Functional Threshold Work Rate

Functional Threshold Work Rate (kcal/kg/h): The maximum Calorie output an athlete can achieve in 1 hour per kilogram of body weight.

You've got inputs and outputs, some of which are measurable and some aren't. Tools like indirect calorimeters use input/output gas exchange to measure the human body's processes, while a direct calorimeter simply measures heat.

Cyclists use power output. It's easy to measure (these days) and efficiency doesn't seem to vary much with training, so this is a decent measure of input too. FTP is in W/kg. Since kJ of output is just power and time (a Joule is a Watt·Second), we combine two fun facts to know that kJ of output is roughly the same as kcal of input. First, 1 kJ = 4.184 kcal . Second, humans are about 25% efficient at taking the input calories to output work, and these two cancel! To this end, FTWR = (W/kg) * 3600/1000/4.184 first converting W into J by multiplying by an hour of seconds, converting the J to kJ, then convering those kJ into kcal by dividing by the conversion. Altogether, FTWR = FTP * .86 kcal/W/h .

Runners use pace. Most apps or fitness trackers (garmin, etc) will use the available data to estimate Calories burned (capital C means kcal). These take into account pace, gradient, and body weight (but not efficiency. Using these output Calorie estimates, it's not so straightfoward to convert into FTWR: efficiency varies by relative pace of the athlete (Barnes 2015). We're looking at a maximal effort here, so at 5 calories burned per liter of oxygen (Scott 2005) and using efficiencies in the range of 15-30% (Hoogkamer 2019) we'll just use 25% for easiest math and say: FTWR = Calories burned * .25 / kg . This isn't very satisfying, still. If you go from pace -> power (W/kg), you could do something like * 10 min/mile or 6.2 min/km: ~3.5 - 4.0 W/kg * 8 min/mile or 5.0 min/km: ~4.5 - 5.0 W/kg * 6 min/mile or 3.7 min/km: ~6.0 - 7.0 W/kg * ~4.5 min/mile or 2.8 min/km: ~7.5 - 8.5 W/kg to account for the nonlinearity, and use the cycling formula.

Weight training, albeit less commonly, uses velocity. Newton's law: F = m·a , so while VBT trackers have velocity, with knowledge of the weight they also have power and work. The values likely aren't comparable to running/cycling over an hour (an hour of deadlifts...).

All this leads me to think that we should measure this with the input rather than the output. Or maybe don't worry about comparing between sports: cycling we can measure output, running we have to measure inputs.