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Walking a mile burns less than 50 calories when done at a slow enough pace by an average person. But the faster you walk, the more calories you burn for every mile that you walk.This is to be expected, as it is in complete agreement with the laws of physics which unequivocally state that kinetic energy equals mass times velocity squared (always then halved to be made consistent with the standard energy unit). Energy requirements grow in accordance with the squaring of velocity - moving faster takes more energy for the same distance, if everything else is equal.Of course, everything is not equal, as strides lengthen and change to become more mechanically efficient as the pace of motion increases. Within the walking stride, everything else remains equal enough (stride length being an obvious exception) such that the escalating energy requirements are easily observed and measured, and they have been largely accepted as accruing in straight line fashion, which has been formulaically codified. But variety between individuals is large, and a big differentiator of that variety is fitness level, which further can be measured by oxygen consumption, and that is the method used by formula in note [10] for linearly relating walking pace (and running pace as well) to energy expenditure.Running is more energy efficient than walking, and as a person's pace approaches a twelve minute mile their gate will switch to a jog and the walking formula will overstate their energy consumption.Repeat: walking a mile over 12 minutes will burn more calories than jogging a mile in 12 minutes!There also appear to be at least two subgroups of gaits which determine energy use within the overall range of the running motion, which also increases largely linearly overall. What is clear, overall, is that running faster burns more calories per mile than running slower (with exceptions). How hard you breathe is an effective determinant of how many calories you are burning, and a range of 100 - 150 calories per mile for an average person, depending on their breathing, is a reasonable estimate.Some reading which I am continuing to absorb, along with the referenced works contained within them all:[1] Energy Cost of Running, 1962Indirect calorimetric measurements were made on two athletes running at different speeds up to 22 km/hr at grades from -20 to +15%; the function was found to be linearly related to speed. Within these limits, the net kilocalories per kilogram per kilometer values seem to be independent of speed and related only to the incline. These values are about 5–7% lower than those found in nonathletic subjects, which shows that training in atheletes does not lead to great improvement. A nomogram is given for easily calculating the energy expenditure in running when the speed and the incline are known. The energy cost per kilometer in horizontal run (1 kcal/kg) is about double that for walking at the most economical speed (4 km/ hr).[2] Energy Cost During Walking and Running a Same Distance is Associated with Vertical Oscillation on Gravity Center, 2007The purpose of this study was to evaluate which factors are involved in energetic cost of running and walking a same distance (2,000 meters). Eight healthy men were submitted to walking (5.5km/h) and running (11Km/h) tests, when oxygen consumption, for energy expenditure of exercise, was monitored, and images of volunteers were recorded for vertical oscillation of gravity center. Both, total oxygen consumption and estimated energetic cost were significantly higher during the running test (p<0.05) (88.66 ± 12.27 L O2, 418.88 ± 59.14 Kcal) compared to the walking one (66.31 ± 10.18 L O2, 319.61 ± 9.06 Kcal), as well as the vertical oscillation on gravity center (3.29 ± 0.42cm and 2.89 ± 0.42cm, running and walking, respectively). These findings suggest that the higher energetic cost of running may be associated with increased vertical oscillation on gravity center during running.[3] The Effects of Running Speed on the Metabolic and Mechanical Costs of Running, 2003This study assessed the influence of speed on the metabolic and the mechanical cost to run a given distance. Trained male runners (n=12) performed 2 treadmill run trials of 8 min duration at each of 6 speeds (range 2.33 to 4.0 m/s). Oxygen uptake values were normalized for running speed providing a metabolic task cost variable (MBTC, ml/kg/m). Mechanical work was calculated from digitized video records using three different algorithms. Values were normalized for running speed giving mechanical task cost variables (MTC, J/kg/m). No change in the group mean metabolic task cost was found across speeds (p=0.25). In contrast, mechanical task cost decreased as running speed increased (p<0.001). The three mechanical work algorithms resulted in MTC characteristics that were significantly different from each other (p<0.001). This study suggests that metabolic cost per distance remains relatively constant across running speeds while mechanical cost per distance decreases as speed increases.[4] Cost of Walking and Running, 1978 Twenty-four young adult male subjects were used to study the relationship between total caloric costs (exercise and recovery costs) incurred and speed of movement over a distance of 1 mile. Caloric costs were determined at walking speeds of 3, 4, and 5 mph and at running speeds of 5, 7, and 9 mph. Energy costs were assessed every 20 sec during the activity and during the recovery until the caloric cost returned to pre-established resting levels. The fitness level of the subjects was considered as a moderating variable. 3regression equations to predict caloric cost from body weight, speed of movement, and VO2 max were also developed. Conclusions for the given speeds were: (1) running is more costly than walking, (2) the cost of walking a mile increases with speed of movement, and (3) for running speeds, total caloric cost and VO2 max are inversely related. The independent variables for the regression equation for walking included body weight and speed squared times body weight (R2 = .86). The independent variables for the running equation were identical to the ones used in the walking equation with the addition of speed times VO2 max (R2 = .62).[5] A Comparison of Caloric Expenditure of Walking Versus Runing One-mileInteresting, on-topic powerpoint presentation from 2002. Included but likely not a professional study done for publication.[6] Energy Expenditure of Walking and Running, 2004Conclusion: Running has a greater energy cost than walking on both the track and treadmill. For running, the Le ́ger equation and ACSM prediction model appear to be the most suitable for the prediction of running energy expenditure. The ACSM and Pandolf prediction equation also closely predict walking energy expenditure, whereas the McArdle’s table or the equations by Epstein and van der Walt were not as strong predictors of energy expenditure.[7] A Study on the Comparison the Energy of Walking and Running, 2010The estimation of the energy expenditure during physical activities has been considered as an important subject and studied consistently for a long time. Nineteen male healthy subjects participated and were required to walk and run on the treadmill with the gas analyzer and a tri-axial accelerometer. The tri-axial accelerometer was attached on the point of middle of left and right posterior superior iliac spine (PSIS). Walking speed were 3.0, 4.0, 5.0 and 6.0 km/h and running speed were 7.0, 8.0 and 9.0 km/h respectively. One trial consists of three periods; ramp-up (1 minute), practice for walking or running (5 minutes), and cool-down (1 minute). After being removed first two minutes during practice, which was expected ‘steady-state’ for minimizing the errors of unstable energy expenditure, the remaining data was then used for analysis. To find a linear relationship between energy expenditure from the gas analyzer and that of accelerometer data, physical activity was calculated by the integration of the accelerometer. The linear relationship between the measured and estimated values were excellent in both walking (r = 0.988) and running (r = 0.895). These results would be expected to apply to health management product such as preventing fatness system.[8] Wikipedia: Running energetics, November 2013Though some recent data may suggest otherwise,[9] it is traditionally well accepted that a strong linear relationship exists between the rate of oxygen consumption and running speed (see figure 1), with energy expenditure increasing with increasing running speed.[1][2][3][4]More recently, it has been proposed that an accurate prediction of the energy cost of running at a given speed can be made from the time available to generate force to support body weight.[10] This theory suggests that smaller animals must take shorter, quicker steps to travel a given distance than larger animals. As a result, they have shorter foot ground contact times and less time to produce force on the ground. Due to this decreased amount of time to produce force, smaller animals must rely more heavily on metabolically costly fast muscle fibers to produce force to run at a given speed. Conversely, larger animals take slower and longer steps, contributing to an increase in the amount of time the foot is in contact with the ground during running. This longer contact time allows larger animals a greater amount of time to produce force. As a result, larger animals do not recruit as many metabolically costly fast muscle fibers in order to run a given speed. All of these factors result in a greater COT in smaller animals in comparison to larger animals.[10][9] Optimal Running Speeds and the Evolution of Hominin Hunting Strategies, 2008This study explicitly forbids the reproduction of its text, but it is the actual study referenced by the Wikipedia article on Running Energetics (immediately above) that, importantly, charts a curvilinear relationship, as opposed to a linear one, between running velocity and energy expenditure, with a very, very strong statistical correlation established.[10] Calculating Caloric Expenditure