Wire Gauge Selection for 45A Motors and 90A Battery in RC Airplane with LiFePO4 4200mAh

Hello there people,

     I'm a freshman at Mechanical Engineering and I've become a member of the Remote Control Airplane Design of my Engineering School. So, we are to design an aircraft for Brazil's national Aerodesign competition, and it's going to be two-engined with electrical motors, and they will be powered in parallel by a 4200mAh LiFePO4 battery. This battery has current discharge capacity above 100A, and each motor's maximum power is obtained with about 45A.

     So, we are required to write the airplane project report, in which we must properly justify that the conducting wires chosen are safe. After some searching, we've found Silicon-insulated wires that can bear high temperatures up to 200ºC. We've been trying to find the minimum cross-sectioned area for the wires going through each motor, having to support 45A as a maximum value of current, and the wire that goes from the battery, which must support the total maximum current (~90A).

     However, the furthest we've got to is a rule of thumb that says that the current capacity of a silicone-insulated wire is approximately given by 25x(cross-sectioned area in mm²). For example, a 2.0mm² cable can handle up to 50A. This is far from a technically competent way to prove that the circuit is safe. So, I'm in search of a way to properly demonstrate the safeness of our airplane's electrical circuit. Can you people help me with this?

     Thanks for the attention!

Matheus firstly the aircraft industry is one of the most regulated around, so if you look and ask around enough you may find some regulations that specify cable sizes.Rules of thumb generally work pretty well, but I'd question this one.  In the field of house electrical wiring, in which I have some experience, we'd use 1.5 mm2 wire for lighting circuits with a 5 or 10 A breaker, and 2.5 mm2 wire for plug circuits with anything up to a 20A breaker.  For an electric stove which might take 25A or more on full load we'd use 6mm2 wire and a 30 or 40A breaker.  Fine, silicone insulated wire is able to carry higher current, and run warmer, than conventional wire, but that's mostly for fire protection, it's not intrinsically able to carry more current and stay cool.  The other side of it is that in aircraft weight is at a premium so you don't want to use bigger cables than you need, but I'd be looking at larger wire than 2.0 mm2.One of our experts is an aerospace engineer and maybe able to give a better answer, I will ask him for  his take on this.

As you refereed to aircraft, albeit a model aircraft, I will point you towards an answer that relates more to a full sized aircraft. 

There is an advisory circular (AC43.13) that represents general repair methods, and is typically pointed towards general aviation.  The AC is approved data for making minor repairs, but can only be used in conjunction other data for major repairs.  In chapter 11, section 5, there is a pretty good set of guidelines for what you are looking for.
This really gives a starting point, though good engineering requires a bit more.  There are more conditions to consider that some directly relate to wire sizing, others relate to other aspects of what the wires are doing.
The first thing that needs to be done is consider the system as a whole.  Where are those wires running, and are there any conditions that you might need to be concerned about.  For example, many of the brushless motor controllers are operating above 20kHz, though are driven by trapezoidal waveforms.  Depending on the rise time, there can be other frequencies in there, and the wires can act as antennas.  There are things that can be done to mitigate this.
You mentioned that the wires can handle up to 200C.  My question is why would you need that (you may, but why)?  If the wires themselves were that hot, then what around it could handle that temperature?  You will be well above the glass transition temperature of any typical composites, and Aluminum at that temperature will have a substantial knockdown in strength.  Perhaps at the connection, but if the electric motors are that hot, then the magnets are starting to degrade, and the insulation on the wires internal to the motor is going to be failing. 

How are you going to attach these wires?  Are they going to be supported, or will they have to support their own weight?
Ok, so if you have gotten this far, do not fear, not all of these things can necessarily be calculated, especially for a project like you are doing.  You will not have access to databases that will have this information, nor will your product have to reach the levels of safety that are required for maned flight.  Risk levels are lower. 

So what do you do?  You use the best engineering information available to you, you then do some testing to validate the assumptions that were used during that engineering assessment to ensure that you have a product that can do what you want, and that all the rest of the systems are unaffected.

Now if this was my model, and I was not having to write a report about it (in other words, I was just doing it for fun), I would probably go to a typical ampacity chart, or look at what others are doing that has been successful.  I might even try and measure the wire gauge that is on the cells, and go with that, do a test run and see if the wires are getting too hot, or if there is too much voltage drop and just go with it.
Adam

A couple of extra thoughts here (and thanks Adam for the above).  If your motors consume 45A each they would be pretty beefy so I'm assuming you're building a fair sized drone here?  Even if they're only 3.7V motors that's 160+ watts.And if you ran such a motor on a 4200 mAh battery, it would power it for less than 1/10 hour, so that's about 5 minutes or so.So I'd say either you will be way off maximum current demand most of the time, in which case you could compromise on your wire sizes a bit, or you'll only have very short flights?

Thank you Adam and David for your attention!David, you brought up some important things: the reason for the powerful motors we have chosen is that the competition envolves carrying the most weight with the lightest airplane possible. Also, we have to drop a payload in a well-determined area on the ground. The airplane's maximum takeoff weight is about 6kg, and that's the reason for the powerful motors we've chosen. Also, indeed it's a short flight, we have estimated that the maximum flight time is about 90s, with the plane flying with takeoff speed. I think it is an important thing to consider, along with the fact that we'll most likely not be flying with maximum power most of the time.
Also, I forgot to mention that the wires that come out of the battery are 10AWG silicone-insulated, which means they have 5.2612mm² of cross-sectioned area. According to the thumb rule, they can handle up to 131.53A. This is the battery model: ZIPPY Flightmax 4200mAh 4S1P 30C LiFePo4 (link:https://hobbyking.com/en_us/zippy-flightmax-4200mah-4s1p-30c-lifepo4-pack.html). As you can see, it has 30C rating, so the maximum current it can deliver is 30x4.2 = 126A
David, you helped me realize that, even if the battery delivered the maximum current, it would last for 120s (4.2A x 3600s / 126A), so, maybe the battery's short discharge period keeps the wires from reaching 200ºC
Adam, you have highlighted an important thing, the possibility of the hot wires affect other parts of the airplane. As to that, we were thinking of wraping  some thermal insulating material around them, but it would be really interesting if none of these would be needed, perhaps increasing the wires diameter enough. You also asked about how we're going to attach the wires and how they will be installed. Well, most of the wire circuit will be inside the wings, and they will run through holes in the airplane's ribs. Any wire extensions are going to be soldered with tin. The motor will be connected with the wires through a XT60 connector (It's not very much known, I think it's very restricted to the RC world)
So, after you guys cleared out some things, I started playing around with some basics eletrodynamics and I wanted to show what I've done to you: