Trebuchet Calculator Program
I found some good web pages with highly detailed answers to predicting the range of a trebuchet. A very simple model we have used in my Intro to Eng class just uses the mass of the projectile (m2), the mass of the counter weight (m1), and the height the counter weight falls (h): Range (max) = 2. (m1/m2). h Now the efficiency of the trebuchet will cause this model to be off by quite a bit.
But once you have a working trebuchet, we find this model works well when we vary m1, m2, or h. We assume we have a take off angle of 45 degrees above the horizon. This solution is based on the classic max range ballistics problem - 45 degree take off angle. It also assumes converting all the potential energy of the counter weight to kinetic energy of the projectile.
That is why the efficiency issue comes up as a lot of energy is lost due to friction in the moving trebuchet. If the projectile spins a lot then it will travel a shorter distance as the potential energy is split into kinetic and rotational energy. Projectile shape and wind will also vary the results.
The students found this worked well enough for their lab work and it was lot of fun. Work = force x distance You (should) know the mass / weight of the counterbalance, and how far it travels during a shot. You should also know the weight / mass of the projectile, and how far it travels before release. Assuming a spherical horse in a vacuum, they can state that work out = work in, and be able to calculate the KE of the projectile.
If they also know the launch angle of the projectile, that should convert quite easily into a predicted range. When they fail to meet the predicted range, they can then work out why, which would be equally as educational as building the weapon in the first place. Well, I was just trying to point him in the right direction and I didn't say it would be easy.:).
Let's see if we can at least help him determine which variables are most important. mass of projectile.
If it's reasonably dense and semi-aerodynamic (eg, rock, bowling ball), you can probably ignore air resistance. Should be able to find a reasonable approximation of effective area and drag online, if wanted. torque of machine. This should just be a function of counter-weight mass and lever lengths. Depending on construction methods, friction may or may not be very important.
Can probably use a fudge factor of, say, 10-20% loss. lengths of rigid arm and sling. I can imagine that computing the launch velocity, with the sling attached, will be rather complicated. This is where a web search would come in handy. I don't think the rigidity of the arm(s) will have that much of an effect (unless they are very flexible). Along the same line, with a suitably strong sling, I don't think stretch will be that big of a deal.
With that data, one should be able to compute launch velocity. I'm not the one, but someone should be able to figure it out.
I have no idea how you would figure out the launch angle. Oh, I've been over-thinking this! Work = force x distance They (should) know the mass / weight of the counterbalance, and how far it travels during a shot.
They should also know the weight / mss of the projectile, and how far it travels before release. Assuming a spherical horse in a vacuum, they can state that work out = work in, and be able to calculate the KE of the projectile.
If they also know the launch angle of the projectile, that should convert quite easily into a predicted range. When they fail to meet the predicted range, they can then work out why, which would be equally as educational as building the weapon in the first place. (I'm going to re-post that as a proper answer - Pi is a physicist, he'll know the relevant equations). Sorry, but I don't think such a tool exists.
Off hand, you would need to factor in; Length of arm. Mass of arm Rigidity of arm Mass of counterweight Kind of attachement of counterweight (rigid, loose etc) Friction at pivot Angle arm turns during preparation Angle arm turns during launch Angle of hook holding ammunition Length of sling holding ammunition Angle of release hook for sling Elasticity of sling itself Mass of projectile Air resistance of projectile So you're best off just building it and seeing how far it goes, or comparing your design to the abilities of existing trebuchets of similar design. All those variables definitely play integral parts in calculations. I am embarrassed to admit, I am a physics teacher and don't have a solution.
My purpose for this is for my students to compete with their individual trebuchets and part of the contest would be to predict accurately their launch distance and accuracy in hitting a target. My only criteria for building the trebs was that they must be able to fit through the door of the classroom.
I've been working on calculations on my spare time.which isn't much of the time so I was hoping to find someone would had already done it. BTW, my students loved the straw rocket design that I lifted from an instructable!
There are a few stuck on high ceiling light fixtures that will be there forever.or until the lights come down. These 2 PDF files probably have everything you need. They have a simple formula for calculating theoretical max range that depends only on the mass of the projectile, the mass of the counterweight, and one angle. I'd keep it simple and focus on the basic physics - projectile motion, principles of work and energy, and maybe efficiency. You could also talk about the basics of mathematical modelling (formulate problem, develop model, test model, refine/simplify model.) Anyway, thanks for putting effort into this for the students.
I wish I had more teachers that did this kind of stuff when I was in High School.
Copyright (c) 2012, James Allison All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 'AS IS' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. This submission provides two main files: treb.m and plottreb.m. Treb.m predicts the projectile range of a simple trebuchet given its fulcrum position and release angle. Other parameters are held fixed (but can be adjusted by the user). Ode45 is used to simulate the dynamic system, including event detection for projectile release and landing.
Plottreb.m samples treb.m to gather range data and then plots it to visualize range as a function of fulcrum position and release angle. Treb.m is intended to be used with an optimization algorithm (e.g., fmincon - bound constraints should be used). The range plot is useful for visualizing the nonsmoothness in objective function that results from discrete elements of the system (such as limits on how high the trebuchet mass can be raised). This nonsmoothness can cause difficulty with gradient-based optimization. Choosing a good starting point that avoids this nonsmoothness helps, but it is also possible to impose the geometric limits as optimization constraints instead of satisfying them implicitly in the simulation, eliminating nonsmoothness from the objective function. A handwritten derivation of the model is also provided (TrebuchetDerivation.pdf) that includes both the trebuchet model and a projectile model using parameters appropriate for a golf ball. This model corresponds to an example video created for ME 149 (Engineering System Design Optimization), a graduate course taught in the Mechanical Engineering department at Tufts University.
Trebuchet Dimensions
The video can be viewed. Andy - I'm glad to hear that this is useful. I use an expanded trebuchet project at several levels. I teach an introductory freshman engineering class where students assemble and test their own trebuchets, but have to make several design decisions. They learn the value of model-based design by using SimMechanics models to tune their trebuchet designs. Physical trebuchet performance goes way up across the board after students use the SimMechanics models.
Trebuchet Formula For Distance
We also use the trebuchets at the UIUC Engineering Open House (a large community event focused on K-12 students), and also at local elementary schools with K, 1st, and 3rd grade students. You can see some photos of these trebuchets by going to: The SimMechanics model is available from: Student instructions are available from: At some point I hope to publish the plan for the trebuchet kits so that others can use them. The unique thing about these kits is the level of adjustability, which makes it possible for students to work through design decisions.