G'day folks,

It's a while since I started a thread and it's a bit off track for the blog but it does involve a mode. I have been working feverously on my latest project which is the construction of a ¹/₃₂ scale model of the Apollo Command, Service and Lunar Modules and the Saturn V launch vehicle.

I will start a detailed threads on the model as I get the various modules finished but for the moment I would like to discuss how I plan to display the Apollo spacecraft.

The plan is to utilize a magnetic levitation device like the one on the right that in conjunction with a rare earth magnet can suspend up to about a 1 kg mass beneath it. The model is primarily constructed from 200 gm^-2 cardboard so it weights bugger all and if I position a NeFeB magnet in the model so it's slightly above the centre of gravity it shouldn't have any problem holding it up.

To sense the position of the model I have built an ultrasonic proximity detector kit that returns a voltage signal that is directly proportional to the position of the model. I also intend to mount a couple of hall effect sensors on the electromagnet that can be used to directly measure the strength of the magnetic field.

To control all this I intend to feed it all into a PICkit 2 microcontroller that will control the electromagnet.

If this all works I would ultimately like to animate the system so that the lunar module starts off on the base then lifts off and lands again.

So far I have found numerous sites out there that discuss different approaches to magnetic levitation but as far as I can see they all use analogue circuitry rather than a microcontroller. To me it seems a little strange as the sites I have looked at state that you can't just use a proportional control loop. This is because you need to take into account the velocity of the object being suspended not just its position beneath the magnet. Getting a differential/proportional control loop working with analogue components isn't that easy whereas with a microcontroller setting up PID (Proportional Integral Differential) control loops is relatively simple. It's also a darn side easier to reprogram a microcontroller than it is to rehash an analogue feedback loop, especially a PID one.

My question is, has anybody ever tried setting up a magnetic levitation system based on a microcontroller and if so what were the end results?

Regards masu.

MASU on Machines: Photovoltaic Cell Energy Payback

Welcome back to the MASU on blog and the first thread for 2008

In this series and other unassociated but similarly themed threads there has been considerable discussion on the subject of the energy that is consumed during the production of photovoltaic PV cells compared to the energy they generate over their operational life. There is an encyclopedic volume of what can at best be described as questionable data and the claim that PV cells do not produce as much energy as they consume. So, what is the reality of the situation, what is fact and what is urban myth?

First off let's have a look at the intensity of solar radiation at ground level. The most commonly bandied about figure and one used in many calculations is 1,000 Wm^-2.

So, is that a realistic figure or not?

The chart below shows the amount of solar radiation that reached the ground in Australia on 24^th January 2008.

It is currently summer in Australia and the Sun is above the horizon for pretty close to 14 hours a day while the average energy to reach the ground is around 25 MJm^-2. We can then calculate a value for the average power per square metre as below:

That's considerably less than the commonly used 1,000 Wm^-2 and we will look at the consequences of that later.

Next off we need to look at the efficiency of Photovoltaic PV cells. This varies considerably depending on the quality of the solar cells, the method of construction, their intended use and a host of other parameters. For example those used in satellites and spacecraft are greatly more efficient, reliable, less massive and considerably more expensive than those used on fixed ground based installations. There are also new manufacturing techniques like sliver technology that not only reduced the cost and materials required to manufacture PV cells but also dramatically increases their efficiency over a greatly increased range of conditions.

For the moment let's assume that we are talking of the average cells that are readily available for ground installations and have an efficiency of around 30%. If we combine this with the data from the chart above, gives us an effective power output of 66 Wm^-2.

It's not realistic to think that we could supply the world's total energy needs from PV cells but it is worth calculating the area that would be required to do so in order to give us some sort of idea about the magnitude of the problem we are facing. First off we need to calculate the average power requirement as shown below:

Next we need to calculate the area of PV cells that would be needed to generate the 16 TW currently being consumed:

However, this doesn't take into account the time that the PV cells are in darkness, under cloud cover or other shadows or other parameters that limit the energy the cells can produce. It also doesn't take into account any increase in power demand or efficiency of so far unknown or undeveloped technology.

If we were to utilize PV cells to supply about 10% of the global energy demand and assume they would only be utilized in places where there was close to 12 hours daylight per day there would be a need to manufacture some 50 x 10⁹m² of PV cells. 50 billion square metres of PV cells is one mammoth production run and would definitely require a coordinated global and multi company program. However, considering semiconductors production has been following Moore's law for several decades will this remain an unrealistic target forever?

Getting back to one of the original questions and commonly quoted factoids is the energy returned during the operational life of PV cells really less than the energy used in their production. This is called the Energy Payback of PV Cells and you will find a fairly extensive review of the information available in 2006 if you follow the link. Some of the main points this article covers are:

• Use of Waste Si Wafers: The wafers that are commonly used in the commercial manufacture of PV cells for domestic and terrestrial use are constructed for Silicon wafers that are not suitable for use in the manufacture of semiconductors. Silicon is produced in ingots that are then cut into wafers that are roughly the same size as a CD/DVD. If the wafers have any imperfections, flaws, occlusions etcetera they are not suitable for the production of semiconductors and are therefore treated as waste. However, these wafers are usually suitable for use in the production of PV cells so in reality PV cells are constructed from the waste products of the semiconductor industry. This then raises the question of whether or not the energy consumed in the creation of the wafers should be used in the calculation of energy required to produce PV cells. After all, if these wafers were not used for PV cells they would be just discarded or recycled to produce new Si ingots.
• Centralized Power Generation: Many of the studies into the energy payback time of PV cells assume that they will be used at centralized locations. The current use of PV cells for domestic and industrial power generation utilizes a distributed system where the power they generate is used locally. Surplus power is then distributed to other energy users over the existing power distribution grids.
• Power Plant Construction: Following on from the previous point many calculations include the energy that is utilized in the construction of centralized power stations. However, since we are talking of a distributed system there is no need for the construction of special purpose built installations. With a distributed power generation system much of the infrastructure and building requirements will already be in place and only require minor modifications to have panels of PV cells installed.
• Operation, Monitoring and Maintenance: Again many calculations assumed that you would need to include the ongoing operation, monitoring and maintenance of centralized power generation. However, with a fully automated and distributed system the need for such work is dramatically reduced.

The conclusion that was drawn by The Environmental Engineer paper was that for a distributed domestic power generating system based on PV cells the energy payback time would be somewhere between 2 and 8 years depending on specific installation parameters. When this is compared to the average expected life expectancy of 20 to 25 years a distributed power generating system based on PV cells will produce between 3-12 times the amount of energy that was used in the production, installation and operation.

Sliver Technology & Other New Technologies.

At the time The Environmental Engineer paper was written sliver technology was still in the very early stages of development. The technology is currently at the trial production level with a test manufacturing facility due to come on line sometime in early 2008 with trial installations coming on line a few months later.

What is sliver technology? Basically sliver technology takes an existing 2 mm thick silicon wafer and cuts it into extremely thin slices. These slices are then rotated through 90° and mounted on a backing substrate. This has several positive results:

• Increased Surface Area: By cutting the wafer into slivers that are 50 μm wide and 2 mm thick then rotating them through 90° the effective collecting area that can be created from a single wafer can be increased by some 10-12 fold.
• Electrode Position: With a normal solar cell the connections need to be mounted on the upper and lower surface of the cell. Since sliver technology rotates the slivers by 90° the connections are now made on the sides of each sliver and has the following effects:
• Bidirectional: Because the electrical connections are at the side of each sliver the cells can generate power regardless of which side is exposed to light. This not only makes the mounting easier but can increase the output if a mirror system is employed that illuminates both sides of the cell.
• Output Voltage: With the current generation of mass produced PV cells there is a disproportionate drop in output voltage as the area exposed, intensity and angle of incidence of light varies. Sliver cells can operate over a dramatically increased range of parameters and will generate their designed output voltage with as little 5-10% of their surface exposed to radiation.

Sliver technology has the potential to reduce the energy payback time by anywhere between 5-10 fold. That would bring the energy payback period down something like 3-18 months.

PV cells have been around for something like 120 years but until around 50 years ago remained nothing more than a scientific curiosity. The first PV cell was constructed from selenium with an extremely thin coating of gold that had an overall efficiency of around 1%. This efficiency increased to about 6% in 1954 when Bell Laboratories accidentally found it was possible to construct PV cells from silicon doped with certain trace impurities. Research into PV cell technology has exploded in the last decade or so and efficiency is now approaching the theoretical maximum of 40%. Over the last century there was undoubtedly a time when the energy consumed in the creation of PV cells exceeded the energy they would produce but with current technology this is no longer the case. The energy payback period is currently somewhere between 5-10 years and is likely to drop to somewhere around 3-18 months in the next few years.

Finally I would just like to differentiate between energy payback and financial payback. Energy payback is only concerned with the energy consumed in production compared to the energy returned over the operational life of PV cells. It does not in any way look into the cost of production, monetary reward or offset of the energy produced by PV cells. Origin Energy Australia are currently offering an off the shelf PV cell based power generating system that has a projected financial payback period of around 5-10 years. Admittedly this payback period is reduced by government subsidies, but Origin Energy are close to completing a pilot plant that manufactures sliver technology PV cells. If sliver technology lives up to its potential then we will more than likely see a reduction in the financial payback period of 20-50%. The financial payback period also does not include inflationary pressures on the price of energy. The more expensive energy becomes, the shorter the financial payback period will become.

In conclusion, The concept that the production of PV cells consumed more energy than that they produced during their operational life may well have been true. However, with the increases in efficiency of PV cells and improved production techniques this is no longer the case. Currently the energy payback period is 5-10 years and is likely to drop to as little as 3-18 months in the next few years.

As usual you can read more about this by following the links below.

• Photovoltaic Cells: Wikipedia
• Energy Payback of PV Cells: The Environmental Engineer
• Moore's Law: Wikipedia
• SI Prefixes: Wikipedia
• World Energy Resources & Consumption: Wikipedia

Continuing with the theme from last week Mars has been the source of legend and myth since mankind first looked at the night sky in detail. However, until recently little was really known about the planet and it has proven to be somewhat of an unwilling subject. In the 1960's NASA and the Russian space agency launched some 13 missions to explore the red planet with all but NASA's Mariner 4, 6 and 7 failing.

The next twenty years 1970 to 1989 were somewhat more successful but even so 9 of the 13 missions failed to operate to their full potential. However, NASA's Viking 1 and 2 proved to be highly successful landing two craft on the surface and one in orbit. The primary mission of Viking 1 and 2 was to look for any sign of life and the initial tests seemed to confirm that there was some form of life present on the red planet. Later detailed examination revealed that the test being used to detect the presence of life was fundamentally flawed leaving the question of Martian life still unanswered.

The embarrassing failure of the Mars Climate Orbiter in 1999 due to mix up between metric and imperial measurements capped ofF yet another decade of failure. Six of the 8 missions failed, but again there was an outstanding success with the Mars Pathfinder mission landing the first successful rover on the surface.

So far the 21^st century has shown a turn around in the luck with only the UK's Beagle 2 apparently crashing while attempting to land on Mars. The Phoenix Lander and Dawn Spacecraft fly by are still on route. To date the two outstanding results have been the Mars Exploration Rovers MER-A and MER-B as depicted in the artist's impression above and to the right,

MER-A or Spirit (see mission patch on right) left Earth on its 207 day journey to Mars on 10^th June 2003. On 4^th January 2004 it successfully landed about 15° south of the Martian equator in Gusev Crater.

After surveying the surrounding terrain as seen in the image above, and carrying out system checks, it commenced its wandering exploration of the Martian surface.

MER-B or Opportunity (see mission patch on the right) departed on its slightly shorter 202 day trip to Mars on 7^th July 2003 successfully landing 2° south of the Martian equator in Meridiani Planum. It is, however, on the opposite side of Mars to its twin rover Spirit.

Again, after surveying its landing site as seen in the image below and carrying out system checks it too started off on its wandering mission of exploration.

The chronicle of failed missions testifies to the difficulty of sending an interplanetary mission to Mars but getting there is only the first step and there are numerous other stumbling blocks that have been the undoing of several missions. Unlike the Moon Mars has an atmosphere so any lander is going to need some sort of heat shield to prevent it from burning up when it enters the atmosphere.

However, it doesn't stop there as the atmosphere is not dense enough to realistically utilize aerodynamic devices like parachutes to slow the descent rate sufficiently to perform a soft landing. In 1976 the Viking 1 lander utilized small rocket braking systems for the final descent but the size of MER landers was too large to use this method.

In 1997 the Mars Pathfinder mission landed the Sojourner rover on the surface of Mars and while Spirit and opportunity were considerably larger engineers believed that the system was sound and could be scaled up to work on the new landers. Basically it was a three stage system as follows:

• Heat Shield: The first stage was the use of an ablative heat shield that both protected the rover and associated equipment and reduced the speed enough to utilize aerodynamic devices to continu the deceleration.
• High Speed Parachute: The next stage was the use of parachute to scrub off as much of the speed as possible. This was no ordinary parachute as the relatively thin atmosphere meant the terminal velocity of the lander after jettisoning the heat shield would tear a normal parachute to shreds. Designing this parachute turned out to be problematic with the original design failing catastrophically at opening. After the opening problems were solved further testing revealed the design has serious stability problems. Time was running out and at one point it looked like the parachutes would not be ready in time for the 2003 launch window but persistence paid off and the deadline was met.
• Rocket Motors: The mass of the landers meant that using only rocket and parachutes would not be practical, but they were not done away with completely.
• Gas Bags: The final stage is the source of the term "Bouncing" in the title and involved the use of several large gas bags. When the craft was close enough to the ground the parachute was released and the lander was cocooned inside several large gas filled bags. These let the lander bounce several times and once the craft came to a complete stop the bags were deflated. Again, during testing the bags proved to be problematic with several unexpected failures but after some redesign and further testing a working system was developed.

Having a failure rate of nearly 55% is bad enough but operating an unmanned roving vehicle on the surface of another planet is even more difficult, complex and literally fraught with mission destroying pitfalls. Real time data and image transmission not only requires considerable band width but the power consumption would be far greater than the primarily solar powered rovers and orbiting Mars Surveyors could supply.

The other major problem is the delay in getting signals to and from Mars. At best the round trip takes 6½ minutes and by the time Mars reaches conjunction this delay has stretched out to almost 45 minutes. Delays like this in critical control and decision making loops would never work as the rover could end up being a pile of debris at the bottom of a cliff for three quarters of an hour by the time the message to stop reached it. The only answer is to build a rover that is for the most part autonomous and capable of critical decisions without input from Earth.

Spirit and Opportunity were scheduled to explore the area around their landing sites for signs of water, life and other geological features for approximately 90 sols (Martian days). However since they were operating well at the end of the initial 90 sols the mission has been extended on several occasions and as of Monday 17^th December Spirit was on sol 1,406 while Opportunity had reached sol 1,386.

The Martian year is 668.6 sols long and as its axis is inclined to the orbital plane by 25.19° Mars experiences seasons in a way similar to Earth except lasting for around twice as long. The initial 90 sol missions were during the summer months at the landing sites and little attention was paid to what would happen when the sunlight diminished as the seasons moved towards autumn and winter. The mission controllers knew that the solar cells that supplied the rovers with their energy would not be able to sustain the rovers during the southern Martian winter. The rovers were parked in a sheltered well lit area and all but the most critical systems were shut down. When the Sun started to get higher in the sky the rovers were carefully started up again and to everybody's relief both came back to life.

The rovers have since been hit with dust storms, have recorded miniature tornado like atmospheric phenomena, explored craters, looked for signs of life, found mineral deposits that seem to indicate there was water once present on Mars but to date no sign of life.

The Spirit and Opportunity have been many times more successful than anybody could have believed and are currently in a race against time to reach the place they will spend their second Martian winter and with a little luck they will both come back to life at the end of the southern Martian winter.

As usual you can read more on the subject by following the links below. I highly recommend visiting the NASA MER Archive page as it has links to a phenomenal amount of information on the Spirit and Opportunity missions.

• Exploration of Mars: Wikipedia
• Spirit & Opportunity: NASA
• Spirit Rover: Wikipedia
• Opportunity Rover: Wikipedia
• Timekeeping on Mars: Wikipedia
• Viking 1: Wikipedia
• Mars Pathfinder: Wikipedia
• Sojourner: Wikipedia
• Mars Explorer Rovers Archive Index: NASA

Once again the end of year is rapidly approaching and MASU is going to take a short break so there will be no new threads for a couple of weeks. I will be checking for new posts in existing threads from time to time. In the meantime I hope you all have an enjoyable and fulfilling festive season and a prosperous and rewarding new year.

Mars the Red Planet

On December 24^th Mars (image at right) will be in opposition, or in non astronomical jargon directly opposite to the position of the Sun as viewed by an observer on Earth. However, six days prior to this Mars will be as close to Earth as it is going to get during this opposition.

"Hang on a minute, that doesn't make sense!"

Well, at least that's what I said when I first read about the orbits of Mars and Earth. The reason for this apparent discrepancy is the inclination of Mars's orbital plane with respect to the ecliptic. Unfortunately it is difficult to describe the concept linguistically or diagrammatically in a two dimensional media like this but the net result for this particular opposition means the date and time of the closest approach happens slightly before the actual opposition.

There are a couple of really good animations on the Windows on the Universe and Illumination web sites that show the relationship between the orbits of Earth and Mars reasonably well and are worth having a look at and play with.

This approach will see a minimum separation of 88,115,332 km which is considerably further than the 2003 opposition when Mars came within 55,758,006 km of Earth. Actually the 2003 opposition is believed to have been the closest since 12^th September 57,617 BC but it is estimated that over the next two millennia the 2003 record will be surpassed on at least 22 occasions.

The table below shows the minimum distance between Mars and the earth between 2003 and 2018.

With a current orbital eccentricity of around 9% Mars has the greatest eccentricity of the major planets. Pluto does have a much greater eccentricity at almost 25% which is not only nearly three times that of Mars, but brings it closer to the Sun than Neptune for a large proportion of its orbit. Unfortunately for Pluto in 2006 the International Astronomical Union decided that Pluto did not fit the definition of a planet and demoted it to the status of dwarf planet. There has been considerable debate over this decision. However, Pluto is smaller (diameters 52 km smaller ) and less massive (3.65 Yg less) than Eris so there was definitely an inconsistency that needed to be addressed.

Until the second half of the 1970's we knew surprisingly little about Mars and many believed it was still possible that there was some kind of life there.

Mars has long been the fictional source of aliens, invaders, ancient civilizations and cultures and host of other "out of this world" ideas. Certainly until the last quarter of the 20^th century relatively little was know about our red neighbor. This all changed in the last quarter of the 20^th century when NASA and other space agencies sent surveying and mapping satellites as well as several landers and automated rovers to explore Mars.

In 1976 when NASA's Viking space craft took the image at right it wasn't long before somebody claimed that it was a face that was too close to that of the sphinx in Egypt to be a coincidence. Theories of ancient civilizations with the capacity for interplanetary exchange of information as well as interplanetary travel abounded and it wasn't long before people were claiming it was proof of an ancient Martian society.

Later high resolution images like the one below, revealed that the face was nothing more than an optical illusion most likely caused by the way our brains try and look for patterns within images. If you have a pair of red-blue 3D glasses then you may wish to go to the NASA Astronomy Picture of the Day site and look at the stereoscopic composite image of the now infamous Face on Mars.

There have been three successful missions to land small autonomous rovers on the surface of Mars with the later two Spirit and Opportunity being far more successful than anyone could have hoped. They were originally designed to explore the surface for 90 days but have now been operating for well over 1,000 days. They have survived more than a full Martian year including a winter and a massive dust storm. By obscuring the Sun the rovers were unable to use their solar cells to generate the electricity they needed not only to operate but to keep the electronics from being destroyed by the cold. All that could be done was to park them in a sheltered place where there was plenty of sunlight and shut down everything but the system that kept the internal temperature within safe limits. When the dust settled the rovers started up again and there was a great sigh of relief when it was found they had survived with little damage.

Mars is roughly 80 Gm further from the Sun than Earth but its day is only about 38 minutes longer than the Earthly equivalent. The Martian axis is inclined by 29.19° to the plane of its orbit and as a result it experiences seasons all be it on a 668.60 sols (686.96 earth days) cycle, in a similar way to the Earth's seasons. It is however considerably smaller, less dense and less massive than Earth and consequently only has a gravity that is 37.6% that of Earth's or slightly more than twice that of the Moon.

Mars has two moons, Phobos and Deimos as shown in the image on the right. They are nothing like Earth's Moon being much smaller and irregularly shaped. It is believed that they are actually asteroids that have been trapped by Mars's gravity and ended up in orbit rather than crashing into the surface.

In subsequent articles we will look at the wealth of information that has and is coming from the spacecraft that are studying Mars from orbit as well as on the surface. If you have some time to spare on a clear night over the next couple of weeks have a look at Mars through a telescope or pair of binoculars because that's about as good as it's going to get till at least 2016. The image below shows Mars's path during the current opposition in daily steps. With any luck I will have my astronomical imaging system working in the next week or so and have some pictures of Mars.

As usual you can find out more about Mars by following these links.

• Mars: Wikipedia
• Mars: NASA
• What Makes Mars Magnetic: Spaceflight Now
• Conjunction & Opposition: Wikipedia
• Mars's Orbit: Window on the Universe
• Mars Today: NASA
• The Face on Mars: Wikipedia

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.