7.8 The table, the fit and the review

Step 3 is where the paperwork gets typed. Working from switches between A distance table and I know the throw ratio — the second for when the number is simply published, and it takes the ratio at both ends of the zoom, the park, the shift travel as typed percentages, and the casting’s sections. Lengths in opens on millimetres, because that is what a drawing prints; switching converts what you have already entered rather than reinterpreting it.

Above the columns is a drawing of the machine with the run each column names dimensioned on it. Point at a header — or land in one of its cells — and that run lights up. It is schematic and never to scale: the question it answers is which run is this, not how long. The faces a distance can be measured to carry clickable markers, the chosen one solid, so Distance measured to can be answered on the drawing instead of in the dropdown.

Step 3 for a front lens: drawing, legend, table and readout — Figure 7.8a Step 3 for a **front** lens, with two rows off the vendor’s throw calculator. The drawing dimensions Distance and Tele — the same picture from two camera positions, which is what a zoom range is — and the inset draws the screen square-on, since an elevation sees it edge-on and could only ever dimension its height. The readout at the foot is the fit.

Two rows solve it; more tighten it. Two points fix a line and nothing fewer does — one row cannot separate a machine that throws wide from one that stands closer.

Worked example — an ET-D75LE20 on a PT-RQ13K, from the vendor’s calculator

Rows (16:10, metres, to the lens tip)	200″ → 7.70 · tele 11.20 · 400″ → 15.48 · tele 22.52
Solved throw ratio	1.806 – 2.6278
Solved apex, past the front face	41.0 mm
Worst miss	0.0 mm
The catalogue’s own entry	1.806 – 2.6278, apex 37.8 mm

The throw ratio lands exactly on the shipped one, and the apex 3 mm past it. That 3 mm is the calculator’s own two-decimal printing: the same rounding on both rows is a constant, and a constant moves the datum rather than bending the line — which is why the fit can miss the rows you typed by nothing at all and still sit three millimetres from the entry the same lens ships with.

The readout shows the throw ratio, the solved apex, the shift where the columns solve one, and the worst miss in millimetres — how far the fitted line sits from the rows you typed.

A bad fit is shown, never blocked

Next is gated on a fit existing, not on it being good. A large miss is evidence, and it usually diagnoses one thing: the guide measures to a different face from the one you picked. Blocking would hide the very number that tells you so — move the datum and watch it collapse. The example above is the same story in miniature: had those rows been read to the front face instead of the lens tip, the apex would have landed 80 mm inside the machine, with the worst miss still reading zero.

The same step, the other three shapes

Step 2’s card is not a label — it is what this step becomes. Each family gets the drawing its own guides are printed against, the columns those guides carry, and the datums that make sense of them. Below is the step as it opens for the other three, before a row is typed.

Step 3 for an L-shaped lens, drawn in plan — Figure 7.8b **L-shaped**, light leaving to the left. Drawn from *above*, because that is the plane its run turns in — pick up or down instead and the drawing becomes a side elevation whose screen is the ceiling or the floor. The two legs are typed underneath, L2 with its own datum, and the distance runs to the near face, the lens tip or the far face — guides use all three. There are no vertical columns: this family’s vertical is its arm.

Step 3 for a rear-fold lens — Figure 7.8c **Rear fold**, folding up over the lid. The light walks the three legs and leaves over the cabinet’s own back, which is why its distances are stated to the *back* face. All three legs are typed; the A min / max columns take the guide’s image-position pair, which is how a sheet states shift when it never says “shift”.

Step 3 for a bolt-on ultra-short-throw — Figure 7.8d **Ultra-short-throw**, bolted onto this chassis. The fold is inside the lens, so the part is drawn as the vendor draws it — machine standing on its feet, screen to the left — and its two runs are typed by name: Barrel to the throw point, Head past it to the end. No Tele column, because every lens of this kind is a prime, and no Drop: that column belongs to the welded-in guides’ inverted wall mounts.

Two of those differences are worth stating as rules, because they decide which figure on a datasheet you are looking at:

Typed sections are the authority. The casting is what you typed, the beam is derived from it, and the rows contribute the throw ratio, the zoom walk and a cross-check. Where the rows put the throw point somewhere the legs do not, the disagreement is reported in millimetres rather than resolved silently in either direction. It also retires a question: the fold’s legs and the bolt-on’s barrel already say where the glass sits, so those two are not also asked for a lens-from-front figure that could disagree.
Drop and image position are two conventions for one thing. A welded-in ultra-short-throw is printed for an inverted wall mount and states the vertical as a drop from its own datum line — hence the Drop column and the Plate → datum figure that places that line on the machine. Everything else is printed standing on its feet and states the vertical as where the image can sit. Feeding one to the other reads the machine upside down, which is why a family is only ever shown its own.

Step 4 reviews it. Two columns, Now and After, listing exactly the fields Apply will write and nothing else: the exit point, the rotation, the throw ratio and its per-format column, the apex at the long end of the zoom, the shift park and travel, and — above them, if step 1 staged any — the body rows.

The wizard's review step, computed against current — Figure 7.8e Step 4. A lens that knew nothing about its own optics — throw ratio 1, and a barrel with no beam behind it — against what two calculator rows solved. Everything the wizard writes is on this page, and one undo takes all of it back off.

What the wizard does not ask for

Coefficients. Some vendors describe a lens as distance = a × diagonal + b, and it is tempting to offer those two boxes — but no datasheet prints them. They live inside a manufacturer’s online calculator, and every machine that has them already ships in the bundled catalogue. That calculator answers “this size, this far” one size at a time, exactly as a printed guide does, so its answers go in as table rows — measured to the lens, so set Distance measured to to the lens tip — and recover the same optics. The worked example above is precisely that: two calculator answers, and the lens comes back.