How the sight-tape model works

What the starting anchor represents

When a value is unknown, the calculator does not pretend that it knows the exact answer. It represents a range of plausible values for a typical modern compound setup, including:

• launch speed and its likely variation;
• arrow drag for common arrow weights, vanes, field points, and broadheads;
• the sight geometry produced by ordinary compound-bow dimensions; and
• normal uncertainty in range measurement and sight marks.

A result made only from these assumptions is labeled an average-setup preview. It is a useful reference, but it is not presented as a tape fitted to your bow.

How your information improves the fit

The Bayesian part

In statistical terms, the typical-bow anchor is a set of informative Bayesian priors. A prior describes which speeds, drag values, and sight dimensions are plausible before considering the user’s measurements. The priors are deliberately broad enough to represent normal differences among bows and arrow builds.

The calculator draws 100,000 possible setups from those distributions. It runs each setup through the flight and sight-geometry models, compares the predicted sight travel with the marks supplied by the user, and gives more weight to setups that agree with those marks. This produces a posterior distribution: the range of setups that remain plausible after combining typical behavior with the user’s evidence.

The displayed sight setting is the posterior median. The 90% interval shows the remaining uncertainty. Approximate shooting-day marks are handled with wider uncertainty. Even a good group includes an allowance for reading the mark, and every mark shares uncertainty from the zero reference. Estimated peep height and sight radius are linked through the same string geometry, so the fit cannot invent a peep height greater than a supplied nock-to-peep distance. These uncertainty allowances are provisional assumptions, not guarantees of field accuracy.

The physics model

The flight model approximates gravity and quadratic aerodynamic drag. It predicts the launch angle needed to intersect the target at each range. The sight model then converts the change in that angle into linear movement along the sight:

predicted sight position
  = effective sight radius
  × (trajectory angle + peep-height correction)

tape travel at a range
  = predicted position at that range
  − predicted position at the zero range

Drag is fitted at the sight-in air density. If hunting elevation differs, the model adjusts drag using the standard-atmosphere density ratio. A change in point category applies a broad drag adjustment and adds uncertainty.

Trajectory and wind

The trajectory calculator holds your sight at a chosen yardage on the generated tape, or at a specified number of millimeters from zero, and follows the arrow to the actual target distance. It uses the same fitted setup and hunting conditions. The flight path includes the arrow’s starting offset below the aiming line.

Wind acts through the arrow’s velocity relative to the air. Enter the direction the wind comes from as you face the target. Results include height above or below aim, sideways drift, ground-relative impact speed, and flight time. Arrow weight is required for energy and momentum.

The 90% intervals carry forward uncertainty in the fitted bow and arrow parameters. They assume a level shot and steady wind along the entire flight; they do not include gusts, shooting-group spread, arrow yaw or broadhead lift. The wind calculation is a point-mass approximation and has not been validated against physical wind-drift measurements.

What the confidence labels mean

Good group, typical shooting day, and rough mark describe how much trust to place in a sight mark. They account for both physical mark measurement and the fact that a sight setting is only as precise as the group and conditions used to establish it.

The calculator also reports whether a result is an average-setup preview, a bow-informed estimate, a calibrated estimate, or strongly calibrated. These labels reflect the amount, spacing, and consistency of the evidence. The optional “For the nerds” section includes posterior parameter summaries, sampling diagnostics, and a “How your marks compare” table that shows the difference between each recorded mark and the estimated setting at sight-in conditions. A Bayesian estimate balances the available information instead of passing through every mark.

Practical limits

This is a calibrated approximation, not a full product-specific arrow simulation. Broadhead tuning, unusual arrow builds, sight construction, weather, shooting form, and measurement error can all matter. Always verify the printed scale and confirm the tape at a safe range before relying on it in the field.