A trebuchet is a type of catapult that converts the potential energy of a counterweight into the kinetic energy of a projectile. The simplest version operates like a see-saw, with the counterweight suspended from a hanger attached to the short arm and the projectile held in a sling attached to the throwing arm. When the short arm is raised and then released, the throwing arm rotates faster because it is longer and the sling rotates even faster as it whips around the end of the throwing arm.

At their inception during the Middle Ages, trebuchets were used to hurl boulders at or over castle walls in an attempt, usually successful, to batter them down. Modern trebuchet designers, lacking castles to besiege and fair maidens to rescue, must content themselves with hurling cooking pumpkins for distance. Competition, however, is fierce, and the winner of the contest can expect any fair maidens present at the pumpkin festival to hurl themselves at him. Thus, it behooves us to put as much study into the ballistics of pumpkins as old-time mathematicians put into the study of cannonballs.

Visit The Ballistic Coefficient of Pumpkins to read the rest of my paper.

Ron Toms, the owner of the Catapult Message Board, dares me to go talk to an engineering or physics professor regarding that nonsense I've been peddling about 45° being the optimal launch angle.

Very well. I will take that dare. Are there any engineering or physics professors on this forum who would like to comment on the accuracy of my paper?

I imagine our local trebuchet expert...who goes by the user name, Trebuchet...will be along before too long. Now, switching to my moderator hat...

Welcome to the BAUT forums, Shaka. Things work a little differently here than at many forums so please take a little time to read up on our rules, linked in my signature line below.

Again, welcome to BAUT.

Edit to add: By the way, if you wondered why your post did not appear immediately, we have use a holding queue as a spam control measure. Posts by new members that contain certain keywords, links, or images are held for moderator approval. Once you have a few more posts under your belt, this will no longer hinder your posting.

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A guy at the Political Forum called MannieG (apparently something else on this forum) told me to come here and ask Trebuchet my question.

I look forward to meeting him.

Hi Shaka. I'm BobP at the CatMess and I'm no great expert by their standards. I've not yet read your paper but would tend to agree with Ron that 45 degrees is only optimal in a vacuum. In other conditions, other angles will likely be better. And it'll vary with the projectile. Tennis balls tend to lose all their momentum and fall vertically out of the sky.

One rule I've learned to live by when doing exhibition type hurling where distance is not the primary objective is that spectators LOVE the high ones. So I tend to lean in that direction.

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One can drastically improve the ballistics of a pumkin by filling it with lead shot embedded in an epoxy matrix...

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If I set the budget, we'd have Ares and more. Unfortunately, I don't set the budget, and Ares is just too expensive and too far out for us to accomplish our goals within the budget we were given.

If we halt the ISS, all versions of Ares, and transport Orion and Altair aboard DIRECTv3's Jupiter family of Shuttle-Derived Launch Vehicles, we just might make it back to the Moon by 2020.

Mugs. Love it. Then you might as well use pellets of depleted uranium .

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A second rate theory explains after the fact.
A first rate theory predicts.
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Now we're talking!

Of course, that might violate a few local, state, and international laws...

Just trying to think outside the trebuchet...

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If I set the budget, we'd have Ares and more. Unfortunately, I don't set the budget, and Ares is just too expensive and too far out for us to accomplish our goals within the budget we were given.

If we halt the ISS, all versions of Ares, and transport Orion and Altair aboard DIRECTv3's Jupiter family of Shuttle-Derived Launch Vehicles, we just might make it back to the Moon by 2020.

Ok, Shaka, I have now read the paper as well as the associated thread on the Catapults Message Board. Link

I'm not a physics professor, nor do I play one on TV. I do have about 10 years designing and building catapults. I can confirm, that contrary to what you believe, hurled objects definitely DO spin coming out of the pouch. Essentially they roll out just as a baseball rolls off the pitcher's fingertips. If a pumpkin is launched from a position sitting on its base you'll see it tumbling in flight. During my last event using large pumpkins I was intentionally selecting those that were taller than their diameter and launching them on their sides, to avoid the tumbling.

A couple of further comments and questions:
1. Have you ever seen an actual trebuchet launch? Other than just on video? If not, I encourage you to try to find one in your neighborhood. Or build your own. A small (1m throwing arm) treb can be built in only a few hours. Throw some tennis balls, and see what they do. If you are on the US East Coast, the World Championships of Punkin Chunkin are in two weeks.
2. You seem to think that 200m sounds like an outlandish distance for a pumpkin. I've thrown them close to that myself, and seen throws of well over 500m.
3. I can't say one way or another on the 45 degree launch angle other than that if I recall correctly, my high school physics teacher said that in an atmosphere, the actual optimum angle is lower. I can tell you that controlling the angle on a real world treb is quite difficult. I tend to have more difficulty throwing too high than too low.

Since I'm sort of "contaminated" by real world experience and exposure to other hurlers, is there anyone on the board who can contribute to the 45 degree question?

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Well, I just wrote a brief matlab script to see if I could get some actual data, accounting for everything except the spin of the pumpkin (I may try to account for that later if I'm feeling ambitious), and here's the result I get:

For an 0.2m pumpkin launched at 60m/s from a release height of 2m, with a density of 0.8 g/cc and a drag coefficient of 0.25, the optimum angle is 42.6 degrees. If I neglect that initial release height, and assume it is launched from the ground, the optimum angle is still <45 degrees (specifically, it is 42.9 degrees).

I can post the code if anyone wants me to.

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I actually would not mind seeing that code, if you don't mind.

For the punkin chunkin veterans, is altering the density of pumpkins as Shaka suggests allowed in most range competitions? It seems like something like that could get out of hand...

Shaka, I have never seen a pumpkin launch in real life but I would expect that a curved flight path would be easily distinguished from an off target shot, since a straight-flying, off target shot would still fly in a plane and not "slice". Since I can make a volleyball or ping pong ball curve visibly in flight at very low velocities, it seems likely that a pumpkin with its higher velocity offsetting its higher ballistic number would also tend to curve.

As for the distance, consider the vertical and horizontal components of the velocity. At a 45° angle the initial drag is the same for x and y but as gravity slows the pumpkin the x component drag becomes higher. Vertical drag drops to zero at the apogee and then switches direction as the pumpkin falls. At impact the vertical speed will be lower than the launch speed, but the horizontal speed will be lower still since it has been continuously decelerated throughout the flight. I suggest that within the simplifications that you suggest, the ideal launch angle will be one in which the angle below 45° at launch is equal the angle above 45° at impact (though I need to remind myself of the math before I can back that up quantitatively).

Here you go - it's a pretty basic code for projectile motion - it should be accurate to around 0.1 degrees in this form (for more accuracy, increase the size of the alpha array when it is defined - it will slow the calculation significantly though):


%% Pumpkin throwing calculation

%This program calculates the distance and ideal angle for a pumpkin of some
%size and density thrown at a user-inputted velocity. A coefficient of drag
%of 0.25 is assumed. Lift based on the spin speed of the pumpkin is not
%accounted for.

clear all
close all
clc


%% User inputs
v=input('What is the release velocity of the pumpkin (m/s)?');
h0=input('How high off the ground is the pumpkin at release (m)?');
d=input('What is the diameter of the pumpkin (m)?');
rho=input('What is the density of the pumpkin (g/cm^3)?');

%% Initial values
% Setting up an array of angles
alpha=linspace(0,pi/2,1000); %rad


%Calculating needed values
mass=4/3*pi*(d/2)^3*rho*1000; %kg
Area=pi*(d/2)^2; %m^2

%Setting constants
rho_air=1.225; %kg/m^3
DeltaT=0.005; %Calculation timestep
n=1;
Cd=0.25;

%Initializing arrays
x=zeros(1,length(alpha));
y=zeros(1,length(alpha));
y(1,:)=h0;
vx(1,:)=v*cos(alpha);
vy(1,:)=v*sin(alpha);


%% Calculating trajectories
while(max(y(n,:)>-.1))
n=n+1;
x(n,:)=x(n-1,:)+vx(n-1,:)*DeltaT;
y(n,:)=y(n-1,:)+vy(n-1,:)*DeltaT;
xDrag=vx(n-1,:).^2*rho_air/2*Cd*Area.*sign(vx(n-1,:));
yDrag=vy(n-1,:).^2*rho_air/2*Cd*Area.*sign(vy(n-1,:));
xaccel=-xDrag/mass;
yaccel=-yDrag/mass-9.81;
vx(n,:)=vx(n-1,:)+xaccel*DeltaT;
vy(n,:)=vy(n-1,:)+yaccel*DeltaT;
end

%Eliminating data points that are underground
x(y<0)=NaN;
y(y<0)=NaN;

%Finding optimum angle
range=max(x);
alpha_optimum=alpha(range==max(range));

Optimum_Angle=alpha_optimum*180/pi %#ok<NOPTS>


(Sorry for putting it in like this, but it seems that .m or .zip files are not allowed as attachments)

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Meh, cut and paste works. Thanks!

Oh, and if you want it to output the range achieved for that optimum angle, just look for the max value in the "range" vector. You can also directly plot range vs alpha, since the range and alpha vectors should directly correspond and be of identical length.

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Nice cut, cjl. Glad they're teaching you straight up there! By the way, the pumpkins spin top over bottom leaving the trebuchet, which imparts a downward force tangent to it's velocity vector, resulting in an higher angle higher than 45 deg in order to achieve maximum distance - if there were no atmospheric drag.

However, atmospheric drag, as you noted, would indeed result in an angle less than 45 deg in order to achieve maximum distance.

Thus, three conclusions:

1. The optimum angle, under precisely one set of conditions, would result in 45 deg, but under all other conditions would result an angle that's either higher or lower than 45 deg.

2. The second consclusion is a question: At pumpkin velocities, with their surfaces shaped as they are, and varying trebuchets, it's impossible to obtain realistic ballistic data as, at the very least, the test load is destroyed each and every launch, and no two test loads are the same.

3. The more powerful the trebuchet, the more drag would be the overriding factor, and the more likely you'd need a lower depression angle.

Shaka, your paper:

Nope. The forward velocity of morter projectiles decreases with time, thus, it carves an ever-shortening parabola. If you assumed a perfect parabola, you'd undershoot the target.

For the purposes of a pumpkin-hurling trebuchet, I'll give you all three. For the purposes of an Iowa-class battleship's 16"/50 caliber Mark 7 gun hurling ton+ shells 20+ miles downrange, all three factors were incorporated into the Ford Instrument Company Mark 8 Range Keeper analog computer.

If they hadn't, she'd have missed her targets by a mile, even on the calmest of days.

Granted.

You make two false assumptions, here.

The first is that the coarseness of the pumpkin's surface results in greater drag, which I would counter by asking you why a dimpled golf ball flies a good deal further than a perfectly smooth one of the same diameter, mass, and radius of gyration.

The second is that an oblong shape would be less aerodynamic than a round one. This is a little more complicated than the first, except that the following is true: If it's flying broadside, it will experience considerably more drag. If it's flying oblong, it will experience considerably less drag.

As well as the following corollary: A trebuchet-hurtled pumpkin doesn't have enough time to tumble into a broadside approach, as it would if it were dropped from a signifcant height (say, a mile).

Really? That's interesting, as it's a critical factor in the question as to which factor overrides the other: spin or drag?

A more accurate test would have been to compare the weight of the pumpkin with it's displacement upon being fully submerged.

So use a small keyhole saw, drilling two holes, and glue the drilled cores back in place with 5 min epoxy. No syringes required.

Only in a vacuum.

Just wanted to insert that you make a lot of assumptions and "fudging," which so far, has rendered whatever tests you may have done null and void.

However, we'll continue on the conceptual front, rather than the mathematical or testing ones:

The effects of a pumpkin's larger Reynold's number (size and mass).

Mach drag rise effects are noticeable at much lower velocities. It's just that they're negiligible.

Ok, you've convinced me that for pumpkins we can discard mach drag rise effects.

This is simple density - given equal masses and geometries, the more dense object will fly further.

For the competition tosses, possibly, but the shorter the toss, the less effect drag has.

I think most people have said the perfect angle is somewhat less than 45 deg. I dare say most trebuchettes conduct field trials, adjusting the lengths of the sling in order to achieve the best release angle for the greatest distance. An optimized trebuchet will use consistantly-massed projectiles with counterweights tuned to the load and the release angle, resulting in the trebuchet stopping dead, thereby imparting the greatest energy to the hurled projectile.

For good reason - that's where their trial and error, if not their calculations, have determined results in the greatest distance.

You mentioned a 30% reduction in distance due to air friction. If that occurs at 45 deg, what do you think would result in greater distance? Increasing the elevation, or decreasing it? If you think both would result in a reduction in distance, you're failing to properly consider/calculate how air friction changes the parabola into something that's very much not a parabola.

Excellent! They're on target!

The real world is very different from simple mathematics, i.e. Trig. Real-world mathematics governing the ballistics of pumpkin-hurling is one of four governing the firing of bullets and shells, and this is called external ballistics.

In fact, while the mathematics are quite complex, and produce very close approximations, they're not good enough for bullseyes, so even today, with the best supercomputers in the world, we generate ballistics tables much the same way as they did in WWII: test firings (aka empiracal measurement).

No. Ron Toms is dead on accurate because he understands (intuitively or mathematically) ballistics. He is absolutely dead on accurate about the horizonatal drag component being the factor which shortens the parabolic arc, and how reducing the angle gives the projectile significantly greater horizontal velocity, and thus greater distance during a slightly reduced hang time.

I highlighted the reality of the situation for you.

False. See highlighted bit, above.

False. See highlighted bit, above.

Continued...

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If I set the budget, we'd have Ares and more. Unfortunately, I don't set the budget, and Ares is just too expensive and too far out for us to accomplish our goals within the budget we were given.

If we halt the ISS, all versions of Ares, and transport Orion and Altair aboard DIRECTv3's Jupiter family of Shuttle-Derived Launch Vehicles, we just might make it back to the Moon by 2020.

True, and for a tailwind you'd adjust the elevation upwards, slightly.

False, as there are two components to wind, the horizontal component, and the vertical component. Since wind moving along the ground moves horizontally, there is little, if any vertical component. Nevertheless, it's the apparent wind, i.e. the "created wind" they're referring to that has two effects, even on a windless day:

1. In the vertical plane, it both reduces apogee and increases drop time.

2. In the horizontal plane, it creates a drag on the pumpkin that's proportion to the square of the horizontal component of it's velocity.

First, you're missing the factors mentioned above. Second, you need to "fire" it at multiple angles, say, every five degrees, but with the proper drag and velocity profiles, in order to obtain an accurate answer.

Your velocity profiles are out to lunch.

Attend a trebuchet event and you'll see plenty of evidence.

Golf balls struck with fairly smooth-faced No. 2 wedges with very slight angles spin rather fiercely, too, I'm afraid. The wedge primarily affects the golf ball's angle, and much less, it's spin. The main effect of spin on a high lob is to cause the ball to "sit" (stop it's forward momentum) when it lands on the green. For drivers, the backspin is serious, and causes upward lift, which gives the ball some seriously extended range.

Following this line of reasoning, I suppose the smooth surface of an airplane's wing fails to have any effect on lift!

You should to a little research before you dismiss the Magnus effect.

Clearly a UFO-like report. Even baseballs, if hit just perfectly, will have a very slight arc to them. No thrown baseball has ever been observed to have a negative (up-turning) arc.

Beach balls and ping pong balls, on the other hand, because of their high surface area to mass ratios, curve upwards all the time when hit/thrown with a backspin.

I think if you could achieve 400 kts combined with a back spin fast enough to rip the pumpkin apart, then, yes, it could certainly achieve positive lift! Unfortunately, no pumpkin on this planet will achieve those forces and lift to tell the tale.

Of course they spin. And of course that spin has an effect on it's ballistics.

Daish is correct.

You are correct on this point. If you're thinking the spin has no effect on a pumpkin's ballistics, however, you'd be incorrect.

Not before correcting your equations and using empiracal evidence to feed your ballistics, it won't.

When you malign the builders of these wonderous machines in this manner, do you really think they'll gather around you so you can tell them how they need to adjust their machines?

He's right - you're wrong. It's called a hook or a slice, and the same Magnus effect that causes a golf ball to hook or slice when it's not struck head-on, thereby developing a left or right spin, identically causes pumpkins to hook or slice.

Frankly, I trust his treb better than your faulty calculations.

They adjust the sling length, which adjusts the release angle. The correct sling length is a function of a lot of things, most notably the mass of the counterweight and the projectile.

Again, no, it won't, as it fails to properly account for the variable drag encountered by a pumpkin throughout flight.

You're wrong on both accounts, as noted above.

See here if you're interesting in correcting your errors.

For those of you interested in a REAL ballistics program, written in Excel, which can be adapted for pumpkin hurling, see here.

It's the Pesja model, which is a highly accurate ballistics model useful for projectiles of all kinds (not just bullets), and includes factors for

Muzzle Velocity (fps)
Bullet weight (grains)
Ballistic coefficient (G1) @MSL
Max range (yards)
Impact Height (inches)
Zero Range (yards)
Wind speed (mph)
Wind direction (o'clock)
Temp (farenheit)
Altitude (feet)
Pressure at altitude
Scope height (inches)
Retardation coefficient rate

with the ballistic coefficient computed from:

Range Separation (yards)
Initial Velocity (fps)
Final Velocity (fps)

The good news is that you can obtain these measurements on the trebuchet field using a side-facing inclinometer at both launch and land, as well as a radar gun and some basic trig to convert the v(x) into v based on the angles.

Good luck, trebuchet afficionados!!!

- Mugs

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If I set the budget, we'd have Ares and more. Unfortunately, I don't set the budget, and Ares is just too expensive and too far out for us to accomplish our goals within the budget we were given.

If we halt the ISS, all versions of Ares, and transport Orion and Altair aboard DIRECTv3's Jupiter family of Shuttle-Derived Launch Vehicles, we just might make it back to the Moon by 2020.

I would actually tend to assume that as the pumpkin is leaving the sling, it would roll out, giving it a net backspin (which would cause some upward lift and further depress the optimum trajectory). I'll see if I can figure out a good approximation for the lift generated though - it's easy enough to implement into the code once I know a rough coefficient of lift, but I don't know how to find a reasonable C_L value for a rotating sphere (or roughly spherical object) at this point. I know some good people to ask though.

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Okay, I never took physics, so this will have no usable math, but I think I can see where the discrepancy is coming in. Maybe someone here with an interest could actually run the numbers on it.

When the treb fires it fires at x m/s. Lets' say 100. If this is at 45* then it will go 100 m/s at a 45* angle. The speed over the ground would be 70.7 m/s. Is that right?

At 25* the speed would be 90.6.

So, at the end of the first second, the 25* shot is already 20 meters further than the 45* one.

Then drag slows it down, and gravity pulls it down. This keeps up until gravity takes away whatever altitude was given and the arc intersects the ground.

My point is, at 45* or 25* drag will be constant per second. So will gravity. But the 25* shot will have a faster horizontal speed downrange, giving gravity less time to pull on it. The 45* shot may travel a lot further (in a high arc) before it reaches the ground, but the 25* will go further having had a greater forward velocity for most of it's flight.

Does this make sense?
Is it sound?

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Reasonably sound, yes, although that same reasoning could cause one to mistakenly conclude that a lower angle would be optimum even without drag.

Here's how I see it:

Without drag, the problem's pretty simple - you just need to find the optimum combination of time in the air and ground velocity. This works out as the maximum of 2*sin(theta)*cos(theta), which occurs at 45 degrees.

In the drag case, the problem is complicated by the fact that the projectile's horizontal velocity is changing, and the vertical velocity is changing both because of gravity and because of drag (so the vertical acceleration is not constant). The average horizontal velocity is higher than the average vertical velocity for a projectile launched at 45 degrees (since the horizontal velocity stays at its initial value for the zero drag case, while the vertical velocity shrinks from that value). This means that proportionally, drag has a larger effect on the horizontal velocity than the vertical velocity, so the horizontal velocity must be proportionally increased to maintain the maximum range condition (in other words, the trajectory must be depressed below 45 degrees).

Does this make sense at all?

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Cool.

Without drag the only thing acting on it would be gravity, in which case keeping it aloft would be more important than average speed. I'd still lean towards 45 as a gut feeling on that. Maybe even a little higher, even though I know better.

Edit: And yes. I think that makes sense, at least to me.

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Thanks guys! Great discussion.

In response to a question several posts up the line, altering pumpkins (other than de-stemming) is strictly forbidden by all hurling competitions. As noted, it would quickly get out of hand. The serious hurlers grow their own, and favor a white variety which is thicker shelled, and thus denser, than common jack-o-lantern varieties.

I have seen pumpkins slice or hook when thrown from a very powerful machine, in fact just a couple of weeks ago. Pumpkins being tossed by the very large machine in Snohomish were consistently slicing to the right, into a corn field where they couldn't be found. This may be due to the sling twisting so that the pouch imparts a sideways spin instead of just over the top. And thinking about it, I believe CJL is correct in saying that you get backspin rather than topspin. I'm not altogether sure however.

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Yikes! Not me - but I love your topic & thread title here! :-D

Are there any experiments there comparing normal pumpkins versus Jack-O'-Lanterns carved up for Halloween? 'Coz now would seem to be around the time to test that .. ;-)

PS. May I suggest this is an ideal topic for just trial & error type experimenting? ;-)

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YIKES!!!! :-O

& I'd like to see you try & obtain the aforementioned pellets of depleted uranium for this purpose! That'd make for an .. uh .. interesting Utube video. LOL!

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I just spent a couple of minutes looking at old Burlington videos to see if I could tell which way the pumpkins spin. Looked like topspin (top going forward) but it's pretty hard to tell. I think I've got one at home which shows one tumbling, I should be able to tell from that.

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My wild guess is that it would be topspin. During the upward swing, the sling would be gripping the pumpkin rather tightly, imparting a topspin.

As the sling releases the pumpkin, it would try to pull the pumpkin into a backspin. My guess is that at this point the webbing is slack and lacks sufficient grip to have much effect. However, this assumes a relatively smooth pumpkin and that nothing like the stem or some big bump "catches" on part of the webbing.

Hi Mugs, et al,

Ron Toms here. I heard my name mentioned, so thought I'd drop by and see what trouble I'm in.

I've seen pumpkins rise in flight. As have many others. They're hollow, the white ones are very strong, and the ridges get good grip on the air. And there's wicked spin on some of these machines too. There have been reports of "pie in the sky" launches from time to time. But that's usually with the air cannons firing them at near the speed of sound, for 4000'+ (4K feet, plus!) shots.

Regarding the spin, here's some empirical evidence some of you might enjoy playing with -
http://www.trebuchet.com/skeet
I'm sorry the photos aren't numbered, but the 10th and 11th photos are 1/6th of a second apart. In photo 10, the bag of flour is about 10 to 15 inches off the ground (about a foot), then 1/6th of a second later, it has moved in a half circle to a height of about 15 feet.

This was a pretty slow machine by today's standards. It's more than 15 years old now. But regarding spin - that's a tunable thing. The two ends of the sling are not attached at the same point. The farther apart the attachment points are, the more the projectile will roll in the pouch as the sling spins around the end of the arm. You'll need a long pouch to get the full effect. But the point is - you might be surprised how much backspin there is on the projectile when the pouch releases it.

And it's always backspin. Never topspin.

Unless, of course, it's a sidespin or even a spiral. Here's a video - http://www.youtube.com/watch?v=6sMIO15gCQI

But never topspin. Nope. really...
ok, ok,ok. When hurling pianos using throw-away slings, you can get topspin. Here- http://www.youtube.com/watch?v=hZxCEkGk6HI

So yeah, weird stuff happens with these things sometimes. My favorite (and unfortunately I don't have a video clip of it), was the T-Wrecks trebuchet hurling another piano. The piano disintegrated during launch, and the soundboard flew out of the sling like a frisbee and flew/sailed about 800 feet downrange, and a little off to one side.

Theory is great, but experience can be a real eye-opener too!

Have fun,
--Ron

OK, so based on the information that there is a significant backspin, I tried adding a lift term to the code. I haven't got a clue what a reasonable value for the coefficient of lift of a rotating pumpkin is, but it does make a significant difference.

For a lift coefficient of 0.5 (a rather extreme case, giving the pumpkin a l:d ratio of 2:1), the optimum launch angle drops all the way down to 20.8 degrees for an otherwise identical simulation to the one performed above, with a range of 383 meters (in the zero lift sim, the optimum range was 278 meters at 42.6 degrees). The trajectory is noticeably flattened at first, and is nowhere even remotely near a parabola. I've attached an image of the ideal trajectory in this lift simulation - the graph is simply range vs altitude, with both axes in meters.

Admittedly, this is not likely to be a realistic lift value, but it does show how sensitive the optimum angle is to lift coefficient.

Ron - you wouldn't happen to know the pumpkin size and weight, flight time, range, and either launch velocity or launch angle for a representative shot, would you? I'd love to have more accurate values for my basic program...

Attached Images

Pumpkin trajectory.png (6.5 KB, 12 views)

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Hi Ron, nice to see you here, since your name was being taken in vain, as it were. Glad you cleared up the topspin/backspin question -- you'd think with all the launches I've seen I would be able remember but I didn't. Looks like several other CatMess regulars have visited as well.

BobP

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I wonder if the OP is coming back...

Not looking like it. He hasn't been back to the catapults board, either. I'd have liked to think maybe he'd learn something. We'll see.

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For the last two hours, I broke out my aero engineering texts, and you're in for a treat:

Given:

12" pumpkin (.1524 m radius)
specific density = 1.0
p 1.2 kg/m^3 density of the fluid
w 221 RPM angular velocity
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 0.225347651 lift coefficient

Spin Ratio = ( w * D ) / ( 2 * linear velocity) 0.75347651

Drag coefficients
sphere 0.47
half-sphere 0.42
cone 0.5
Angled cube 0.8
rough sphere 0.4

Fd = Cd * 1/2 * p * v^2 * A

Where
Fd 38.05181357 kg
p 1.2 kg/m^3
v 44.7 m/s
A 0.072965877 m^2
Cd 0.435

Conclusions:

A 12" pumpkin has a mass of 14.8 kg. If hurled at 100 mph (44.704 m/s) would require a backspin of 221 RPM (3.68 revolutions per second) in order for the force created by the Magnus effect to equal its weight.

That force, precisely, would be 14.853 kg.

Now, that's the calculation. In reality the greatest variable is the pumpkin's lift coefficient.

Regardless, if hurled fast enough, and with enough backspin, the smaller pumpkins could indeed curve up! But just barely...

So Hurler aka Ron Toms was right! My earlier wag was incorrect.

You'll also notice that the drag on a 100 mph, 12" pumpkin is 38 kg, a little more than twice it's weight, so it's decelerating pretty quickly. However, that seems high, as the Cd of a human in freefall position is more than 1.0, and terminal velocity (where Fd=weight) isn't reached until about 120 mph...

So I'm rusty at crunching aero numbers. If someone wants to check my math on these basic calculations, have at it.

- Mugs

__________________
If I set the budget, we'd have Ares and more. Unfortunately, I don't set the budget, and Ares is just too expensive and too far out for us to accomplish our goals within the budget we were given.

If we halt the ISS, all versions of Ares, and transport Orion and Altair aboard DIRECTv3's Jupiter family of Shuttle-Derived Launch Vehicles, we just might make it back to the Moon by 2020.