Reciprocity revisited.

gainer submitted a new resource:

(there was a url link here which no longer exists) - Reciprocity revisited.

The equation I used to represent available experimental reciprocity data is:
T = Tm + Tc
Where:
T is the exposure time corrected for reciprocity characteristics.
Tm is the time indicated by your exposure meter's calculator.
Tc is the correction to be added to Tm.

Through much curve fitting I found that:
Tc = a*Tm^b
Where a and b are constants for a given film but vary with the film. Thus, for HP5+ film:
Tc = 0.11 * Tm ^ 1.62
Fortuitously, this equation graphs as a straight line...

Click to expand...

(there was a url link here which no longer exists)

comments from the previous article system:

By pnance - 05:48 PM, 05-25-2006 Rating: None
Is there any reason this would not be applicable to paper? The only real difference is that paper is already in the seconds range.

By JeffD - 04:17 PM, 07-29-2006 Rating: None
This is pretty interesting. I wish I had an equation as convenient that would help me determine development time, so my contrast would be *normal*, when processing film that has been exposed to account for reciprocity failure.

By jstraw - 10:00 PM, 09-15-2006 Rating: None
I love your formulas but I find I struggle to make the clear to myself. I can't be on the right track with this one.
Tri-X at 60 seconds:
.17(Ff) * 60(seconds) ^ 1.62 = 43.04 + 60(seconds) = 103.4(seconds)
My 3 charts say 480 seconds, 600 seconds and 832 seconds (this big discrepency is why I want a new handle on this problem).
Where am I losing my grip on your formula?

Now that this is back, I'd love to pick up this conversation again.

Sandy:

By chance would you happen to have the coeficients for other films? I remember when you first published your findings a number of us pubished tables which made it easier to calculate the new exposure times. I published a set of tables and a chart at Dead Link Removed

Really would like to expand to include XP-2 and Pan-F

Thanks

Mike

Sean said:

comments from the previous article system:

...
By jstraw - 10:00 PM, 09-15-2006 Rating: None
I love your formulas but I find I struggle to make the clear to myself. I can't be on the right track with this one.
Tri-X at 60 seconds:
.17(Ff) * 60(seconds) ^ 1.62 = 43.04 + 60(seconds) = 103.4(seconds)
My 3 charts say 480 seconds, 600 seconds and 832 seconds (this big discrepancy is why I want a new handle on this problem).
Where am I losing my grip on your formula?

Click to expand...

Exponentiation has higher precedence than multiplication. Using substitution, the complete formula for calculating the exposure time is as follows:

T = Tm + Tc
Tc = a * Tm^1.62
T = Tm + ( a * Tm^1.62 )

using your example above, we get the following:

T = 60 + ( 0.17 * 60^1.62 )
T = 60 + 0.17 * 759.64
T = 60 + 129.14
T = 189.14

which is more in line with the numbers you were expecting, although certainly less than the published numbers.

Here are the calculations for the four films, using the factors published above:

TXP TMX HP5+ Delta
1 1.17 1.07 1.11 1.05
2 2.52 2.22 2.34 2.15
3 4.01 3.41 3.65 3.30
4 5.61 4.66 5.04 4.47
5 7.31 5.95 6.49 5.68
6 9.10 7.28 8.00 6.91
7 10.98 8.64 9.57 8.17
8 12.94 10.03 11.19 9.45
9 14.97 11.46 12.87 10.76
10 17.09 12.92 14.59 12.08
60 189.14 113.17 143.56 97.98

The formatting is a bit hard to read, but if you import the data into a spreadsheet, it'll be readable.

I just made an excel sheet with calculations from 1 second up to ~72 hours at one stop intervals. Tri-X would have to be exposed for approx. 1100 days for a metered 72 hour exposure. Anyone interested in the sheet?

Here's the chart, I'm gonna try to make it a bit more readable during the weekend...

https://spreadsheets.google.com/ccc?key=0AqToPM-vcpx4dFl3WlVIQlRHSHJxblhUZFd0VDNQNnc&hl=sv