there is a similar graph for temperature
Most developer formulations nowadays contain two developers working in concert, so I'm afraid one will need to measure temperature-vs-time by experiment with those.
This is a more convenient way of calculating the development time, especially if you don't have a computer at hand or can't be bothered with regression analysis. Also, it requires only one data point (development time; temperature) and the temperature coefficient which according to Mees is independent of the film.Mees-James, 3rd edition (1966), page 371, says:
The temperature-dependence on the rate of development can be expressed roughly in terms of the temperature coefficient. This coefficient is the ratio of the rate at a particular temperature to the rate at a temperature 10 [degrees] lower on the Centigrade [...] scale.
A table of coefficients follows. For example, the coefficient of D-76 is 2.8, which is 1.108/degree, or 10.8%/degree. That means for each degree rise in temperature, development rate increases by 10.8%. Coefficients vary widely, from 3.9 for Windisch 665 down to 1.9 for Agfa 15.
Would you be kind and explain how you got that from the graph?If you use Metol alone, as in D-23, the graph above says the constant is 10 ^ (log(2/1.07) / 5) = 1.133 which is 13.3% per degree C.
It's OK, I think I've worked it out. Had to scrape away some adult brain sludge to rediscover school maths.Would you be kind and explain how you got that from the graph?
Presumably this is like working out compound interest?This is a more convenient way of calculating the development time, especially if you don't have a computer at hand or can't be bothered with regression analysis. Also, it requires only one data point (development time; temperature) and the temperature coefficient which according to Mees is independent of the film.
Almost. Choose the sign of your temperature difference, for example positive temperature difference means you are developing at at temperature (t) lower than the temperature (t_ref) for which the development time is known (Time_ref). Then the equation isTo be correct, you need to calculate t x coefficientdifference in temperature for a lower temperature, or t / coefficientdifference in temperature. Is that right?
Great, thanks. So what I was heading towards was to make an Ilford-style time-temperature chart for a metol-only developer. I think this is right, but it would be kind if someone would check it.Almost. Choose the sign of your temperature difference, for example positive temperature difference means you are developing at at temperature (t) lower than the temperature (t_ref) for which the development time is known (Time_ref). Then the equation is
Time = Time_ref * coefficient^(t_ref - t)
If the difference is negative (development at higher temperature) the same equation is used. It is equivalent to Time = exp(a + b*t) that I used to plot the curve.
It's OK, I think I've worked it out. Had to scrape away some adult brain sludge to rediscover school maths.
You read the time values for the relatively straight line segment from 17 to 22 deg C, which are respectively 2 and 1.07 units on the y-axis. Although the y-axis is plotted logarithmically, the numbers shown are not log values (misleading description!). Development time at 17 deg must be 2/1.07=1.87 times greater than at 22 deg. You take the log of 1.87 to get it into the same x-y space as the plotted curve. It's a 5 deg range, hence you divide that log value by 5 to get the log change per degree. Take the antilog (10 to the power of ...) of the result, and you have a multiplication factor per degree for times in ordinary units. A multiplication factor of 1.133 is the same as 113.3% or an increase of 13.3% for every degree.
Have I got that right?
I was heading towards was to make an Ilford-style time-temperature chart
Great, thanks. So what I was heading towards was to make an Ilford-style time-temperature chart for a metal-only developer. I think this is right, but it would be kind if someone would check it.
View attachment 322934
The family of curves is for different films or developer concenrations, right?
It appears that your base temperature is 22 degrees, and that the curves represent the base times of 2, 3, 4, 5, 6, 7, 8. By looking at the topmost curve, I estimated that your temperature coefficient is 1.13, which agrees with an earlier posting. Looks good to me.
I suppose a good test is to develop a strip at 19.5 degrees for 4 minutes, and another at 25 degrees for 2 minutes, and verify that their densities are equal.
Yes, we are talking about the same thing here. If you shoot a different film your known development time will be different for the same temperature of 22 degrees. You pick a curve closest to your time and trace along this curve to the desired temperature. Thus, each film will have its own curve. The same is true for developer concentrations.Not exactly. If you know your dev time at a given temp, you find that point on a curve, then trace it along to the temp you want. To make the curves I started with whole numbers of minutes at 22 deg. As Ilford do, I’ve not over-cluttered the graph, as it’s easy to imagine intermediate curves.
Yes, but I’ll have to leave that to someone else as I don’t have a densitometer.
I’ve got a decent darkroom now, and find it easy to raise my chemicals to a standard 22deg C. That wasn’t always the case - I often had to process at ambient temperature.So who would need such resource?
Fair caution, although as it happens I am currently favouring Double -X and a version of the Leitz 2–bath developer, both of which were developed over 50 years ago!I would feel uneasy relying on a temperature coefficient that was determined over 50 years ago.
Great idea, thanks! Not sure that I need any maths, do I? All I need is to determine what dev time at (say) 17 deg gives me the same density as the reference time and temperature, as you suggested a couple of posts back. I will try this in due course and report back.Actually, you do have a densitometer: Your light meter. Hold each strip over the meter's sensor with a bright light nearby, subtract the readings and multiply that by 0.3. That's the density difference.
You determine your temperature coefficient from the development times at three temperatures (technically two is sufficient, but the third gives you some estimation of the quality of fit). This data is provided in the film and developer datasheets.I would feel uneasy relying on a temperature coefficient that was determined over 50 years ago.
You determine your temperature coefficient from the development times at three temperatures (technically two is sufficient, but the third gives you some estimation of the quality of fit). This data is provided in the film and developer datasheets.
I just computed the coefficient for XTOL and TMAX-400; it's 3.2 (12.3% rate-gain per degree).
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