Maddenation
PunkinChunkin
On the way home from Hyde Park, mom, Ed, and I decided to stop at a roadside stand to get some apples. As we pulled in, we heard this loud, rushing sound that for a second caused me to think I had blown a tire; or worse. As we proceeded to park, we noticed a sign that advertised “Pumpkin Cannon today: 1 PM.” There is was, off to the side; a large truck trailer supporting a long “gun barrel” attached to two compressed air tanks mounted at a 45 degree angle and pointing off across the farm fields to the woods beyond.
In a few minutes, their diesel-powered compressor had filled the tanks and they were ready to fire again. I watched excitedly as the pumpkin was blasted almost out of sight before cresting and eventually landing a mile away in the wooded area. Holy Cow! This was neat. Ed and I quickly got our cameras ready and started calculating what the pressure might be, and how high/far the pumpkin sailed, and how much pressure it would take to shatter the pumpkin before it left to cannon, and other questions engineers ask. I decided immediately to use my cell phone stopwatch to time the pumpkin’s “hang time” so I could calculate how high it went (and ultimately estimate how far it would travel in a vacuum). So yeah, this is another physics problem for you phythathisths out there. The best hang time I recorded was about 15 seconds.
By the way, we talked to the operator for a while and he told us that the world record for “punkin chunkin” was… I’d better not tell you lest I give you a good clue to solving the problem. Anyway, the world championships will be held in Delaware in early November, and I plan to be there. In addition to the compressed air devices, they also have other classes, such as Centrifugal, Catapult, and Trebuchet. Anybody want to join me?
Dad • Events • 10/08/07 • 4 comments
Comments
Patrick • 10/24/07 • 2:15 AM:It’s called “chunkin,” not “chuckin”? And, yes, I’m with you, but you gotta lead the way, engineerman!
Dad • 10/24/07 • 8:39 PM:Yeah; makes it sound like a contest for chopping pumpkins into “chunks.” Of course, when they hit the ground…
Dad • 11/08/07 • 11:54 PM:It’s been long enough. Now it’s time to solve the physics problem. For answers to lots of questions, check out this site. It has lots of trajectory formulas for virtually every situation. It gives you a formula for calculating range based on launch velocity (and angle), but it doesn’t tell you how to calculate range from hang time.
I did it this way. First, we know that, without air resistance, the distance traveled will be the horizontal component of velocity times the hang time. Vertically, the pumpkin will rise to the maximum height in half the hang time (7.5 sec.) and descend the rest of the time. On the way down, the vertical velocity component will increase according to the formula: v = gt, where t is half the hang time. By symmetry, the ending velocity is equal to the initial velocity. Also, because of the 45 degree angle, the vertical and horizontal components of velocity are equal. So v = 32 × 7.5 = 240 ft/sec. Distance = 240 ft/sec x 15 sec = 3600 feet.
How high does it go? Use the old standby equation: s = 1/2 gt^2, and apply it to the second half of the trajectory—the peak to the ground.
s = 16 x (7.5)^2 = 900 ft.
Technically, one should take into account that the pumpkin comes out of the barrel well above ground level, especially for some of those big air cannons. See the website for this calculation.
Dad • 11/25/07 • 9:00 PM:OK, it’s been even longer, and now it’s time to talk about air resistance. The reason air resistance is so often neglected is not that the effect is small—it’s huge—but that it makes the problem too hard to solve easily. I have played with it a bit, and taking air resistance into account dramatically increases the initial velocity required to reach a given distance. This is not surprising, because the drag force is a function of the square of the velocity, and it is well known that falling objects reach a terminal velocity in the neighborhood of 200 mph because of air resistance. This means that a pumpkin traveling that fast would experience a drag force roughly equal to its weight.
We know from the calculations above that the weight of the pumpkin slows its vertical velocity to zero in 900 feet. Admittedly, the drag force decreases sharply as velocity slows, but the point is that air resistance has a huge effect on the speed of the pumpkin. For the case described above, adding air resistance reduces the distance traveled by about half. However, the same distance can still be reached by increasing the “muzzle velocity” and reducing the launch angle (45 degrees is no longer optimum). Interestingly, the “hang time” is close to the same for the same distance, with or without air resistance. So my little “hang time” calculation produces a reasonable first approximation to the actual distance traveled.
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