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I n d u c t i o nEddy Current Losses in a Transformer

Group Project

IntroductionInduction is a process where an electromotive force (EMF) is generated due to a change in magnetic flux passing through a conductive loop. This process was first extensively documented by Michael Faraday in the 1830s. A famous experiment by Faraday had two sets of coils insulated from each other wrapped around an iron torus. This allowed him to observe induction and develop the formulas below. Heinrich Lenz was also involved in the formulation of thetheory of induction. (Serway, 2010).

It was observed by Faraday that induced EMF was directly proportional to the rate of change in flux for a given number of loops of conductor. It was also observed that for a constant rate of change in magnetic flux that the induced EMF was directly proportional to the number of conductive loops. (Serway, 2010) These observations form a substantial platform on which a formula which describes induction can be built.

Where £ is the induced EMF,N is the number of conductive loops,

and is the rate of change in magnetic flux passing through these loops with respect to time. Although Faraday made this observation as well, Lenz' contribution to the field was to note that the direction of the induced EMF was such that it would set up a magnetic field so as to oppose the change in the magnetic flux passing through the coil. For the purposes of the above formula this means that we need to take a negative sign out the front of the formula to represent this process. This gives the final formula for characterising induction.

The method by which the flux passing though the conductive loops changes is not limited to physical processes such as moving a magnet closer or further away from the loops, or even just changing the angle of the flux incident the coil. It can also be changed by a time varying current in a nearby conductor (Kane, 1988) .This is because a current traveling through a conductor produces a magnetic field whose strength and polarity is proportional to the current in the conductor. Effectively what this means is that if a conductor has a time varying current traveling through it near another conductor, it can induce a current in this second conductor. This is the

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principle (mutual induction) behind transformers (Kane, 1988).

There are several important considerations in transformer design. If these considerations are taken into proper account then the transformer can be very efficient. Efficiencies in excessof 98% are often found associated with transformers in industrial use (International Copper Association, 2011).

The first big consideration when dealing with transformers is selecting a material that will thread nearly all of the flux from one coil through another coil. If just air is used this is essentiallythe same as taking the permeability of free space and the flux will head at the ends (very roughly speaking) in all directions instead of heading through the other coil. Some materials have permeabilities much higher than free space. Steel, for example has a relative (to free space) permeability of 100. (Nave, 2011) Almost like electricity, the flux will seek the path of highest permeability (lowest resistance). This means that the vast majority of flux will thread the steel core, rather than just head out (Nave 2011). This consideration is used when designing transformers. So transformers are constructed with cores made of a material with a high permeability so that as much flux as possible threads from one coil through the other and often the choice is something like steel.

There is a problem with simply using a steel bar as a core. As mentioned above a change in flux threading a conductor, with respect to time, induces and EMF and hence a current in the conductor. This is not just limited to coils, but can also happen in the core. What this means isthat the EMF induced by the changing current in the coils will cause currents to form in the core. These currents are called eddy currents (Serway, 2011). Now there will be some small amount of electrical resistance in a core made of just pure steel and consequently these currents will dissipate energy via resistive losses (Kane, 1988). This can be overcome by designing a core with a high permeability but with a low conductivity and certain materials, such as amorphous metals (discussed further in the discussion) have these properties. A more traditional method of reducing eddy currents (used in many home appliances) is to place non-conductive laminations between sheets of metal (Elliot, 2011). This keeps the high permeability of the metal, while restricting eddy currents to a much smaller size (introduction figure 1) and hence limiting losses to eddy currents.

HypothsisThis effect should be observable in first hand investigations and forms the basis of this experiment's hypothesis, which is that core materials with high conductivity, but no laminations will experience greater losses than those with laminations.

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Introduction Figure 1

AimThe aim of this project is to investigate the dissipation of power in a transformer due to eddy currents. This will lead to the investigation of effect of different using different core materials and then lead on to investigate possible ways to improve upon current transformer design.

Materials and Procedure

Required Materials

Item Quantity Notes

Voltmeter 2 This can actually just be a multimeter as long as it has reasonable accuracy for AC voltage in the 12V range.

Ammeter 2 This can actually just be a multimeter as long as it has reasonable accuracy forAC current. Note that many multimeters don't measure AC current.

Transformer coils 2 The ratio of coils does not really matter because power is being measured, but for this experiment a ratio of 1:1 was used.

Steel Core 1 This should be large enough that it fits snugly inside the coils. For this experiment four iron rods were used to achieve this. Ideally there should be one bar the same

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shape and size as the inside of the coils.

Laminated Iron Core 1 This should be large enough that it fits snugly inside the coils. For this experiment such a bar was available and laminations were spacedat roughly 1mm intervals throughout the bar.

Copper Core 1 This should be large enough that it fits snugly inside the coils. For this experiment a round bar which fitted snugly inside the coils was found, however it did not fill the entire inside as the inside of the coils were in the shape of a square.

Aluminium Core 1 This should be large enough that it fits snugly inside the coils. For this experiment a round bar which fitted snugly inside the coils was found, however it did not fill the entire inside as the inside of the coils were in the shape of a square.

Laminated Iron Horseshoe 1 This should be a laminated iron core in a horseshoe configuration. For this experiment such a core was available and laminations were spaced at roughly 1mm intervals throughout the core. This horseshoe core was of such a shape that it matched up nicely with the laminated iron core to form a closed loop.

Wires There should be enough For this experiment banana

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wires to complete the hookups required, and shown, in Method Figure 1.

plug leads were used as all the other equipment accepted these leads.

12 AC Source 1 This should be able to deliver in excess of 5amps of current as some configurations may draw this much current on the primary coil.

Resistor 1 This may just be a rheostat but it should be able to handle fair high powers (5W+) as someconfigurations may provide that much power. The benefit if a rheostat is that different power resistances can be used so that the voltage and current across and passing through the coils can be changed. (The power on each side should stay more or less the same however).

Procedure1. The experiment needs to be setup such that the voltage across and the current traveling though each coil can be measured. This should be done as shown in method figure 1. Seeing as in the experiment performed, multimeters were used as AC ammeters, care had to be taken to not to blow the fuses on the multimeters. Particular care needs to be taken on the primary side (the side connected to the AC power source) where the currents are quite often large (several amps). This can be done by selecting the correct range on the multimeter.

2. After the circuit is configured the coils should be "warmed up" so that resistive losses can be discounted from comparisons. This can be done by simply turning on the power supply with no core between the coils and letting one of the coils warm up. Then swap the coils and repeat. As long as the experiments are performed at a reasonable pace the coils should stay consistently warm throughout the experiment. A key point to note here is the aim is to get the coils "warm", not hot. At any point during the experiment should the coils get too hot to hold by hand then they are too hot and the experiment should be paused until the coils cool down. The point of this step is to try and warm up the coils so that the first measurements don't have less resistive losses than the other ones so the aim should be to keep the temperature consistent throughout the experiment.

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A safety note here is that the experiment's safety could be increased by using a normally open momentary switch in series with the primary coil. This means that the coils could not overheat accidentally by leaving the power supply on.

3. After these initial preparations have been completed then start by placing the laminated iron core through the coils and keep the coils right next to each other. Turn on the power supply and note down the voltage and current on the primary and secondary side. This can be used to calculate the power for each side by P=IV. Turn off the power supply and changethe setting on the rheostat (if using one), turn on the power supply and take down a new set of measurements. Do this until three sets of results have been obtained. Repeat for all the different cores available.

4. When dealing with core with a lower permeability it may be that the current and voltage on the secondary side are too small to measure with the range used for cores with higherpermeabilities. If possible change the range on the multimeters to pick up these smaller values.

5. A set of measurements for an air core should also be taken this is done by simply placing the coils right next to each other but with no core threading through each coil.

6. A set of measurements for a closed core can also be taken by using the laminated horseshoe and laminated iron bar and forming a closed loop with the coils on either side.

7. The results collected can then be used to calculate efficiencies for each configuration.

Method Figure 1

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Results

High Permitivity Cores

Primary Voltage (V)± 0.05

Primary Current (A)± 0.005

Primary Power (W)

Secondary Voltage (V)± 0.05

Secondary Current (A)± 0.005

Secondary Power (W)

Efficiency (%)

Laminated 12.2 1.39 16.87 ± 1.7 0.37 0.581 ± 3.46 ±Open 0.49 0.13 0.876Horseshoe

Laminated 12.3 0.74 9.06 ± 0.49 4.3 0.58 2.50 ± 0.26 27.8 ± 4.39ClosedHorseshoe

Steel Bar 11.8 1.83 21.6 ± 0.92 3.7 0.50 1.76 ± 0.22 8.10 ± 1.36

Laminated 11.9 2.07 25.6 ± 0.79 2.8 2.87 0.8 ± 0.22 3.22 ±Core 0.985Straight

Low Primary Primary Primary Secondary Secondary Secondary EfficiencyPermitivity Voltage (V) Current (A) Power (W) Voltage (V) Current Power (%)Cores ± 0.05 ± 0.005 ± 0.05 (mA) (mW)

± 0.5

Aluminum Bar

11.2 4.12 45.97 ± 0.91

0.1 45 6.16 ± 3.4 1.3 x 10-2

± 7.7 x 10-3

Copper Bar 11.2 3.92 43.73 ± 1.03

0.1 42 4.15 ± 0.97 9.5 x 10-2 ±2.4 x 10-2

Air 11.1 4.13 45.81 ± 1.05

0.2 28 5.61 ± 0.89 1.2 x 10-1 ±2.2 x 10-2

*Italicised columns are calculated not measured.Results Table 1

Error Calculation

Error was taken for the multimeter to be ± half the least significant figure displayed. As the three sets of results were averaged in each case (for voltage, current and power), the power error calculation is the range of powers calculated divided by two.The efficiency error number was calculated using the primary power percentage error + secondary power percentage error.

Important Comparisons

Obviously because of the large range of results in the above table it is important to select situations where the conditions were most similar and compare the results for these setups.

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Straight CoreThese results relate to the configuration shown in the diagram below, where coils were placed next to each other with the core material traveling trough both coils, but with each end of the core material "open" (not joined back to the other side).

High Primary Primary Primary Secondary Secondary Secondary EfficiencyPermeabili ty Cores

Voltage (V)± 0.05

Current (A)± 0.005

Power (W) Voltage (V)± 0.05

Current (A)± 0.005

Power (W) (%)

Steel Bar 11.8 1.83 21.6 ± 0.92 3.7 0.50 1.76 ± 0.22 8.10 ± 1.36

Straight Laminated Core

11.9 2.07 25.6 ± 0.79 2.8 2.87 0.8 ± 0.22 3.22 ± 0.985

Low Permeabili ty Cores

Primary Voltage (V)± 0.05

Primary Current (A)± 0.005

Primary Power (W)

Secondary Voltage (V)± 0.05

Secondary Current (mA)± 0.5

Secondary Power (mW)

Efficiency (%)

Aluminum Bar

11.2 4.12 45.97 ± 0.91

0.1 45 6.16 ± 3.4 1.3 x 10-2

± 7.7 x 10-3

Copper Bar 11.2 3.92 43.73 ± 1.03

0.1 42 4.15 ± 0.97 9.5 x 10-2 ±2.4 x 10-2

Air 11.1 4.13 45.81 ± 1.05

0.2 28 5.61 ± 0.89 1.2 x 10-1 ±2.2 x 10-2

Results Table 2

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It should be noted that as expected the laminated core actually did have a higher efficiency than the core without laminations.

The low permeability cores also produced some interesting results. As expected air performed the best in terms of efficiency. An unusual result was obtained where aluminium was vastly less efficient than copper despite having a lower conductivity and a higher permeability.

Results Figure 1

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Results Figure 2

Laminated Horseshoe CoreThese results correspond to a transformer configuration shown below (with or without the end bar). The purpose of these results, somewhat tangentially, was to highlight the importance of threading all (or as much as possible) the flux through the coils of a transformer.

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High Permeabili ty Cores

Primary Voltage (V)± 0.05

Primary Current (A)± 0.005

Primary Power (W)

Secondary Voltage (V)± 0.05

Secondary Current (A)± 0.005

Secondary Power (W)

Efficiency (%)

Laminated Open Horseshoe

12.2 1.39 16.87 ± 0.49

1.7 0.37 0.581 ± 0.13

3.46 ± 0.876

Laminated Closed Horseshoe

12.3 0.74 9.06 ± 0.49 4.3 0.58 2.50 ± 0.26 27.8 ± 4.39

Results Table 3

Results Figure 3

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DiscussionThe aim of this project was to measure the eddy current losses in a transformer given different core materials and then, if possible, propose a better core material. This experiment did test various core materials and the results do show that different transformer configurations do result in vastly different efficiencies. The results do show the effect of eddy currents but because of various experimental design issues they really don't provide the platform from which to quantify theses losses.

If considering a comparable pair of configurations, the "straight laminated iron bar" and "steel bar", an expected but interesting result can easily be seen in results table 1. The laminated bar had a higher efficiency than the steel bar with no laminations. This is consistent with the theory discussed in the introduction which essentially predicts that without the laminations there will be larger losses due to eddy currents.

The percentage uncertainties for these results were quite large, and there was potential uncertainty introduced by experimental design. The metals that were used were not necessarily identical. This can have quite an effect as trace elements can drastically change permeability (Nave, 2011). Also as noted in the material notes the steel bars were round and did not snugly fill the inside of the coils, unlike the laminated iron bar. This could mean that different amounts of flux were threading the coils in each case. This could reduce the efficiency in some cases, as changing flux not threading the coils could dissipate energy into the environment.

An improvement for this particular source of error and uncertainty would be to select identical metals to compare. A practical way to do this would be to take strips of iron and form a bar with conductive paste between them, then take another set of strips, laminate them, then form abar out of the laminated strips. This would mean that metals with identical permeabilities would be being compared and it would be potentially much easier to isolate the losses due to eddy currents.

Although the experiment yielded the theoretically "correct" results the above improvements would mean that the experiment was more reliable than the one actually conducted. These improvements could very likely show an increase in the relative difference between the two different core materials, further highlighting the losses directly caused by eddy currents.

Both systems were quite inefficient. Commercial and industrial transformers have efficiencies up in the high nineties (International Copper Association, 2011) while these setups did not get over 10%.This indicates that a large amount of energy was being lost, and unfortunately these very large losses could come from other sources than eddy currents, especially in the case of the laminated core. These losses should be considered, not because they caused the wrong result to be obtained, but because the reduce the certainty of the results and the ability to calculate losses specifically due to eddy currents.

A possible explanation for the reduction in efficiency could come from experimental design. As the coils are used for extended periods of time their temperature increases quite markedly due to resistive heating. This heating reduces the conductivity of the coils. The order that the

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measurements were taken, laminated then not laminated or vica versa This is because more energy would be lost due to resistance rather than due to eddy currents. This explanation is unlikely to have distorted the relative efficiencies of each setup. This is because the coils heated up during preliminary testing, before any results were taken down, and it is unlikely, althoughnot impossible, that one set of measurements had substantially more resistive losses than another.

One possible fix for the problem outlined above could be done by characterising the sensitivity of the resistivity of the coil material to the temperature and then measure the temperature of the coils during eddy current measurements to calculate, and hence compensate for, resistive losses. Specifically for this case an easy way to measure the coil's sensitivity to temperature changes would be to measure the resistance of the coil at room temperature (20 degrees)and then heat the coils up until they reached some chosen temperature, say 80 degrees and then remeasure their resistance. Assuming the relationship is linear this would allow for the calculation of the resistance of the coil at a given temperature and hence the magnitude of the resistive losses expected in the coil during eddy current measurements. This could be used to remove these losses and further isolate eddy current losses.

There are another set of results that are worth looking at. They are the ones which are from selecting cores with low permeabilities as presented in results table 2 and results figure 2. The results here are also consistent with theory, for the most part. The air core, as shown in results figure 2, has the highest efficiency.This is to be expected as they all have more or less the same permeability (see discussion table 1) but air is by far the least conductive of the set. This would suggest that air should not have eddy current while the other two should. This is actually exactly what the results suggest happened.

There is a counter intuative result with the aluminium. Aluminium is slightly less conductive than copper (so there should be fewer eddy currents) and it has a slightly higher permeability than copper (so more flux should be threading the coils and less being lost to other elements in the environment). This is not reflected in the result. There is possible explanation for this however. As noted in the materials section above the experiment was conducted with not much aluminum going through each core. (See discussion figure 1 for an image) It is quite possible that this difference acted to affect the experiment but it is still not clear why it didn't have a result similar to air. The reason a comparison to air, in the case should be made is because the limiting case of less aluminium would be air so one would expect that if there was less aluminium then it would behave more like air.The way to minimise this uncertainty would be to get a square rod of aluminium to fit inside the coils. The same should likewise be done for the other materials should be conducted to give a more reliable set of results.

Material Relative Permeability (relative to freespace)

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Discussion Figure 1

Air 1.00000037 (Cullity, 2008)

Copper 0.999994 (Clarke, 2008)

Aluminium 1.000022 (Clarke, 2008)

Air 5 x 10-15 (Pawar, 2009)

Copper 5.96 x 107 (Grifiths, 1999)

Aluminium 3.5 x 107 (Serway, 1998)

Discussion Table 1

An aditional source of uncertainty which affected almost all of the results was the fact that for many measurements the multimeters were giving results at the edge of their measurement range. This means that there was a higher percentage uncertainty for several results such as for the aluminium bar. Ideally more accurate multimeters should be used to get more accurate results and greatly increase the certainty in the results.

Another set of results to look at is the closed and open horseshoe configuration show in results table 3 and results figure 3. While this configuration does not actually further the isolation of eddy currents it does show the importance of getting the flux to thread through both coils when designing efficient transformers. Huge efficiency gains were had by closing the horseshoeand ""forcing" the flux to thread each coil. Interestingly even after closing the flux loop the efficiency was still not over 50%. Commercial transformers, as already noted get much higher efficiencies.

Although not all other sources of inefficiency in the setups in this experiment have been isolated it is possible to see that there is a reduction in efficiency due to eddy currents. In other word

Material Conductivity (Sim)

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power is being consumed by eddy currents instead of being transferred to the secondary coil. With the comparison between the steel bar and the laminated iron core there is a roughly 3% (50% relative) reduction in efficiency with some of it attributable to eddy currents. In the case of air - copper there is a roughly 0.02% (10% relative) reduction in efficiency. In this case, for these particular transformer coils, with a conductive core at least 10% of losses are probably attributable to eddy currents. Because of experimental limitation there is not much certainty in these numbers however. Most of this uncertainty comes from experimental limitations such asnot having snugly fitting cores, rather than measurement uncertainties which are relatively small as can be seen in the results charts above.

In terms of designing a transformer with a better core, research has focused on selecting cores with a high permeability but low conductivity. This is done to minimise eddy currents, as discussed in the introduction. In common transformers used around the home this is often done with "E" type transformers where the primary and secondary coils are wrapped around the middle "leg" of the E and the flux is threaded around using the other legs with a connecting bar at one end(Elliot, 2001). This is shown in diagram to the right.

This is efficient because it keeps the eddy currents small while allowing the magnetic flux to be threaded through each coil. The coils are also placed in close proximity, sometimes on top of each other, to maximise flux threading each coil.

There is ongoing industrial research and practical implementation of cores made of amorphous metal. This metallic material has the property that it has a high permeability while having a relatively low conductivity. This is ideal in the case of transformers as it allows almost all of the flux to be threaded through each coil and it also also prevents large eddy currents from forming and causing losses (General Electric Company, 2011).

Hysteresis losses are another type of loss that can occur because of the core material but these losses are most prevalent at high frequencies, much higher than the 50Hz used in theabove experiment. These losses are also reduced by selecting an amorphous metal core. North American wind farms are currently making extensive use of these cores because they allow for the production of extremely efficient transformers. (General Electric Company, 2011).

ConclusionThis experiment aimed to isolate losses due to eddy current. While quantitative value of the losses could not be reliably determined because of experimental limitations, the losses could be qualitatively isolated. By this it is meant that losses, which were predicted by theory were observed in the results as theoretically predicted, but these losses were not consistent enough

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to quantify. Research into secondary sources provided more information on how a transformer core may be selected or designed to minimise eddy current losses and maximise efficiency was conducted. On the whole this experiment was largely successful given the limited resources available.

ReferencesClarke, R. 2008, "Magnetic properties of materials", University Of Surrey [online] available at http://info.ee.surrey.ac.uk/Workshop/advice/coils/mu/

Cullity B. D & Graham C. D. 2008, Introduction to Magnetic Materials, Wiley IEEE Press, New Jersey

Elliot, R. 2001, "Transformers - The Basics (Section 1)", Elliott Sound Products [online] available at http://sound.westhost.com/xfmr.htm

General Electric Company (Producer). "Prolec GE High-Efficiency Transformers Chosen for North American Wind Farms", General Electric Company [online] available at http:// www.genewscenter.com/content/detail.aspx?releaseid=3635&newsareaid=2

International Copper Association 2011, "Higher Efficiency Copper-Wound Transformers Save Energy and Dollars", International Copper Association [online] available at http:// www.copperinfo.com/energy/transformers.save.html

Kane, W.M. & Sternheim, M.M. 1988, Physics Third Eddition, John Wiley & Sons, Singapore.

Nave, C. R. 2011, "Magnetic Susceptibilities of Paramagnetic and Diamagnetic Materials at 20°C", Georgia State University [online] available at http://hyperphysics.phy-astr.gsu.edu/hbase/ tables/magprop.html

Pawar, S. D. & Murugavel, P. & Lal, D. M. 2009, "Effect of relative humidity and sea level pressure on electrical conductivity of air over Indian Ocean". Journal of Geophysical Research 114

Serway, R.A. & Jewett, J.W. 2010, Physics for Scientists and Engineers with Modern Physics eighth eddition, Brooks / Cole Cengage Learning, California.

Serway, R. A. (1998). Principles of Physics (2nd ed), Brooks / Cole, Texas

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Acknowledgements

We would like to acknowledge and thank the demonstrators for their help in carrying out this experiment.

We would like to acknowledge and thank the lab staff for their help sourcing equipment and materials for this experiment.

We would like to acknowledge each other's hard work in carrying out this experiment.

ApendixBelow is a table of raw results for many configurations tested.

Config Vp Ip Pp Vs Is Ps E

Laminated 12.1 1.4 16.94 1.5 0.4 0.60 3.54%

Open Horseshoe

12.2 1.34 16.35 2.6 0.27 0.70 4.29%

12.2 1.42 17.32 1 0.44 0.44 2.54%

Closed Horseshoe

12.3 0.71 8.73 4.8 0.56 2.69 30.78%

Laminated 12.3 0.79 9.72 3.4 0.64 2.18 22.39%

Closed Horseshoe

12.3 0.71 8.73 4.8 0.55 2.64 30.23%

Aluminium 11.1 4.23 46.95 0.2 5.00E-02 0.01 0.0213%

11.2 4.09 45.81 0.1 3.13E-02 0.00 0.0068%

11.2 4.03 45.14 0.1 5.36E-02 0.01 0.0119%

Copper 11.1 4.04 44.84 0.1 4.20E-02 0.00 0.0094%

11.2 3.89 43.57 0.1 5.10E-02 0.01 0.0117%

11.2 3.82 42.78 0.1 3.16E-02 0.00 0.0074%

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Air 11.1 4.11 45.62 0.2 3.04E-02 0.01 0.0133%

11.1 4.23 46.95 0.2 3.13E-02 0.01 0.0133%

11.1 4.04 44.84 0.2 2.24E-02 0.00 0.0100%

Laminated Core Straight

12 1.97 23.64 2.6 2.00E-01 0.52 2.20%

11.9 2.12 25.23 2.9 3.20E-01 0.93 3.68%

11.9 2.11 25.11 2.8 3.40E-01 0.95 3.79%

Steel 12 1.79 21.48 3.9 4.00E-01 1.56 7.26%

11.9 1.91 22.73 2.9 6.90E-01 2.00 8.80%

11.6 1.8 20.88 4.2 4.10E-01 1.72 8.25%

Note the follwing results have no uncertainties. They were conducted with a resistor hooked up at 250hm for the load.

Copper Round Bar

10.5 3.92 41.16 0.2 0.0133 0.00266 0.006462585

Neodymnian Magnet - Iron backed

10.7 3.54 37.878 1.3 0.0644 0.08372 0.221025397

Neodymnian Magnet - Tube

10.5 3.9 40.95 0.4 0.0226 0.00904 0.022075702

Iron Magnet Bars 10.7 3.59 38.413 1 0.05 0.05 0.130164267

Iron Bar - Homebrew Horseshoe - Opposite Sides

12.1 0.74 8.954 5.2 0.11 0.572 6.388206388

Iron Bar - Homebrew Horseshoe - Same Side

12 0.78 9.36 7.2 0.26 1.872 20

Iron Bar - Homebrew with tissue laminations

12.1 0.86 10.406 6.4 0.23 1.472 14.14568518

Pole on a 12.2 0.83 10.126 6.5 0.23 1.495 14.763973

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laminated horseshone

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Double Horseshoe - Laminated Next to each other

12.2 0.51 6.222 8.8 0.33 2.904 46.67309547