Sight Tape Calculator: Two Marks In, a True-Scale Tape Out

How Do I Make a Sight Tape From My Own Marks?

Fill in at least two marks below. Positions are read from one fixed scale on your sight, such as the blank setup tape that came with it or the printable setup ruler further down this page. Everything runs in your browser; nothing you type is sent anywhere.

How Do I Take Sight Marks the Calculator Can Use?

The calculator only knows what your marks tell it, so the marks are where the accuracy comes from. Here’s the routine I’d follow. It mirrors what the makers describe: HHA’s instructions have you lock the needle at 60 yards on a 0–80 setup tape and roll a tape until its 20 falls on your 20 yard mark, and S&S Archery’s Black Gold walkthrough uses pencil marks at 20 and 60 yards the same way.

1. Put a scale on the sight. Use your sight’s blank setup tape or print the setup ruler below and stick it where the tape goes. It has to stay put until you’re done. Setup-tape numbers aren’t millimeters, so if you read those, pick Sight’s scale numbers in the calculator and measure how many millimeters one unit spans.
2. Level the sight first. Set the 2nd and 3rd axis before you take a single mark; a forum poster in a Black Gold Ascent setup thread put that first: “Make sure the 1st, 2nd, and 3rd axis is set correctly before anything”.
3. Zero at your short distance. Shoot groups at 20 yards with the arrows and head you’ll actually use, adjust until dead center, lock the housing and read the scale under the pointer. Half a millimeter is a realistic reading. If your broadheads and field points don’t group together yet, tune the bow first; marks taken on a bow that isn’t tuned move when it is.
4. Shoot your long distance. Move back, adjust only the elevation, and read again. 60 yards is the common choice; farther gives a better tape if your groups at that range are tight.
5. Add a middle distance. 40 yards is enough. It’s your check: if it doesn’t agree with the other two, one of the three readings is wrong, and the calculator tells you.
6. Measure peep height and get a speed. Peep center to arrow center along the string, and a chronograph reading of the same arrow. A speed worked out from the bow’s rating runs high, since IBO numbers come from a light test arrow.

Don’t mix arrows, heads or release settings between marks. Each change moves the impact point, and the calculator will happily fit a tape through numbers from two different setups.

How Does the Calculator Turn Two Marks Into a Whole Tape?

As far as I can tell from how they’re matched, every pre-printed tape set is built on the same idea, even when the maker doesn’t spell it out. Spot-Hogg ships 40 tapes “for varying bow speed” with calibration tapes to pick one, and the Black Gold Ascent Verdict comes with 54 sight tapes. Each tape in a set is one shape of curve. Your two marks pick the shape that passes through both of them. I wanted the shape to come from the arrow’s flight instead of a chart, so here’s what the calculator does.

• ψ(d) comes from physics. The calculator flies a point-mass arrow in 2-D, starting h below your eye, with gravity and the same drag constants every ArcheryEra tool uses (speed falls as v = v₀·e−k·s; k is set by fletching and head). It solves for the launch angle that brings the arrow back to your line of sight at d.
• a and b come from your marks. They’re fitted by ordinary least squares on a straight-line model, since s is linear in tan ψ. Two marks give an exact fit. Three or more leave residuals, and those are your quality check.
• The leave-one-out check. With three or more distances, each one is dropped in turn, the tape is refitted on the rest, and the dropped mark is predicted. That prediction is independent of the mark it’s compared against. A mark that misses by more than three reading steps (or 1 mm, whichever is larger) gets flagged.

Two things fall out of this that I didn’t expect before running it. First, b is your sight radius. If your marks imply a 9-inch or 70-inch radius on a flat slider, a reading or a distance is wrong, and the calculator stops instead of printing nonsense. Second, the short end of the tape is strange. Your eye sits a few inches above the arrow, and at 10 to 20 yards most of the aiming angle goes to lifting the arrow up to your line of sight. That’s why short marks bunch up.

How Much Does a Wrong Speed or Peep Height Move the Marks?

This was the question I cared about most, because most people don’t own a chronograph and nobody measures peep height to a hundredth. So I pinned a modeled 280 fps sight at 20 and 60 yards and asked the engine for the tape with the speed entered wrong.

Inside the bracket, a 30 fps mistake is worth about 0.2 mm, which is less than you can read on the scale. At 100 yards the same mistake is 0.71 mm, roughly 3″ of impact. The 10 yard mark is the most sensitive of all, but 1 mm there is only 0.4″ at the target.

Which pair of distances should I shoot?

The widest pair you can shoot well. Here’s the same 30 fps speed error with three different brackets, measured at the 80 yard mark:

Archers who set up these sights by hand found the same thing. In a Rokslide thread on Spot-Hogg tapes, one poster wrote “20-60 works better than 20-50, but 20-90 works even better than 20-60 in my experience.” The math agrees with him.

Why Doesn’t My Chronograph Speed Match the Tape Number?

It comes up constantly. In the same Black Gold thread, one archer said “I needed to go several tapes higher FPS than the chrono reading”. The model gives a plain reason. A tape’s speed label describes how far apart its marks are, and that spacing also scales with sight radius. I took one 280 fps arrow, put it on three sight radii, and asked which speed would produce the same 20-to-60 spacing on a tape drawn for a 32″ radius:

Peep height, a different drag build and the sight’s own scale all push the same way. Treat a tape’s speed number as a family name, not a measurement. This calculator never has to guess that family, because it fits the stretch (b) directly from your marks.

How Do I Print the Tape at True Size?

The SVG and the print are drawn in millimeters, but browsers, printer drivers and PDF viewers can rescale a page without telling you. Check every print.

1. In the print dialog, set scale to 100% or Actual size. Turn off Fit to page or Shrink to fit.
2. Measure the 100 mm check line with a steel ruler or calipers. If it reads 99 mm, every gap on the tape is 1% short; on a 30 mm tape that’s 0.3 mm at the far end.
3. Cut on the outline and stick the tape so your shortest measured distance sits under the pointer with the sight set there. Then check the longest one.
4. If you downloaded the SVG, print it from a program that respects its size, again at 100%.

I tested the print and download files in Chromium; I haven’t been able to test every printer driver, and that’s exactly why the check line is there.

How Do I Check the Tape Before I Trust It?

Shoot it. Start at a distance between your marks you didn’t use for the fit, then the longest mark you plan to use, then a short one. Lancaster Archery’s piece with 3D shooter Cara Kelly makes the point that a homemade tape should be confirmed mark by mark, and that a micro-click sight can’t always stop between two clicks, so a mark that falls between clicks will be off by part of a click no matter how good the tape is.

If a check distance misses, take that as a new mark, add it to the table and reprint. The fit only gets better.

Recheck a couple of marks after anything that moves the string or the peep: a new string, a peep that has rotated, a cable or limb-bolt change. The tape is only as current as the bow it was shot on.

Which Sights Does It Work With?

Any sight whose elevation is set by moving a housing along a scale you can read. The table shows what’s documented and what isn’t.

If you’d rather buy a pre-printed HHA tape than print one, the HHA Optimizer Lite tape guide walks through picking one from your 20-to-60 differential.

How Did I Check the Math?

I didn’t want the tape to depend on a formula that only looks right. So the engine is checked by a separate script that flies the same arrow with a different integrator, written without reference to the page’s code, and compares.

• Trajectory solve: 108 cases (220 to 340 fps, three drag builds, two peep heights, 10 to 100 yards). Worst disagreement: 0.0025 mm at the sight.
• No-drag limit: matches the hand-solved vacuum parabola.
• Two-mark fit: reproduces both marks exactly and recovers a known 32″ sight radius within 1%.
• Bad-mark test: a deliberate 3 mm misread at 40 yards in a five-mark set gets flagged; clean half-millimeter readings don’t.
• Input checks: a single distance, half-filled rows, out-of-range values and impossible sight radii are all refused with a message instead of a tape.

One finding from that work: the site’s older trajectory shortcut (drop = ½gt² with drag-lengthened flight time) overstates drop by roughly 3 to 14% against a full 2-D flight with the same drag in the cases I ran, more for slow, high-drag arrows at long range. That’s small for a pin gap but too much for a millimeter tape, so this calculator uses the full solve. The formulas are also written out on the calculator methodology page.

Frequently Asked Questions