George, I'm going to guess this post is somehow related to your series of inflammatory posts about broken ring gears on twelve volt conversions. And it appears your point is that if you run your 6 volt starter on twelve volts you're going to submit your ring gear and starter drive to FOUR TIMES the force they were designed to handle. If that's your point, I'm afraid you're wrong.
First off, Ohm's "Law" isn't actually a scientific law. It's simply the definition of electrical resistance. So it stands to reason it accurately describes the behavior of purely resistive electrical loads. But your starter motor isn't a resistive load, particularly when it's cranking an engine. You might be able to adequately describe its behavior using a second-order differential equation, but simple alegbra isn't going to cut it.
The real question is: "How much more force does the ring gear experience when the starter voltage is doubled?" To answer this, we need to look at the instant the starter drive engages with the ring gear. That's when the starter's torque is greatest. Let's assume for a moment that the drive engages the instant your hit the switch (it doesn't, but bear with me). Its torque will be a function of the current through the starter. If we double the voltage to the starter, we double the initial current as well. So we DOUBLE the initial torque.
Now what this model doesn't take into effect is the torque resulting from the armature's inertia. The armature does have some angular velocity when the drive engages (otherwise it wouldn't engage!), but it hasn't had time to accelerate to no-load speed. So there is some shock contributed by the starter's inertia, but it shouldn't be significant. (That assumes the drive isn't sticky and engages almost instantly.)
Yes, running twelve volts to a six volt starter is going to increase the likelihood of ring gear damage. But so will installing a twelve volt starter. After all, if we didn't get more torque from 12 volts than six, our tractors would all have six volt systems.
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