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It could be that you are not following two fundamental rules of cornering: 1) Looking deep into the turn: You can only know that your trajectory is one foot off if you are looking close in front of your bike. 2) One steering for the whole turn: You may be adjusting your steering along the turn in order to achieve your goal trajectory. Think of the unintended consequences that you are creating if you are doing so, like diversion of attention, disorientation, over-stressing the front tire, etc. The way I visualize cornering trajectory: to me it is like shooting a ball into the basketball hood from a distance, you feel the cross-wind, you estimate the distance and the angle, you gut-calculate the whole flight of the ball and then you impart your best directed push hoping for the best. Sometimes you miss for little and sometimes you nail it. The hard mental, visual and calculation work in cornering happens prior the turn-in point, which is equivalent to the moment of actually pushing the ball. Let the bike "fly" describing that natural arc, free of unnecessary minute steering inputs and lean angle adjustments. Missing an apex for 12 inches may add a few feet to the corner's total trajectory, which is not a big difference for a bike that moves 88 feet per second (60 mph). Distracting your attention from proper throttle control and from reference points and from spatial location may slow your bike much more.

Welcome, Don! Very true, as soon as we are not 100% mentally riding ahead of the bike, the perception (false or true) of excessive speed and lack of time and available space overwhelms our fears of not surviving the situation. "A superior pilot uses his superior judgement to avoid situations which require the use of his superior skills" - Frank Borman

You are welcome, Jaybird What you have been analyzing and trying to understand is very complex dynamics, reason for which most riders don't even bother learning the "why" of these things. The books that explain the whole interconnection of steering, wheels, masses, forces, etc. in a motorcycle are very dense to read and difficult to comprehend. I believe that there is value in understanding the basics of the Physics behind riding a motorcycle in a proficient way. It is difficult to explain those principles to inexperienced riders without going too deep into the subject and causing confusion. Most mentoring/teaching is limited to "do this to achieve that and go practice it". The experienced rider has the advantage of having tested what works and what does not, of having felt those forces and the reactions of the machines during enough time to make sense of those principles. If serious about this, by persistent observation during thousand of miles, an educated rider becomes more aware and more sensitive about the dynamics of riding and develops a finer input of all the controls and sense of balance. The Physics then becomes less abstract and more in harmony with our senses and minds. In order to function as a motorcycle rather than as a bag of potatoes, all the forces and moments acting over a motorcycle in different directions must be in balance. If our control inputs or road conditions break that balance, a brief transition period follows, during which the machine does its magic to self-adjust to a new state of balance. If that state is not physically achievable, a fall will follow. Counter-steering is a clear example of that: the rider intentionally steers the bike out of balance (out of its rectilinear path), inducing many reactive forces, movements and moments for a very brief period of time, forcing the machine into a new state of balance (onto a curvilinear path). If the machine continues on in one of the two states of balance, the rider is doing nothing or too little to modify those, like it happens in the No BS bike demonstration. If the machine is upset by incorrect control inputs from the rider, like closing the throttle during a big rear tire slide, the machine can go from stable cornering balance to unstable transition to out of balance (highside fall) really quick. The speed of the motorcycle is very influential about the steering, gyroscopic reactive forces, rolling and balance, reason for which counter-steering is so powerful in a superbike at high speeds, but almost negligible for a trial bike at walking speeds. http://www.dynamotion.it/eng/dinamoto/8_on-line_papers/effetto giroscopico/Effettigiroscopici_eng.html

Talking about chairs, it has occurred to me that we can discuss the actions of monkeys (passengers) in sidecars races. By moving around for each corner, they do what you describe about your folding chair: they relocate the total or combined center of gravity as far from the motorcycle or as close to the rear tire as possible. Rather than trying to make the motorcycle and sidecar roll, they compensate the natural rollover tendency during fast cornering as much as possible. That rollover tendency is induced by the combination of centrifugal effect and height of the center of gravity respect to the road. A regular sidecar could be comparable to the situation that you have pictured above: a motorcycle with a dramatic asymmetrical weight to its side. Would the bike yield to the induced roll? Let's say that thanks to the third wheel, that weight does not roll the bike over and instead keeps it vertical. If we weld the steering to the frame keeping the steering bar perpendicular to the bike and then make the bike and sidecar gain speed on a straight trajectory, the contraption will describe a straight line. As the bike happily cruises along, if we suddenly remove the sidecar wheel, even with the stability induced by the two remaining main gyroscopes of the contraption, that asymmetrical mass or weight will be able to roll the bike until the sidecar axis hits the ground (the lateral balance will be lost). The bike, even while leaned over, will try to keep going along the straight line (assuming no dragging forces from that dragging axis) because the steering has not changed. Riding with a Motorcycle Sidecar: http://www.steves-workshop.co.uk/vehicles/bmw/sidecar/riding/sidecarriding.html Yes, a substantial weight with some lateral leverage is able to roll a motorcycle in movement or tip the stationary chair of your example over. Nevertheless, without the complicity of the steering capability, the bike will not turn, even if leaned over. The following video shows that the steering capability of a motorcycle, with or without a sidecar, has a powerful influence regarding directing it onto either a straight or a circular trajectory in a precise and controlled manner ....... and what it seems more important: combined with speed and rider's skill, it is able to lift that asymmetrical weight and keep it balanced at will, even on a left turn, in which the centrifugal effect tries to take the chair down. The maneuver is known as "flying the chair". https://www.youtube.com/watch?v=k6ZSSPY32Jk

https://motomatters.com/interview/2012/04/12/casey_stoner_explains_how_to_slide_a_mot.html Casey Stoner Explains How To Slide a MotoGP Bike: "It's something that only works in certain corners in this type of racing, it doesn't work in all the corners. When it does work, sometimes it can be a bit scary; you can go into the corner, and if you make a small mistake when you are sliding, the finish of it can be a catastrophe. When your heart beats really hard is when you slide when you don't really want to,"....... "There's different techniques to different corners and when they should be used, depending on grip levels, and a lot of different things. Unfortunately, most of the time these days, sliding is not the fastest way, there's only some corners where it can still work." About teaching a 5-year child how to shift gears, I recommend you this reading: https://books.google.com/books/about/Casey_Stoner_Pushing_the_Limits.html?id=npA1AgAAQBAJ

Unless you have a fixed fulcrum to exert leverage against, you move the bike away from you (roll it a little) as you move your body off in the opposite direction. The total center of gravity (yours plus bike's) remains along the vertical line that crosses the imaginary horizontal line that connects both contact patches. If the steering is kept perfectly fixed and aligned with the contact patches, the bike does not have a reason to turn. If instead the steering is free to adjust by itself, the geometry of the front tire and angle of suspension, combined with the total weight and gyroscopic reaction (please, refer to your video and see that a left roll of the bike induces a left steering) , will slowly turn the steering towards the side upon which the bike has rolled (only if steering angles, tire's profile and pressure are neutrally set, so there are no over or under-steering tendencies). That slight counter-steering will induce a balancing slow roll towards the side upon which the rider is hanging off and the bike will commence a turn. That is the same self-balancing principle that allows a rider-less bike keep going for a while while speed is relatively high. That is a very different situation than exerting "a force (weight) at a lever point away from the center of rotation". We are starting from an out-of-balance situation. In that case, the bike will be forced to roll due to the moment created by the total center of gravity being initially far away from the line that connects both contact patches. Either or not the self-balancing capability of the steering will be strong and fast enough to compensate for that initial lack of balance depends on several factors, such as magnitude of off-set weight, weight's lever, mass of front tire and linear speed of the bike.

Absolutely! That is the whole reason for the need of selective gears: to keep the engine rotating within the range of rpm's that produces usable torque (and work) for a wider range of rpm's of the rear wheel (which translates into forward speed of the motorcycle). Except during the brief periods of coasting and engine breaking, the work of the engine pulls the motorcycle forward against the resisting forces of inertia (during acceleration) aerodynamic drag (at relatively high speeds) and (when climbing a hill) gravity. The only thing that dramatically changes the torque (and work) that the engine can deliver is the "twist of the throttle": more entering fuel and air means more powerful internal combustion, which means more internal heat and delivered torque (and work). That is true for certain range of engine's rpm and until we reach the point of full open throttle (maximum intensity of combustion and delivered torque), which is what dyno charts show. The work developed by the rear tire is always the product of its rotational speed (rpm's) times the torque it is able to deliver, which is exactly the same value as the product of its linear speed (forward speed of the bike) times the rearward force exerted over the pavement. The value of the work developed by the engine is always a little higher than the previous one, as some energy (in the form of transferred forces down the gears and chain and sprockets) is lost in the links between the crankshaft and rear tire. When the bike is moving at sustained 60 mph on a horizontal road, the position of the throttle is fixed, allowing intake of the exact amount of fuel and air that keeps two forces in balance: pushing forward force and resisting rearward force. If the bike starts climbing a hill and the throttle remains fixed (work delivered by the engine remains the same), the force resisting the rotation of the rear wheel increases due to the addition of the gravity effect. As no additional work from the engine is available, the other factor of the formula (torque X rpm) must decrease, resulting in a new state of balance at lower rpm's. The natural reaction to that is the slowing down of the rotational speed of the rear tire and forward speed of the motorcycle and reduction in rpm's of the engine. We can only allow certain amout of that reduction of the rpm's of the engine before the engine becomes real weak. If we wish keeping the same on-flat-road during the climb, we need to open the thottle up (more work delivered by the engine translates into resuming speed). If the steepness of the hill is excessive to achieve a new state of balance, even at full open throttle (no additional available work), we need to sacrifice bike speed in order to increase force on the rear contact patch via dowshifting. Returning to your original question: When the bike is moving at sustained speed on a horizontal road, the two forces are in balance: pushing forward force and resisting rearward force. If you open the throttle up some (more delivered work), the bike will accelerate due to additional torque reaching the rear tire, until reaching a new rpm X torque balance. If you open the throttle up a lot, the bike will do a wheelie due to excessive acceleration and abundant traction. If traction is not that abundant, then the additional available work must go to break the grip between the contact patch and the surface, spinning the rear wheel.

In order to communicate with the same terms, are you refering to the rolling motion of the motorcycle? Is your question limited to the reactions of the bike and steering and trajectory following a lateral weight shift of the rider? Sorry, I couldn't clearly understand your question.

Because all the gears and sprockets that link the crankshaft with the rear wheel act like a lever: the rotational speed of the rear wheel gets reduced while its applicable torque increases. For the same degree of openning of the throtle, resisting load and rpm's, the engine generates certain amount of torque or rotational force. We have to work around that more or less constant amount of torque, playing with the gears, just like it happens with a bicycle. For a greater resistive load (going uphill, for example), we have to sacrifice rotational speed of the rear wheel in order to have greater torque there; hence, we switch to lower gears. One trick for riding in the rain is to corner using a taller than normal gear, which "weakens" the available torque of the rear wheel, which creates an extra safety margin regarding any mistake with excessive throttle that could overwhelm the marginal available traction. https://www.youtube.com/watch?v=3Tc3VIDQvh0

There is more force applied onto the rear contact patch when the transmission is working in lower gears. On surfaces of poor traction (grass, dirt, etc.), the rear tire has more authority (breaks loose and pushes the bike around easier) when first or second gears are engaged.

Welcome! Perhaps the bike needs to regain the trust in the rider. Available traction can suddenly disappear under us, if the surface of the road is contaminated with Diesel, oil, sand, etc. Always be careful when the road is wet and consider that street tires may never warm up properly in those conditions, because they are cooled down by the water and spray around them. The road can be awfully slippery during a light drizzle of rain, because there is no enough water to wash away the dirt and contaminants mentioned above. Also avoid the outer half of any runabout and curve, where Diesel leaking out of trucks and sand tend to accumulate.

Accelerating hard (enough to lift the front tire) at extreme lean is equivalent to hard braking at extreme lean: the tire will slide. The very essence of the trail braking technique is the trade off between the longitudinal force of braking and the lateral force of cornering. https://www.sportrider.com/sportbike-riding/riding-skills-series-traction-circle https://www.motorcyclistonline.com/leaning-bike-code-break Our natural gauges to feel and evaluate braking force are the degree of compression of front suspension and forward pressure of our weight on knees and hands. Our gauges for evaluating cornering force are the lean angle and the pressure of our butt on the seat.

This shows the experimental process and the result for a 2013 BMW R1200GS: http://www.me.unm.edu/~starr/moto/cm.pdf

Regarding the bicycle coasting question: The forces acting over the contact patches in the case of coasting are only the portion of the total weight that each tire carries (vertical force vector pointing down) plus the lateral force trying to deviate the bike from a linear trajectory (horizontal force vector pointing towards the center of the circular trajectory described by the bike). Fortunately, the magnitude of that lateral force for a particular tire depends on the portion of the total weight that that tire carries. The other two factors on which that horizontal force depends are the radius of that circle (the smaller the radius, the stronger the force) and the square of the speed (the faster the bike, the stronger the lateral force, squarely. The possible reasons for the slides of those rear tires in the video are many. As Hotfoot pointed above, the rear tire could be worn, improperly inflated, too hot or too cold or under excessive braking or accelerating forces. Even when both tires were made of the same material (possible same brand and pattern) and being rolling over similar surface and trajectory, the available traction of the front tires in each case were higher than the one for the rear tires. Disclaimer: I am not expert; only an enthusiast of Physics, Math and motorcycling. Without being scientifically rigorous, this is what I have learned from books and from riding many miles in all weather conditions: 1) Understanding what is happening in the relatively small areas of both surfaces where rubber and asphalt meet (contact patches of both tires) is extremely important, as much for avoiding crashes as for high performance riding. The proficient rider develops a fine sensitivity about this; he/she can almost feel what is going on there, based on visual evaluation, comparative experience and feed-back from suspension and steering. 2) Traction or grip is the capability of both materials in contact (rubber and asphalt) to persist on staying together, not dramatically and uncontrollably sliding respect to each other, whether or not lateral forces (excerted in any direction that is parallel to the surface) are applied onto that contact patch. Physics tells us that such capability only depends on two things: nature of materials in contact (molecular structure and superficial roughness) and force that is exerted in a direction that is perpendicular to the contact surface (also known as normal force). After many laboratory tests, a "coefficient of friction" is obtained for each combination of materials, which is just the rate between the magnitude of the lateral force that is able to induce an slide and the normal force. That coeficient is a fixed number, which means that both forces are proportional and that in order to achieve more traction, you must increase the perpendicular or normal force. Example: double normal force in magnitude gives you double traction or friction, being the contact patch able to resist double lateral force in magnitude. 3) Considering only the available traction of each contact patch of our machines: While rolling at high speed over a less than flat and perfect asphalt surface, our tires deviate some degree from that pure Physics concept of traction. Static perpendicular or normal force: Static weight on each contact patch is the available perpendicular or normal force . That is only true for a horizontal surface; if there is camber of the track or road, that normal force becomes smaller than the weight. If the bike is going up or down a sloped road, there is more static weight on the lower tire and less on the one located higher. Dynamic perpendicular or normal force: Then, there is a dynamic load, which is fluctuating (greater and smaller than the magnitude of the weight in static conditions). When a tire rolls over a crest of the road's surface, its contact patch "feels" a higher weight or load (the suspension compresses and the available traction improves), the opposite happens when the tire rolls over a valley. When we accelerate or decelerate (brakes or engine brake), we dramatically change the distribution of the total weight of bike, fluids and rider between both contact patches and suspension (from 50/50 up to 0/100). Notice that it is much more difficult for the overloaded suspension to follow the crest and valleys of the track's surface, also that the overloaded tire suffers more dramatic changes in tire profile and contact patch area. Coeficient of friction: Between a rolling tire and asphalt, this is not as constant as the lab experiments demonstrate. We are not dealing here with a loaded chunk of flat rubber that resists slidding. In the case of a rolling tire, any contact patch is rapidly disappearing to be followed by the next contact patch a few inches ahead (reason for the side-walking of the tires while cornering hard, when combined with lateral deformation of each contact patch, the next one lands off track). There is the molecular attraction of the two materials, but there is also the number of macro-imperfections of the asphalt and how deep the rubber "flows" into those; hence, bigger area and higher pressure of contact improves traction. Then, we have the dependence of the rubber on temperature: too cold and does not deforms well enough to dig into the surface, too hot and the integrity and resilience of the rubber degrades and slippery oils start to come out. There is also the time factor: being a flexible solid behaving as a very viscous fluid, rubber needs time to "flow" down and sideways and to get twisted: too quick the load application and the rubber reacts as a hard rock (imagine the water resistance on your body diving from 30 foot trampoline versus walking into a pool); hence the advice about smooth control inputs. Finally, foreigner material that eventually infiltrates between both surfaces, such as sand, water, Diesel, dramatically reduce the coefficient of friction (bassically sliding friction becomes rolling friction, as those molecules and small particles act like little balls). 4) Finally, considering only the horizontal forces that the contact patches "feel" as reaction forces back from the asphalt (those trying to slide or detach both surfaces in contact, inducing a skid or a slide) on each contact patch of our machines. There are three fundamental types of these horizontal forces: A) Longitudinal forces (horizontal force vectors pointing directly forward (accelerating) or rearward (decelerating). B) Lateral force (horizontal force vector pointing towards the geometric center of the circular trajectory). C) A combination of A and B above (horizontal resulting vector pointing at certain angle between the trajectory and radius lines), which happens when we simultaneously corner/accelerate or corner/brake. The magnitude of those forces are limited by the traction that is available at each moment, which can be represented as an imaginary circle around each contact patch. Each time that one of these forces grows beyond that limiting circle (available traction), the inexorable laws of Physics punish us with a skid or a slide (excessive entry speed, for example). Exactly the same result happens each time that the circle of available traction suddenly shrinks and its diameter becomes smaller than the the magnitude of any lateral force for that tire (cornering and crossing over a patch of sand, for example). I find "A twist of the wrist 2" book to be very accurate about the Physics of motorcycling. It is not scientifically rigorous, but it seems to me that the principles that it explains were based on accurate and objective observations. I have extensively experimented with its tips, techniques and advise, and all work regarding performance and safety. Once again, excuse me for the long post.

All excellent answers, gentlemen! Based on those, and talking in forces and traction terms only, why are the rear tires sliding in this video, while the front tires are not?

Please, excuse the math and the physics; it was just an attempt to show and quantify the limits that we are dealing with in this discussion. Allow me to insist on some basic concepts, which are very important for you and for any rider to visualize and understand in a clear and solid way. You should know and apply these things without thinking too much about them while riding a fast motorcycle in a proficient way. The limit to "roll it harder, sufficiently enough to lift the front" is the available traction of the rear tire in those cornering conditions. If you can do it without inducing a slide of the rear tire, it is only because your tires have not been loaded enough (with cornering speed) in the previous stages of cornering: your entry speed was lower than it could have been. In other words, you will be trying to compensate a slow entry with a fast exit. Why is that? I believe that this is the point that unfortunately I have failed to explain properly. Hence, I will try the questioning approach, hoping to make you see some limits: 1) Would a unicycle corner better that a bicycle? Why? 2) Do you believe that a motorcycle doing a wheelie becomes a motorized unicycle? Please, explain. 3) What limits the maximum speed at which a sport motorcycle can negotiate a turn of 200-foot radius? How does rain affects that? 4) What forces are acting over the contact patches of a bicycle that is cornering and simultaneously coasting? 5) Regarding turning a motorcycle along a corner, should the lean angle be considered a consequence or a cause? Please, explain. 6) What causes a wheelie (for a vertical attitude of the bike)? How can it be controlled? Why? 7) What forces are loading each contact patch during a wheelie?

I was corroborating your statement, which I found to be correct. I agrre with your last post as well. Sorry about the confusion.

1. The bikes want to follow a straight line, if they can, if not forced otherwise (remember the Newton's law we described priorly?). A sphere rolling on a flat surface can't make a curvilinear trajectory. A disc (like a coin or a tire) can, if rolling over the same flat surface off a vertical position (leaned). For keeping that leaned attitude, someone or something must have initiated the leaned rolling. The Newton's law manifests itself in the case of the rolling leaned disc, however, there is a force making the disc deviate from the straight trajectory, turn instead over a circle: a portion of its own weight constantly pulls the disc towards the center of that disc. Same force is what keeps the motorcycle leaned and turning in that out of-the-curve wheelie. If that centripetal force (portion of the weight) equals the centrifugal effect of the circular movement, the bike as well as the disc will keep describing the same circle over and over again. Yes, your wheeling bike will keep turning even after the end of the curve (you must put your front tire down and counter-steer to decisively straighten the trajectory up). If that centrifugal effect becomes bigger that the centripetal force (portion of the weight), then the bike tends to open the circle (to constantly increase its diameter). That is what makes a leaned bike that is excessively accelerated (greedy application of throttle) run wide and subsequently reduce the lean angle. That is also the reason that the leaned and turning bike in that wheelie will tend to return to a straight trajectory, if enough acceleration and time is provided. 2. You could accelerate harder than 0.2 g, let's say 0.9 g and achieve 10/90 weigth distribution. Consider that your rear contact patch will be loaded with harder longitudinal forces (exactly 90% the magnitude of the combined weight of your bike and your body, because F = mass x acceleration). If the rubber of your good racing tires is able to achieve traction of 1.1 g, then, your rear tire can only deal with around 0.3 g of cornering lateral force (around 20-degree lean). Then, you will be forced to slow down to prevent a slide (like riding on wet-dirty pavement). There it goes your excess of acceleration due to the need to moderate your speed. Even if you make the turn in those conditions, you will only have a fraction of the grip that you could have in the front contact patch (only 10% of the weight on there, remember?) for countersteering out of the turn. 3. Let's do some math: Sustained acceleration of around 1.0 g (32 ft per second or 22 mph of additional speed per each second in the curve) will give you a nice sustained wheelie. If the limit of available traction allows a maximum speed of 80 mph in that curve, that will be your leaving or exiting speed. If it takes 3 seconds to complete the curve in the described conditions of strong acceleration, your maximum entering speed must be 80 mph - (22 mph x 3 seconds) = 14 mph. Your average speed through the curve would be (80 + 18) / 2 = 49 mph. Another rider following the recommended 40/60 weigth distribution (acceleration of 0.1 g) would increase the speed at a rate of 2.2 mph per each second, which means same exit speed of 80 mph and entering speed of 80 - (2.2 x 2 seconds) = 75 mph, being his average speed of 77 mph. Note that he used 2 seconds while you used 3 seconds (gross approximation only). Hope those numbers help you see the dramatic difference. There is more than maximum available traction involved in this picture of moderate or recommended weight distribution: steering, suspension, tire performance, stability, as mentioned in my previous post. Practical considerations: You want to keep your steering tire loaded with a decent amount of weight or available traction. To force a speeding heavy bike in and out of a lean angle requires muscular effort and a solid fulcrum, which is a gripping front contact patch. That loaded front tire can save you in an emergency swerving and in a slide of the rear tire. Imaging going through a quick chicane with only 10% of the total weight on the front tire? Please, excuse my long post.

I believe that the answer to your question can be found in the last section of that chapter: Stable suspension. Perhaps re-reading Chapter 3 could help you see the whole picture more clearly.

We care the most about inducing the 40/60 weight distribution via throttle control when we need maximum performance from the tires and the suspension, when cornering on asphalt as fast as possible. If, while cornering like that, we put more weight on one tire, we compress that suspension and load that tire beyond the optimum state or conditions. The suspension becomes harder, the contact patch becomes a little bigger and the profile of the tire less pliable. Following the irregularities of the pavement is more difficult for the tire. The rubber becomes less elastic and it changes its shape more slowly. Once the weight carried by that tire while cornering hard reaches a crtical point, the available traction that the over-loaded tire can offer rapidly decreases. During a leaned wheelie, all the weight of the bike and the rider is on the rear tire and on the rear suspension. That tire would not be able to develop the traction demanded by the lateral forces of extreme cornering, which normally surpass the value of that weight. The wheelie always happens during the way out of the corner and at a lean angle that is much smaller than the max lean angle required by that turn. If the rider tries to wheelie the bike at that max lean angle, when the lateral forces of cornering on the contact patch are close to the max, the tire would slide. The tire would not slide only if the rear contact patch has been unloaded enough from lateral forces in a way that its performance can be reduced by the the extra weight.

Using arm's force to countersteer and make any bike turn, we cancel the self-correcting property of the steering geometry. Motorcycles don't really need a rider to avoid cornering:

First Newton's law of motion: In an inertial frame of reference, an object remains at rest or continues to move at a constant speed along a straight line path indefinitely, unless acted upon by a force.

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. https://m.youtube.com/watch?v=3idIpc0Bv_I

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.

Revisiting your #1 question, asphalt riders push the bike under them sometimes. Both types of riders are improving the agility of the bike to lean over the desired side when they "disconnect" the mass of their upper bodies from the mass of the bike. Yes, the result is an exaggerated final lean angle, but that could be beneficial on asphalt as well as the front tire turned at full lock will describe a smaller radius with a greater lean angle. The first five minutes of this video show the dramatic differences in steering inputs, accuracy of lines and available traction between dirt and asphalt: https://m.youtube.com/watch?v=BzF_q5ivlKE