I originally wrote the full “Technical Field Guide for the Discerning Analog Photographer” as a quick reference for technical photographers in the field. This is why I chose to print all 918 pages on 5×5″ waterproof paper, bound on a single brass ring, to make reference quick, on-the-go.

A Technical Field Guide for the Discerning Analog Photographer - cover shot
A Technical Field Guide for the Discerning Analog Photographer – cover shot

You can purchase the original guide here →

This extremely comprehensive guide has been praised as “an inspired compendium”, “unique”, “unequivocal”, “on point” and “concise and to the point”, by Hamish Gill of 35mmc (in his usual meandering fashion) but it has come to my attention that many photographers — once having read the 900-plus-page volume several times through — have come to mostly use the appendices as an even quicker and pocketable reference.

Assuming you are all already well-versed in the full field guide, I decided to release a copy of just the four appendices. This, of course, makes for an even smaller reference in the field, while maintaining a certain level of in-depth mathematical analysis of certain photographical concepts which is nearly impossible to find elsewhere.

Additionally, the smaller brass rings that this appendix requires, cost significantly less.

In this article – Appendix A – I walk you through how I arrived at my push and pull development formulae, which are used throughout the field guide. The pushing formula, specifically, is heavily relied on in the guide.

Showing its derivation will allow you to tweak as you see necessary for your particular practice.

Pushing calculations

In all of our film pushing calculations thusfar, we have used the formula:

t_{df} = 0.025 \sigma^3 - 0.05 \sigma^2 + 0.425 \sigma + 1

Where t_{df} is our development factor, and \sigma is stops pushed.

This is derived from the following 4 points given by Digital Truth’s black and white push processing tables:

(0,1), (1,1.4), (2,1.85), (3,2.5)

…where the x-value is “stops pushed” and the y-value is the development time factor.

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The point (0,1) implicit in the fact that a zero-stop push results in a development time factor of 1.

Of course, there exists a unique cubic for any given set of four points, hence our equation.

Example pushing table using ILFORD FP4 PLUS with TETENAL Ultrafin T-Plus developer

ILFORD FP4 PLUS development times using T-Plus
Exposure IndexStops PushedDev Time
12509m 15s
500217m 7s
8542.7721m 33s
60005.5857m 4s

Pulling Calculations

The author, not having much hands-on experience in pulling film, solicited anecdotal data from Twitter. From that, using the following formula did not seem unreasonable, if not entirely speculative and derivative (in the literary sense).

t_{df} =\frac{1}{ 0.025 \tau^3 - 0.05 \tau^2 + 0.425 \tau + 1 }

…where t_{df} is our development factor, and \tau is stops pulled.

Example pulling table using ILFORD HP5 PLUS with TETENAL Ultrafin T-Plus developer

ILFORD HP5 PLUS development times using T-Plus
Exposure IndexStops PulledDev Time
40009m 15s
2500.687m 18s
1251.685m 27s

I hope this helped clear up some of the numbers used throughout the guide.

Next time, for Appendix B, I will go through some of my formulae for metering for multiple exposures. But, until then, keep pushing (or pulling).

~ David

Editor’s note

When David first for in touch with me about publishing the appendices of ATFGFTDAP I honestly couldn’t have been happier to help him share these wonderful nuggets of technical insight with the community at large.

Your immediate reaction may be one of confusion and frustration at “not getting it”. This is normal and will pass. If you are able to get a copy of the full ATFGFTDAP, some of the examples may provide clarity sooner. If not, stick with it.

Thanks for reading, see you in part two.

~ EM

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About the author

David Allen

Tried to use photography to replace mathematics. Was paid for mathematics.


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  1. Brilliant:). Thank you.
    In the push/pull examples, surely the column header “Exposure” should read “Development Time”?

    ILFORD FP4 PLUS development times using T-Plus
    Exposure Index Stops Pushed Exposure
    125 0 9m 15s
    500 2 17m 7s
    … etc.

    1. Oh dear. And in the ‘example pulling table’ with HP5, “Stops Pushed” should be Stops Pulled, else the values ought be negative. Details details…