Launch system wire resistance.
Yesterday at the scout launch, Charlie asked about what gauge wire should be used if he were to replace the existing cables on the club launch controllers. Time for a little engineering and math.
The electrical resistance of wire varies with its length. The longer the wire, the higher the resistance. It also varies inversely with its diameter. The resistance of a length of wire is determined from the following equation:
R = 𝛒L/A
where:
R — RESISTANCE (in ohms Ω)
L — LENGTH (in meters)
A — Area (square centimeters cm²)
𝛒 — resistivity constant (for copper wire, it is 1.725×10⁻⁸ Ω・m)
Wire gauge (AWG) is the wire diameter in circular mils. 16 gauge has a diameter of 0.05082 inch and 22 gauge has a diameter of 0.02535 inch. Converting these to metric, the diameters are 0.129cm and .065cm respectively. The areas in cm², from πr² or π(d/2)², are 0.013cm² and 0.0033cm² respectively.
Putting these into the resistance equations using a 1 meter unit yields:
R₁₆ga. = 1.725×10⁻⁸ Ω・m (1) / 0.013cm² = 1.725×10⁻⁸ Ω・m (1) / 0.0000013m²= 0.01327 Ω/m
R₂₂ga. = 1.725×10⁻⁸ Ω・m (1) / 0.0033cm² = 1.725×10⁻⁸ Ω・m (1) / 0.00000033cm² = 0.05227 Ω/m
What does this mean for our launch controllers? Assume 100feet of cable. 100feet is approximately 30 meters. That means that a cable 100 feet in length of 16AWG wire has a resistance of 1.327Ω and a 100 foot length of 22AWG has a resistance of 5.227Ω. That's on a difference of 4Ω per 100ft between 16AWG and 22AWG wire.
The club typically sets up the launch pads approximately 25feet away from the launch controller. Thus, the total resistance for the paired cable is 0.664Ω for 16AWG and 2.61Ω for 22AWG.
Usher in Kirchoff's and Ohm's law.
E/R = I
In a 12V system, that means there's 18A* for the 16AWG system and 4.6A for 22AWG. The current in both, assuming that the batteries are well charged and fresh, is more than adequate to fire the typical Estes igniter.
(*) It's highly suspect that the batteries can supply this current.
So is the answer then "use whatever you want"? 🤔
Good research! Thanks for sharing.
When I was learning about building launch controllers I also saw some considerations about the internal resistance of the batteries used and the non-ignition current of the typical igniter for continuity checks. But for this question specifically I agree it probably doesn't matter, in fact the physical handling characteristic probably matter more! That is, having some extra strands to account for longevity/breakage and the jacket UV and abrasion resistance. Then there's cost.. Fun to think about!
The point is that the big heavy 16AWG wire is pretty much overkill for the small distance we maintain to the pads. The heavier wire, however, does often pull the igniters out of the rocket.
So then why not have the best of both worlds. Have a heavier wire (18awg?) for most of the run to the pad, but step it down to something smaller (22awg) for the last 5ft. Make that transition a plug connector of some sort so one could easily switch out the fried ends once in awhile. Doesn't need to be those big 110v lamp plugs we currently have in the wires for some unknown reason.
But before we do this, are we heading towards building new controllers as we've discussed but never committed to? Should this be part of that design consideration?
🤷
The main reason I would like to use 16 awg is so we can do clusters. I have seen several failed cluster launches that I chalk up to not enough amperage. I plan to do a little more testing testing, I hope. I believe one controller has 16 awg and the other 18 awg.. I will let you know.
The reason for the extra plug and sockets was to be able to add extra length if needed without changing the whole run. Not a great reason. My fault.
Charlie
Quote from Ckirlew on May 14, 2023, 5:42 pmThe main reason I would like to use 16 awg is so we can do clusters. I have seen several failed cluster launches that I chalk up to not enough amperage. I plan to do a little more testing testing, I hope. I believe one controller has 16 awg and the other 18 awg.. I will let you know.
If you remember, Jeff Miller launched his 7-motor cluster off of my small wireless unit.
When it comes to clusters, the igniter are wired in parallel, not series. The problem with series is that if one ignitor goes before the others, the circuit is broken and none of the others will ignite a motor. In this case, the total resistance, let's call it R𝑡, it the sum of the resistance of all the igniters. Estes inters have a resistance between ~0.75Ω and 1Ω. I = E/R with a 12V battery and .75Ω ignoring leader resistance, means you drawing 16A. Again, I doubt the batteries have that. However, igniters are wired in parallel to better insure that all igniters can start a motor. This is because current still flows if one igniter burns through. In parallel, the resistance is 1/R𝑡 = 1/R1+1/R2+...+1/Rn or R𝑡 = R1R2...Rn/(R1+R2+...Rn). Assume a three motor cluster and an igniter of 0.75Ω. the resistance of the clustered igniters is 0.75³/(3•0.75) = 0.422/2.25 or 0.1876Ω. I=E/R means 12/0.1876 or ~64A. CERTAINLY, not happening with the present batteries.
What's needed for a good cluster ignition, it a battery that can supply a very high current for a brief interval. In my radio units, that means, with present battery chemistry technology, lithium batteries. I use two Li/FeS₂ with a voltage of 1.8V (1.5V𝑛𝑜𝘮) and two 14500 Lithium Polymer batteries with a voltage of 4.2V (3.7V𝑛𝑜𝘮). The total peak voltage is 2(1.8) +2(4.2) = 3.6V + 8.4V or 12V.
Small lead-acid gel AGM batteries are good but they need to be charged to peak when used for clusters.
The reason for the extra plug and sockets was to be able to add extra length if needed without changing the whole run. Not a great reason. My fault.
If their connections are clean, their contributions should be negligible.
- The plugs aren't necessarily a bad idea, just was unknown to me. The concept you mentioned is sound. I think they could be done a little more "elegantly," but I wouldn't call it anybody's "fault" as I don't think it is a fault.
- I have launched 2 and 3 engine clusters on our pads several times (wired in parallel with my 3 lead harnesses), however - on one occasion we couldn't ignite any of the cluster on the 1-6 rack. We moved it to the 7-12 rack and it launched, all 2 or 3 ignited just fine. (It was my "Titan Flex" which can fly on 1, 2, or 3 engines. I don't recall what it had on this occasion.) I also have launched my "Flying Machine" on the 1/4" rod, wires 11 or 12, with my harnesses to the 3 engines in parallel. So that controller seems to have the guts needed. The 1-6 controller definitely has less. If I recall, we switched batteries too, with no change. So there is a big difference between resistance of the 2 controllers, for whatever reason.
- If you ever read the directions Estes has for launching clusters, they instruct one to connect the igniters in series. Aside from being too far apart on my cluster rockets, I never had the warm and fuzzies with that setup.
Quote from Eric Becher on May 14, 2023, 10:01 pmIf you ever read the directions Estes has for launching clusters, they instruct one to connect the igniters in series. Aside from being too far apart on my cluster rockets, I never had the warm and fuzzies with that setup.
I don't know where that's been written. It's always been wired in parallel for cluster ignition. Here's a collection of Estes Classic Educator Series Technical Reports. TR-6 covers clustering techniques. It states in parallel throughout the read. It's the difference between the old Christmas tree light strings wires in series where one bulb out means they're all out or newer strings with blues in parallel where if one bulb goes out the rest stay lit.
https://estesrockets.com/wp-content/uploads/Educator/2845_Classic_Collection_TR-TN.pdf
Never saw the TR, but I thought that I've seen them wire up the igniters in series somewhere. I wouldn't do it, but I know I've seen it somewhere on a diagram. Might have been on something old.