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Estimating Methods, Variability, and Sampling for Drop-Test Data

Introduction

For nearly six decades, the Forest Service has been using a procedure known as drop testing to analyze the ground patterns made by aerial drops of fire retardants or suppressants (Suter 2000). The procedure involves dropping firefighting chemicals from an airtanker flying over open cups arranged in a regularly spaced grid (figure 1). The ground patterns allow operators and managers to:

  • Compare the performance of aerial delivery systems
  • Compare the drop characteristics of firefighting chemicals
  • Determine whether an aerial delivery system is suitable for contracting height, drop speed, volume, flow rate, and other factors

Photo of an airplane dropping retardant.
Figure 1—TBM (Avenger) aircraft dropping fire retardant over a test grid.

After more than 25 aerial delivery systems were tested during the early 1990s, three concerns arose:

  • Estimation methods
  • Variability
  • Sampling

The first concern deals with the process of making estimates using the data collected from the grid. It is not feasible to collect every gram of retardant that hits the ground. Instead, the drop is sampled at regular intervals with estimates made for points in between. Historically, linear interpolation was used to estimate between sample values. Linear interpolation assumes uniform change between points, an assumption that may be inadequate for drop data.

The second concern relates to the variability of estimates and of the test. Any time a quantity is estimated, the variability associated with the estimate should be provided

Replicate drops can help investigators obtain a measure of the variation inherent in the test. Replication also reduces the variability of mean line length for each drop type. Because of the cost of other testing constraints, replicate drop tests are usually not conducted, making it impossible to estimate reliably the error variance due to the test.

The third concern, sampling, pertains to grid arrangement and cup placement. Although hundreds of drops have been conducted over grids, little testing has been done to determine the appropriate cup spacing and grid dimensions (Suter 2000). Usually, the length and width of the grid are estimated based on flow rate, volume, and ground speed. Some steps have been taken to achieve greater consistency. For instance, cups are placed at a uniform height and spaced in a regular pattern. For most drop tests, a denser area has been constructed in the middle of the grid where the majority of retardant is expected to fall. Constraints on time, budgets, and labor must be taken into consideration when developing a sampling scheme.

This report uses data collected from six airtanker drops to investigate estimation methods, variability, and sampling.