{"id":782,"date":"2019-08-28T23:39:11","date_gmt":"2019-08-29T03:39:11","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/physicsforlifesciences1phys1108\/?post_type=chapter&#038;p=782"},"modified":"2019-10-03T10:56:33","modified_gmt":"2019-10-03T14:56:33","slug":"5-3-drag-forces-on-the-human-body","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/physicsforlifesciences1phys1108\/chapter\/5-3-drag-forces-on-the-human-body\/","title":{"raw":"5.3 Drag Forces on the Human Body","rendered":"5.3 Drag Forces on the Human Body"},"content":{"raw":"<h2 class=\"entry-title\">DRAG FORCES ON THE BODY<\/h2>\r\n<div id=\"post-1097\" class=\"standard post-1097 chapter type-chapter status-publish hentry chapter-type-standard\">\r\n<div class=\"entry-content\">\r\n<figure id=\"attachment_1290\" class=\"wp-caption aligncenter\" aria-describedby=\"caption-attachment-1290\"><img class=\"wp-image-1290 size-large\" src=\"https:\/\/openoregon.pressbooks.pub\/app\/uploads\/sites\/42\/2018\/08\/1024px-Gabriel_Skydiving_23-1024x682.jpg\" alt=\"\" width=\"1024\" height=\"682\" \/><figcaption id=\"caption-attachment-1290\" class=\"wp-caption-text\">A skydiver maintains a horizontal (flat) body position with arms and legs spread, which reduces the terminal velocity and increases the fall time. Image Credit: \u201c<a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:Gabriel_Skydiving_(23).jpg\">Gabriel Skydiving<\/a>\u201d By Gabriel Christian Brown, via<span>\u00a0<\/span><a href=\"http:\/\/wikimedia.org\/\">Wikimedia Commons<\/a><\/figcaption><\/figure>\r\n<a class=\"footnote\" title=\"&quot;Gabriel Skydiving&quot; By Gabriel Christian Brown [CC BY-SA 4.0 (https:\/\/creativecommons.org\/licenses\/by-sa\/4.0)], from Wikimedia Commons\" id=\"return-footnote-1097-1\" href=\"https:\/\/openoregon.pressbooks.pub\/bodyphysics\/chapter\/drag-force\/#footnote-1097-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a>\r\n\r\nCorrect and thoughtful body orientation is an important part of\u00a0 skydiving because the orientation of the body affects the amount of<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-3841\">air resistance<\/button><span>\u00a0<\/span>experienced by the body. In turn, the air resistance affects the<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-4026\">terminal speed<\/button>, as we will see in the next chapter.\r\n<h1 id=\"chapter-1097-section-1\" class=\"section-header\">DRAG<\/h1>\r\n<figure class=\"wp-caption aligncenter\"><img src=\"https:\/\/media.giphy.com\/media\/IEWzCQ2RnXd1m\/giphy.gif\" alt=\"Fluid moves around a sphere and curls toward the sphere on the back side before forming a vortex that detaches from the sphere and swirls away downstream.\" width=\"646\" height=\"486\" \/><figcaption class=\"wp-caption-text\">Simulation of fluid flowing around a sphere.<span>\u00a0<\/span><a href=\"https:\/\/www.grc.nasa.gov\/WWW\/k-12\/airplane\/dragsphere.html\" target=\"_blank\" rel=\"noopener noreferrer\">\u201cDrag of a Sphere\u201d<\/a>\u00a0by\u00a0<a href=\"https:\/\/www.grc.nasa.gov\/WWW\/k-12\/aerores.htm\" target=\"_blank\" rel=\"noopener noreferrer\">Glenn Research Center Learning Technologies Project<\/a>,\u00a0<a href=\"http:\/\/www.nasa.gov\/\" target=\"_blank\" rel=\"noopener noreferrer\">NASA,<\/a>\u00a0<a href=\"https:\/\/giphy.com\/gifs\/drag-sphere-IEWzCQ2RnXd1m\">via GIPHY\u00a0<\/a>is in the\u00a0<a href=\"http:\/\/creativecommons.org\/publicdomain\/zero\/1.0\/\" target=\"_blank\" rel=\"noopener noreferrer\">Public Domain, CC0<\/a><\/figcaption><\/figure>\r\n<a class=\"footnote\" title=\"&quot;Drag of a Sphere&quot;\u00a0by\u00a0Glenn Research Center Learning Technologies Project,\u00a0NASA,\u00a0via GIPHY\u00a0is in the\u00a0Public Domain, CC0\" id=\"return-footnote-1097-2\" href=\"https:\/\/openoregon.pressbooks.pub\/bodyphysics\/chapter\/drag-force\/#footnote-1097-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a>\r\n\r\nAir resistance limits the<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-4026\">terminal speed<\/button><span>\u00a0<\/span>that a falling body can reach. Air resistance is an example of\u00a0 the<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-4027\">drag force<\/button>, which is force that objects feel when they move through a fluid (liquid or gas).\u00a0\u00a0Similar to<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-3957\">kinetic friction<\/button>, drag force is<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-3894\">reactive<\/button><span>\u00a0<\/span>because it only exists when the object is moving and it points in the opposite direction to the object\u2019s motion through the fluid. Drag force can be broken into two types:<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-4028\">form drag<\/button><span>\u00a0<\/span>and<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-4029\">skin drag<\/button>. Form drag is caused by the resistance of\u00a0 fluids (liquids or gases) to being pushed out of the way by an object in motion through the fluid. Form drag is similar to the<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-3839\">normal force<\/button><span>\u00a0<\/span>provided by the resistance of solids to being deformed, only the fluid actually moves instead of just deforming. Skin drag is essentially a kinetic frictional force caused by the sliding of the fluid along the surface of the object.\r\n\r\nThe drag force\u00a0 depends the density of the fluid (\u03c1), the maximum<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-3975\">cross-sectional area<\/button>\u00a0of the object(<img src=\"https:\/\/openoregon.pressbooks.pub\/app\/uploads\/quicklatex\/quicklatex.com-af2a49a0b900175f892860b4a50bcb59_l3.svg\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A_x\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" \/>), and the<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-4032\">drag coefficient<\/button><span>\u00a0<\/span>(<img src=\"https:\/\/openoregon.pressbooks.pub\/app\/uploads\/quicklatex\/quicklatex.com-b07f5335022864eeceabf15295e5faa4_l3.svg\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C_d\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" \/>), which accounts for the shape of the object. Objects with a low drag coefficient are often referred to as having an aerodynamic or streamlined shape. Finally, the drag force depends on the on the speed (<em>v<\/em>) of the object through the fluid. If the fluid is not not very<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-4033\">viscous<\/button><span>\u00a0<\/span>then drag depends on<span>\u00a0<\/span><em>v<sup>2<\/sup><\/em>, but for viscous fluids the force depends just on<span>\u00a0<\/span><em>v<\/em>. In typical situations air is not very viscous so the complete formula for air resistance force is:\r\n<p class=\"ql-center-displayed-equation\"><span class=\"ql-right-eqno\">(1)<\/span><span class=\"ql-left-eqno\">\u00a0<\/span><img src=\"https:\/\/openoregon.pressbooks.pub\/app\/uploads\/quicklatex\/quicklatex.com-000123d803f185109777d26aca0cfbea_l3.svg\" height=\"31\" width=\"101\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"\\begin{equation*} F_d = \\frac{1}{2}C_d \\rho A_x v^2 \\end{equation*}\" title=\"Rendered by QuickLaTeX.com\" \/><\/p>\r\nThe image below illustrates how the shape of\u00a0 an object, in this case a car, affects the<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-4032\">drag coefficient<\/button>. The table that follows provides drag coefficient values for a variety of objects.\r\n<figure class=\"wp-caption alignnone\"><img src=\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/5\/58\/Aerodynamic_Drag_of_Car.jpg\" alt=\"A graph with drag coefficient on the vertical axis and year on the horizontal axis. The drag coefficients of of vehicles manufactures in various years are plotted. 0.6 in 1925, 0.5 in 1945, and 0.3 in 1975. The shapes of the vehicles and the shapes that would have a similar cross sectional area are also shown: A plate for 1925, a cylinder for 1945 and an oval for 1975.\" width=\"754\" height=\"396\" \/><figcaption class=\"wp-caption-text\">Drag coefficients of cars (vertical axis on left) have changed over time (horizontal axis). Image Credit:<span>\u00a0<\/span><a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:Aerodynamic_Drag_of_Car.jpg\">Drag of Car<\/a><span>\u00a0<\/span>by Eshaan 1992 via Wikimedia Commons<\/figcaption><\/figure>\r\n<a class=\"footnote\" title=\"Drag of Car By Eshaan 1992 [CC BY-SA 3.0 (https:\/\/creativecommons.org\/licenses\/by-sa\/3.0)], from Wikimedia Commons\" id=\"return-footnote-1097-3\" href=\"https:\/\/openoregon.pressbooks.pub\/bodyphysics\/chapter\/drag-force\/#footnote-1097-3\" aria-label=\"Footnote 3\"><sup class=\"footnote\">[3]<\/sup><\/a>\r\n<table id=\"import-auto-id1165298535568\" summary=\"A table lists typical values of draft coefficient C for different objects. Values include 0.28 for a Toyota Camry, 0.64 for a Hummer H2 SUV, 0.7 for a skydiver feet first, and 1.0 for a horizontal skydiver.\">\r\n<tbody>\r\n<tr>\r\n<td>Object<\/td>\r\n<td>Drag Coefficient (<em>C<\/em>)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Airfoil<\/td>\r\n<td>0.05<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Toyota Camry<\/td>\r\n<td>0.28<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Ford Focus<\/td>\r\n<td>0.32<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Honda Civic<\/td>\r\n<td>0.36<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Ferrari Testarossa<\/td>\r\n<td>0.37<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Dodge Ram pickup<\/td>\r\n<td>0.43<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Sphere<\/td>\r\n<td>0.45<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Hummer H2 SUV<\/td>\r\n<td>0.64<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Skydiver (feet first)<\/td>\r\n<td>0.70<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Bicycle<\/td>\r\n<td>0.90<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Skydiver (horizontal)<\/td>\r\n<td>1.0<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Circular flat plate<\/td>\r\n<td>1.12<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div><a class=\"footnote\" title=\"OpenStax,\u00a0College Physics. OpenStax CNX.\u00a0Jan 17, 2019 http:\/\/cnx.org\/contents\/031da8d3-b525-429c-80cf-6c8ed997733a@14.5\" id=\"return-footnote-1097-4\" href=\"https:\/\/openoregon.pressbooks.pub\/bodyphysics\/chapter\/drag-force\/#footnote-1097-4\" aria-label=\"Footnote 4\"><sup class=\"footnote\">[4]<\/sup><\/a><\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Reinforcement Exercises<\/h3>\r\nWhich body orientation would put the largest<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-4027\">drag force<\/button><span>\u00a0<\/span>on a human body moving vertically through a fluid?\r\n<ul>\r\n \t<li>body horizontal and sideways (side first)<\/li>\r\n \t<li>body vertical with arms in (feet first)<\/li>\r\n \t<li>body flat with arms out (front first)<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n\r\n<hr class=\"before-footnotes\" \/>\r\n\r\n<div class=\"footnotes\">\r\n<ol>\r\n \t<li id=\"footnote-1097-1\">\"<a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:Gabriel_Skydiving_(23).jpg\">Gabriel Skydiving<\/a>\" By Gabriel Christian Brown [CC BY-SA 4.0 (<a href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\">https:\/\/creativecommons.org\/licenses\/by-sa\/4.0<\/a>)], from<span>\u00a0<\/span><a href=\"http:\/\/wikimedia.org\/\">Wikimedia Commons<\/a><span>\u00a0<\/span><a href=\"https:\/\/openoregon.pressbooks.pub\/bodyphysics\/chapter\/drag-force\/#return-footnote-1097-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">\u21b5<\/a><\/li>\r\n \t<li id=\"footnote-1097-2\"><a href=\"https:\/\/www.grc.nasa.gov\/WWW\/k-12\/airplane\/dragsphere.html\" target=\"_blank\" rel=\"noopener noreferrer\">\"Drag of a Sphere\"<\/a>\u00a0by\u00a0<a href=\"https:\/\/www.grc.nasa.gov\/WWW\/k-12\/aerores.htm\" target=\"_blank\" rel=\"noopener noreferrer\">Glenn Research Center Learning Technologies Project<\/a>,\u00a0<a href=\"http:\/\/www.nasa.gov\/\" target=\"_blank\" rel=\"noopener noreferrer\">NASA,<\/a>\u00a0<a href=\"https:\/\/giphy.com\/gifs\/drag-sphere-IEWzCQ2RnXd1m\">via GIPHY\u00a0<\/a>is in the\u00a0<a href=\"http:\/\/creativecommons.org\/publicdomain\/zero\/1.0\/\" target=\"_blank\" rel=\"noopener noreferrer\">Public Domain, CC0<\/a><span>\u00a0<\/span><a href=\"https:\/\/openoregon.pressbooks.pub\/bodyphysics\/chapter\/drag-force\/#return-footnote-1097-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">\u21b5<\/a><\/li>\r\n \t<li id=\"footnote-1097-3\"><a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:Aerodynamic_Drag_of_Car.jpg\">Drag of Car<\/a><span>\u00a0<\/span>By Eshaan 1992 [CC BY-SA 3.0 (<a href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/3.0\" rel=\"nofollow\">https:\/\/creativecommons.org\/licenses\/by-sa\/3.0<\/a>)], from Wikimedia Commons<span>\u00a0<\/span><a href=\"https:\/\/openoregon.pressbooks.pub\/bodyphysics\/chapter\/drag-force\/#return-footnote-1097-3\" class=\"return-footnote\" aria-label=\"Return to footnote 3\">\u21b5<\/a><\/li>\r\n \t<li id=\"footnote-1097-4\"><span class=\"name\">OpenStax<\/span>,\u00a0College Physics. OpenStax CNX.\u00a0Jan 17, 2019<span>\u00a0<\/span><a href=\"http:\/\/cnx.org\/contents\/031da8d3-b525-429c-80cf-6c8ed997733a@14.5\" rel=\"nofollow\">http:\/\/cnx.org\/contents\/031da8d3-b525-429c-80cf-6c8ed997733a@14.5<\/a><span>\u00a0<\/span><a href=\"https:\/\/openoregon.pressbooks.pub\/bodyphysics\/chapter\/drag-force\/#return-footnote-1097-4\" class=\"return-footnote\" aria-label=\"Return to footnote 4\">\u21b5<\/a><\/li>\r\n<\/ol>\r\nNote:\u00a0 Special thanks to\u00a0<a href=\"https:\/\/openoregon.pressbooks.pub\/bodyphysics\/chapter\/drag-force\/\">https:\/\/openoregon.pressbooks.pub\/bodyphysics\/chapter\/drag-force\/<\/a>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"<h2 class=\"entry-title\">DRAG FORCES ON THE BODY<\/h2>\n<div id=\"post-1097\" class=\"standard post-1097 chapter type-chapter status-publish hentry chapter-type-standard\">\n<div class=\"entry-content\">\n<figure id=\"attachment_1290\" class=\"wp-caption aligncenter\" aria-describedby=\"caption-attachment-1290\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1290 size-large\" src=\"https:\/\/openoregon.pressbooks.pub\/app\/uploads\/sites\/42\/2018\/08\/1024px-Gabriel_Skydiving_23-1024x682.jpg\" alt=\"\" width=\"1024\" height=\"682\" \/><figcaption id=\"caption-attachment-1290\" class=\"wp-caption-text\">A skydiver maintains a horizontal (flat) body position with arms and legs spread, which reduces the terminal velocity and increases the fall time. Image Credit: \u201c<a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:Gabriel_Skydiving_(23).jpg\">Gabriel Skydiving<\/a>\u201d By Gabriel Christian Brown, via<span>\u00a0<\/span><a href=\"http:\/\/wikimedia.org\/\">Wikimedia Commons<\/a><\/figcaption><\/figure>\n<p><a class=\"footnote\" title=\"&quot;Gabriel Skydiving&quot; By Gabriel Christian Brown [CC BY-SA 4.0 (https:\/\/creativecommons.org\/licenses\/by-sa\/4.0)], from Wikimedia Commons\" id=\"return-footnote-1097-1\" href=\"https:\/\/openoregon.pressbooks.pub\/bodyphysics\/chapter\/drag-force\/#footnote-1097-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a><\/p>\n<p>Correct and thoughtful body orientation is an important part of\u00a0 skydiving because the orientation of the body affects the amount of<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-3841\">air resistance<\/button><span>\u00a0<\/span>experienced by the body. In turn, the air resistance affects the<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-4026\">terminal speed<\/button>, as we will see in the next chapter.<\/p>\n<h1 id=\"chapter-1097-section-1\" class=\"section-header\">DRAG<\/h1>\n<figure class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/media.giphy.com\/media\/IEWzCQ2RnXd1m\/giphy.gif\" alt=\"Fluid moves around a sphere and curls toward the sphere on the back side before forming a vortex that detaches from the sphere and swirls away downstream.\" width=\"646\" height=\"486\" \/><figcaption class=\"wp-caption-text\">Simulation of fluid flowing around a sphere.<span>\u00a0<\/span><a href=\"https:\/\/www.grc.nasa.gov\/WWW\/k-12\/airplane\/dragsphere.html\" target=\"_blank\" rel=\"noopener noreferrer\">\u201cDrag of a Sphere\u201d<\/a>\u00a0by\u00a0<a href=\"https:\/\/www.grc.nasa.gov\/WWW\/k-12\/aerores.htm\" target=\"_blank\" rel=\"noopener noreferrer\">Glenn Research Center Learning Technologies Project<\/a>,\u00a0<a href=\"http:\/\/www.nasa.gov\/\" target=\"_blank\" rel=\"noopener noreferrer\">NASA,<\/a>\u00a0<a href=\"https:\/\/giphy.com\/gifs\/drag-sphere-IEWzCQ2RnXd1m\">via GIPHY\u00a0<\/a>is in the\u00a0<a href=\"http:\/\/creativecommons.org\/publicdomain\/zero\/1.0\/\" target=\"_blank\" rel=\"noopener noreferrer\">Public Domain, CC0<\/a><\/figcaption><\/figure>\n<p><a class=\"footnote\" title=\"&quot;Drag of a Sphere&quot;\u00a0by\u00a0Glenn Research Center Learning Technologies Project,\u00a0NASA,\u00a0via GIPHY\u00a0is in the\u00a0Public Domain, CC0\" id=\"return-footnote-1097-2\" href=\"https:\/\/openoregon.pressbooks.pub\/bodyphysics\/chapter\/drag-force\/#footnote-1097-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a><\/p>\n<p>Air resistance limits the<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-4026\">terminal speed<\/button><span>\u00a0<\/span>that a falling body can reach. Air resistance is an example of\u00a0 the<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-4027\">drag force<\/button>, which is force that objects feel when they move through a fluid (liquid or gas).\u00a0\u00a0Similar to<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-3957\">kinetic friction<\/button>, drag force is<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-3894\">reactive<\/button><span>\u00a0<\/span>because it only exists when the object is moving and it points in the opposite direction to the object\u2019s motion through the fluid. Drag force can be broken into two types:<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-4028\">form drag<\/button><span>\u00a0<\/span>and<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-4029\">skin drag<\/button>. Form drag is caused by the resistance of\u00a0 fluids (liquids or gases) to being pushed out of the way by an object in motion through the fluid. Form drag is similar to the<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-3839\">normal force<\/button><span>\u00a0<\/span>provided by the resistance of solids to being deformed, only the fluid actually moves instead of just deforming. Skin drag is essentially a kinetic frictional force caused by the sliding of the fluid along the surface of the object.<\/p>\n<p>The drag force\u00a0 depends the density of the fluid (\u03c1), the maximum<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-3975\">cross-sectional area<\/button>\u00a0of the object(<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/openoregon.pressbooks.pub\/app\/uploads\/quicklatex\/quicklatex.com-af2a49a0b900175f892860b4a50bcb59_l3.svg\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A_x\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" \/>), and the<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-4032\">drag coefficient<\/button><span>\u00a0<\/span>(<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/openoregon.pressbooks.pub\/app\/uploads\/quicklatex\/quicklatex.com-b07f5335022864eeceabf15295e5faa4_l3.svg\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C_d\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" \/>), which accounts for the shape of the object. Objects with a low drag coefficient are often referred to as having an aerodynamic or streamlined shape. Finally, the drag force depends on the on the speed (<em>v<\/em>) of the object through the fluid. If the fluid is not not very<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-4033\">viscous<\/button><span>\u00a0<\/span>then drag depends on<span>\u00a0<\/span><em>v<sup>2<\/sup><\/em>, but for viscous fluids the force depends just on<span>\u00a0<\/span><em>v<\/em>. In typical situations air is not very viscous so the complete formula for air resistance force is:<\/p>\n<p class=\"ql-center-displayed-equation\"><span class=\"ql-right-eqno\">(1)<\/span><span class=\"ql-left-eqno\">\u00a0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/openoregon.pressbooks.pub\/app\/uploads\/quicklatex\/quicklatex.com-000123d803f185109777d26aca0cfbea_l3.svg\" height=\"31\" width=\"101\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"\\begin{equation*} F_d = \\frac{1}{2}C_d \\rho A_x v^2 \\end{equation*}\" title=\"Rendered by QuickLaTeX.com\" \/><\/p>\n<p>The image below illustrates how the shape of\u00a0 an object, in this case a car, affects the<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-4032\">drag coefficient<\/button>. The table that follows provides drag coefficient values for a variety of objects.<\/p>\n<figure class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/5\/58\/Aerodynamic_Drag_of_Car.jpg\" alt=\"A graph with drag coefficient on the vertical axis and year on the horizontal axis. The drag coefficients of of vehicles manufactures in various years are plotted. 0.6 in 1925, 0.5 in 1945, and 0.3 in 1975. The shapes of the vehicles and the shapes that would have a similar cross sectional area are also shown: A plate for 1925, a cylinder for 1945 and an oval for 1975.\" width=\"754\" height=\"396\" \/><figcaption class=\"wp-caption-text\">Drag coefficients of cars (vertical axis on left) have changed over time (horizontal axis). Image Credit:<span>\u00a0<\/span><a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:Aerodynamic_Drag_of_Car.jpg\">Drag of Car<\/a><span>\u00a0<\/span>by Eshaan 1992 via Wikimedia Commons<\/figcaption><\/figure>\n<p><a class=\"footnote\" title=\"Drag of Car By Eshaan 1992 [CC BY-SA 3.0 (https:\/\/creativecommons.org\/licenses\/by-sa\/3.0)], from Wikimedia Commons\" id=\"return-footnote-1097-3\" href=\"https:\/\/openoregon.pressbooks.pub\/bodyphysics\/chapter\/drag-force\/#footnote-1097-3\" aria-label=\"Footnote 3\"><sup class=\"footnote\">[3]<\/sup><\/a><\/p>\n<table id=\"import-auto-id1165298535568\" summary=\"A table lists typical values of draft coefficient C for different objects. Values include 0.28 for a Toyota Camry, 0.64 for a Hummer H2 SUV, 0.7 for a skydiver feet first, and 1.0 for a horizontal skydiver.\">\n<tbody>\n<tr>\n<td>Object<\/td>\n<td>Drag Coefficient (<em>C<\/em>)<\/td>\n<\/tr>\n<tr>\n<td>Airfoil<\/td>\n<td>0.05<\/td>\n<\/tr>\n<tr>\n<td>Toyota Camry<\/td>\n<td>0.28<\/td>\n<\/tr>\n<tr>\n<td>Ford Focus<\/td>\n<td>0.32<\/td>\n<\/tr>\n<tr>\n<td>Honda Civic<\/td>\n<td>0.36<\/td>\n<\/tr>\n<tr>\n<td>Ferrari Testarossa<\/td>\n<td>0.37<\/td>\n<\/tr>\n<tr>\n<td>Dodge Ram pickup<\/td>\n<td>0.43<\/td>\n<\/tr>\n<tr>\n<td>Sphere<\/td>\n<td>0.45<\/td>\n<\/tr>\n<tr>\n<td>Hummer H2 SUV<\/td>\n<td>0.64<\/td>\n<\/tr>\n<tr>\n<td>Skydiver (feet first)<\/td>\n<td>0.70<\/td>\n<\/tr>\n<tr>\n<td>Bicycle<\/td>\n<td>0.90<\/td>\n<\/tr>\n<tr>\n<td>Skydiver (horizontal)<\/td>\n<td>1.0<\/td>\n<\/tr>\n<tr>\n<td>Circular flat plate<\/td>\n<td>1.12<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div><a class=\"footnote\" title=\"OpenStax,\u00a0College Physics. OpenStax CNX.\u00a0Jan 17, 2019 http:\/\/cnx.org\/contents\/031da8d3-b525-429c-80cf-6c8ed997733a@14.5\" id=\"return-footnote-1097-4\" href=\"https:\/\/openoregon.pressbooks.pub\/bodyphysics\/chapter\/drag-force\/#footnote-1097-4\" aria-label=\"Footnote 4\"><sup class=\"footnote\">[4]<\/sup><\/a><\/div>\n<div class=\"textbox exercises\">\n<h3>Reinforcement Exercises<\/h3>\n<p>Which body orientation would put the largest<span>\u00a0<\/span><button class=\"glossary-term\" aria-describedby=\"1097-4027\">drag force<\/button><span>\u00a0<\/span>on a human body moving vertically through a fluid?<\/p>\n<ul>\n<li>body horizontal and sideways (side first)<\/li>\n<li>body vertical with arms in (feet first)<\/li>\n<li>body flat with arms out (front first)<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<hr class=\"before-footnotes\" \/>\n<div class=\"footnotes\">\n<ol>\n<li id=\"footnote-1097-1\">&#8220;<a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:Gabriel_Skydiving_(23).jpg\">Gabriel Skydiving<\/a>&#8221; By Gabriel Christian Brown [CC BY-SA 4.0 (<a href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\">https:\/\/creativecommons.org\/licenses\/by-sa\/4.0<\/a>)], from<span>\u00a0<\/span><a href=\"http:\/\/wikimedia.org\/\">Wikimedia Commons<\/a><span>\u00a0<\/span><a href=\"https:\/\/openoregon.pressbooks.pub\/bodyphysics\/chapter\/drag-force\/#return-footnote-1097-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">\u21b5<\/a><\/li>\n<li id=\"footnote-1097-2\"><a href=\"https:\/\/www.grc.nasa.gov\/WWW\/k-12\/airplane\/dragsphere.html\" target=\"_blank\" rel=\"noopener noreferrer\">&#8220;Drag of a Sphere&#8221;<\/a>\u00a0by\u00a0<a href=\"https:\/\/www.grc.nasa.gov\/WWW\/k-12\/aerores.htm\" target=\"_blank\" rel=\"noopener noreferrer\">Glenn Research Center Learning Technologies Project<\/a>,\u00a0<a href=\"http:\/\/www.nasa.gov\/\" target=\"_blank\" rel=\"noopener noreferrer\">NASA,<\/a>\u00a0<a href=\"https:\/\/giphy.com\/gifs\/drag-sphere-IEWzCQ2RnXd1m\">via GIPHY\u00a0<\/a>is in the\u00a0<a href=\"http:\/\/creativecommons.org\/publicdomain\/zero\/1.0\/\" target=\"_blank\" rel=\"noopener noreferrer\">Public Domain, CC0<\/a><span>\u00a0<\/span><a href=\"https:\/\/openoregon.pressbooks.pub\/bodyphysics\/chapter\/drag-force\/#return-footnote-1097-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">\u21b5<\/a><\/li>\n<li id=\"footnote-1097-3\"><a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:Aerodynamic_Drag_of_Car.jpg\">Drag of Car<\/a><span>\u00a0<\/span>By Eshaan 1992 [CC BY-SA 3.0 (<a href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/3.0\" rel=\"nofollow\">https:\/\/creativecommons.org\/licenses\/by-sa\/3.0<\/a>)], from Wikimedia Commons<span>\u00a0<\/span><a href=\"https:\/\/openoregon.pressbooks.pub\/bodyphysics\/chapter\/drag-force\/#return-footnote-1097-3\" class=\"return-footnote\" aria-label=\"Return to footnote 3\">\u21b5<\/a><\/li>\n<li id=\"footnote-1097-4\"><span class=\"name\">OpenStax<\/span>,\u00a0College Physics. OpenStax CNX.\u00a0Jan 17, 2019<span>\u00a0<\/span><a href=\"http:\/\/cnx.org\/contents\/031da8d3-b525-429c-80cf-6c8ed997733a@14.5\" rel=\"nofollow\">http:\/\/cnx.org\/contents\/031da8d3-b525-429c-80cf-6c8ed997733a@14.5<\/a><span>\u00a0<\/span><a href=\"https:\/\/openoregon.pressbooks.pub\/bodyphysics\/chapter\/drag-force\/#return-footnote-1097-4\" class=\"return-footnote\" aria-label=\"Return to footnote 4\">\u21b5<\/a><\/li>\n<\/ol>\n<p>Note:\u00a0 Special thanks to\u00a0<a href=\"https:\/\/openoregon.pressbooks.pub\/bodyphysics\/chapter\/drag-force\/\">https:\/\/openoregon.pressbooks.pub\/bodyphysics\/chapter\/drag-force\/<\/a><\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":9,"menu_order":4,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-782","chapter","type-chapter","status-publish","hentry"],"part":327,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/physicsforlifesciences1phys1108\/wp-json\/pressbooks\/v2\/chapters\/782","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/physicsforlifesciences1phys1108\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/physicsforlifesciences1phys1108\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/physicsforlifesciences1phys1108\/wp-json\/wp\/v2\/users\/9"}],"version-history":[{"count":1,"href":"https:\/\/pressbooks.bccampus.ca\/physicsforlifesciences1phys1108\/wp-json\/pressbooks\/v2\/chapters\/782\/revisions"}],"predecessor-version":[{"id":783,"href":"https:\/\/pressbooks.bccampus.ca\/physicsforlifesciences1phys1108\/wp-json\/pressbooks\/v2\/chapters\/782\/revisions\/783"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/physicsforlifesciences1phys1108\/wp-json\/pressbooks\/v2\/parts\/327"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/physicsforlifesciences1phys1108\/wp-json\/pressbooks\/v2\/chapters\/782\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/physicsforlifesciences1phys1108\/wp-json\/wp\/v2\/media?parent=782"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/physicsforlifesciences1phys1108\/wp-json\/pressbooks\/v2\/chapter-type?post=782"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/physicsforlifesciences1phys1108\/wp-json\/wp\/v2\/contributor?post=782"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/physicsforlifesciences1phys1108\/wp-json\/wp\/v2\/license?post=782"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}