Personalized Helmet Design

In this project, our group was tasked with designing a racing helmet using physics principles to guide our design.  We began by conducting research into helmet safety standards.  Using the fruits of this research, we calculated important characteristics of our helmet relevant to safety.  We next used technical sketching to produce orthographic and perspective concepts of our helmet.  Lastly, after completing an introductory tutorial activity which taught a variety of relevant concepts in Fusion360, we made a 3D model of our helmet.

The Report, Sketches, and Renders

Concept Sketches (Orthographic and Perspective)

For reference, the raw 3D model may be found at https://drive.google.com/file/d/1vS1Pha5sshssZXpBvjCOfJ0ROPuFMPCD/view?usp=sharing.

Core Concepts

Acceleration

Acceleration is the change in velocity over time.  Quantization of acceleration is exceedingly important in the design of a helmet due to the fact that a collision involves high accelerations; these must be managed in order to prevent the helmet's occupant from suffering debilitating injury.  Since acceleration involves both velocity and time, we must alter one or both of these in order to reduce it.  While velocity is uncontrollable, the time it takes to decelerate is controllable by allowing the wearer of the helmet to decelerate over a greater distance (thereby taking more time); this is precisely the purpose of padding within a helmet, which allows the user to decelerate into the padding rather than stopping immediately.

Acceleration is often described in terms of G-force, which measures acceleration relative to the acceleration of Earth's gravity.  1G is 1 times the acceleration of Earth's gravity, 10G is 10 times the acceleration of Earth's gravity, and so on.

Crumple Zones

Via the above principle, to reduce the dramatic effects of an impact we wish to allow the occupant to accelerate into something malleable rather than stopping immediately on something hard.  These deformable materials are frequently called crumple zones and have a wide variety of applications.  For example, cars are designed with crumple zones in the front that are designed to deform should the car be involved in an impact; this allows the car to come to a stop over a distance equal to the length of the crumple zone rather than stopping immediately, increasing the time of impact and thereby decreasing the acceleration experienced.

Inertia

The problem of impacts is brought about through the existence of inertia.  When an object moves at a given velocity, it will continue to move at said velocity without the imposition of outside forces upon it.  This is Newton's first law.  But likewise, any outside force imposed on the object must equal the momentum of the object in order to cause the object to come to a stop.  By this token, objects moving at high speeds — that is, objects with great momentum — will take exceedingly high impulses (forces over a period of time) to stop.  Since force is mass times acceleration, high impulses means high forces which means high acceleration.

Force

A force is an interaction between two bodies which imparts acceleration.  In a collision, there is a force exerted on the crashing car by the object which it crashes into precisely equal in magnitude but opposite in direction to the force the car exerts on the object it is crashing into.  This is Newton's third law — that for every force exerted by one object on another there is an equal but opposite force exerted on that object by the other.  Note that there is also a force exerted by the crashing car on its occupant, equal to that of the force exerted on the car.

Newton's second law states that force equals mass times acceleration.  We can draw two conclusions from this in relation to an impact:

• For an object with a large mass, like a car, the force exerted on it (and by extension, the occupant) must be very large.

• For an object moving at high speeds, like a car, the acceleration will be great (recalling that acceleration is equal to the change in velocity over time) and therefore the force exerted on it (and by extension, the occupant) must be very large.

These factors make it apparent why collisions are so dangerous; the forces involved are enormous.

Friction

Friction is the force exerted on an object as it rubs against another.  Two contacting surfaces will always resist motion; however, there is notably a difference between resisting motion while not moving and resisting motion while already moving.  This distinction is the distinction between static friction, which occurs between two contacting objects that are not moving (such as someone's foot on a carpet while they are standing), and dynamic friction (or kinetic friction), which occurs between two contacting objects that are already in motion.  Dynamic friction is of particular interest to the application of the helmet as the helmet is indeed a moving object — and while it may not be apparent what the helmet is rubbing against, it is indeed experiencing friction, as we will see.

Drag

Drag is the frictional force of air against a moving object.  It is thus a form of dynamic friction.  While moving through the air, our helmet experiences drag; to avoid exerting too much force on the wearer's neck, we wish to minimize drag to the greatest extent possible.  Drag force is defined by the equation F = 1/2⍴v²CA, where ⍴ indicates the density of the air (something out of our control), v is the velocity of the object (also out of our control, given that we cannot reasonably ask the car to drive slower), C is the coefficient of drag (within our control), and A is the cross-sectional area of the object.

The coefficient of drag is a specific kind of coefficient of friction.  A coefficient of friction describes how "rough" an interaction is.  A very bumpy helmet will have a higher coefficient of drag against the air than a smooth one will; for this reason, our helmet is very smooth.  Likewise, the cross-sectional area describes how much of an object is presented to the airflow; making the helmet as sleek and streamlined as possible reduces this area as much as can be done without making it uncomfortably small, which is what we have done in our design.

Reflection

This project was quite short, but I believe we met the challenge well.  We first and foremost demonstrated our critical thinking skills in the calculations section of our report.  Figuring out how to do the math to accurately calculate the required constraints for our helmet to be considered safe was a significant effort, and producing a reasonable number in the end for the thickness of the foam confirmed intuitively that our calculation was correct.  Additionally, our communication for this project was fairly strong.  We were able to create a detailed report explaining every aspect of our helmet's design and the math behind how we came up with it.

This project did have some issues.  We came right up against the deadline, so the conscientious learning might have been improved.  While we were given just a handful of days to complete the project, we delayed work by one day due to other work for our Capstone project.  In hindsight, this work could have waited, and the time would have been better allocated for this extremely short-timeline project.  Our collaboration was also not perfect; some members did more than others in working to complete the project, and while everyone did help and put forth their best, not everyone got started as early.  Ensuring that everyone is on the same page at the very start is important for the future.

Despite this, I would call the project a moderate success due to the fact that we pulled it off without any question.  We were able to put a significant level of detail into the project despite having very little time to do so.