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Pop can hang time.I'm going to toss this out for discussion. Find the hang time in this video. You can hear the can land. The thud is not very loud due to the distance. The sound reaches the mic after the landing due to speed of sound.
Here is the exercise. Find the hang time. A photo of the launch to landing is included below. From the hang time, what is the approximate apogee? The can was a full 12 oz soda. From the height, what was the approximate muzzle velocity? [youtube]http://www.youtube.com/watch?v=0MzvW1Fy34E[/youtube] Here is the landing. Watch the orientation of the center court net as we approach. It landed just past 1/2 court. [youtube]http://www.youtube.com/watch?v=VaRLTvw74NM[/youtube]
what angle was the cannon fired at because that will determine weathe i use kinematics or 2D kinematics
AHahahahah!!
Cannon angle was hand held, but close to vertical with just enough lean to ensure we didn't get hit on the head. In degrees, it is unknown. A close approximation can be found when the remainder of the parameters are close.
Use the Ballistics tool in GGDT to model the hang time and distance. The soda was not sugar free. Edit; Played with the cannon values and plugged in the can weight. The distance works for an elevation of about 81 degrees.
the delay in time before the sound reaches the microphone creates about 0.026871198 second of difference so the can hits the ground about 0.02687 second sooner then is heard, neglecting air resistance one way you can solve for this is:
~muzzle velocity(in fps)=(time recorded between launch and impact 0.026871198)16.087 pretty simple, I wouldn't bother with 2D kinematics because for all I know the wind could have affected the horizontal trajectory, but if you insist I would still use the equation only let the answer equal the vertical initial velocity, then the horizontal initial velocity = (distance between launch and impact site)/(time recorded between launch and impact) then plug in the horzontal and vertical values into this Pythagorean therom based equation ~muzzle velocity=sqrt( (horizontal initial velocity)^2 + (vertical initial velocity)^2 ) did anyone measure the time in audacity
I think the delay is a little longer than that. SOS is just over 1,000 feet/second. The distance is about 300 feet, so wouldn't the delay be closer to 0.3 seconds?
Please check the figures. Thanks for taking the time to give this a try. I was wondering if anyone came up with numbers like I am getting. Does anyone know the CV of a falling pop can projectile? I'm still trying to figure that portion out. Edit: I think the decimal point is simply off one position. I'll check the rest later. I do know that velocity going up is considerably more than velocity going back down. I can tell from the damage a can sustains when launched directly at a tree vs falling and making a splat on the ground. Does anyone know the terminal velocity of a pop can in free fall? If a skydiver drops a can of soda on the way down, does the skydiver or pop can fall faster?
I thought you said 30ft away
The flight path is provided in the original post with the map scale in the lower left corner. 30 feet is the distance from the road where I parked the car to the compressor on the other side of the row of trees. The car provided power to run the compressor at the launch site. The extension cord is way too short to reach the landing site.
The launch angle appears to have been within 10 degrees of vertical.
Without knowing the Cd it is really impossible to determine the muzzle velocity from hang time or apogee height.
Even an 0.3 second error due to the SOS is pretty irrelevant in this case. In the video it looks like the hang time is about 13 seconds, so an 0.3 second error is only about 3%. The accuracy of the velocity calc in the absence of a decent estimate of the Cd is probably in the range of at least 50%. The terminal velocity of a soda can is probably in the vicinity of 100 fps. Since that is probably significantly less than the muzzle velocity any calc that doesn't take into account the Cd is wothless. The equation for hang time to muzzle velocity ignoring friction is; Muzzle velocity = gt/2 where g is the acceleration due to gravity (32 fpss, 9.8m/s^2) and t is the hang time. So, on the moon, (assuming the moon had earth strength gravity) the muzzle velocity is just 16 times the hang time. A 10 second hang time would mean a 160 fps muzzle velocity. Using what appears to be reasonable estimates for the Cd of a 120g spud a hangtime of 10 seconds corresponds to a muzzle velocity, ignoring air drag, of ~160 fps. Using a couple different estimates for the Cd of the spud, 10 second hang time corresponds to muzzle velocities in the range of 250 to 600 fps. So, inclusion of Cd in the model increases the calculated muzzle velocity anywhere from 50% to 400%. (So a 3% error in the time from the SOS is pretty darn insignificant.) http://www.inpharmix.com/jps/Hang_Time_ ... ocity.html
The projectile shape is known. What is typical Cd's for a short cylinder. I was approximating between 0.7 and 1.1.
@ Jimmy, well done. You are in the ballpark.
0.8ish... if it's flying nose into the air flow. However, the concave shape of the ends would lead me to guess a drinks can was higher than that. As your second video testifies though, it was not constantly flying nose into the flow (else it wouldn't have landed on its side). The problem is, there are two variables in this equation. If we knew the muzzle velocity, we could estimate the ballistic coefficient of the can (which would be useful for other trajectory modelling) from the hang time. If we knew the ballistic coefficient, then we could guess the muzzle velocity. Basically, if we're guessing one of the variables, then we're basically guessing both. If we know one of the variables, then we can actually solve for a meaningful result.
Does that thing kinda look like a big cat to you?
I'll help out. The can was launches somewhere in the 300400 FPS ish range. We didn't measure it. This is based on cannon performance from prior measurements and approximate pressure used. The end first orientation is effective for only the very fist part of the flight.
As far as I can tell, the can wobbles on the way up and soon flies sideways. The sideways flight continues on the way down and is a stable orientation for falling soda cans. All high lobs I've done with full soda cans land flat on the side with no exceptions. This turning of the can sideways does seem to scrub off quite a bit of velocity from the shot. I have considered adding a tail to a can to see if it helps. The school I mentored on a shirt launcher has added streamers to shirts they launch to maintain the end first profile. They are getting much better range by doing that even with the drag of the streamers. I'll post some picks of shirts with streamers later to show this. I remember hitting the wall at trying to exceed 400 feet with a rolled up shirt. It is a difficult distance to pass. Lower pressure shots flew further than high pressure shots, etc.
this ought to help I'd say around .81 the angled cube should give some good insight for the general affect of the angled can
they may seam like the landed flat on their side, but with the length of the can I doubt it, they're probably flying at an angle but as soon as the further most point hits the ground the can would yaw, especially with the distribution of mass being spread out fairly evenly along the length rather than at the tip I highly doubt that a tail would improve the velocity, a homogeneous projectile should tend to position itself in a position with less drag if it's fairly stable falling in a sidewaysish position then that's probably the close to the position with the least drag, then adding a tail would just increase the overall drag
Do you have any data or references to back that up? My understanding is that there is no driving force to minimize drag if the shape has uniform density. That is, if the center of drag is the same as the center of mass, which it is true for most simple solid geometric shapes like balls, cylinders, cubes, "bullet" shapes, cones etc. Energetically, high drag and low drag aspects are the same to the object. There is no energetic advantage to falling faster, or slower. I believe there are a very few highly specialized shapes that don't obey the simple laws in terms of stability in flight (wasp waisted at high velocities?). If a soda can actually does tend to fall oriented horizontally then it is a higher order affect than simple drag and center of mass. Perhaps a (nearly) horizontal aspect takes advantage of the odd shapes, and perhaps lower drag/area on the ends of the can? For a shape that tumbles you probably need to actually measure an effective Cd based on projectile mass, dimensions, measured muzzle velocity and hangtime.
We have landed soda cans on pavement and examined them. There is no indication they landed on a corner and then laid flat. There was no evidence of a crumpled corner. Cans if they were a cat and had feet, would always land on it's feet, never the head or tail. (maybe back or side).
Hmm... that makes me think. Homogeneous monostatic objects  those with only one stable point of equilibrium do exist. (For a relatively famous example, take the Gömböc.) Obviously, that pertains to gravity, not drag. However, it is certainly possible to manufacture homogenous projectiles which do have a driving force to minimise drag  but those are exceptions, not the rule.
Does that thing kinda look like a big cat to you?
 
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