The horsepower ratings on routers are technically true, but misleading. First, lets talk about what 3-1/4 hp means. If there are no electrical losses (resistance, friction, heat, etc.) in a motor it takes 746 watts to generate a horsepower. Thus it would take ~2425 watts to generate that much power. In reality there's about 10% wasted due to friction heat, etc. and about 10% lost due to how motors work on AC (in technobabble, the voltage and current waves not being in sync over time). The combined effect is a motor that's in the 80 percent efficient range. At that efficiency, it takes about 25A at 120V to generate 3-1/4hp.
Induction motors behave much differently than induction motors under load. An induction motor delivers its rated power, and that's it. If the load goes up a bit, the motor essentially stops.
With an induction motor, when the load exceeds the rating the motor keeps turning and just draws more and more current (and provides more and more torque) until the resistance in the wiring eventually outweighs the ability for the router to draw more power.
As the power consumed goes up the heat generated by the router goes up very quickly, exceeding the fans ability to cool it. Additionall, the electronics is rated for certain amounts of current and, if overloaded, can fail as well.
The 3-1/4hp rating is the peak horsepower the motor can generate, as its generating heat much faster than it can reject it. Essentially, as it is burning itself up.
A side-note for when people here are using routers with speed control. As you are slowing down the router, you are slowing down the cooling fan. Does this mean you shouldn't slow down your router? No. Just keep an eye on how warm your router is or isn't getting when you are spinning a large bit taking heavy cuts at slow speed for a long time, as the router may warm up. The cooling system should be designed to take it but you're definitely loading the router more than normal, for two reasons.
Just my $0.02.
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