This is non-trivial as the body has 3 different, but connected, metabolic subsystems, see Nutrition for Health, Fitness, & Sport, or How does one train for sports when the three metabolic pathways interact?. So a sprinter will likely only anaerobically consume the ADP present in their muscles, and possibly utilise some energy held in their blood sugar. Both these subsystems / conversions have a lesser overhead than that of aerobically converting energy to / from fat, ATP and ADP.

Anyway ignoring sprinting, burning calories is essentially an aerobic process, so generally can be approximated / modeled from the oxygen consumed and pumped to your muscles by your heart (volume of O2 [VO2] and Heart Rate [HR]).

A number of external variables affect the calories required to travel a given distance: body mass, speed, wind resistance, gradient, temperature, heart size.... but essentially it's the heart rate and oxygen volume that determine, and can be used to estimate, the amount of energy consumed in a given period.

There are several studies / regression equations that attempt to model the dependencies between the variables listed above, such as the ACMS equations, but in your case the MET tables are probably of more interest. As they list for various activities / speeds the relative energy cost, of an individual performing them.

Possibly also worth a read of: How reliable is this study for the relationship between heart rate and calories burned?

The following maths I've lifted from my earlier answer to: Metabolic Equations for Anaerobic Exercise? (below).

MET = vVO2Max = VO2Max / 3.5 = kCalBurnt / (bodyMassKg * timePer formingHours)

estimated VO2 = (currentHeartRate / MaxHeartRate) * VO2Max

where: MaxHeartRate = 210 - (0.8 * ageYears)

Kcal/Min ~= 5 * massKg * VO2 / 1000

Note: The 5 calories / min constant, assumes just carbohydrates are being converted, over a short period. If the exercise is sustained aerobically for a period this value drops to 4.86 to reflect a mix of fats and carbohydrates are being converted into energy.

A number of sites have MET estimates for specific activities eg.

• Compendium of Physical Activities
• procon.org - MET Values for 800+ Activities
• Metabolic Equivalents (METS) in Exercise Testing, Exercise Prescription, and Evaluation of Functional Capacity

So just use the formula above to estimate the calories spent performing a particular exercise eg. If you spend 6 mins on an Elliptical trainer (moderate effort), which has been assigned a MET score of 5.0, and you weigh 80Kg, you'dend up with:

KCalBurnt = MET * bodyMassKg * timePerformingHours
          = 5.0 * 80 * 0.1 
          = 40 KCal

The ACMS equations may also be of interest:

Arm Ergometry VO2 = (3 * workRateWatts) / bodyMassKg + 3.5

Leg Ergometry: VO2 = (1.8 * workRateWatts) / bodyMassKg + 7

Stepping: VO2 = (0.2 * (steps in a Min)) + 1.33 * (1.8 * stepHeightMeters * (stepsInAMin))

• 3.5

Walking: VO2 = (0.1 * metersWalkedInAMin) + (1.8 * metersWalkedInAMin) * (fractionalGrade) + 3.5

Running: VO2 = (0.2 * metersRunInAMin) + (0.9 * metersRunInAMin) * (fractionalGrade) + 3.5