atomic_fungus (atomic_fungus) wrote,

#859: It's not an estimate. Physics is my friend.

In the comments for #858 Anonymous poster told me, "For what its worth..I think your speed calculations are grossly underestimated." I was writing a reply, explaining why I could not be wrong--it is literally physically impossible--and realized it was far too long for a comment. But my calculations are calculations, not estimates: I used actual physics to come up with my numbers.

That's why I said "calculations" and not "estimation". Its true that my description is leavened with "about" and "approximately" but that's because I didn't want to write the precise numbers, which were 2.09165 seconds, leading to a velocity of 95.61828 feet per second, which is 65.19428 miles per hour.... That gets tedious, and the rounded numbers were close enough for my purposes. (And I have, in fact, truncated the numbers. Actual speed at impact: 65.194287781876016725571846165079 miles per hour....)

But I did "run the numbers"--twice, to make sure I'd gotten the correct answer...and I'm sorry to say that unless the information I got from the article was wrong, the answer I got cannot be wrong. It's the laws of motion in action!

So let's take a look at things again:

Distance equals 1/2 acceleration times time squared: D=0.5*a*t^2.

The car could not possibly fall faster than it did. In order to strike the tree 15 feet from the ground it had to fall for two seconds. In a one G field, it takes a full second just to fall 16 feet, but at the end of two seconds, you've fallen 64 feet. (And at the end of 2.09165 seconds, you've fallen 70 feet.) That's why we say an acceleration is some measure of distance per second per second: you add X many units per second of velocity every second that you're under acceleration.

The article says that the car left a runway that was 85 feet above the surrounding terrain, traveled 200 feet, then struck a tree 15 feet from the ground. It therefore had to fall 70 feet before striking the tree. In order for the car to have enough time to fall 70 feet--traveling a distance of 200 feet after leaving the runway but before striking the tree--it could not have been moving faster than 70 miles per hour.

As I said in my initial post, at 100 MPH they would have fallen only 29 feet before striking the tree, and they would have hit it 56 feet above the ground rather than 15. At 100 MPH they would have had only 1.3 seconds of "air time", and that's not enough time to fall 70 feet. It's only enough time to fall 29 feet. As I said.

According to the information given in the article, it can't be otherwise.

* * *

However, there is one point I insufficiently amplified, which I will amplify now.

After you fall for two seconds, your speed is 64 feet per second, which is about 43 miles per hour. The car did not just slam into the tree with a horizontal speed of 70, but with a vertical speed of 43 MPH.

If the car had not hit the tree, those five kids would be just as dead as they are now, but for a different reason.

The typical car is not built to have much crash protection along its yaw axis. The vertical drop test is not one that is usually evaluated by manufacturers or government safety inspectors, because cars are not meant for stunt driving. Most people do not operate their cars in a regime where such a collision is likely.

Although the chassis of a car has significant rigidity to withstand road-induced flexion and compression, it's desgined to operate in a rather limited envelope and does not have the strength to withstand a generalized impact at such speeds.

If I am generous, and allow 0.1 second for the duration of acceleration, then the car experienced 20 gravities of acceleration when it struck the ground. That alone would have totaled it even if it had not struck the tree. 0.1 second is a long time for a collision; I'm deliberately overestimating the compressibility of dirt in order to make a point: a car pancaking onto the ground at 43 MPH is going to be destroyed. In fact, a duration of 0.05 seconds is probably more reasonable, shooting the acceleration to 40 G.

And since the human spinal column does not respond well to compression, I wager those kids would also still be dead.

It is possible for a human to survive much greater shock than 20 G--see this Wikipedia article on John Stapp--but he has to be strapped in securely. A typical automotive safety harness--while safe in most collisions--is not sufficient.

The other factor is, of course, that the car would have pivoted on its pitch axis.

Anonymous poster claims to have survived a 70 MPH collision with a tree, and I don't disbelieve him--but his collision and this one occurred under differing circumstances.

The BMW was not, as we have established, merely striking a tree; it was striking a tree after falling 70 feet. But it was also rotating about its center of gravity.

The front wheels left the runway first. This means the front end of the car began falling before the rear--a few milliseconds--which means that the car, as it fell towards its rendesvous with destiny, had a slight moment of rotation about its center of gravity induced by this asymmetrical application of gravity.

This diagram shows all the forces acting on the car. There is its residual speed, Vs, its velocity due to the acceleration of gravity Va, and its rotational component, omega, which I'll represent in text here with "w". W is the key to why the car experienced such enormous damage and disintegrated so spectacularly.

Cars are designed for collisions in the "x" plane--the plane defined by the car's roll and pitch axes, the plane which is perpendicular to its yaw axis. Most collisions occur in this plane. The car is designed for a certain amount of "rollover protection"--it can withstand a certain amount of impact on its roof--but nothing like what it can stand from the front or sides.

I would wager that Anonymous' accident involved skidding off road and striking a tree--all in the X plane, with little or no other component to the collision. This is the kind of collision that a car is designed for.

In the case of our ill-fated BWW, however, it would have struck the tree at an angle: 70 MPH in one direction, 43 in another. On the roof.

But, what the hell. Dead is dead.

* * *

I am interested to learn that the morons may have been drag racing. Interested, but not terribly surprised.

I see, all the time on Pennock's Fiero Forum, people who argue that as long as street racers don't endanger others, they should be allowed to do whatever they want to.

Here is an example of what happens, though, when street racing is taken to a "safe" venue: people still end up dying.

It's obvious that the driver of the 2008 BMW in question did not know how to drive his car at that end of its performance envelope; and in fact I'd question his ability to comprehend that "faster speed" means "it's going to take longer for you to stop". God alone knows what his speed was before he started braking; but physics tells me that he was going 70 when he left the runway, and it's no stretch for any modern production car to break 100 MPH. In all probability his speed was somewhere north of 130 when he started braking. He couldn't stop fast enough, went off the end, and the rest is history.

This is why the people who find "deserted roads" to street race aren't any better--nor any smarter--than the morons who do it in populated areas.

When you race at a track, the people who run the race are there to help you minimize the risks you are taking. They have no emotional involvement in your success or failure as a racer; all they care about is making sure that you have an environment in which you can "go that way, really fast" without putting anyone else or yourself in any more danger than is strictly necessary. They do this by requiring certain amounts of safety equipment and by holding the race in an environment specifically designed for it.

So that if you do lose control of your car, you don't hit a light pole or a tree, but a safety barrier which is designed to extend the duration of impact as long as possible, in order to reduce the forces you experience. Lowering acceleration.

The environment also has plenty of visual cues for the driver to let him know when he is running out of room; and many drag strips have a "sand pit" at the far end, where an out-of-control car gets bogged down in loose sand.

A deserted road--or landing strip--has none of this.

In the end, regardless of the particulars, an age-old equation has again been satisfied: youth plus stupidity plus speed equals dead bodies.

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