}
  const mid = Math.floor(sorted.length / 2);
  return sorted.length % 2 === 1 ? sorted[mid] : (sorted[mid - 1] + sorted[mid]) / 2;
}

[Figure: ResultsTldr]

## Question

Paper tuning is simple in theory: shoot an arrow through paper and use the
tear to infer how squarely the arrow is leaving the bow. The tricky part is
distance. Too close, and the arrow may not have fully revealed the launch
error. Too far, and the arrow may already be recovering.

The practical question is: for an out-of-tune launch, where is the arrow
yawing the most? That is the distance where paper should be most sensitive
to tune error.

## Method

We used the 2026 front-of-center slow-motion yaw fits for the torqued
shots. The torque condition deliberately injected launch error, which
makes it a useful proxy for an out-of-tune or inconsistent launch.

Each build was fit with a damped sinusoid. For this article, we subtract
the fitted centerline offset and look for the maximum oscillation
magnitude. That avoids treating a camera or model offset as tuning error
and focuses on the yaw motion itself.

[Figure: PlotSections]

## What the Fits Show

Across all {curves.length} torqued builds, the fitted yaw motion peaked
between {bandLabel}. The median peak was around {medianPeak} ft.

The exact peak moved a little by build, but the range was tight enough to
be useful. It lands right in the common paper-tuning neighborhood: not
directly off the rest, and not so far downrange that the arrow has already
started to clean itself up.

## Takeaway

Based on this test, paper tuning should be conducted around **10-15 ft
from the shooter** if the goal is to make launch yaw as visible as
possible.

A few caveats:

- This was one bow setup, not a universal proof across every compound
  platform.
- It did include multiple arrow builds, so the estimate is not tied to a
  single arrow configuration.
- The result uses fitted slow-motion yaw data, not direct paper tears. It
  tells us where yaw error should be most visible, not that every paper
  setup must use the same distance.