How to Design the Perfect Trebuchet

the trebuchet is one of the most famous siege engines of all time in designing and optimizing the powerful machine involves some tedious work to understand how to optimize the design of a trebuchet to lay siege to your neighbour's house first we need to understand exactly what designs and principles make one up a trebuchet in its most pure form involves a counterweight that falls completely along a vertical axis and a swing arm attached to the end of the swing arm is typically something like a sling to increase rotational velocity but it is an essential to trebuchet design potential energy is stored in the lever mechanism as the large counterweight is lifted high off the ground once it's dropped the potential energy stored in the counterweight is transferred through linear motion into rotational kinetic energy for the projectile it's important to note that no compound motion or mechanism is involved in the trebuchet rather it's one simple lever arm along with the counterweight once the mechanism is understood the variables controlling flight begin to appear being such a simple design the only things you can vary are the lever arm length the height the counterweight weight and where to position the fulcrum along the lever arm while the constraints may seem limiting optimizing all of these factors can produce a highly efficient machine the physics behind a trebuchet are more complicated than the mechanism might suggest by placing the fulcrum much closer to the counterweight a higher linear velocity can be achieved by the projectile it will go faster this becomes simple lever physics but you also don't want to have the fulcrum too close to the counterweight or your mechanical advantage will begin to dwindle there will also come a point where increasing the weight of the counterweight on a trebuchet will do absolutely no good other than putting strain on the trebuchet frame no matter the weight of the counterweight it's limited by its freefall velocity the sling on the end of the trebuchet releases upon an angle alpha at which point the counterweight does no more work on the projectile you can change this release angle by adjusting the angle of the holding pin at end of the lever arm the more inline with the lever arm the holding pin is the smaller the release angle alpha is you may be beginning to see how calculating the design of a trebuchet could be a little difficult but luckily we have engineers who have widely studied the design of trebuchet zijn already determined optimized designs dr. Donald B siano is one of those engineers he published a paper in 2001 titled trebuchet mechanics detailing an intensive study into optimizing all variables in the war machines design these are some of the key facets of design he found to be true throughout his testing number one the length of the payload arm should be three point seven times longer than the counterweight arm number two the length of the sling should be the same length as the payload arm and finally number three the initial angle between the counterweight arm and the support should be 45 degrees at launch there is a whole slew of other equations and optimization techniques included in C ah nose paper including many page long derivations in differential equations depending upon your age if you want to relive your past differential equations woes or see what you might be encountering in the future I would highly recommend giving it a read to get deeper into some of the optimization physics we need to understand the ratio of payload arm to counterweight arm called the beam ratio there have been many trebuchet designs that used ratios closer to four to one or even five to one increasing the ratio increases the launch velocity of the projectile but it also means that the counterweight must be larger to provide the necessary force when you start to grasp the idea of the ratios in relation to the moment arm of the trebuchet simply put the length of the arm this might become a little easier to understand to determine what ratio you need to use you need to take into account your available material strength as well as consider the counterweight weight next we'll need to examine how heavy to make the counterweight the generally accepted ratio is 133 to 1 or the counterweight needs to be 133 times as heavy as your intended projectile if you want to determine your specific counterweight ratio the math is fairly simple it's called Persis you can read the equation states that the mass ratio of the counterweight to projectile is equal to the beam ratio times 20 using these ratios optimizing your counterweight weight and launch arm length shouldn't be too difficult to tie up a few loose ends in the design process the height of your support should be high enough to keep the counterweight freely moving throughout all of its rotation sizing of the trebuchet is going to come down to the distance you need to launch the projectile in order to size your trebuchet based on the range you want it to shoot you would need to back calculate the launch velocity of the projectile using projectile motion equations from here it would be a simple matter of plugging that launch velocity into trebuchet sizing equations and you can derive your sizing constraints from there on a final notes unless you're designing a trebuchet of great scale it's generally a good idea to build components that are adjustable out in the field everything can look good on paper but once you get out there and have your trebuchet set up you want to make sure you can hit your neighbor's house perfectly thanks for watching if you want to check out more of our content you can click here and here if you haven't subscribed yet you can do that here and if you want to make sure that we can keep producing content every week you can support us on patreon here [Music] you

Channel: Concerning Reality

Views: 151,160

Rating: 4.674118 out of 5

Keywords: Trebuchet, trebuchet design, how to design a trebuchet, catapults, design a catapult, swing arm, Potential energy, kinetic energy, trebuchet physics, siege weapon, mechanism, counterweight, Donald b. Siano, payload, launch velocity, lever physics, lever mechanics, medieval battle, projectile motion, Phsstpok's Rule, how to build a trebuchet

Id: bmSl9AqmVyc

Length: 6min 0sec (360 seconds)

Published: Tue Jun 12 2018