Bore and Stroke have no effect on Horsepower (Part 2)

KTM X-Bow Engine [via]

Last week  I explained the relationship between horsepower and torque.  For this post, I will explain the second concept – how torque is calculated inside a bike engine

Engine torque calculation

The torque that an engine develops is a result of the torque exerted by the piston on the crankshaft.  (For multiple pistons, remember to add the torque for each piston).

Picture 1 below shows how the downward force of the piston is translated into a torque ‘force’ on the crankshaft via the connecting rod.

We can see that torque and piston are related in someway, but how so? Like this:

Torque = Piston Force x Crank pin offset  — (Picture 2)

Still with me so far? Good.

So how do we calculate this Piston Force and Crank Pin offset?

Piston Force          =    Pressure on piston face x piston face area  =    P x π x (Bore/2)2

Crank Pin offset    =    Stroke / 2

See the Picture 3 below for a clearer explanation

So back to the equation

Torque   =    [Piston Force] x [Crank pin offset]    =    [P x π x (Bore/2)2 ] x [Stroke / 2]

This is the equation I need to prove that Torque (and hence horsepower) is independent of Bore and Stroke.

Lets go back to the table.

2 similar capacity engines with different bore and stroke combinations

Since pressure is constant in both these engines, we can leave it as P.  Plugging in the bore and stroke values into the above equation:

Torque of Engine 1            =          P x [π x (58/2)2 x 47.3 / 2]  — [formula for capacity]

=          P x 125 / 2

Torque of Engine 2            =          P x [π x (52.37/2)2 x 58 / 2] — [formula for capacity]

=          P x 125 / 2

So there you have it, a mathematical proof that torque is independent of Bore and Stroke, and hence has no effect on horsepower.

I hope you’re still with me, and that you benefited from my learning.  More to come next time.

If I made any mistakes, comments and critique are most welcome below!