The Iron Man suit is perhaps the greatest invention in the superhero universe. Developed by the billionaire genius Tony Stark to initially aid his escape from captors, we were first introduced to the Iron Man suit in cinema in the 2008 film Iron Man, the first film in the Marvel Cinematic Universe (MCU). The suit represents the ultimate wearable technology and undoubtedly many people around the world have dreamed of wearing one.

Just like any aircraft, the Iron Man suit experiences a drag force due to its motion through the atmosphere. To optimize his flight path and minimise the drag force Iron Man experiences during flight, his AI computer system, Jarvis in the first MCU films and currently Friday, will continually make calculations in relation to the drag force experienced by the suit while in flight. However, a recent paper by Sathish Sanjeevi and Johan Padding in Journal of Fluid Mechanics on the drag force experienced by particles in airflow could have important repercussions for the drag force felt by the Iron Man suit.

In their study of non-spherical particles in airflows, Sanjeevi and Padding revealed that the drag coefficient, a number that gives a measure of how much an airflow is acting against the motion of an object, can be calculated for any particle placement or alignment. The formula used to calculate the drag coefficient includes one of the most famous trigonometric relations – the sine formula. In fact the formula includes a sine-squared term. To use the formula you only need to measure the drag number when the particle is parallel to the flow and when the particle is at right angles or perpendicular to the flow. Once you have these two numbers you are ready to use Sanjeevi and Padding’s drag formula.

Sanjeevi and Padding also found that their drag formula is accurate for particular types of flows. One number used by people working with fluids is Reynold’s number, named after Osborne Reynolds (1842-1912) who made a number of key contributions to our understanding of fluids. Basically the Reynold’s number (Re) is the ratio of the forces trying to stop a velocity change in an object and the forces exerted by the airflow when you are trying to change the airflow. In this case, the particle is trying to change the airflow. Sanjeevi and Padding showed that their formula is valid for Reynolds number (Re) up to 2,000.

This formula can have implications for the processing of biomass particles, which are usually non-spherical, in fluidized bed reactors to produce biomass fuels. By knowing more about how these particles move in airflows can improve the design of these reactors to maximise output of biomass fuel.

But how does this finding on the drag coefficient impact on Tony Stark and the Iron Man suit? Like the non-spherical particles in airflow, the Iron Man suit will have a Reynolds number associated with its motion. Imagine Tony Stark is flying his Iron Man suit at 50 km/h into a headwind of 50 km/h. Let’s assume that the Iron Man suit can be approximated as a non-spherical “particle” with a thickness of 0.4 m. When flying into this headwind the Iron Man suit has a Reynolds number (Re) of roughly 600,000. Although this number is higher by two orders of magnitude than the maximum value studied by Sanjeevi and Padding, the authors are confident that their formula is valid for higher Reynolds number.

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The consequences for Tony Stark are simple. He could now use Sanjeevi and Padding’s non-spherical particle formula to calculate the drag force on the Iron Man suit for any alignment of the suit relative to the headwind, provided he knows the drag force on the suit when it is parallel or perpendicular to the head wind. As a result some of his computational resources can be assigned to other tasks such as weapons, life support or energy management. Stark could also use the formula when designing the next generation of Iron Man suits, particularly when doing aerodynamic tests of new suit designs in wind tunnels – just like Formula 1 teams test the aerodynamics of their latest Formula 1 cars before the start of a new season. Iron Man could also use the formula when designing the shape of the small rockets and weapons that he fires from his suit when in battle.

Life really doesn’t need to be a drag for Iron Man!