# Soapy solution to empty fuel tanks

Engineers at Purdue University are using a computer model that explains the mathematics behind soap bubble formation to predict when satellites will run out of fuel.

Satellites keep their position 22,500 miles above Earth by firing small rocket thrusters, but these must be replaced shortly before they run out of hydrazine, a rocket fuel that is worth more than its weight in gold. Enough fuel must remain to get the satellites out of orbit to make room for their replacements.

The engineers, led by Steven Collicott, an associate professor of aeronautics and astronautics, used a model created by Kenneth Brakke to help improve fuel gauging. The model was initially used to describe the mathematics behind such phenomena as the formation of soap bubbles. It also helped to solve the following problem: When a straw is placed inside a glass of water, why does the water level inside the straw rise higher than the level in the glass?

‘The exact same physics, the wicking action, is responsible for positioning fuel inside the tank,’ Collicott said. ‘Here on Earth we see this capillary action only on very small length scales because gravity generally overwhelms it. But in space the weight of the liquid is irrelevant.’

Consequently, the effect is exaggerated in space, making it more difficult to predict the liquid’s movement and its location inside the tank.

However, Collicott’s application of the model is said to make it possible to use routine temperature data from the satellite to monitor how much fuel is left in the tank. Those data come from heaters, which are needed to keep the fuel from freezing, and temperature sensors located on the outside of the fuel tank.

Areas of the tank that contain fuel take longer to heat, while portions of the tank that are empty heat up faster. The more fuel that is present, the longer it takes to heat.

Information returned to Earth from satellites reveals how fast different areas of the tank are heating up, indirectly indicating where the most fuel is located. The model uses the temperature information to provide a detailed, three-dimensional understanding of where fuel is located inside the tank. That information can, in turn, be used to calculate how much fuel remains in the tank.

‘One practical benefit of this gauging method is that it makes use of hardware that is already a standard part of these satellites,’ Collicott said. ‘As such it can even be applied to satellites launched before this work began.’