Headlamp question

Cracked is correct. A good example is, we used to use 220V lamps in our 120V socket in my Mom's wellhouse in winter. This created a very low power heating element that lasted a very long time. It didn't need much, as the wellhouse was insulated, so only the coldest nights were a threat

Example.......a 220/240V 200W lamp is about .9 amps

The very same bulb operated on 120V draws 1/2 the amperage at 1/2 the voltage

So 120 X .45A is 54 watts, about 1/4 the wattage that it generated on rated voltage

Both is true of either light or heat. As the voltage sags, so does the amperage, so the wattage doesn't drop by 1/2, it drops by a factor of 4 (or 1/4)