# Introduction

One of the critical tests of any new propulsion method is to determine if it works in a vacuum. A successful test in a vacuum chamber will eliminate a considerable number of variables, for example, ion wind and reaction propulsion due to the movement of gases including air[1]. It is also a necessary step before the technology can be used in space. This section outlines the type and setup of the vacuum chamber used in the tests.

# Setup

The vacuum chamber used for these tests is a modified MDC sputtering vacuum chamber 30" high by 25" in diameter as shown in figure 1. Although the chamber is capable of a high vacuum, only a roughing pump as shown in figure 2, was used which means a medium vacuum or 10-3 torr.

## Design of Acrylic Port Window

One of the modifications of the cavity was to add a large acrylic window to the end of the cavity which will allow easy filming of and access to the interior. The stronger acrylic called "cell-cast" acrylic was used and comes in standard sheets 48" wide and of various thicknesses. For 28" of the sheet, necessary to cover the 25" diameter opening, typical prices are as follows:

• 2" thick - $1200CND • 1.5" thick -$900CND
• 1" thick - $265CND Clearly the 1" Acrylic sheet is the best price, but the question is, does it have enough strength to hold back the air pressure vacuum over a diameter of 25"? Using existing equations[2], the safety factor for a given window strength versus diameter of a vacuum chamber window was calculated. For an acrylic window with 25" diameter of unsupported space and 1" thick, it has a safety margin of 3 to 6x depending on the acrylic rupture strength. In other words, the window can handle over three times more air pressure before breaking. For a 1.5" thick window, it has a safety factor of 15 times and for 2" thick piece, 27 times. Here are the calculations carried out: First, calculate the stress on the window for a known thickness versus radius (from the power point slide): $S_m=k\left ( \frac{wR^2}{t^2} \right)$ where  $S_m$ - the stress on the window in psi $k$ - is the coefficient for circular plate and 1.1 was used, which is a conservative estimate. This constant is described in the power point presentation. $w$ - the uniform pressure across the window, which, because Edmonton is ~2300ft above sea level, means our air pressure is 13.66psi. $R$ - is the radius of the unsupported part of the window, in our case 12.5" or half of the 25" diameter $t$ - is the thickness of the window which in our case is 1", 1.5" or 2"  The stress from air pressure for a 1" thick acrylic window is 2300psi, for 1.5" thick window it is 1043psi and for 2", 587psi. The safety factor of cast acrylic is then calculated by:  Stress Factor = Modulus of Rupture / Max Stress  where the Modulus of Rupture for Acrylic is typically 13,000 to 16,000psi. The safety factor is then = 16000/2300 = 7x which clearly means the 1" thick acrylic is thick enough to handle the air pressure with a safety margin. ## Build First, a vacuum chamber was found on eBay ($1660USD), purchased and then a cart with enough strength was found and everything modelled in 3D. The cell-cast acrylic was then water jet cut and everything mounted. The extra ports were covered with acrylic windows to provide light inside the chamber and a strut added under the top shelf.

The strut was necessary to avoid putting too much weight on the top shelf of cart which can only support 250lbs. The vacuum chamber is roughly 150lbs and the next heaviest component is the acrylic window(s). If acrylic weighs 0.0426lbs per cubic inch (apparently), then the rough weight of the front window will be about 40lbs, assuming a 30" by 32" square 1" thick piece. That leaves about 60lbs for everything else including ports, DUT and other variables.

A bungee cord was all that was necessary to keep the front port closed because suction during pump down was more then enough to pull the acrylic tight.

## Testing

As shown in figure 11, the gauge with red numerals on the bottom right shows 49.0 microns, vs 760 microns at atmosphere. With a longer pump down, we have pumped the cavity down to 19 microns which is only 2.5% of atmosphere and only 1 micron above the lowest expected, 18 microns. The lowest expected pressure was determined by capping the hose to the vacuum pump and testing the lowest it would go ((figure 10). We were using the timer on the iPhone, bottom left of Figure 11, to time how long the vacuum chamber could keep the vacuum and it loses about 40 microns of pressure in the first five minutes. Our experiments will be less then a minute long and even at the current state of leakiness, the chamber is useful. It takes about 15 minutes for the chamber to pump down.

Under vacuum, the 1 inch thick acrylic deflects inward about 9mm, as shown below in figures 12 and 13:

# References

1. Jets of gas in the vacuum of space will create a force, as is used by the Space Shuttle with it's Reaction Control System. However, if Shawyer's cavity has no air inside it, then the heating of a gas cannot be the cause of a unidirectional force.
2. Practical Knowledge of Vacuum Windows, Rev 1.1, Ali Durney, Senior Optical Engineer, Steward Observatory, University of Arizona, Power Point Slide