Sorry, but I have to respond to this. As an electronics engineer and fanatic, I can't help it, I just have to.
You have a bit of a strange idea about power, current, and so on.
An 8 ohm load draws only half the current of a 4 ohm load. You say that the input current is about just as high. Well then, where does the rest of the current go then? And more, since
U = R x I (voltage = resistance x current)
P = U x I (power : current x voltage)
we can derive
P = R x I²
That would mean that, if indeed the current would be constant, the 8 ohm speaker delivers twice the power of the 4 ohm...
Sorry man, wrong there...
What does "power run freely" mean? An output stage of an amp delivers some current to the load, and depending on the output impedance (which should be as low as possible) that results in a voltage across the load, and some voltage across the output impedance, called "loss". That's why them things get hot!
Keeping that in mind, you will understand that the loss is lower when the amp is loaded with 8 ohms instead of 4 ohms.
That's not how it works, however going deeper into this would take me far into schematics and theory.
It is indeed ALWAYS better to install power supply cables as thick as possible, with as low resistance as possible. Even a very low resistive loss costs power at the end. Suppose that the cable from battery to amp has only 0,1 ohm resistance, which is not bad at all! For a 240 watt RMS amp it would carry 20 amps, meaning a loss of 2 volts! So your amp wouldn't be getting 12 volts, but only 10... (Simplified calculations). That's also where these big electrolytic capacitors come into play: they flatten out the load peaks, so the current in the supply cables is less peaky, and you'll have a more steady supply, and less loss.
I see where your coming from and indeed I am worng in some areas, I did mention it's been a while & I'm probably not using the right words to get across what I am trying to say, but so to are you in some assumptions with speaker loads seen by the amp.
Without acutally measuring the amps current draw in a given setup I'd be inclined to say that no matter what load on the output side the amp itself, running full volume would try to pull the amps it needs to produce it's RMS figure.
Of course this most probably will change if using an 8ohm speaker as below.
An 8ohm speaker/load will not stress the amp so much and that is a fact, the lower the impedance the easier it is for the amps power to flow though into the speaker. Crude way of explaining it but thats a simple term.
Some ampifiers are not rated to a 2ohm load on the bridged output, as the lower the speaker impedance the more amps/current will flow through the amp. This you can see from the amps load tests/specifications, an amp connected to a 4ohm load will give X amount of power while the same amp connected to a 2 ohm load will give Y which is more RMS power.
A 4 ohm speaker delivers twice the power of an 8ohm dont you mean? You may be refering to what I have possibly come across as saying.
4ohm is less of a load on the amp compared to using an 8ohm speaker, the amp will produce more power connected to a 4 ohm speaker than an 8ohm one.
In essence you do not want the lowest impedance rating you can get, unless of course your amplifier is capable of running down to 1 or 0.5ohm even. This is how the top boys get mega bass from small amps, if the amp is stable down to really small impedances then you can configure a group of subs to load the amp down to say 0.5ohm and inturn it will produce lots of power.
The lower the speaker impedance the higher power output you will get from the amp as there is less restriction to the power output.
Another crude example is a hose pipe with a bung in the end, with the end of the pipe blocked up the water pressure behind it builds up.
If it can burst the pipe it will, no restiction to flow means the water will flow more freely. The same results happen with amplifiers if the impedance is to low for it to handle, this I know first hand.
That's also where these big electrolytic capacitors come into play: they flatten out the load peaks, so the current in the supply cables is less peaky, and you'll have a more steady supply, and less loss.
I can agree that they smooth power once inside the amplifier yes, but will not necassarily smooth power into the amp from the power cable.
In this instance you will need a dedicated smoothing capacitor of 1 farad or above, a clue to needing one of these is your lights dimming with the bass hits. That and a high output alternator or better battery.
When it comes to working out current draw for a give power supply or output this maths is beyond me so your experince here is invaluable.
But when it comes to ICE & speaker wiring I do know a lot as I have been there blowing amps up which are not loaded correctly.
Also, when connecting a 4ohm subb to the BRIDGED output of a 2 channel amp you are halving the 4ohms across 2 outputs of the amp. Hence the amp will be running @ 2ohm's bridged mono.
Dedicated MONO amps are different again.
Subb wiring diagrams explain in most cases the various ways of wiring up 1 or more subbs to provide a given impedance value for the amp to see.
Of course there are some amps that regardless of load on the speaker side will give the same RMS power if it was driving an 8, 4, 3 or 2 ohm subb. JL Audio amps are one such make.
On the basis of amps running hot, an amp running a 2ohm load will be hotter than the same amp running a 4ohms load.
If MR JP can give us the specs of his amp then you could probably work out it's current draw and recommend the correct size cabling he needs?
This is cool, I'm having to remember what I've done myself in the past.
P.S. Just found this : Home Toys Article - Speaker Impedance, Your Amplifier And You.
Another : OHM SWEET OHM
Good reading and the first one makes references as I do to a water hose pipe.
I'm not 110% on my electrics, I used to be an electrical/mechanical engineer but didn't do much sutdying in electric circuits more wiring and programming.