Spring Landing Gear Material Selection

Not sure if anyone else would find this interesting, but maybe there are some landing gear nerds out there! At some point I had a chance to do some independent research into the optimum material to use for a cantilevered spring gear on an aircraft. A lot of companies have arrived at different solutions, using various aluminum, steel, carbon fiber, or fiberglass designs. I was curious if the industry was being overly restrained in those selections, maybe there's something that hasn't been considered for whatever reason but could be measurably better? What about Kevlar or boron fibers? What about the best natural materials? What benefits could futuristic materials provide?

Just to orient people not familiar with landing gear, a cantilevered spring landing gear is among the most basic landing gear concepts and is used on a variety of small aircraft designs. An image of one such example is below:

The most important thing to know about landing gear design is that it is not just a matter of strength, but rather energy absorption. Over the stroke of the landing gear deflection, energy is absorbed per the integral of force×deflection. When trying to absorb that energy in a material, it's stored as the integral of stress×strain. Therefore, when trying to find a good material for a spring landing gear, we want to find a material with a high strength, a low modulus, and because this is an aircraft, a low density. The material-science term for this is resilience, modulus of resilience, or specific strain density. The equation for that is below:

Confusingly, despite sometimes being called specific strain density, it does not take into account the density of the material. I can't find an official term for it (maybe someone here knows) so let's just call it specific resilience.

For landing gear material selection, the obvious answer that I'm sure a lot of people would assume is the best choice is carbon fiber. It is a strong material, and has a low density, but it has a big downside, which is its high modulus. This means that the integrated stress×strain isn't necessarily very high.

Another option to consider might be spring steel, as it's designed specifically to deform and absorb energy. However, the obvious downside is density; it's too high to overcome any strain×stress advantages. It also has a high modulus, lowering the specific resilience. A lot of aircraft structures are made from aluminum, but they start yielding at a pretty low strain, preventing it from elastically absorbing a lot of energy.

So how do we objectively compare all of the materials? I created an imaginary aircraft and an analysis spreadsheet that analyzes a constant rectangular cross section, cantilevered gear for that aircraft. It determines the energy absorbed in that gear along with the max stress. I can then optimize the gear design parameters (gear length, leg width, leg thickness), and then optimize those parameters for a variety of different gear leg materials. The results were surprising in a few ways:

After optimizing the design parameters, all of these gear designs have the same energy absorption, maximum applied load, and stress margins of safety of 0, which means that they all equally meet our requirements. In the table, the leg weight is progressively increasing. I hope other people appreciate the inclusion of some oddities... One obvious thing to point out is that these results show that the strongest materials aren't always the best choice. The same is true of modulus, as there isn't an obvious trend between modulus and leg weight.

Surprisingly given this visualization, spring steel landing gear designs aren't entirely uncommon. Cessna uses them on a decent amount of their airframes, as does the Citabria. Aluminum isn't rare either with Grove making a variety of replacement aluminum landing gear legs for various aircraft. I think the primary benefit to aluminum and steel is the manufacturability, as it's relatively cheap after the tooling is completed.

After plotting leg weight against a variety of inputs and combination of inputs, I found that it does trend very well against a certain parameter...

The optimized gear leg weight trends perfectly with the inverse of specific resilience, and it shows that the optimization is working as expected. Remember that I didn't calculate those leg dimension values directly. Instead, I used Excel to optimize the design parameters until the gear weight was minimized, and the end result tracks perfectly along that curve.

Ignoring some of the quirky sci-fi materials (although a spider-silk gear leg would be highly marketable), the material that a lot of landing gear engineers end up implementing ended up the best in my analysis, which is S-2 glass. Originally developed by Owens Corning for military applications, its combination of high strength, low stiffness, and low density make it ideal for spring landing gear. It's used on a variety of small aircraft, such as the MQ-9 Reaper:

These properties also enable it to be useful as an alternative material in truck leaf springs to save a dramatic amount of weight (although not exactly a novel idea, the composite leaf springs were used in the C4 Corvette almost 40 years ago). Aircraft seats are another application where the goal isn't to necessarily just be strong but also absorb energy in the event of a crash more slowly. This can reduce the maximum shock loads applied to a passenger.

A few caveats to this conclusion! When you drop testing a landing gear, you're generally testing two primary cases, a limit energy and a reserve energy. At the limit energy, the regulations require the gear to absorb all of the energy elastically, which is to say no permanent deformation is permissible. However, plastic deformation is permissible in the reserve energy case. This means that I should be running two sets of calculations, one using yield strengths and moduli, and another allowing for ultimate stresses and strains for that reserve energy case. I don't think the order of materials would change dramatically, but it is something to consider when you're getting into the weeds of landing gear design.

I mentioned earlier that my spreadsheet assumes a constant cross section gear. In reality, you'd want to ensure that at the maximum gear deflection, the entirety of the gear leg is near the maximum strain limit. This indicates that all of the gear leg material is absorbing the maximum amount of energy possible. Below is a plot of two landing gear drop tests of two different legs, with strain sensors located at various locations on the gear legs. The test on the left clearly shows that the strains are not consistent along the gear leg, and we could be using the material in the lower part of the leg more effectively. The test on the right is my adjusted design and shows that the strains are very consistent along the leg, which indicates that the material is being used very efficiently.

Another big caveat is one of the issues with cantilevered spring gear design as a general concept! Sure, you've created a landing gear that can absorb a lot of energy, but where does that energy go? Usually right back into the aircraft. This is why the landing gear drop test data above oscillates endlessly. It's easy to accidentally bounce an aircraft with a spring landing gear design. There are ways to quantify how well materials dissipate energy into heat after they've been deformed, and that should play a factor in the material selection.

Most aircraft that want to dissipate that energy quickly without bouncing the aircraft use Oleo struts, which are pressurized systems that force oil through a port to dissipate the impact energy as heat. The obvious downsides to Oleo systems are that they are more expensive, difficult to optimize, and difficult to maintain. I'm curious if there are any examples of systems that integrate both with a simple unpressurized oil damper and a spring gear (similar to how most cars operate)? Maybe someone more knowledgeable than me has seen something like that implemented.

If anyone would like to correct me on anything I misunderstand or reported incorrectly, please do so! If this was helpful to anyone, I might do another article on my 2D FEM design method I use to optimize systems like this very quickly.

Also, this article is the materialization of my excess free time! Let me know if you know of any projects that might need another engineer to support their project. In the meantime, I'm going to get back to tinkering on side projects, which hopefully I'll be able to talk further about soon!

Contact: Byron Young, (720) 480 - 4605, [email protected]