I think the answer to my central question of this thread is more simply than any of us realized. The reason the rates of change of ET and BT show a similar correlation is that the design of the hottop leaves the beans exposed a significant amount of radiant (infrared) heating. This means that as the heater cycles on and off, it both affects the rate of change of the air in the roaster (perhaps even directly heating the ET probe) and the rate of change of the beans.

Every time the heater cycles on, both my ET probe and the beans recieved a "kick in the pants" from the infrared radiation of the heater. This is probably also a significant source of noise in the ET-BT vs. delta BT graph that we've been plotting.

Lesson learned? well, the HOTTOP is more responsive to heater power changes than a convection/conduction roaster. In this roaster, (and in roasters like the behmor) the air doesn't need to heat up in order to heat the beans up - the beans are directly heated via the element.

Remember, however, that the changes i'm talking about only become apparent in a graph of the derivatives of ET and BT. Overall, the roasts are very smooth and ET does show a destructive "cycling" with respect to time

Jim, I know you became frustrated as i seemingly got sidetracked on this issue. What do you think of all of this? I know you roast with an air-roaster, but i'm sure you're familiar with drum roasters where the beans are directly exposed to the heating element.

I have not had an opportunity to play with a hot top but when originally working on my Galloping Gourmet convection top and a Behmor the cycling of the thermostat drove me crazy when trying to steer the roast and analyze the data. Sometimes the cycling would occur at ok moments and other times not such ideal timing. I wouldn't say the cycling is disastrous to the roast but more annoying with the data. With the open mesh drum of the Behmor the cycling and radiant heat effect (30-50* fluctuations) definitely hit the beans. I had installed a BT probe and a "Kill A Watt" meter set on watts being used to correlate the cycling and with the BT readings.

The quality of my HotTop roasts jumped a notch when I dumped the internal control.
Input power is controlled via the variac, so remains constant.

Several years ago as a test, I roasted several batches of Colombian with stock and manual control to the same profile for a long weekend away. Several couples, coffee drinkers all, were unknowingly subject to a test of drip coffee made in a crusty old Krups. I'd alternate between the stock and the manual to see if anyone noticed. After a couple of pots, several made unsolicited comments that the manual was 'smoother', 'more balanced' and the stock was 'flat.' Some thought it was a different bean. By the end of the weekend, it was "don't give us any of that stock crap"

cafeIKE wrote:The quality of my HotTop roasts jumped a notch when I dumped the internal control.
Input power is controlled via the variac, so remains constant.

I'm a believer. When I'm applying 94volts to finish a roast why would I want an element firing at 122v then kicking off. I shoot for a super clean and even roast and getting rid of the thermostat and maximizing agitation really helped.

Hi,

I was referred to this year-old thread from this current thread on CG: http://www.coffeegeek.com/forums/coffee...053&Page=1
(see page 2)

I've been roasting less than a month in my Popcorn Pumper, with no probes or other test equipment, and I regulate the roast with an on/off switch. But I am fascinated with the idea of tooling up and being able to control roasts better, maybe even having the computer control the roast rather than me. I could get tired of squatting for 20 minutes outdoors next to the on/off switch I've put on the extension cord to the popper. Maybe I need to haul out a lawn chair for these roasts ...

A brief comparison of my analysis (details below) with Jim's:

To summarize Jim's analysis (in my words, please correct me Jim if I'm wrong), he says (dBT/dt) / (ET - BT) should be constant: the more heat you apply to beans, the more they heat up, and the rate constant is at most a fixed property of the bean. He then observes that that quantity is somewhat constant empirically, supporting his point. But it fits much much better to say dBT / dt = .76 BT + .18 ET + 23 , although he does not analyze the implications of this equation which are actually quite a bit different. How can BT have a positive coefficient!?

To summarize my analysis, which is free of data analysis because I am free of test equipment, I treat the inside and outside of the bean separately. (dBT/dt) / (ET - BT) is not a constant, but a measure of IT, the inside bean temperature that is not directly observable. [Later thought: it should probably be a measure of BT - IT rather than IT itself. Will think about that more ....] BT is the temperature of the outside of the bean, but I am more interested in IT as an indicator of what the cup will taste like. With some further figuring I derive dBT / (ET - BT) as the incremental cooking of the inner bean. I have no implication that it's constant, although it is reasonable to expect (or hope) it to progress somewhat steadily during a well performed roast.

So Jim thinks it's fairly constant because it has to be constant; I think it's fairly constant because the example roasts were done reasonably, but the deviations from linearity late in the roast are consistent with the very fast roasting action and touchy timing that is typical after first crack. And I think the accumulation of dBT / (ET - BT) is a time-independent measure of the doneness of the inner bean.

Here are the detailed steps of my analysis:

Mostly I guess we are trying to cook the inside of the beans in a certain way, but that is unobservable (other than by cracks and smell, for which we have no automatic sensors). The closest we can come is to observe the temperature of the outside of the beans, roughly BT. We can also observe the color of the outside of the beans. We often use time measurements to help us guess what's going on inside the bean.

I propose (dBT/dt) / (ET - BT) as a proxy for bean internal temperature:

IT = k (dBT/dt) / (ET - BT) for some value of the constant k.

Rationale: if the inside is much cooler than the outside, the application of additional heat to the bean exterior won't make the outside heat up as fast. A correction may be needed because we measure temperature but the fundamental thing being transferred is heat; I'm not sure. (dBT/dt) / (ET - BT) has units of (1/time) which is not very intuitive ...

Now suppose the amount of cooking effect C inside the bean is proportional to (t IT), the product of time and internal temperature. If IT can change over time, make that

C = integral (IT dt)

the integral of IT over time. Now substitute in the equation for IT:

C = integral [ k (dBT/dt) dt / (ET - BT) ]
= k integral [ dBT / (ET - BT) ]

because dt cancels itself out! k is a constant and can go outside the integral.

Now we have a peculiar quantity to be regulated

integral [ dBT / (ET - BT) ]

that is calculated to measure the amount of cooking that has occurred inside the beans, has no time dependency and is dimensionless.

There are a couple dBT vs. (ET - BT) plots in this thread on page 2. Fixing dt (so comparisons are fair) it would be interesting to compute that integral over various completed roasts that taste good or taste like different levels of doneness, to see if that integral is predictive of doneness in the cup.