I'm using host power on this.
Swat, I understand what you're saying, but momentum has little to do with speed if memory serves. The mass just means that it accelerates more slowly. I'd say 500 miles would be pushing the envelope. The only person who is siding with you on this is blazer who is the direct beneficiary. Also your graph axes have no labels.
Wikipedia has some nice equations on railguns. If you can give us the specs for the longbow (OOC for the sake of your own security) ahead of time and not edit the post you put them in so we know there's no BS going on, and plug those numbers into Wikipedia's formulas, factor in fins and all that other stuff and still tell me with total honesty that the longbow can have a range of that sort, then it's real and there will be no further challenges.
Frankly, I doubt that the Longbow is reasonable. Give me the math, and I'll believe you. Until then, the Longbow is limited to known railgun range (250 miles).
I feel that this is an equitable solution given that the current numbers don't seem to correlate to knows railgun performance and we are limited in our technology to the present plus a couple years. This way, I get proof and Swat gets to show us all how smart he is.