I seem to recall seeing a photo in Autocourse somewhere around '89 or '90, the aftermath of a meeting between a manhole cover that wasn't properly secured and a Group C car. There wasn't much left of the car.
Any math/science nerds looking at this? There is an error with units in my math. Can you find it? You don't have to be a math wizard to find it; just keep track of the units that I am using for different variables.
There is also an error in the second-last paragraph. That one should be really easy to find. I'll fix both of them as soon as somebody finds them.
This stuff happens all the time when you do math. You just have to keep checking, and usually have somebody else look at it as well.
Jeez you guys. OK, here are the errors.
1) time_over_manhole = tray_length/car_speed. tray_length is in feet, and car_speed is in MPH. Not gonna work.
2) In the graph, it shows that the cover gets to about 0.8 inches because of the racecar. In the second-last paragraph, I say that it got to 0.067 inches. I should have said 0.067 feet, which is the same as 0.8 inches. All my calculations were done in feet, and then I converted to inches for the graph by multiplying the cover height s(t) by 12.
I'm posting this because a) I love this stuff, and b) I'm hoping that I can show you how technical problems can be solved with fairly simple math, on the computer. I'm not crunching these numbers myself. I'm just typing in the equations and some variables, and Mathcad (my math app) is doing all the calculations. If this looks like fun to you, maybe you should consider getting into the tech field. If you are good at math, you don't need Mythbusters so much. If some good young engineers don't start showing up, old geezers like me are going to keep doing engineering (and raking in the big bucks) until we are senile.
jcolbert, I would convert to SI in a real project. I stayed with English units here because most people in the US are comfortable with pounds and feet.
I am making a lot of simplifying assumptions. For example, I am ignoring the situation when the manhole cover is PARTIALLY covered by the racecar. I am also ignoring the possibility that the cover may come up at an angle.
What if a second racecar comes along while the manhole cover is raised? Either it will hit the cover, or it will raise it some more, making it nearly inevitable that the cover will strike the bottom of the second car. I haven't shown this in my math. Remember, this is a 110-pound hunk of iron. You don't want this anywhere near your delicate little racecar.
Here is a much more elegant way to do this math. In Mathcad, which I am using here, there is a conditional statement which is just like an if-then-else statement: x = (if a, b, c). If condition a is true, then x = b, otherwise x = c. For a brief interval, the force on the manhole cover is from the racecar. Afterwards, it's gravity alone. By using the conditional statement, I've combined both force conditions into one function. Now I can divide force by mass to get acceleration (F = ma). And I can integrate acceleration over time to get velocity. Then I can integrate velocity over time to get position of the cover. Now the entire motion profile of the cover can be shown on a graph.
Last edited by Motie; 05-14-2013 at 08:18 PM.
Your data correlates to the Myth Busters experiments findings
I didn't watch the Mythbusters episode. Keep in mind that I am not saying this is exactly how it's going to happen. My method gives you an idea how these problems are tackled, and gives you a template where you can plug in your actual numbers for things like lift force, car speed, etc. The main thing that can go wrong is that the car doesn't make enough lift force to move the cover. The lift force is a function of the car's aerodynamics, the area of the undertray, and the car's speed. Calculating the lift force would be horrendous. You would probably want to get that from a CFD model or a measurement on the actual car.
What happens if there is a small hole in the manhole cover? The car is over the cover for only 0.02 seconds. That's not enough time for much air to flow through a small hole. If the volume of air under the cover is large, I don't think a small hole will make any difference. Also, as soon as the cover lifts a little, there is a huge air leak all around the circumference, so I don't think the small hole is significant. On the other hand, if the air volume under the cover is small or zero, then the vacuum due to the undertray will quickly get under the cover as soon as it starts moving, and the lift will be much less.
A hot racecar tire is virtually molten and some adhesion from that can contribute to the lift.
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