# Are there hidden units in the Pandolf equation?

I've been reading up on several fitness areas and rucking caught my attention. I stumbled across the Pandolf equation for how many calories you burn, which is as follows (link to site where I found the explanation):

M = 1.5 W + 2.0 (W + L)(L/W) 2 + n(W + L)(1.5V2 + 0.35VG)

Where

M: your metabolic rate in watts

L: the weight of your pack (kg)

G: the grade of any incline (%)

n: a “terrain factor” that adjusts the results for different surfaces

What I am wondering is are there hidden units in the 1.5, 2.0 or the 0.35? ignoring the variables the units don't make sense to me

watts = kg + kg + kgm2/s2 + kgm/s

### Yes there are!

I found the original paper1 and the terms of the equation are defined:

(1) A metabolic cost for standing without load (M1); this is proportional to the weight of the body and is calculated as 1.5 watts per kilogram of body weight (M1 = 1.5W).

This indicates that the actual units for 1.5W is (watts/kg) * kg = watts.

(2) A metabolic cost of load bearing while standing (M2); this is affected by the total weight (subject + load) and is fitted as a function of the load to weight ratio squared (M2 = 2.0 (W+L) * (L/W)2)

As this term also cancels to kg, it can be presumed that the metabolic rate is 2 watts when (W+L) * (L/W)2 = 1.

The formulation of the last term is somewhat obfuscated, but based on the previous terms, it can be assumed that the original researchers determined that the metabolic rate was 1 watt when the third term totaled out to 1.

Essentially, there is a hidden (watts/unit) in front of each (unit), which cancels to (watts).

1 K.B. Pandolf, B. Givoni, R.F. Goldman. "Predicting energy expenditure with loads while standing or walking very slowly". J Appl Physiol, 43 (4) (1977), pp. 577-581