In the final few minutes of a spacecraft landing, it is moving at hypersonic speed through many layers of atmosphere. Knowing the air density outside the vehicle can have a substantial effect on its angle of descent and ability to hit a specific landing spot. But air density sensors that can withstand the harsh hypersonic conditions are uncommon. Researchers developed an algorithm that can run onboard a vehicle, providing important real-time data to aid in steering the craft, particularly during the crucial entry, descent, and landing stage.

The algorithm starts without knowing anything about the air density. It gathers data from accelerometers and gyroscopes available on any vehicle to gather data and combines it with prior knowledge about maximal rate of acceleration to obtain a time-varying estimate of air density. It learns and changes its estimations onboard, based on the input data it receives.

The researchers used data acquired from the entry, descent, and landing of the Phoenix lander — a Mars science probe — representing the last 220 seconds (the ballistic phase) until parachute deployment. The craft cannot be steered at the later portion of that stage, so it is important to immediately know the air density in the rarified flow regime, from about 80 kilometers and up. When it enters that later portion, its flight path angle gets fixed and the vehicle just descends; it is barely affected by the direction of the wind.

There is often an assumption that there exists a fixed model known in advance and control methods can be determined that lead the vehicle to land. It's often not the case because due to the speed and the impact with air, hypersonic vehicles change shape slightly during the flight and that changes their dynamics during flight. There is no unified model that describes the entire flight because the dynamics change gradually over time. With the new algorithm, using the maximal rate of change, that knowledge can be exploited to create an estimate.

There are other fields to which this knowledge can be applied such as in electro-surgery to predict the temperature field during a surgical operation so that the surgeon can know how deep the cut is.

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