharper angles (15° to 30°) of pull increased the peak force by nearly 1,000 N (225 lbf). Schwab et al. (1985) expanded on the principle of boundary shear identified by Cowin and Trent (1980) and combined it with the Janssen (1895) equation for predicting granular pressures, with an approximated human surface area, to develop a model for predicting the force required to extract a person trapped in grain. No other researcher has published a prediction model since, nor has much work been done to refine the originally proposed model for determining extraction forces exerted on a victim entrapped in granular material. The purpose of this article is to reintroduce the prediction model, explore sensitivity anal- yses of the independent variables, update the anthropometric data used in the calculations, and produce extraction force estimates for adult male victims with different body shapes submerged below the grain surface.
Original Prediction Model The original prediction model is divided into two conditions based on the victim’s po- sition relative to the grain surface. The first condition is when the victim is completely submerged below the grain surface. The second condition, not included in this article, is when the victim’s head and shoulders are above the grain surface. The original prediction model for the first condition used the mass of the victim, vertical loading from the grain above the victim, and the frictional loading on the victim. These three components for the first condition are expressed in equation 1:
gwRA ky2 FgWextraction 1exp kR (1) gS wR R ky3 ky2 yy32 exp exp ykRR1 where W = mass of victim (kg) g = standard acceleration of gravity (m s-2) w = bulk weight of granular material (kg m-3) R = hydraulic radius of cylindrical bin (m) A = top surface area of victim (m2) = coefficient of friction of grain on grain (dimensionless) k = ratio of vertical to lateral pressure (dimensionless) S = surface area of victim (m2) = coefficient of friction of grain on victim’s surface (dimensionless) y1 = distance from top of victim’s head to bottom of feet (m) y2 = distance from top of victim’s head to top surface of grain (m) y3 = distance from bottom of victim’s feet to top surface of grain (m) Fextraction = force required to extract victim from grain (N). The three distance measurements (y1, y2, and y3) related to the victim and the top surface of the grain are shown in figure 2.
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Figure 2. Three distance measurements (y1, y2, and y3) related to submerged victim and top surface of grain used for estimating extraction force.
Prediction Model Limitations The prediction model was only intended for the enveloping flow conditions in a cylin- drical bin with a grain height to bin diameter ratio of 2.0 or less (ASABE, 2016). When the grain height to bin diameter ratio is larger, the stored grain does not create an enveloping flow pattern on the top surface and greatly reduces the potential for submersion. The pre- diction model was not intended to estimate the extraction force for a victim submerged from a collapsed grain bridge. Those conditions typically involve non-free-flowing granu- lar material because bridging results from frozen or spoiled grain. Prediction Model Sensitivity Analysis A direct sensitivity analysis was conducted on the extraction force prediction model. Partial differentials of equation 1 were made for each variable in equation 1. The distance from the top of the victim’s head to the top surface of grain (y2) was not included because that variable is dependent on y1 and y3. The direct sensitivity analysis did not provide any useful information about the variables in the prediction model. A sensitivity coefficient for the variables, as described by Hamby (1994, 1995), was calculated using the partial differential equations and the quotient of the variable and re- sulting force of extraction to normalize the product. The sensitivity coefficient for each independent variable was calculated for different fractions of the base variable. This di- mensionless sensitivity coefficient was graphed, and the results did not provide any useful information about the independent variables. The one-at-a-time sensitivity measure was also used. Each independent variable was varied by -10%, -7.5%, -5%, -2.5%, 0%, 2.5%, 5%, 7.5%, and 10% of a set base value (table 1). The percentage of the extraction force (dependent variable) was calculated and plotted based on the fractional change in the base variable (independent variable).
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Table 1. Independent variables for extraction force prediction model and associated base values used in the sensitivity analysis and in the base extraction force predictions. Variable Symbol Base Value Coefficient of friction of grain on grain 0.38 (dimensionless) Hydraulic radius of cylindrical bin R 2.3 m (7.5 ft) Bulk weight of granular material w 730 kg m-3 (45.6(lb ft-3) Surface area of victim S 1.77 m2 (19.0 ft2) Distance from top of victim’s head to bottom of feet y1 1.829 m (6.0 ft) Coefficient of friction of grain on victim’s surface 0.6 (dimensionless) Ratio of vertical to lateral pressure k 0.5 (dimensionless) [a] Distance from bottom of victim’s feet to top surface of grain y3 3.05 m (10.0 ft) Mass of victim W 75 kg (165.0 lb) Top surface area of victim A 0.058 m2 (0.62 ft2) Extraction force Fextraction 8594 N (1932.0 lbf) [a] The 3.05 m depth for the base value was selected because the victim must be below the grain surface for condition 1 of the model to apply.
Two independent variables (coefficient of friction of grain on grain, and stature of the victim) were the only two variables that yielded an inverse influence (fig. 3). As the victim stature increased, the percentage of the extraction force decreased. The reverse was also true: as the victim stature decreased, the percentage of the extraction force increased. Three independent variables (mass of victim, hydraulic radius of bin, and top surface area of victim) had a negligible influence on the dependent variable and were documented as having less than 1% change in the dependent variable for a maximum change of 10% in the independent variable (fig. 4). An unexpected outcome of this sensitivity analysis was the small impact that the top surface area of the victim had on the predicted extraction force. Initially, this variable was expected to have more influence. The most influential independent variable appeared to be the distance from victim’s feet to top of grain (fig. 5). When this independent variable changed by 10%, so did the de- pendent variable of extraction force. Four other independent variables (bulk weight of grain, surface area of victim, coefficient of friction of grain on victim, and ratio of vertical to lateral pressure) had impacts on the dependent variable that were less than the most
115 (%) 110 Force 105 coefficient of friction of grain on grain 100 Extraction stature of victim of 95
90 Percentage 85 0.90 0.95 1.00 1.05 Fraction of Base Variable
Figure 3. Percentage of prediction model extraction force (dependent variable) versus fractional changes in two base variables (independent variables) with inverse relationships.
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101 (%)
weight of the victim Force
100 hydraulic radius Extraction
of top surface area of the victim
99 Percentage 0.90 0.95 1.00 1.05 Fraction of Base Variable
Figure 4. Percentage of prediction model extraction force (dependent variable) versus fractional changes in three base variables (independent variables) with low observable influence.
115 coefficient of friction of grain on victim
(%) 110
bulk weight of grain Force 105
victim feet to top of 100 grain Extraction
of
95 ratio of vertical to lateral 90
Percentage surface area of the victim 85 0.90 0.95 1.00 1.05 Fraction of Base Variable
Figure 5. Percentage of prediction model extraction force (dependent variable) versus fractional changes in five base variables (independent variables) with the largest observable influence. influential independent variable (distance from victim’s feet to top of grain). Therefore, focus was warranted on these five independent variables: surface area of victim, bulk weight of grain, distance from victim’s feet to top of grain, coefficient of friction of grain on victim, and ratio of vertical to lateral pressure. Anthropometric Data The physical measurements for a victim that were used in the original prediction model were from anthropometric measurements reported by Dreyfuss (1959). The anthropometric data for a 50th percentile male adult was used to estimate the surface area of a submerged victim using simple geometric solids (i.e., right ellipsoidal cylinder, frustum of a right cone, and obelisk). The surface area of a submerged victim was estimated by summing the dif- ferent body part calculations, as shown in table 2.
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Table 2. Surface area values for 50th percentile male with corresponding geometric solids used.[a] Surface Area Body Part Geometric Solid m2 ft2 Head Right ellipsoidal cylinder 0.12 1.3 Shoulder Obelisk 0.09 1.0 Torso Right ellipsoidal cylinder 0.75 8.1 Thigh Frustum of a right cone 0.38 4.1 Calf Right ellipsoidal cylinder 0.29 3.1 Feet Partial obelisk 0.14 1.5 Total surface area 1.77 19.0 [a] Source of data: Schwab (1982).
When the prediction model was developed, these were acceptable body dimensions and surface area values. However, the standard shapes of contemporary human beings are con- siderably different from the standard body shape defined over four decades ago. More va- rieties of human shapes exist than the standard idealized shape used in past anthropometric models. The technology used to collect physical shape data, changes in the general popu- lation, and the ability to estimate surface area have also changed. The anthropometric data for stature and body mass index (BMI) for a 50th percentile male from a government report (DHHS, 2016) and the University of Michigan Transpor- tation Research Institute (UMTRI) human model were used to construct a computer-gen- erated 50th percentile male model that could be used in a comparison of total surface area calculations with the initial estimate of 1.77 m2 (19.0 ft2) (table 2). Two major differences were the body shapes between these two 50th percentile males and the method used for calculating the total surface area of the victim using crude geometric solids (fig. 6). The computer-calculated surface area of the 50th percentile male UMTRI model was deter- mined to be 1.88 m2 (20.25 ft2). The 6% difference between these two surface area calcu- lations is reasonable, given the different methods used for estimating surface area and the variation due to physical changes in the average human body in recent decades.
(a) (b) Figure 6. Comparison of (a) 1981 geometric solids body model and (b) 2018 computer body model.
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Extraction Force Predictions for Males A question that has been repeatedly asked refers to the extraction force predictions for males who are not 75 kg (165 lb), 1829 mm (6 ft) in stature, and considered in perfect physical shape. This research examined three male statures (tall, medium, and short), as shown in figure 7, and four male BMI values (underweight, normal, overweight, and ex- treme obesity), as shown in figure 8. Several calculations were performed to determine the extraction force predictions for these conditions, which varied the depth at which the vic- tim’s feet were buried below the grain. A total of 60 human male models were constructed using DHHS (2016) anthropometric data and UMTRI (2018) male human model files. The sample size of 60 resulted from inputting four different BMI values, three different statures, five ages (20, 30, 40, 50, and 60 years), and a fixed ratio of 0.50 for erect sitting height to stature (SHS) into the online interface for the statistical body shape of a male standing model. The purpose of these
Short stature Medium stature Tall stature (1542 mm) (1700 mm) (2007 mm) Figure 7. Computer-generated models of three statures with normal body mass index.
Underweight Normal Overweight Extreme obesity (19 BMI) (23 BMI) (29 BMI) (40 BMI) Figure 8. Computer-generated models of four body mass index (BMI) values with medium stature.
84 Journal of Agricultural Safety and Health human male model samples was to determine the influence that the variables stature, BMI, and age had on the calculated surface area of a victim. There were good relationships of surface area with stature and BMI. These relationships are shown in figures 9 and 10. Vic- tim age had no significant relationship with victim surface area and was not considered in the extraction force prediction model. The same 60 human male models that were used for the surface area calculations were used for top surface area calculations. The purpose was to determine the influence that the variables stature, BMI, and age had on the calculated top surface area of a victim. There were good relationships of top surface area with stature and BMI. These relationships are shown in figures 11 and 12. Victim age had no significant relationship with victim top surface area and was not considered in the extraction force prediction model. The original extraction force prediction model was slightly modified for the purpose of this research. Because the mass of the victim is a constant variable in the extraction force prediction, it does not directly influence other components of the prediction model. Indi- rectly, variations in the influence of the victim’s mass are managed through the influences of stature and BMI on the victim’s surface area and top surface area. The variations in
3.0
2.5 ) 2 2.0
1.5
1.0 y = 0.0285x + 1.0913
Surface Area (m Surface Area R² = 0.3354 0.5
0.0 15 20 25 30 35 40 45 BMI (dl)
Figure 9. Estimated relationship of victim surface area with body mass index (BMI).
3.0
2.5 ) 2 2.0
1.5
1.0 y = 0.0016x 0.9826 R² = 0.6596 Surface Area (m Surface Area 0.5
0.0 1500 1600 1700 1800 1900 2000 Stature (mm)
Figure 10. Estimated relationship of victim surface area with stature.
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0.20
0.18 ) 2 0.16
0.14
0.12
0.10 y = 0.004x + 0.0081 R² = 0.8279 0.08 Top Surface Area (m Area Top Surface 0.06
0.04 15 20 25 30 35 40 45 BMI (dl)
Figure 11. Estimated relationship of victim top surface area with body mass index (BMI).
0.20
0.18 ) 2 0.16
0.14
0.12
0.10
0.08 y = 7E-05x 0.0059 Top Surface Area (m Area Top Surface R² = 0.1571 0.06
0.04 1500 1600 1700 1800 1900 2000 Stature (mm)
Figure 12. Estimated relationship of victim top surface area with stature. surface area are not tied to variations of 4.4, 8.8, or 22.1 kg (2, 4, or 10 lb) in the victim’s mass as much as they are to the victim being underweight or overweight based on BMI. The extraction force prediction model contains the victim’s mass and the partial extraction force, as shown in equation 2. The partial extraction force represents the two terms of the original extraction force from equation 1 that are dependent on the victim’s surface area and top surface area, as shown in equation 3:
FgWFextraction partial extraction (2)
gwRA ky2 Fpartial extraction 1exp kR (3) gS wR R ky3 ky2 yy32 exp exp ykRR1
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The partial extraction forces for twelve male human body conditions, combining the three statures and four BMI values, were calculated for submersion depths (y3) of 3.05 to 6.10 m (10 to 20 ft). The body conditions were tall underweight (TU), tall normal (TN), tall overweight (TO), tall extreme obesity (TE), medium underweight (MU), medium nor- mal (MN), medium overweight (MO), medium extreme obesity (ME), short underweight (SU), short normal (SN), short overweight (SO), and short extreme obesity (SE). The par- tial extraction forces for these twelve conditions are presented in figures 13, 14, and 15. Estimating the extraction force requires addition of the victim’s mass to the partial extrac- tion force from the graph values (eq. 2). A comparison of the partial extraction forces between two extreme conditions is shown in figure 16. The upper condition (tall extreme obesity adult male) is shown with the lower condition (short underweight adult male). As a reference point, a medium height, normal weight adult male is also included. There is considerable variation between the two extreme conditions, which ranges from 5,581 N (1254.6 lbf) at shallow depths to 14,577 N (3,277 lbf) at greater depths.
30000
TU TN 25000 TO TE 20000
15000 Partial Force Extraction (N) 10000
5000 3.0 3.5 4.0 4.5 5.0 5.5 6.0 Depth of Grain (m)
Figure 13. Estimated partial extraction force for victims with tall stature of 2007 mm (79 in.) and four body types: TU = tall underweight, TN = tall normal, TO = tall overweight, and TE = tall extreme obesity.
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30000
MU MN 25000 MO ME 20000
15000 Partial Extraction Force (N) 10000
5000 3.0 3.5 4.0 4.5 5.0 5.5 6.0
Depth of Grain (m)
Figure 14. Estimated partial extraction force for victims with medium stature of 1700 mm (67 in.) and four body types: MU = medium underweight, MN = medium normal, MO = medium overweight, and ME = medium extreme obesity.
30000
SU SN 25000 SO SE 20000
15000 Partial Extraction Force (N) 10000
5000 3.0 4.0 5.0 6.0 Depth of Grain (m)
Figure 15. Estimated partial extraction force for victims with short stature of 1542 mm (60.71 in.) and four body types: SU = short underweight, SN = short normal, SO = short overweight, and SE = short extreme obesity.
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30000
SU 25000 MN
TE
20000
15000 Partial Extraction Force (N) 10000
5000 3.0 4.0 5.0 6.0 Depth of Grain (m)
Figure 16. Estimated partial extraction force for three body types representing extreme conditions of short underweight (SU) and tall extreme obesity (TE) and an intermediate condition of medium normal (MN).
Summary This article presented the existing extraction force prediction model, explored sensitiv- ity analyses of the input variables, updated the anthropometric data used in calculations, and produced extraction force estimates for adult male victims with different body types for various depths when the victim was below the grain surface. The model presentation and sensitivity analyses provide a better understanding of the variables that are used in the model. It also helps focus additional research efforts on the variables that have the greatest influence on extraction forces. The ability to generate different human models permits exploration of how certain hu- man variables can influence the extraction force estimates. A victim classified as tall and extremely obese can now have an estimated extraction force that differs from that of a victim classified as short and underweight. At a grain depth of 3.048 m (10 ft), the esti- mated extraction force ranges from 12,261 N (2,756.4 lbf) for a tall extreme obesity person to 6,680 N (1,501.7 lbf) for a short underweight person. These results increase the general understanding of the original extraction force prediction model and help focus new re- search on topics that can further improve the model. These results also address the question of what the extraction force would be for male victims who are not 75 kg (165 lb) in mass, 1829 mm (6 ft) in stature, and in perfect physical shape. Acknowledgements Journal paper of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa. This work was supported by the USDA National Institute of Food and Agriculture (Hatch Project IOW05542) and by State of Iowa funds.
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