Evaluating Crumple Zone Performance
This lab is designed to align with AAOT science outcome #1: Gather, comprehend, and communicate scientific and technical information in order to explore ideas, models, and solutions and generate further questions.
- writing utensil
- digital device with spreadsheet program
- digital device with internet access
- Apply the Laws of Conservation of Energy and Conservation of Momentum to predict the effectiveness of peak forces during collisions with and without crumple zones.
- Experimentally investigate the effectiveness of crumple zones by measuring average and peak forces during collisions with and without crumple zones.
- Compare the model predictions with the experimental results.
For the simplified case of a car hitting a solid barrier that doesn’t move, let’s compare the force peak applied to occupants for the theoretical case of a perfectly elastic car and a perfectly designed crumple zone. We will simplify our problem by analyzing the case of a car hitting a solid immovable barrier. We start by analyzing the first half of the collision (as the car/person comes to rest before bouncing back) and including the car and barrier in our system. We will assume the crumple zone provides a constant resistive force as it crumples and dissipates kinetic energy into thermal energy.
Crumple Zone Model
First we start with the Law of Conservation of Energy:
The crumple zone is designed so that it does not store elastic potential energy. Instead, internal work is done within the car-barrier system to convert kinetic energy (KE) to thermal energy (TE). We will assume that work was done by a constant force applied over the total crumple distance, . In that case the work done was , so that must be the change in thermal energy of the system:
The change in kinetic energy is initial subtracted from final, but the final kinetic energy is zero when the car finished crashing:
We can then use the initial speed in the formula for kinetic energy,
1) Symbolically solve for the constant force applied. Show your work.
Rigid Frame Model
We want to compare your previous model equation for forces with a crumple zone to a similar model for rigid frame car. We will assume the whole point of a rigid frame is that it does not crumple (permanently deform) during the collision. Instead, the frame only temporarily deforms a slight bit, but not enough to get into the failure region of it’s stress vs. strain curve. Therefore, the frame acts like a spring and bounces back to original shape and we will model it as a spring. This also means that the car will bounce off the barrier. However, it does have zero speed for just an instant as it stops and begins the return bounce. We will only need to analyze the collision up to that point in order to make our comparison. Again we start with the Law of Conservation of Energy:
In the ideal elastic collision internal work is done on the car-barrier system to convert kinetic energy (KE) to elastic potential energy (PE) and no energy is converted to thermal energy. As before, we expanding the change in kinetic energy and setting the final kinetic energy to zero:
We will model the elastic material as a spring, so change in PE is .
Writing the as allows us to easily introduce the Force into the equation.
We recognize that for a spring and make that substitution:
2) Just as for a spring, the maximum force is applied at maximum compression distance, which we have called . Symbolically solve for the peak force. Show your work.
3) Compare your model equations for the peak force of the elastic collision (rigid frame) and the peak force of the dissipative collision (crumple zone). Which is larger, and by how many times?
4) Assuming the seatbelt holds the person firmly to the seat so that they always have the same velocity as the car and come to a stop over the same distance (and time). Therefore our model of the forces applies to both the car and the person and find the forces on the person we would simply use their mass in the equations instead of the car mass. Most importantly, the relative size of the peak forces in our two models gives us an idea of the relative size of peak forces on the occupants of the vehicles. Does our model predict that crumple zones are effective at reducing collision forces on people? Explain.
Real collisions can be more complex than our idealized model. For example, the colliding objects may have similar mass, the case of the elastic collision will not be perfectly elastic, and the crumple zone will likely not produce perfectly constant force. Friction from the bottom of the seat also acts on the occupant. We are assuming the model still captured the overall behavior of each collision type to provide us with the correct ranking of peak forces and the correct conclusion about the effectiveness of crumple zones, but we still want experimental verification.
Collision experiments were performed for a rigid frame, a springy frame, a crumple zone built from soda can aluminum, and finally a crumple zone built from aluminum foil. The velocity of the cart was measured by the cart’s optical sensor and the force on the simulated occupant of the cart was measured with a force sensor. All of the necessary data is available in an online spreadsheet. You can copy and paste the data into your own sheet for analysis.
5) Create a single graph containing plots of the the velocity vs. time data for all 3 trials shown in the datasheet. This will allow you to quality check your data. Make sure you have a complete dataset that includes the maximum speed reached by the cart for each trial. Be sure to name your graph and label the axes, including units. Also be sure to add a legend so you or anyone else can identify which dataset in your plot is which trial.
6) Create a single graph containing plots of the the force vs. time data for all 3 trials shown in the datasheet. This will allow you to quality check your data. Make sure you have a complete dataset that includes the maximum speed reached by the cart for each trial. Be sure to name your graph and add axis labels with correct units. Also be sure to add a legend so you or anyone else can identify which dataset in your plot is which trial.
7) Use the MAX spreadsheet function to find the peak speed for each trial. (The datasheet contains empty rows at the top for you to apply this function). Are the collision speeds for each trial all the same to within a few percent? Show your calculations below.
8) Based on the experimental data, rank the collisions by peak force applied to the occupant, from lowest to highest.
9) Change the axes limits on the force graph to zoom in on the impulses for the two non-rigid collisions. Describe the shape of the impulses for the spring collision and crumple collision.
Max and Average Force Hypotheses
10) Use the MAX and AVERAGE spreadsheet functions to find the peak force and average force for each trial. (The datasheet contains empty rows at the top for you to apply this function). In the space below, record the peak force and average force for each type of collision.
11) Considering your results, when comparing rigid frames, spring systems, or crumple zones, which is the best safety system?
12) During our modeling of the crumple zone we assumed that the crumple zone provided a constant force during the entire collision. Based on the experimental force data does this assumption appear reasonable? Explain your reasoning.
13) What changes could we have made to our experiment to more accurately recreate a real collision between cars?
It might initially seem like building cars to be rigid would be a good idea because the occupants would be “protected” by a cage that would not deform. However, we have shown that a rigid frame actually increases the force on the occupants. It might then seem like an very compressible elastic frame would reduce the force and also prevent permanent damage to the car. However, we have shown that the elastic collision still puts more more force on the occupants than a crumple zone collision. In fact, the elastic collision is even worse than we have found in this case because of the bounce-back that occurs for an elastic collision. If the car bounces back but the person’s head continues forward due to inertia, then the relative impact speed between their head and the dashboard has been amplified. Just as crumple zones reduce forces and prevent the car from bouncing back into your head moving inside the car, airbags are designed to reduce forces and prevent your head from bouncing back into your brain moving inside it. Airbags have holes to allow deflation as your head hits them, rather than bounce your head back the way a beach-ball would.
Overall, the crumple zone decreases the impact speed between your skull and the airbag while the airbag decreases the impact speed between your brain and skull.
During our experiment we could not use the motion sensor to measure the bounce-back speed of the cart because the fan was in the way. However, we can use the Impulse-Momentum Theorem to find the change in velocity for the occupant of the vehicle. The larger the change in velocity, the more bouncy the collision was. The cart mass doesn’t change during the collision, so the Impulse Momentum Theorem looks like this: .
14) Solve the impulse momentum theorem for the change in velocity.
15) Find the impulse on the car for each collision by multiplying the average force for each collision by the duration of the collision.(You will notice in the data that all of the collisions have the same duration. Record the impulse values here:
16) The mass of the “occupant” in this experiment was 0.05 kg. Calculate the change in velocity for each collision. Show your work.
17) Rank the each collision type by the magnitude of change in velocity.
18) After analyzing this new factor to worry about, the bounce back indicated by change in velocity, does your conclusion about the effectiveness of crumple zones change or become more solid? Explain your reasoning.