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.

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.

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 Index Stops Pushed Dev Time 125 0 9m 15s 500 2 17m 7s 854 2.77 21m 33s 6000 5.58 57m 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 Index Stops Pulled Dev Time 400 0 9m 15s 250 0.68 7m 18s 125 1.68 5m 27s 20 4.32 2.24

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