Medieval Myth Busting with Engineering Simulation

As an avid of fan of HBO’s uber-popular medieval fantasy series Game of Thrones, I’ve often been curious about the feasibility of the weaponry we see in the show’s epic battle scenes. I took a particular interest in the massive trebuchets, a fancy name for a catapult, used in many of the show’s siege battles. This powerful catapult uses a swinging arm and counterweight to hurl projectiles over and through fortified castle walls and at battalions of oncoming soldiers. Of course, only an engineer like me would be able to suspend their disbelief for dragons and ice zombies while obsessing over the plausibility of a trebuchet But still I wondered, would the computer-generated mechanisms depicted on screen stand up to the laws of physics?

The best way to understand how the trebuchet would behave is to put it to the test. I used Altair InspireTM Motion to create a simulation model, define the design constraints and performance goals, then simulate the catapult in action. We can then transfer the motion loads onto the structure to assess the feasibility of the initial design and even optimize the geometry to create a stronger and better performing final design.

One of the advantages of working with Altair Inspire is how it lets users build concepts quickly and easily simulate multiple iterations. There’s little risk in experimenting … in fact we recommend it since this iterative approach is especially helpful for businesses to get to market quicker and mitigate risks. In my case as a geeky application engineer and super-user, Inspire is ideal in helping me satisfy my recreational curiosities by building a few virtual models and putting them to the test.

So, back to Game of Thrones… I came across this blog that addresses some feasibility issues with the trebuchets shown in the show’s siege of Meereen. Clearly, I’m not the only one thinking about these things.

Trebuchets on Screen: Game of Thrones

The author lays out a few basic issues:
1. The counterweight would be insufficient
2. There is not enough structure to support the required counterweight
3. How would you load the projectile?
4. How to would you light the projectile?

Items three and four are very obvious and don’t require analysis to prove or disprove. I wanted to look at the counterweight mass and structure. Rather than trying to recreate the structure exactly, I just wanted to know if its feasible to build a wooden structure that can handle the required counterweight and dynamic loading.
The kinematics are set up to mimic the CGI trebuchet and I ran a few studies varying counterweight mass to determine the ideal weight for this design and payload mass. From there I used motion-generated loads and topology optimization to see what kind of structure would be needed to survive the predicted loading.

I settled on a 200lbm payload mass after doing a little online research-about the mass of an ACME anvil. Since this is a fantasy trebuchet, that seems about right. After a few studies, I selected a counterweight mass. I used the 10,000lb mass given a 50 percent increase or more in loading isn’t worth the effort for an extra 50 meters of distance.

The predicted range is around 350m, which is more than a bow and arrow, and with that mass would certainly pack a punch. In the picture below, the darker block is an iron counterweight and the larger brown block is a wooden counterweight. In the Game of Thrones trebuchet, we don’t see anything that heavy.

I checked the release velocity of the projectile and ran a quick script in Altair Compose to generate a projectile motion plot.

The beauty of working with Inspire Motion is that loading is seamlessly transferred to structural analysis and optimization. I directly applied the loads to two optimization studies.

In this animated motion study, the counterweight is lifted with a 10 to 1 reduction coupler at the top. This generated vertical and lateral loads on the frame from the lifting process. Then, the counterweight is released and finally, the projectile is unleashed to wreak havoc.

Maximum Stiffness Design 50 percent mass reduction

Minimize Mass Design

After running the optimization, the optimized shape from the Minimize Mass study was wrapped in Inspire using Polynurbs.

Analysis of Minimize Mass Design Showing Factor of Safety contour for a 10000lb counterweight and 200lb projectile.

Results plot (worst case across all time step) iso plot showing factor of safety.

Is This Design Feasible?

So, after all this analysis, what have we determined? The exact trebuchet from the show isn’t feasible as shown.  It would absolutely require a larger counterweight.  However, with a little more engineering and a LOT more wood, it would be doable. Regarding lighting of the projectile, we can solve that problem in another blog post.

Crawl, Walk, Run

When creating simulation models, I recommend a crawl, walk, run approach. Start by defining the goal of the simulation and let that determine the level of detail needed in the model. You can start with a simple stick figure like I did in this study in order to get simple design feasibility results. If you need more detailed results, additional complexity can be added to the model, such as actuators, contact sets, and stress analysis driven from the motion loads.

Want to try this for yourself?

If you’re not an Inspire user already, you can sign up for a 15-day trial.

I’ve also created these tutorial videos which walk you through the initial stages of the process for setting up your own trebuchet experiment.

• Tutorial Video 1: Ground, Rigid Groups, Joints and Contacts and Results
• Tutorial Video 2: Actuators, Motors and Springs

In addition, our Altair Forums are a great place to interact with other users and our expert moderators to ask questions you can’t find answers for in the help or tutorials.

Have you ever felt like your design was overweight or unnecessarily exceeded its structural requirements? This could mean you are using excessive material which can directly affects the overall cost.

Or has your single part has been patched up with structural Band-Aids so many times due to ever-changing requirements that it has become an inefficient, overweight monster? This could mean your casting or molding is in dire need of ribs, but you don’t know where they should be placed.

Or have you often sat wondering what the right combination of gauges is for your complex assembly in order to find the optimal balance between weight and performance? Perhaps you’re starting from a clean slate? You know the space available and the structural requirements to meet but you jusr are not sure what the optimal architecture would be or even where to begin drawing?

Need a solution to circumvent these situations? Altair OptiStruct is a finite element-based tool that creates lightweight efficient designs through an iterative process.

Identifying which areas to modify in size when there are multiple, often conflicting, loading scenarios are  being considered can be overwhelming and tedious. Sometimes, whether from a faulty inception or due to multiple evolutions during its life, the structure does not follow the main load paths. This makes the design automatically, not optimal.

Using the various techniques in Altair OptiStruct, in the examples that follow, we will take a simple, clearly over-designed, tubular structure and optimize it to reduce material and cost. These concepts can be utilized on your own designs, both simple or complex.

The structure we are using is made up of standard 2“x2”x0.12” tubes welded together to support a 440-lbs mass (shown in red) from the front overhanging tube. It’s supposed to withstand g loads, including horizontal directions, with deflection requirements. It is bolted to the floor at five locations.

The current design weighs about 130lbs and easily meets the deflection requirements. Don’t you think this structure is slightly overdesigned? Let’s see what design iteration OptiStruct can perform for us.

1. Gauge Optimization

Gauge optimization will determine the lightest combination of gauges that meet the requirements of the structure. To respect the symmetry in the architecture, the tubes are grouped by different colors and the gauge of each group can vary. The base plates are excluded from the optimization as they do not contribute to the structure’s performance.

This picture shows the outcome of gauge optimization with the total mass of the structure under 33lbs. (thickness in mm, starting from 3mm in the original design)

The tubes in grey show a very low thickness which indicate they can be removed. The lower fifth support is eliminated as well as some of the redundant tubes in the upper half of the structure.

However, the results are not easily obtainable and would require special order tubes.

Taking this into account, a new analysis was conducted by limiting the gauges to a few standard values. The new results put the total weight of the structure under 48 lbs. With new constraints, the mass increase from the previous analysis is a logical outcome.

2. Shell Topology Optimization

Shell topology optimization will identify the areas of the existing tubes that can be eliminated and still meet the structural requirements.

The structure shown, weighs just under 22lbs and highlights the areas that are necessary to the design. Considering the gauge optimization already preformed, these results correlate well.

It is difficult to create this structure with tubes because some sections are incomplete in areas, but this provides valuable information to the user about the lightest design available that will still meet all the structural requirements.

3. Size and Shape Optimization

Size and shape optimization allows users to modify some parameters of the geometry to reach a more optimal design. Within the tubular structure, the cross-section of each tube can be modified in size, adjusting the overall dimensions, and shape, changing the tube to be square, rectangular, horizontal or vertical.

The picture below shows how much the sections have grown in either direction to determine the lightest structure (about 60 lbs) that meets the requirements.

In size and shape analysis, parameters can be set to force the structure to use standard sized cross-sections and varying the gauges can also be added to the analysis for a more accessible solution.  This picture shows the shape change on the left and the thickness value on the right for a final solution to the comprehensive size and shape optimization.

This type of optimization can be used for many geometric parameters other than tube cross-sections.

4. 3D Topology Optimization

Sometimes it’s possible to completely re-design the architecture of the structure and start from a clean slate. 3D topology optimization will identify the optimal load-paths from the design space available based on the loading scenarios set and the constraints placed.

For the considered structure, the design space is shown in blue. The inside of the structure was left open, just like the original design. The overhanging tube was excluded from the 3D topology optimization, as it does not affect the overall load-paths.

During the analysis, 3D topology optimization carves out the unnecessary material, only showing the main load-paths of the structure.

These results match up with the previous gauge optimization because Altair OptiStruct has removed unnecessary tubes. It also shows a unique, more optimal, design of the sides of the structure. The mass of this structure is not relevant until the material layout is interpreted into a manufacturable design.

If the design space in blue is modified to include the inside area that was left out in the previous analysis, a different material layout can be obtained.

5. 1D Topology Optimization

To speed up analysis time, the structure can sometimes be modeled with 1D beam elements.

The outcome of a 1D topology optimization shows density values indicating the necessity of a tube for the overall structure. These values can be seen on the left and while the right shows all the required beams isolated. The lower the value is, the more unnecessary the beam is.

The results of this 1D optimization are compatible to the results seen in the previous analyses. Both the overall layout design and the removal of unnecessary beams appear in each of the results thus far.

And then more…

All the above techniques illustrate some of the approaches that can be used to optimize a structure into a lightweight, efficient design that meets all structural requirements.

Gauge optimization, size and shape, and shell optimization, can be used to improve an existing design without altering its overall architecture. 3D topology optimization can be used when a significant re-design is desired because it identifies the optimal load paths of a structure and recommend material reduction. The material layout produced in the 3D topology is then interpreted into a concept design which is dimensioned and fine-tuned with the gauge, size, and shape approaches resulting in a final structure.

Do you want to learn how to execute all the techniques mentioned?  are available now for download!

Within Altair HyperMesh and Altair OptiStruct there are many other optimization techniques not covered above that can be leveraged in the design process.

Topography optimization allows you to design bead features on the surface of the design, which is a great way of tuning a localized stiffness. Multi-material optimization allows you to distribute different materials across an assembly to optimize stiffness, strength, and weight. Design exploration and optimization through Altair HyperStudy can be used to evaluate many different designs parameters and extract an optimal combination.

All techniques have potential for optimizing a design but each have a place in the design process. For example, size and shape optimization (including gauge) should not be initiated until the material layout is known and this is usually done through 3D topology optimization.

Learn more about Altair OptiStruct and download the step-by-step tutorials!