  Using the unique capabilities of the Variable Density Turbulence Tunnel at
the Max Planck Institute for Dynamics and Self-Organization, G\"{o}ttingen, we
report experimental result on classical grid turbulence that uncover fine, yet
important details of the structure functions in the inertial range. This was
made possible by measuring extremely long time series of up to $10^{10}$
samples of the turbulent fluctuating velocity, which corresponds to
$\mathcal{O}\left(10^5\right)$ large eddy turnover times. These classical grid
measurements were conducted in a well-controlled environment at a wide range of
high Reynolds numbers from $R_\lambda=110$ up to $R_\lambda=1600$, using both
traditional hot-wire probes as well as NSTAP probes developed at Princeton
University. We found that deviations from ideal scaling are anchored to the
small scales and that dissipation influences the inertial-range statistics at
scales larger than the near-dissipation range.
