Collier et al data

[From Bill Powers (950806.1340 MDT)]

Bruce Abbott (950805.1900 EST) --

Now you're talking. The Collier, Hursh, & Hamlin experiment is just what
we need. Nice and simple, great density of data points, no futzing
around or fancy fiddling with parameters, drugs, etc., and lots of
patience -- plenty of time to get to asymptote. And I'll bet they
checked to see that 10 days per schedule was enough! From ratios of 1
to 60 the animals maintain their food intake constant at about 21 +/- 1
gram per day. We can mine this kind of data for all kinds of good
information.

     Bill P.: can we get an estimate of calories expended per lever-
     press if we know the force requirement and lever movement-distance?
     In this experiment the lever force requirement was 25 g (0.25 N)
     and I would guess at a lever travel-distance of perhaps 1 cm.

Way ahead of you; I got the necessary numbers together a few days ago,
but didn't know the force or travel of the lever.

Work = force * distance, so 0.25 newton applied through 1 cm is 2.5E-3
N-meter. 1 Kg-M = 2.3427 gm-cal and 1 Kg = 9.8 N, so 1 N-M = 0.23905 gm-
cal. Therefore each press uses 2.5E-3 * 0.23905 gm/cal or 5.98E-4 gm-
cal. This is 5.98E-7 Kg-cal per press.

At 71,720 presses per day, the energy used is 0.0429 kg-cal per day. A
diet of 14.67 g per day (at 326 pellets per day, 0.045 g/pellet, 4 Kg-
cal per g) provides 58.7 kg-cal per day if the _Joy of Cooking_ applies.

So the energy required to depress the lever is negligible relative to
the energy contained in the food. However, the efficiency of muscles at
such low loading is probably very low. The real energy usage for
pressing the lever is probably much higher than calculated, but it would
have to be 1000 times higher to make any big difference. By far most of
the energy goes for metabolism and other activities beside bar-pressing.

From your remarks, it seems that these fat slothful lab rats quickly

turn their bulk from flab into muscle, gaining a bit of weight but
probably increasing their density and strength. Adding muscle tissue
would increase their capacity to make fast movements, but would not
necessarily increase energy efficiency at light loads. Up to a point,
this experiment is like pumping iron. These rats can go to their home
cages afterward and beat up the other rats who kicked sand in their
faces.

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Best,

Bill P.