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I'm in the process of buying an ebay bike (http://www.ebay.co.uk/itm/121337863485) which I won for maybe 60 - 75 % of its expected value. In the description the owner states that the bike dyno'd 10,000 miles ago. I don't know what that means but it sounds bloody scary. Can anyone shed some light on what this means mechanically?

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tl;dr: it's fine. dyno-ing = measuring. See @Paulster2's answer. –  Bob Cross May 19 at 18:39
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Basically, it sounds like they put the bike on a chasis dynomometer (or "dyno") which was made to run motorcycles. This dyno was used to measure the power output of the bike at the rear wheel. What happens is, the rear wheel of the motorcycle engages a large roller on the dyno. The bike is then strapped down so it won't go anywhere. The engine is started, the bike is put into gear, and is then ran up to speed. When brought up to speed, the dyno is engaged, which puts a measureable load on the roller. The tester will then throttle the bike up to wide open throttle (WOT) to get a reading on what the bike is capable of as far as output. The reading is taken and you have your rear wheel horsepower of the bike. For a bike, 125hp is quite a bit of HP (I'm thinking Hyabusa here ...). And unless it's obvious to you, the owner has riden the bike 10k miles since he did the dyno run on the motorcycle.

Here is an example of a motorcycle dyno made by Dynojet.

If you are wondering about how Torque and HorsePower relate to each other, I wrote this diatribe a while back which may give you some understanding.

EDIT: I did want to add that the "B" in your "125BHP" refers to "brake horse power". This is kind of an antiquated term, but refers to the brake action used to measure the output, with the output given being before the power losses caused by gearbox, alternator, water pump, power steering pump, A/C, etc. BHP is a very inaccurate measurement of the HP output of an engine. More commonly used now is the term Rear Wheel Horse Power (or Front Wheel Horse Power if a FWD vehicle). This is the power output (which is actually what was being measured on your bike) measured where the rubber meets the road and is a more accurate measure of what the vehicle's capability will be.

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Oh thank goodness! I was thinking it was some kind of malfunction of the flywheel at speed. I imagined all kinds of wobbling and control issues. It's great to hear that I'm just an over-energetic-worrier and the previous owner is just a bit of a nut... Thanks for the great explanation. Come to think of it, I've seen this contraption in a garage. Just didn't know it was called a dynomometer. –  grenade May 19 at 18:46
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"most likely refers" should be replaced with "definitely refers" - BHP always == brake horsepower –  Bob Cross May 19 at 19:45
    
@BobCross ... I don't like to assume things, especially when they are using the terms "brake HP" and "chassis dyno" ... seems to me the two should mutually exclusive. –  Paulster2 May 20 at 1:06
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@Paulster2, BHP is the unit for brake horsepower - if they're using a chassis dyno, they're almost certainly applying some multiplier to "correct" for gearbox/transmission/etc loss. How accurate is that? Good question. <-- Bob gives Paul a meaningful look indicating opportunities to write even more words in a lengthening answer ;-) –  Bob Cross May 20 at 11:55
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@Paulster2, don't forget differential losses, even in a close-to-1:1 gear. I'm less charitable and suspect that the dyno operator took a measurement and applied a rule of thumb (e.g., 20% drivetrain losses sounds about right!) I totally agree that wheel horsepower is always more useful since none of us drive an engine stand to work. –  Bob Cross May 20 at 19:26
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