Can I jump in here as I believe everyone is saying this correctly.
This will be directly from the horses mouths
, being Newton, Watt, Da Vinci etc. It is all locked by equations developed from these people. Please bear in mind I am not getting at anyone as I see conversations following on in part from others, and at times it's easy for a reader to get mixed up if you are only reading from part way.
We need Energy input (fuel) to get the Work Done. Energy comes in many forms and as it goes in, will branch off in many directions using up parts of this energy blob as frictional heat etc, eventually getting some Work Done hence producing a final output. I view energy as being a blob that goes into a system, various parts are used up as losses and getting the Work Done, and what's left is your output. In our case the desired output is Horse Power, where this unit of power was created as a starting point or benchmark. It is still used throughout industry, on just about every induction motor there is a plate saying the output HP and equivalent Watts.
Energy is time related as it is calculated in one way of using Energy (Watts used over a period of time) = Power (Watt) * Time (seconds) as in your home elec bill of E=Watts per Hour. Torque is not time related as it is measured in force of Newtons/Meter. Horse Power output is time related as 1 Watt = 1 Joule (of energy) per second.
What we now have is torque being produced (by the engine using Energy and getting the Work Done) at the rear wheel, but torque is producing an angular force, and hence a linear tangential (right angled) force in one direction only at the point of contact (tyre and road). With torque not being time related, then the power output means nothing and cannot exist without time now being added to the equation. So torque will move you forward in one linear direction only, but cannot produce power output at this moment as time is needed for the power output equation (HP).
So we have some equations developed by the guys with the sore heads, and we have at one point a torque equation that is in Newton/Meters (no time involved), but is trying to push the bike forward in one direction only. Then a following equation of Power comes along that requires time and hence HP output can be calculated..
So if you try and go from the fuel going in, to the Horse Power out in a sequence of events using calculations, then the torque equation comes along, with the Power equation following after.
Final sum up;
1. Mechanical Power is defined as the 'rate' at which Work is done.
2. Torque is the rotational analogue of Force. Force causes linear acceleration, torque causes angular acceleration.