Part 2 Design & Engineering

In part 1 we looked at the overall design and discussed various concepts and background. We also calculated the maximum loads the airframe would be capable of withstanding as shown in Table 1 directly below:

In part 2 we will look at the calculations and properties of materials that will be used to guide the process of selecting materials, then designing and engineering a replacement for the existing retractable undercarriage as detailed on the plans by Brian Taylor.

Material Properties

The majority of the main undercarriage is constructed from 16, 12 and 8 gauge ASTM A228 steel and the first task is to gather the appropriate material properties in order to ascertain the required strengths for any structural element.

Table 2 contains the relevant information about the materials used in the original design.

Wheels

Figure 1 shows an outline drawing of the Mosquito that has been loaded into a CAD package and scaled to represent the 1:8 scale model with dimensions in mm.

The plans call for 127 mm (5 in) wheels on the main undercarriage and a single 57 mm (2¼ in) tail wheel which clearly is somewhat different to the scaled drawing in Figure 1 that calls for 155 mm main wheels and 70 mm tail wheel.

Clearly there is a difference and there are a couple of factors that are at work here.

• Firstly there isn't an infinite range of sizes of model aircraft wheels available so there is a need to compromise somewhat.
• The next is by far the most important and that is mass. The 127 mm wheels as recommended in the plan each weigh about 143 g while the closest to the scaled size with a diameter of 152 mm has a mass of 245 g.
• The final factor that comes into play is the space available within the airframe to house the wheels when they are retracted. As the structure of the model is not identical to the real aircraft the space available can vary making the use of smaller wheels than the scale would suggest.

The end result with the redesign was to stay with the 127 mm main wheels while the tail wheel was increased to 70 mm matching the scaled size exactly.

Structure & Mechanisms

The actual structure and retracting mechanism is somewhat more complex and requires a considerable amount of work in order to ensure that everything will work correctly. As discussed earlier there are three ways to go about redesigning the main undercarriage.

Reverse Engineering

The first part of the reverse engineering process is to calculate the strength of the existing components then use that information as the design parameters for the new design. The existing design utilizes what is commonly referred to as music wire which is otherwise known ASTM A228 and is a carbon, iron, manganese alloy that is cold drawn into various diameters and often used to construct springs. In this case 16, 12 and 8 gauge music steel is utilized.

This is where things start to get vague, confusing and terribly frustrating as there are no less than 10 wire gauge standards that cover music steel none of which even remotely match what is detailed in the drawings. According to the standards I have managed to locate 8 gauge music steel can have a diameter anywhere between 127 μm and 508 μm. To quote Jim Lovell Commander of the Apollo 13 Lunar Mission

"Houston, we've had a problem."

Clearly four 70 mm long elements at most half a millimeter in diameter couldn't even support the static load of a 6.2 kg model let alone the shock loading that the undercarriage is likely to be subjected to.

We "aren't totally up the proverbial creek without a paddle" as the original drawings do show the details of the undercarriage in enough detail to get an idea of the actual diameters of the structural elements.

It turns out that the closest standard is American Wire Gauge but interestingly AWG specifically precludes "music steel" and is not meant to be used on ferrous and spring wires as it is here.

It's a classic example of how the imperial system of weights and measures is a cobbled together mess of standards that are difficult to understand, prone to miss interpretation, time wasting and easily capable of causing catastrophic failures due to misinterpretation. We live in a global society where people communicate on a daily basis as a matter of course, yet we are still messing about using measurement standards that for the most part were created in the dark ages and have no place in a highly technical global society. It is up to those living in the last two countries on Earth stubbornly hanging onto a system that is atrociously out of date to bring pressure to bear on the appropriate authorities to move to a universal acceptance of the SI system of weights an measures.

We can now put all the data we need to perform the calculations that will give us the loading specifications we need for the new design. Table 2 shows what we have so far.

With the original design there are four load bearing elements that are constructed from the 8 gauge steel with several additional elements that are made from 12 and 16 gauge steel which are primarily used to extend and retract the undercarriage.

The four primary elements are about 140 mm long but are supported by the retracting elements at their mid point. The lower 70 mm have the axles that support the main wheels attached at the lower extremity. This gives us a column that is fixed at the top, free at the other end and has an overall length of 70 mm.

Before we can calculate the ultimate load the undercarriage can withstand we need to calculate the Area Moment of Inertia. I for round load bearing members like the ones utilized here. For a solid cylindrical load bearing element I is calculated as follows:

Therefore Area Moment of Inertia for the 8 gauge steel I_8g is:

Likewise we can calculate the Area Moment of Inertia for the 12 gauge steel I_12g

We can now utilize Euler's formula to calculate the maximum load that each of these load bearing members can withstand prior to failing due to bending but first we need to get all the information together.

• E = 210.0 GPa Modulus of Elasticity
• I_8g = 5.44 x 10^-2 Area Moment of Inertia
• A₀ = 8.37 mm² Initial Cross Sectional Area
• L₀ = 70.0 mm Initial length
• K = 2.00 Column Effective Length Factor

Since each load bearing member of the undercarriage can take a maximum load of around 590 N the four together will be able to carry an all up load of approximately 2.36 kN.

If we compare this to the previously calculated maximum loads that the airframe can take in Table 1 it is clear that the undercarriage will fail while the airframe is only at 50% of its maximum load. This is close to what we would expect to see according to the constraints discussed earlier and is a good check to show we havn't made a fundamental error in the design so far.

Now we have the maximum loadings we can utilize the information to redesign the undercarriage. You could back track substituting the characteristics and profiles of different materials but this can be time consuming and error prone. The simplest way is to use the information to date to create a spreadsheet that does all the calculations for you. It's then a simple matter to plug in the specifications, dimensions and profiles of readily available materials and then select the most suitable material and profile for the job.

Table 3 shows a comparison of 16, 12 and 8 gauge music wire with all the relevant data with solid aluminium, thin and thick walled aluminium tube in standard imperial sizes and aluminium tube in metric sizes.

Reengineer from Scratch

Pretty much all of the work to reengineer from scratch has been done during the reverse engineering process and you can use the data in Table 3 to select the appropriately sized components.

Scaled Engineering

The final possibility is to utilize a direct scaled version of the undercarriage on the real aircraft and then check to make sure it is capable of handling the loads required.

To get the scaled dimensions for the undercarriage I loaded the image shown in the image below into the CAD system and scaled it to represent the dimensions of the model in mm as done when selecting the sizes for the wheels

The averages then give us the three diameters 4.7 mm, 11.4 mm and 16.7 mm that would be required to construct the undercarriage.

It's now a fairly simple matter to use these diameters and the spreadsheet created in the reverse engineering stage to generate the data in Table 5

There are two problems that clearly stand out here:

• Increased Mass: The mass of the scaled replacements are all greater than the original elements. Mass is always a problem and to increase it this dramatically just for cosmetic reasons is not a good idea.
• Increased Load Bearing Capacity: If we look at the load bearing capacities of the scaled replacement elements with the maximum calculated loads the airframe can withstand in Table 1. it is clear that if the undercarriage were constructed along these lines it would be easily capable of transferring loads that were greater than the airframe could handle without suffering structural damage.

This clearly eliminates using the scaled engineering concept as it does not comply with either of the primary constraints of not being able to damage the airframe and reducing mass.

Final Comparison & Selection

We can now compare the maximum loads the airframe can withstand in Table 1 with the data in Table 3 and Table 5 to ascertain which option is the most desirable

The comparison shows that in most cases the forces that could be transferred to the airframe could over stress it and cause structural damage. The best solution would therefore be the reverse engineering solution that utilizes 3.0 mm and 5.0 mm aluminium tubing. It would also be possible to utilize the imperial sizes as well but as there is only one diameter that could fulfill the requirements it would mean an increase in overall mass and a less aesthetically correct result.

There is, however, a further possibility and that is the introduction of some sort of shock absorbing or force damping system that could decrease the shock loads applied to the airframe. This would enable the use of the scaled engineering results, but would add to the mass and complexity.

In future articles we will look at techniques for construction items like pneumatic shock absorbers and actuators, but for the moment the design will be based on utilizing 3.0 mm and 5.0 mm aluminium tubing.

In a future article we will look at the final design and construction of the undercarriage that will include the use and construction of various types of actuators.