# Riding the Curve – The Theoretical and Practical relationship Torque and Power in your machine?

It’s a good day to ride, you put your gear on and go out for a spin – roam the streets, burn some rubber, paint the town glowing red with the heat from your engine. Yes, we know all too well what we need to do and how we need to do it!!

What we are yet to understand is how it works when you need it to!!

That feeling of power, that pull of your bike, that wind speed hitting your face, that feeling is something I am sure you know all too well – there is no need to try and comprehend that, because for each one of us it’s a totally different scenario governing that comprehension.

What you read here and now is not a theory about how you feel when you ride your bike – it is in fact the causality caused by that certain “thing” of sorts that happens under your seat, between your legs, above the ground and inside your chassis that lets you on an everyday note achieve that feeling. It’s the power you feel, the thrust that pushes you and the speed that gets you going every time you shut the visor on your lid and pull that accelerator in the hope of riding to kingdom come.

Today we talk about the understanding your bike has with itself, the intelligence it works with and the relationship it creates between the power it holds and the torque it shows.

Plainly said by a motorcycle manufacturer about half a century ago when asked how much power can you put in between two wheels, his reply was simple yet intellectually elegant – “Torque is measured but Power is calculated”. It is that power and torque, that secret which I will let you in on calculating for yourselves today.

The character of a motorcycle, the way it feels, the way it rides, is determined by a combination of many factors. Two of those characteristics are torque and power, and these are probably the most important. Here we try to explain what torque and power mean, and how they influence the way a motorcycle feels.

What is Torque?

Taking your motorcycle’s engine as an example – to be specific the Pistons and Cranks. The piston moves up and down, and the force for that comes from the fuel that is burned. Connected to the piston is a rod, the connecting rod, and that rod is connected (with the ability to turn) to the crankshaft.

When you try to compare that system to a bicycle for example (since a cycle was and always will be the father of two wheels), you would compare the rotation point between connecting rod and crankshaft with the bicycle pedal. The force that you apply to the pedal, with your leg muscles, is comparable with the force that is applied by the piston on the crank. The distance between the pedal to the rotation point is comparable to the distance between the crank and the middle point of the crankshaft, and in the same way as in the bicycle example, the distance “counts” for 100% when the point of the crank that is connected to the rod has an angle of 90 degrees with the direction of the piston, and for 0% when that point is in the highest or the lowest position.

Newton-Meters

The amount of torque is expressed in Newton meters: (N-M).

In technical specifications of motorcycles, you often see a number for the maximum torque, and the number of revolutions per minute at which that torque is delivered (in R.P.M., revolutions per minute).

Maximum torque

A piston, therefore, delivers a varying amount of torque. The torque at a certain rpm is the average torque that the piston delivers during the revolution stroke. And when your motorcycle has more than one cylinder, the torque of the individual pistons add up. The rpm where the maximum torque is delivered, is the rpm where the fuel is burned most efficiently: it is at that rpm that the piston delivers the maximum torque on the crank.

The gearbox transmits the rotation of the crank onto (ultimately) the wheels. The amount of power tells how fast work can be done.

Power is expressed in kilowatt (KW) or in Horsepower (H.P.).

When you know the torque of your motorcycle with a given rpm, you can deduce the power, by multiplying the torque with the number of revolutions per minute (and of course with a constant factor to adjust the different dimensions like R.P.M., H.P. and N-M).

So what’s the relationship between horsepower and torque when we talk about engines?

Horsepower = Speed (R.P.M.) x Torque (ft-lbs) / 5252

To find the horsepower at any given R.P.M., multiply the torque at that R.P.M. by the R.P.M., then divide by 5252. This will generate a horsepower curve by calculating the horsepower at various R.P.M’s.

Find the peak of this curve (the highest horsepower number), and that is the horsepower rating of the engine. Depending upon the torque curve of the motor, maximum horsepower may occur at low or high RPM. Generally it is near the maximum RPM of the engine.

Now I am sure you all must have some certain doubts about this theory here so at this conjecture I will clarify some of the few questions you might have swirling around in your head.

Firstly, the mathematics – that we shall get to in the next few lines I promise.
Secondly, one of the two following questions must be poking at your brain.

Why does torque drop after a certain RPM?

Torque starts to decrease because the engine cannot breathe as well. Due to the speed, the cylinder does not fill with air as well.  A designer can get around this problem with “tuned intake” which sets up a resonance to pack the cylinder with air, but it only happens at a certain R.P.M.

The next evolution of design is to make a variable system which packs the cylinders with air at all RPM; this is usually called “variable tuned intake runners” or something like that and involves valves which open and close to create a different size for the air box and manifold.

Why does power continue to increase after torque decreases?

Remember that the power is essentially the product of the R.P.M. and the torque.  When the torque peaks at a certain R.P.M. and starts to drop off, the decrease is small and is not enough to offset the increasing R.P.M., so the overall product still increases.
Eventually the decrease in torque becomes large enough that it outweighs the increase in R.P.M. and we see the power start to drop.
Because of this, the power peak will always be after the torque peak.

An Explanation of sorts!!

Talking about peaks here, the whole point of this article is to tell you what is going on in your machine and without a basic diagram of sorts that can be quite difficult to understand, so here as promised is the derivation of the mathematics of this theory and the graphs of the two peaks to show you when, where and how exactly your bike pulls out the relationship between torque and horse power without you asking for it every moment that your bike is turned on and running.

For me to get into these nitty-gritties about torque and power. First we must understand the definitions of both these ideas in the most basic sense.

Torque is defined as a FORCE around a given point, applied at a radius from that point.

Power on the other hand is the measure of how much WORK can be done in a specified time.

There are some facts that need to be cleared off before we get into this –

1. Power here in an engine is dependent on Torque and R.P.M.
2. Torque and R.P.M. are the measured quantities of an Engine’s output.
3. Power is always calculated.

Taking into consideration the above, we can now get into the mathematics of this article which by way of definition I shall prove to be very easy.

From the definitions above, we can speculate –

So implied,

Also, a wheel in your bike is a circle (unless we have some futuristic designers to prove me otherwise, I shall stick to this theory), which means that – distance travelled in one revolution of your wheel is basically the circumference of a circle (don’t worry the formula is right here just in case you’ve forgotten) or in plain words – the length of a circle. Hence,

Distance/Revolution = 2 X π X Radius

(That weird symbol being Pi – I know you all know what that is)

So now,

Distance per minute = 2 X π X Radius X Revolutions per Minute (R.P.M.)

And from the definitions above we can also speculate that –

Power = Force X Distance per Minute

We already know what Force is and we also now know what the Distance per Minute is, hence combining both we can see a pattern coming into form here which is as follows – Power here is –

Power = (Torque / Radius) X (2 X π X Radius X R.P.M.)

Cancelling out the radius’s here for obvious reasons that they can be, we now get –

Power = Torque X 2 X π X R.P.M.

On a side note – not everything can be determined and found out, so Google being the brain here now, we know and can find out that –

1 H.P. (Horse Power) is defined as 33,000 foot-pounds of work per minute which plainly says

Horse Power = Power / 33,000

From the above equations we know now,

Horse Power = (Torque X 2 X π X R.P.M.) / 33,000

Another one to Google here that (2 X π) = 6.2832. So the equation now becomes –

Horse Power = (Torque X 6.2832 X R.P.M.) / 33,000

Taking out all the numbers here, basically taking out a calculator, we now know for a fact that –

Horse Power = (Torque X R.P.M.) / 5252

This being the one and only equation that relates torque and horse power, coincidentally also shows us the same equation as mentioned above and also concludes that dreaded mathematics part of our article too.

For the graphic part of this article, we now will show you where, why and how your torque and horse power relate to each other when they are put together to correlate.

That small intersection you see, the point where the red and blue line cross – the point where your torque and horse power intersect.

That point, that R.P.M. is 5252. This is the exact point that the Torque and Horse Power match equally and then rise and fall in exact opposite quantities after this point is crossed.

So the next time you take your bike out and want to know what is happening inside it that makes your hair fly or your body pull back and why out of the blue you start to stabilize yourself – you give this article a read and tell me then what is it you feel – because if it not just the feeling you are looking into and want to know the cause & causality of that feeling – you have come to the right place.

Learn – Unlearn – Evolve

That is our motto, and this is how we show you what the Evolve part in Motovation is all about.

Until the next article, stay tuned and most importantly – Ride Safe and Ride On.

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