Power and speed
If 55 bhp gives 125 mph (personally I doubt that many Shadows ever did 125 mph, so I'll settle for 120 mph) then to get 165 mph, you need 165/120 squared, x 55 = 103 bhp. The Vin is naked, the modern bike isn't, so 95 bhp would seem more reasonable for a faired bike. However, from my own experience of publishing power figures on oilfield downhole motors, knowing that drilling "engineers" were uneducated nerds, more testosterone than brains, who were impressed by numbers they didn't understand, bhp became an abbreviation for "brochure horse power". We always looked to see what the opposition were claiming, then fiddled the numbers to get more. A flash reading of 125 on the brake, miraculously survived, became "delivers a reliable 125 bhp". Who would ever know? It's capitalism, baby. Caveat emptor. As many bankers - some, but not enough, busted - would tell you.
The doyen of UK Aermacchi tuners, Dick Linton, quotes an American tuner (sorry, forgotten his name) who said that horsepower sells bikes, but torque wins races, and this is true. When the torque falls off a cliff (on the Manx, about 7200) the speed is still increasing, but now more slowly. Knowing this, I shifted at about 7000, and only let it run (to about 8300) in top. This works. One of the highlights of my racing career was out-accelerating a 55 bhp Gilera four replica on a 50 bhp Norton at about 110 mph. He had the power, but I had the torque IN THE RIGHT PLACE. (Noisewise there's no comparison. I got the full Doppler as I eased past him. Orgasmic.)
I've never put the Vin on a brake, but it would be interesting. Meantime, it goes from 30 to 100 in top, at which point I need to deploy the Vulcan Death Grip to stay on board, and I'm too old for any undignified lying on tanks. Would it do 125 mph? Doubtful, but WTF cares? Not me.
However 103 bhp (and now you know what bhp means) is close enough to a claimed 125 bhp to bear out the rule. The horsepower to reach any speed has a square law relationship with the speed difference, starting from about 36 bhp to see 100 mph on a naked bike.
And if you want to check the veracity of brochure claims, try weighing your Fireblade or whatever. Most of the claimed weights are only true if the bike is without oil, petrol - and crankshaft. Would-be customers are known to look particularly at weight. So lie. Who'll ever know?
Thought for the day: a "cynic" is what an idealist calls a realist.
Tom