Measuring work done in the gym
Not quite off-topic. I'm trying to work out how much energy gets burnt up doing strength training in the Powerhaus and the Mermet etc.
So, today, squats.
I did :
12 x 20kg (empty bar)
8 x 60kg
5 x 100kg
5 x 5 @ 145kg as my work sets. The prior sets were warmups.
Depth is I think ~0.8m, I'll take that as a good enough guess for now.
How much work is that. in terms of tonnage it's really only worthwhile to look at the work sets, so I lifted 3,625kg as my working load.
That's one measure, but it's not all that useful really. My 1rm for these full squats is probably around 163kg if I use Brzycki's equation to extrapolate from my 5 rep sets, which isn't 100% accurate, but it'll do... So I'm lifting ~88% of 1RM 25 times. Reasonably intense. But still not what I'm interested in here.
Work is defined as force x distance
Force is mass x acceleration
Mass is easy! 145kg ... Acceleration is gravity, 9.8m/s^2 - we'll assume the weight is moved upwards slowly, it's too hard otherwise.
Distance is 0.8m
So our force is 145 x 9.8 : 1421 N, which gives work as 1421 x 0.8 : 1136.8 joules - roughly. Let's say 1100 as close enough (conservative estimate). 25 reps all up at that weight : 27,500 joules. Roughly 27 Kilojoules. Is that much? Nope! The human body is around 25% efficient. So to get 27 Kj the body will use around 4 times that, so roughly 100Kj. My BMR is around 11,000 kj per day. 100 kj isn't very much!
This lot of sums doesn't take into account the energy used to build muscle after the training session, the effect of extra muscle on RMR and BMR etc, it's purely a rough (very) estimate of how much energy gets used to do these lifts. Have a look at wikipedia's brief summary of EPOC for more on post exercise energy use.
Power's another interesting measure. If I assume I'm lifting the weight in ~1.5 seconds (pretty close, but I haven't timed it), let's see how many watts that is.
Power is work / time
So for a 145kg squat, lifting 0.8m in 1.5s, what's that in watts?
We already know work from above, each rep is about 1100 joules, divided by 1.5 seconds, that's about 733 watts.
Compare that to a 50kg clean, where the weight moves from the ground to the shoulders (in me, that's about 1.5 meters), in a second (a clean is very quick). Work : (50kg x 9.8m/s^2) x 1.5 : ~735 joules - not much compared to the squat at 145kg, but it is a lot less weight (to get the same work, the clean would have to be ~75kg), power is, assuming 1 second for the lift : 735 watts. That's more than the squat at 145kg. It's no wonder that 5 reps at 50kg doing cleans feels as hard as 5 squats at 145kg!
It's so much easier to do these sums on a bike, Powertaps and SRMs make it a doddle ... They just tell you the numbers. For weights work, one of these does, but it's not cheap and it ties you to their website where they store your data - no thanks.
We had a good night at DISC tonight, everyone did sprints! Fun!