{"id":790,"date":"2019-09-16T11:00:42","date_gmt":"2019-09-16T18:00:42","guid":{"rendered":"https:\/\/c21-wp.phas.ubc.ca\/index.php\/energy-cost-of-transport"},"modified":"2020-01-08T13:50:42","modified_gmt":"2020-01-08T21:50:42","slug":"energy-cost-of-transport","status":"publish","type":"article","link":"https:\/\/c21.phas.ubc.ca\/article\/energy-cost-of-transport\/","title":{"rendered":"Energy Cost of Transport"},"content":{"rendered":"
Work and Energy<\/strong><\/p>\n The amount of energy required to get from A to B is equal to whatever force is required to push the object in the direction it is going in, multiplied by the distance travelled, i.e. the mechanical work done. How much force do you need? If you are moving at a constant speed, then the only reason a force is needed is to overcome friction or drag[note] Cars versus bicycles \/article\/energy-use-cars-6-gasoline-cars-vs-bicycles<\/a>[\/note]. For travelling on land or water, physics puts no constraints on how small this force can be<\/em>. For flight, physics imposes fairly strict limitations on how low the transport cost can be (because one has to move fast to stay aloft). However, when the transport cost is expressed in appropriate units, remarkable similarities can be seen in very different modes of locomotion.<\/p>\n <\/p>\n Units<\/strong><\/p>\n When dealing with generalities, the most useful units for the expression of transport costs are something like:<\/p>\n $ \\dfrac{\\textnormal{energy}}{\\textnormal{(distance)(mass)}} \\tag{1}$<\/p>\n Energy can be given in J, kJ, MJ, GJ or kWh<\/p>\n Distance is usually given in km<\/p>\n Mass, in kg or tonnes, can refer to that of the entire vehicle or only that of the useful load. Or, it can be a single passenger or 100 passengers [note]D. MacKay, Without hot air, p.121 http:\/\/www.withouthotair.com<\/a>[\/note].<\/p>\n Dimensional Analysis<\/strong><\/p>\n If you want to make an educated guess about what the energy cost of transport should be, consider a dimensional analysis approach:<\/p>\n $\\dfrac{\\textnormal{J}}{\\textnormal{kg}\\cdot\\textnormal{m}} = \\dfrac{\\textnormal{kg}\\cdot\\textnormal{m}^2\\textnormal{\/s}^2}{\\textnormal{kg}\\cdot\\textnormal{m}}= \\textnormal{m\/s}^2 \\nonumber \\tag{2}$<\/p>\n So transport cost has the same dimensions as acceleration. What is the most relevant acceleration when considering moving stuff from A to B? The acceleration due to gravity, g<\/em>, is the most likely culprit. If g<\/em> were equal to 0, you could push ten-tonne loads around with your little finger, albeit rather slowly.<\/p>\n The acceleration due to gravity in energy units is 9.8 J\/(kg\u00b7m) or 9.8 MJ\/(tonne\u00b7km). This would be the energy cost of lifting an object vertically, or of sliding it along the floor if the coefficient of kinetic friction, \u03bc\u00a0<\/em>k<\/sub> = 1. Of course, we can do better than this, as we have wheels and wings. However, the efficiency of our engines, \u00a0the ratio of mechanical work done to chemical energy in the fuel burnt to do it, is never much bigger than about 30 or 40%, and this works against us. Hence the energy cost of most forms of transport is somewhere between 3 and 6 times better than our dimensional estimate, as can be seen from table 1.<\/p>\n