The right side doesn't look right - too flat.

Holy cow, Trebuchet, that J-Buchet is unreal!

It may look too flat, but I've been over the code about 10 times now, and I'm convinced that for the values I found, it is accurate.

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Unfortunately they didn't compete this year. The scuttlebutt had it that they were doing some practice/demonstration hurling and came close to having a serious accident potentially involving injuries. They decided to withdraw until they had the safety issues worked out.

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Send me the code. I've seen too many ballistics graphs. Admittedly they weren't for pumpkins, but even in a vacuum it's not that flat.

In a vacuum it's flatter than that - the descent is noticeably steeper than the rise, which wouldn't happen in a vacuum. The code is posted above.

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It's flatter than an airless parabola. Somethings not right, and I suspect it's your x-component drag factor.

An airless parabola can be as flat as you want - that depends on initial angle and velocity.

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Here's a comparison to show just how significant aerodynamic effects are in my code. Here are the optimum trajectories for 5 different spin rates (300, 600, 1200, 1600, and 2000rpm) as well as a vacuum optimum. All are launched from 30m off the ground at 120m/s, around 270mph. This also demonstrates that my x-drag is working just fine.

Attached Images

Aerodynamic effects 120 meters per second.png (18.0 KB, 14 views)

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I think your spin rates are a little high, and that could actually be the problem if you've got very high backspin in the descent phase, as that would considerably flatten the trajectory.

I think 400-800rpm is believable honestly, which gives a 38-40 degree optimum angle (depending on other specifics). Higher than that does seem implausible.

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Today was the final day of the World Championships of Punkin Chunkin. A very large treb called Yankee Siege threw 2034 feet on Saturday, setting a new record. I haven't seen any results from today (Sunday) yet.

According to the WCPC site, Yankee Siege won't be returning next year now that they've done 2000 feet. They said it costs them $15,000 to haul the machine to the chunk each year. Wow! I don't think I've spent $1500 in ten years. Of course I've only thrown 500 feet. The owner of Yankee Siege is, IIRC, a dentist.

Thanks for the great discussion, CJL & Mugs. Too bad the OP didn't stick around to learn something, once it didn't agree with his preconceived ideas.

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Can you link to your latest?

I'm very glad you mentioned this, cjl - it shows your mind is ticking away, weighing possibilities against realities, an indication of your groundedness.

Earlier today, while watching a load of laundry spin, I though of spinning pumpkins and decided to get a better feel for how fast my laundrey was spinning (3,600 rpm), and how fast most pumpkins could safely spin before ripping themselves apart.

Without testing many pumpkins on something like a lathe, I don't know. I have my suspicions, however, that most would not remain intact through a regimen of 3,600 RPM and .6 g deceleration upon leaving a trebuchet at 100 mph. I would hazard a guess that 90% would remain intact at rpms less than about 600 rpm (10 revolutions per second).

That's what I came up with this morning, and your estimate of 400-800 rpm puts mine smack dab in the middle, which I find a reassuring confirmation.

Now - what to do with it.

I loaded it back into my own pumpkin ballistics spreadsheet and came up with a 14.8 kg pumpkin being lifting by a 63 kg Magnus effect.

Since that would produce a rather serious upward curvature, which we simply do not see in trebuchet'd pumpkins, this leaves me to doubt that pumpkins leave trebuchets with spins less than that required to create an initial upward curvature.

So, up the velocity to 200 mph, what spin would be required to produce an initially flat trajectory?

143 RPM.

Next we have to take a look at the arms of trebuchets, and in particular, their slings, to see if their angular velocity ever approaches 143 rpm.

Couple of videos later (looked at through very slow mo):

It appears most of the pumpkins travel through the 120 of potential spin-imparting stage in between 1/5 and 1/2 of a second, with about 1/4 to 1/3 being most common. Thus, even if 100% of the sling's angular momentum were imparted to the pumpkin, we're still talking angular velocities of, at max, 15 rps (the J-buchet), which is 900 rpm. On average, though, we're looking around 10.5 rps, which is 630 rpm.

This is a third confirmation that your "400-800 rpm" ballpark figure and my "600 rpm" wag were both very close!

So, from now on, I'm using 630 rpm, with the caveat that this is represent's the slings maximum angular velocity, and that in all likelihood, less than 100% of this is imparted to the pumpkin. In fact, I'm guessing that less than half is actually imparted, so I choose to use 300 rpm.

I also looked over a bunch of old test data on various objects and adjusted a few other factors, as noted below.

Will someone please measure the three-axis diameters of their roughly 12" pumpkin and post it here? That's one diameter about each of the three (x,y,z) axes. Then, please weigh that pumpkin on an accurate scale and post that here, as well. Thanks!

My numbers to date in the next post.

Example:
1. 12" pumpkin and 16" pumpkin 0.1524 m and 0.2032 m RADIUS
2. Launched at 30 mph and 100 mph 13.4112 m/s and 44.704 m/s
3. Launched with 30 rpm and 300 rpm

Magnus effect

F = 1/2 * p * w * r * V * A * l 22.5720425 kg
Water density 1000 kg/m^3
Volume of pumpkin 0.014826666 m^3
Mass of pumpkin 14.8266662 kg
32.61866565 lb

Where

p 1.2 kg/m^3 density of the fluid
w 300 RPM angular velocity 5.00 RPS
r 0.1524 m radius of the ball
V 44.7 m/s velocity of the ball
A 0.072965877 m^2 cross-sectional area of the ball
l 0.252281879 lift coefficient

Lift Coefficient - may be determined from graphs of experimental data using Reynolds numbers and spin ratios.

Spin Ratio = ( w * D ) / ( 2 * linear velocity) 1.022818792

For smooth ball with spin ratio of 0.5 to 4.5, typical lift coefficients range from 0.2 to 0.6

0.5 0.2
4.5 0.6
4 0.4
slope (m) 0.1
y-intercept (b) 0.15
y=mx+b

Drag coefficients
sphere 0.47
half-sphere 0.42
cone 0.5
Angled cube 0.8
rough sphere 0.4 Re=10^6

Cd = Fd / ( 1/2 * p * v^2 * A
or
Fd = Cd * 1/2 * p * v^2 * A
1.474968012 G Drag Force
Where
Fd 21.86885837 kg drag force
p 1.2 kg/m^3 mass density of the fluid
v 44.7 m/s speed of the object relative to the fluid
A 0.072965877 m^2 reference area
Cd 0.25 coefficient of drag

For spheres, the reference area = pi * r^2

Dentists buy talent. People like you and I are our own talent!

Our pleasure, Treb! It's been an enlightening experience!

I'd like this thread to continue, as it's loaded with basic aero-engineering concepts. One thing that would really help is if you, Treb, could supply some sort of ballistics info from your recent pumpkin-chunkin contest so that we longhairs can crunch some more numbers.

Here's what we would need:

Pumpkin mass: ___

Pumpkin mean circumference (as measured by either the most median circumference, or by a triple-axis measurement): ___

Angle of launch (as measured by a side-looking video with correct aspect ratios): ____

Vx (the horizontal exit velocty as measured by a level, downrange dude with a radar gun): _____

Distance (from sling release point to level impact (hopefully, you're not launching them off the top of a hill... )): ___

Seriously: mass, circumference, angle, horizontal exit velocity, and distance are all we need. But we need that for a variety of launches.

Oh, and, uh, launch winds would be nice, too, but... Perhaps I'll write a government grant proposal for exploring "the ballistics of trebuchet-launched pumpkins as a means of inferring operational payload ballistics of middle-ages-era weapons for civil defense and seige during nuclear winter."

No?

Seriously, Trebuchet, armed with this basic information, we could glean a wealth of pumpkin-chunkin' knowledge and refine out ballistics tables and computational algorithms to match The Great Pumpkin!

More seriously, Treb, I already have the trebuchet calculations which consider armateur mass, mass distribution, dimensions, payload, and sling length. Given that and the ballistics, I can easily optimize a pumpkin-chunkin machine!

For considerably less than $15,000...

ETA: With a little ingenuity and the application of techniques used for

- Mugs

Your laundry was spinning 3600rpm? That's fairly impressive - I would have guessed slower than that.

I definitely agree that most pumpkins would be destroyed at several thousand rpm. It could be an impressive demise to watch though.

I really don't see how you're getting this value. Using your value in your example post of a Cl of ~0.25, v=44.7m/s, r=0.15m, here's what I get:

Reference area=pi*r^2=0.0707 m^2
Dynamic pressure=1/2*rho*v^2=1.224 kPa
Lift=q*A*Cl=1224*0.0707*0.25=21.6 newtons (~2.2 kgf)

As I've said above, I'm almost convinced that your numbers are all a factor of 9.8 too high (since your formulas should be outputting in newtons, not kgf)

This doesn't agree at all with my code - as I said, I believe you are overestimating aerodynamic forces by a factor of 9.8.

This is good information - I'm glad to have separate confirmation of the guesses I had before on spin rate.

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The motor's synched to 60 hz. Says so on it's side, and in spin cycle, timed with an ignition timing strobe hooked into 60 hz city power supply, ka-ching! it's a 3,600 rpm.

Yes! More! Spin 'em more!

Ah-ha, I understanding.

All units are kg; m; and s. Please standardize your units to SI.

Please check your unit math.

Hmm, no cursor in the typing window. That makes it "interesting".
Competition pumpkin mass is 8-10 pounds. Unfortunately that's about all I can really tell you. They are all over the place with regards to proportions. Most are relatively squatty. Hurlers tend to place those on their base in the sling prior to launch so they would be tumbling in flight and probably get no Magnus effect anyhow. The last year I threw large ones I started selecting tall ones and laying them on their sides, which would be the way to do it to get the right kind of spin. But I had a very underpowered machine that year. I'd guess they tend to be about 10" diameter and perhaps 8" tall for the squatty ones.

As for the rest, launch angles etc are all over the place. I don't know of any good video from the side, most tend to be taken by folks in the pits looking from behind. Being in the pits also makes it hard to tell launch angles by eye.

By the way, controlling launch angle is something I have found very difficult. It's dependent on just about every parameter of the system, including pumpkin mass. Either having the sling too long or too short can cause a high trajectory, which has been my problem most of the time.

Wind is another issue. At Snohomish this year, the wind at ground level wasn't too bad. At the elevations Barbaric was reaching, above the nearby treeline, it was a different story!

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In that case, you need to check your units - your force is in newtons. The newton is the base SI unit of force (since a newton is 1 kg*m/s^2).

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Gents, although I haven't been very active on here, I have been following your postings, as they are of great interest to me.

I wish I could follow the equations better but perhaps I can lend a little insight that may clear up a couple of things a bit.

I noted one comment concerning Sling angular rate, as it applied to Payload spin.
Although in very rare cases, the rotation direction of the Sling is the same as the Payload spin direction, in almost all cases, they are opposite. Payloads tend to have back-spin (top towards the origin of launch.) As I think I said before, the 'forward' spin applied by the Sling rotation does have an effect on the Payload rotation, but only in the sense that it will slow it down a bit, not add to it or even be the primary method of rotation impartment.

There is much debate, in the hurling community, about how much spin there is and exactly what causes it. I have my own opinions but no imperical data to support them. I do believe though that the friction between the Pouch and the Payload accounts for majority of the impetus. This may seem silly, given the very short period of time allowed for this action to take place in, namely that time between when the Sling releases and the friction between the two drops to a point too low to be of use. However, I attempt to account for this by the fact that there is a very large loading factor taking place at that point. So the next question is:

How many G's does a Payload endure at maximum?

As friction is proportional to the force, even if the time period is short, that could be enough to account for the back spin rate. Also consider the speed at which the Payload must travel, in relation to the Pouch, as it is exiting. Friction/Time/Force....in the right proportions, shouldn't that do the trick?

There are indeed very few vid's of Payloads (pumkin' or otherwise) that give a good record of spin rate. I'll try to put out 'the word' though and see if anybody as something in their files. We have some real nut cases...er...devoted people in this hobby.

Pumpkin sizes: Ouch. They vary a lot. Never mind the differences between species, the differences between what each person will choose, as a good candidate, will also vary greatly. Some want round and smooth, some want more ridges, some less, some want squate, some want density, etc. Depending on what they select, they may opt for setting it in the pouch on end or on its side. As many variables as you can think of, somebody is doing it.

I don't believe it is possible to get 'good' numbers for Pumpkins, in terms of aerodynamics, by educated guessing or modifying tables until the results look good. There are too many unkown variables. One could get 'good' results but for the wrong reasons.

So, how do I get good numbers? Build a wind tunnel and start tossing gourds into it?

Gents, although I haven't been very active on here, I have been following your postings, as they are of great interest to me.

I wish I could follow the equations better but perhaps I can lend a little insight that may clear up a couple of things a bit.

I noted one comment concerning Sling angular rate, as it applied to Payload spin.
Although in very rare cases, the rotation direction of the Sling is the same as the Payload spin direction, in almost all cases, they are opposite. Payloads tend to have back-spin (top towards the origin of launch.) As I think I said before, the 'forward' spin applied by the Sling rotation does have an effect on the Payload rotation, but only in the sense that it will slow it down a bit, not add to it or even be the primary method of rotation impartment.

There is much debate, in the hurling community, about how much spin there is and exactly what causes it. I have my own opinions but no imperical data to support them. I do believe though that the friction between the Pouch and the Payload accounts for majority of the impetus. This may seem silly, given the very short period of time allowed for this action to take place in, namely that time between when the Sling releases and the friction between the two drops to a point too low to be of use. However, I attempt to account for this by the fact that there is a very large loading factor taking place at that point. So the next question is:

How many G's does a Payload endure at maximum?

As friction is proportional to the force, even if the time period is short, that could be enough to account for the back spin rate. Also consider the speed at which the Payload must travel, in relation to the Pouch, as it is exiting. Friction/Time/Force....in the right proportions, shouldn't that do the trick?

There are indeed very few vid's of Payloads (pumkin' or otherwise) that give a good record of spin rate. I'll try to put out 'the word' though and see if anybody as something in their files. We have some real nut cases...er...devoted people in this hobby.

Pumpkin sizes: Ouch. They vary a lot. Never mind the differences between species, the differences between what each person will choose, as a good candidate, will also vary greatly. Some want round and smooth, some want more ridges, some less, some want squate, some want density, etc. Depending on what they select, they may opt for setting it in the pouch on end or on its side. As many variables as you can think of, somebody is doing it.

I don't believe it is possible to get 'good' numbers for Pumpkins, in terms of aerodynamics, by educated guessing or modifying tables until the results look good. There are too many unkown variables. One could get 'good' results but for the wrong reasons.

So, how do I get good numbers? Build a wind tunnel and start tossing gourds into it?

Funny that the record breaker is an old-school design, every part easily recognizable by a medieval siege engineer, instead of the floating arm or similar modern designs.

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TreBarbaric is also an old-school design. Although both Yankee Siege and Barbaric have one major modification -- they are able to roll back and forth on the throw. That upped Barbaric's best from 1300 feet to 1700 when they implemented it. Although many old depictions of medieval catapults show wheels, I doubt if the ground conditions allowed them to move much on the throw.

The other thing they both have in common is shear size! I think YS uses more than 10,000 lb of counterweight. Your medieval siege engineer would be scratching his head at using that to throw a small payload a long distance instead of a large one from just out of bowshot.

By the way, the record Barbaric broke was held (for just a couple of weeks) by a machine from Belgium which is a modern design.

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Howdy. I'm new here; basically the only reason I'm posting is that I feel a need to clarify something that Shaka wrote in his little screed. I'm the builder of the machine that threw 24 degrees, or whatever it was. A video was posted to You Tube. That was the third throw ever from that treb in an experimental mode, a throwing arm that was "cranked" at the fulcrum. No claim was made that it was either 45 degrees or that the throw was at anything like an optimal angle. The verbal info with the video clearly stated that it was an experimental setup and that much tuning needed to be done.

The fact that Shaka continues in this misrepresentation gives a good idea of his "scientific" methodology.

Thanks for your time in reading this.

BTW, the reason for the cranked arm was to raise the counterweight somewhat more than normal to increase the gravitational potential energy in the system. Unfortunately I wasn't able to transfer the extra energy to the missile (a tee-ball), so performance wasn't improved. It was almost exactly the same as with a straight arm, which is a lot easier to make.

That was my guess, but it's good to have some confirmation from someone who knows a bit more about long distance gourd-chucking than me.

That is a good question, and one which my program can't really answer. I would guess that the number is quite high though - if you look at how quickly the sling is swinging around a fairly large radius, I would have to imagine that the G-force is quite significant.

It should, but there would be a tremendous amount of handwaving involved in getting any of those numbers, and I'm not sure I would trust the results. The best result would be something like high speed video of a pumpkin leaving the pouch, which (unfortunately) seems nowhere to be found.

That would be excellent - to get an actual spin rate would allow the other parameters to be pinned down to much better accuracy.

Well, a wind tunnel would be ideal, but I honestly don't think that the numbers for a sphere with fully turbulent flow are going to be that far off. I have access to a wind tunnel here at the University of Colorado - I wonder if they'd let me throw a pumpkin into it...

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My guess would be that the main reason for this is that the floating arm or similar designs put significantly more strain on certain parts, and because of structural concerns, nobody has upscaled a floating arm design to the same size as the truly large traditional trebuchets mentioned above (YS, TreBarbaric). It would certainly be a significant challenge.

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Compared to the rest of your parabola, the right side is too flat.

It's not right.

Rough wag of the extreme end? 0 to 200 mph in half a second: 179 m/s/s, which is 18 g's. Most hurled gourds probably see 10 g's.

The problem with "back spin" is that the pouch is spinning forward. During release, however, if the forward line is the one that's released, the pumpkin will roll out of the pouch in a way that develops backspin, even if it initially had forwardsping due to the rotating pouch.

Yes, as mentioned.

I strongly disagree! By constraining the pumpkins to be relatively round, the only variables of consequence would average circumference, density, and ridge depth. Armed with those three, and a lot of launches recorded by a side-lookng video camera with calibrated launch angle, max altitude, and distance overlays, ballistics tables would be a snap to produce.

That's a big wind tunnel!

First, you'll want a flat, open field with a lot of trebuchets launching a lot of pumpkins.

Then you'll need to select only relatively round pumkins, and find:

1. Average circumference (use a tape measure and measure around all three axes).

2. Weight

3. Ridge depth - use a ruler while you have the tape measurer, and simply measure the distance from your average crease to the tape.

Next you'll need to accurately determine the following, preferably using a video camera stationed a consider distance away, while shooting through a clear overlay on which calibrated angle and altitude information has been inked. Water ski jumpers use one to determin altitude and distance - just what you need for pumpkins, so head to your local water ski store and ask around.

4. Launch angle

5. Max elevation

Finally, you'll need an intrepid spotter downrange to report how far the pumpkin travelled, so:

6. Distance.

It would be helpful, though not absolutely necessary, to also have exit velocity. A simple hand-held radar gun stationed about 100 yds away might suffice to provide the x-component of the launch velocity. Since we know the launch angle, we can calculate the exit velocity.

So:

7. Launch velocity

Throw those measurements into a spreadsheet and send it to me, and I'll run the ballastics.

Trust me, it is. Take a look at the image in which I included a dragless trajectory if you want more proof.

I've checked it many times, in several different ways, and I'm basically 100% convinced that my code is correct.

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PUNKIN CHUNKIN premieres Thursday, November 26 at 8 p.m. e/t on Science Channel

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