On Reaching Dizzying Heights In Bicycle-Vehicle Collisions

"If a car traveling at 46.5 kph hits a cyclist, the force of impact would be sufficient to send the cyclist up to the thirteenth floor of a building."

- Traffico, a journal by the Directorate General of Traffic of the Spanish Ministry Of The Interior

I happened to come across this quote on some helmet advocacy website a few days back. I forgot to bookmark the darn site but had copy pasted this statement exactly as it was into a word file on my computer. Anyway, I was struck and bothered by such a bold claim. While it sounds scary, is there any real truth in it? 46.5 kph is around 29mph, which is a low speed for a vehicle. Despite this, the momentum of the vehicle is a hell of a lot considering its high mass with respect to the cyclist. So can the momentum transfer in the above collision really rocket the cyclist up to as high as thirteen floors before crashing to the ground? If such were the case, the cyclist could be in serious condition, even dead.

If you know your college physics, the topics to recall would be Newton's laws, impact and momentum transfer, conservation of energy, collisions and projectile motion. But hold on. Its a tricky challenge. There are many variables to consider : the masses of the three bodies, height of the cyclist, the gradient of the road, point on the vehicle first struck, orientation of the bicyclist before impact, the launch angle, coefficients of restitution and friction, and victim's behavior post impact (wrap, vault, forward projection, somersault etc).

Physicists and engineers across the world have come up with all sorts of equations to study vehicle-pedestrian collisions. They're interested in things such as - how one can devise a good comprehensive mathematical model that will approximate well the speed with which the vehicle first impacted the victim, or what the total throw distance of the victim would be given other data, or would the model ultimately validate real world behavior - questions of that nature. Such models could then be incorporated into manuals and computer tools that could be used by police officers and forensic investigators to catch criminals and help serve justice.

Example of a Post Impact Scheme Adopted By Bogdanovic and Batista, 2004

In America, most commercial buildings are 10 feet in height per floor : 8 feet head room, 1 foot above drop ceiling (pipes, electrical, etc.), and 1 foot for infrastructure (beams & support structures). Can a cyclist rocket to 130 feet in the air upon a collision? We may never know exactly, because not a single bit of data is provided by Traffico other than the car's speed at impact which is given to be 46.5kph=29mph.

Lets make an effort to find out.



1. LOOKING AT VIDEOS


Forget the theoretical part for a moment. Lets look at a couple of real collision videos involving a two wheeler and a car.

Here's a guy on a bicycle getting hit by a car. The latter was decelerating hard after the driver spotted the rider coming into his view but it was too late to stop an impact. Note how the right corner of the car impacts the cyclist first. The rider then hits the windshield and bounces off it before falling onto the road on the right side.



The victim is pretty lucky. He just gets up and immediately starts yelling his frustrations. I'm so surprised he didn't smash his head onto the ground. But hey, neither did he fly any higher than the car itself. Just a few feet. The car itself could have been doing 15 or 20 mph before impact.

Here's another video. This time, its a vehicle colliding with a motorcyclist who fled a red light only to meet his deadly fate.



If it had been a bicycle in the video, which is much lighter than a motorbike, it would have been thrown off a farther distance. The car was moving much faster than the first video. It could well have been doing 35 or 40mph before coming to an abrupt stop after the collision. The airbags must have surely deployed since the driver appears disoriented. The motorcyclist is shown spinning in the air at a stomach sickening angle before landing onto the hood of the car and bouncing off it straight onto the road, right in front of the stopped vehicle. Its anyone's guess how many bones he could have broken that day.

And finally, here's a simulation of a car-bicyclist collision. It was done by Crash Teams, the largest crash reconstruction company in the world.




All three of these videos don't show the cyclist being propelled to dizzying heights after the collision. At least not thirteen storeys high.



2. FIELD EXPERIMENTS

Jim Green is a triathlete and Professional Engineer with over 20 years of experience in reconstructing bicycle accidents. In the 19th chapter of his book "Bicycle Accident Reconstruction For The Forensic Engineer", a table of vehicle-bicycle collision data is presented to us. The analysis was done on the field by Rusty Haight and Jerry Eubanks who set up an experiment in which different kinds of motor vehicles were used to strike an exemplar bicycle with a dummy cyclist at various speeds.

Here's the field data that shows the linear throw distance of the dummy cyclist after impact.

Determination of the throw distance of a bicycle and cyclist at various impact speeds

I have highlighted some rows of data for cars close to 29mph. For example, a 1979 Honda Accord hitting the dummy cyclist at almost 27 mph in a 60 degree orientation would throw the rider some 58 feet. Although the field experiment did not measure for the maximum height of the cyclist in the air, I highly doubt that the dummy really went as high as thirteen floors for a throw distance of 58 feet. I don't believe that's what the researchers really observed.



3. PROJECTILE MOTION

Coming back to physics, the cyclist on impact would be a projectile because his motion is only governed by gravity. But can we use the equations from projectile motion to find out what his height achieved could be in an ideal case scenario?

Lets use some simple assumptions like the following before any calculations :

a) the cyclist is a particle of mass 70kg
b) the head-on collision is elastic
c) the bike is immediately separated from under him after impact
d) the cyclist hits the windshield and is launched forward at an angle
e) during the collision between him and the car, there is zero effect on the velocity of the car itself due to its very high mass and that all the car's impact velocity is transferred to him
f) the car comes to a complete stop just after impact, leaving the cyclist with the forward motion velocity
g) there isn't much deformation to the car, or injuries to the cyclist AT impact and the co-efficient of restitution is essentially at or very close to 1.
9) the analysis is strictly restricted to a two dimensional plane, with no regard for the z dimension.

Using the equations for a projectile, we can apply a simple applet to solve for height.

For head-on elastic collisions, the velocities of the car and cyclist would be :



Assume the car has mass m1=2000kg, and the cyclist has mass m2=70kg.

v(car) = 13m/s (46.5kph, given by Traffico).

So, v(cyclist) = 25.12 m/s.


According to the equation for maximum height in a trajectory, we find that range is shortest and peak height is maximum when the launch angle is exactly 90 degrees with respect to the horizontal. This is because sin(90) = 1.



Since we assumed that the cyclist hits the windshield, lets give him a launch angle of 80 degrees. Solving :

With air resistance factored in, the cyclist would make a 30.82 m max height, or 101 ft. Add the height of the car's impact point to this figure and it still gives us something under 105 feet. This height, given such idealistic assumptions we made earlier, is still lower than 13 floors. In America, commercial buildings are usually 10 feet in height per storey. 13 floors would be about 130-140 feet. Hence, in the real world, one probably cannot come close to anywhere this high. Real world videos or simulation show us different and complicated outcomes. There usually isn't a good bounce between the car and the victim just after collision. Moreover, kinetic energies could be absorbed in the collision as heat, light, or deformation energy and the neither does the cyclist and the bike follow ballistic trajectories like a cannon. Lets remember that the cyclist sits on a bike and that fact coupled with how he impacts the car are very likely to influence how far or high he's thrown. Hence, I cannot validate the calculations above for real world observations. I may believe it if you're talking about a collision on the surface of the moon where the acceleration due to gravity is 1/6th that of the earth. Or if we're talking not about a human cyclist, but a ping-pong ball.

CONCLUSIONS

The idea that a cyclist will launch as high as 13 storeys seems like a wonderfully wacky proposition. I support the wearing of helmets for protection but don't support the spreading of false information by agencies in putting together a helmet wearing agenda.

As an end note, I just thought of something in my hindsight. Maybe Traffico is right. What if, in Spain, the 13th floor of a building is considered so unlucky that there is no 13th floor at all in its elevator's options.

What Traffico then must have actually meant through their quote is : You're one unlucky bastard to be hit by a moving car at 46.5kph!



Concluding video presentation : James Green, PE discusses bicycle accident scene investigation from the perspective of a forensics engineer.