# CORNERING VS. RPM INCREASE

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Hello,

Just became a member and wanted to post a question.

I watched this video that shows the rpm increase when the bike leans over to the edge of its tire without throttle input nor gear changes.

So, you are moving down the straight at 100mph, 4th gear, X RPM, fixed throttle position and you enter a corner.

You are now at full lean and riding on the edge of your tire therefore on a smaller diameter. The tire should now spin faster and increase your RPM.

Is there any truth to this?

Why do the RPM increase without throttle input?

Sorry that the video is in Italian but it has subtitles and I'm sure you all get it.

Ciao

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Other than the slip between tyre and road, the engine is mechanically linked to the tarmac. By that it means that for any given speed, rpm is constant for a particular gear, regardless of throttle position. Let's say you need 5000 rpm to go 60 mph in 4th gear. Regardless of where the throttle is, be that full off or full on or anywhere in between, you will have exactly 5000 rpm at 60 mph in a straight line. Unless the tyre is spinning or the clutch is slipping.

Now, if you lean over, the circumference of the tyre is reduced. This has a similar effect to lowering the gearing. But while lower gearing mean that the engine must turn more revolutions in order to get the wheel turned a certain amount of times, now the wheel must turn faster to maintain the speed, bringing the engine along with it.

This could probably be explained much simpler, but as long as you remember that when the engine turns over X times it always makes the tyre turn Y times in gear Z. A smaller wheel must turn faster than a larger diameter wheel for any given speed, and so the engine must turn X+n to compensate.

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Welcome, Kneedragger727

What the video shows is very close to be true.

They show two different engine's rpm's (in and out) for the same speed of the bike.

If you carefully watch between 3:33 and 4:00 times, you can detect an error: entering and leaving speed/engine rpm's ratios must be exactly the same when the bike is perfectly vertical.

Why do the RPM increase without throttle input?

Because Newton's first law of motion:

"In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force."

Because the masses of bike and rider try keeping a constant velocity, the engine "is forced" (see further explanation below) to spin faster by a smaller rear wheel that is forced to spin faster.

Rear wheel and engine are solidly connected by a gear train (there is no relative slipping or jamming).

In order to follow the constant speed or inertia of the bike, the leaned rear wheel must cover the same linear distance in the same period of time as when vertical, having now a smaller diameter and perimeter.

The only way for the wheel to achieve that is by spinning faster (increasing its angular velocity) in the same proportion in which the diameter gets reduced (10% reduction in diameter induces 10% rpm's increase).

Velocity of bike = Radius of wheel x Angular velocity of wheel

Further explanation: When the throttle is full open, the engine is not really forced to spin faster.

There is still enough pressure in the combustion chambers as for the engine keep pushing the rear wheel to rotate, although not at peak torque.

The inertia phenomenon explained above unloads the engine (less torque applied over the rear wheel is needed), which performance point moves over the torque curve to a new state of lower delivered torque and higher rpm's.

Nevertheless, if the leaned situation would last long enough, the speed of the bike and the rpm's of the engine will go down some.

Because of all that, at the end of the curve the leaving speed is slightly lower than the entering speed of the bike.

The whole story is that the engine and the gear train have their own rotational inertia and tend to conserve it due to the very same first law of motion........"unless acted upon by a force."

A portion of that force is provided by the impulse or the change in momentum of the moving masses of bike and rider (the rest of the force is provided by a weaker engine off the peak torque).

Impulsing the engine to spin faster plus the additional internal friction losses of engine and gear train cost energy.

The kinetic energy (read speed) of the bike pays for that energy demanded by additional rpm's of the engine.

If rather than moving at high speed, your bike with a wheel of smaller diameter (or a much bigger rear sprocket) would start from repose, the final speed of the bike and the the rpm's of the engine would end up being lower at full open throttle.

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Thank you so much for your quick and thourough responses. I really appreaciate the highly technical nature of your responses as well.

Reading your response has brought up another question on how throttle position would effects final speed and rpm.

If for example you are moving at 100 mph, 4th gear, 50% throttle with X RPM and a rear tire diameter of 27 inches.

You then restart from repose with a smaller tire diameter, say 22 inches.

Will you reach the same linear velocity of 100 mph (obviously on 4th gear with 50% throttle and higher rpm); or do you reach the same X rpm but with a lower velocity?

Thanks again.

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That is impossible to answer. If the large wheel meant 7000 rpm, the smaller wheel would give 8600 rpm. If the engine had a torque dip at 7k, it may be able to go faster with the smaller wheel at the same throttle opening. Same if the load his high, like climbing a steep hill, you would likely benefit from the extra rpm and resulting extra power to give a small increase in speed. Another thing to consider is mapping; 50% throttle will not give the same amount of fuel at high rpm as at lower rpm, meaning mapping could be better or worse if you increase rpm for any given speed.

However, for most engines the extra energy required to rev higher due to more internal friction, you would not go as fast with the smaller tyre - if you have an instant fuel consumption read-out on your bike (or car) you can see how much more energy is required to go a certain speed in a lower vs a higher gear.

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You are welcome

The difficult part of your question is the 50% throttle: something hard to get precisely accurate.  Full or partial throttle only means that the power delivery of your engine would be maximum or partial, leading to similar results than in the OP's case.

The power plant of any bike delivers the necessary torque (rotational force) at the necessary rate (rpm's or torsional speed) to compensate for the forces that resist the acceleration and movement (internal friction, hills and aerodynamic drag mainly).  At partial throttle, you are taming the engine to deliver exactly what you need to achieve certain final speed or rate of climbing or acceleration (a specific amount of resistive forces).  At full throttle, you are full feeding the engine to generate maximum torque-rpm's combination (HP), which will be naturally resisted by certain amount of resistive forces (aerodynamic drag force grows with the square of the speed), which will result on maximum acceleration and speed on a level road.

Electric motors have a delivery of power that is more or less linear with the "throttle opening".  They will burn themselves trying to give you exactly what you ask.  That is the reason for which electric bikes need few or no gear box to select gears.

An internal combustion engine is a pneumatic machine that very much depends on "breathing" and over-the-piston pressure.  That breathing is determined by intake, valving and exhaust and rpm's.  That pressure is determined by the expansion of the gases due to the heat of the combustion.  That makes them have a delivery of power (HP) and torque that is a curve rather than a line.  For partial throttle, the amount of mix (air plus fuel) is artificially restricted (carb(s) or FI alike) via increasing intake resistance (butterfly damper(s)).  For full throttle, the amount of mix is allowed to be has high as possible.  After certain point along the range of rpm's, the breathing or mix intake gets compromised due to turbulences, needed time to expel the exhaust gases and valve floating (lack of time to fully close) and torque followed by HP begin to decrease.

A good selection of the transmission steps and sprockets (the equivalent to manipulating the diameters of the wheels in the OP) tries to match max speed with the point of rpm's on the curve where the engine is stronger.  That selection is always a compromise for tracks of different configurations (max acceleration out of curves (max torque) versus max speed on straight sections (max HP)), in order to complete the circuit as quickly as possible.  If you wrongly select that 22-inch wheel for a track of few fast turns only and long straights, that other bike with a 27-inch will have an advantage over yours, reaching max speeds that are higher than yours. At full open throttle, the engine of your bike will reach its max HP about the same rpm's than the other engine, but it will not reach the max speed of the other bike with the bigger wheel.

What happens is that your engine will deliver higher rearwards force onto the contact patch of the smaller rear wheel than needed to counteract the resistive forces generated by that speed (excess of rear wheel torque), but will restrict its own breathing or choke itself as soon as it tries to turn that smaller wheel faster to keep up with the other bike, resulting in less torque to fight the resistive forces (returning to the balance point).  That is what happens when  you extend a gear (second gear, for example) beyond the proper point of switching, the engine keeps screaming, but the bike does not move faster.   When you switch to the next gear is the equivalent to replacing your rear wheel with a bigger one: you are simultaneously slowing down the rpm's of the engine and increasing the resistive torque, moving the operational point of the engine back over the curve of HP to a state in which it can deliver higher torque by breathing better.

In extreme cases, when the engine is unloaded too much, even when the delivered torque cannot push that wheel (downhill, for example), it will reach the rpm's limiter, which is designed to prevent the auto-destruction of the engine due to excessive forces of its internal alternating parts, cutting the ignition and temporarily killing its strength.  In essence, the proper diameter for your theorical wheel (sprocket and/or transmission selection in practical terms) should make your engine rotate at the optimum average rpm's (between top torque and top HP) demanded by the track conditions.

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