Say for example a 125cc motorcycle with 6 gears has a top speed of about 75mph, why can’t they make it with 7 gears and surely that’d increase the top speed?
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Gears just increase the speed range in which the engine works on optimal rpm. But there is a limit to it, gears don’t give the engine more power than it has, and moving fast requires a lot of power
So from high school physics, power = force multiplied by velocity. If you make a higher gear to go faster, but have the same amount of power, the force you’ll apply in this gear will be less. And, the faster you go, the greater force you need to apply to overcome wind resistance.
In fact in most cars, you can’t go top speed in the highest gear… the higher gears are only added for fuel economy. You’ll go fastest in the 2nd or 3rd highest gear.
Gears don’t add more speed. The engine has a certain amount of force it’s putting out, and that force is what determines speed.
The function of gears is that combustion engines have to spin between a certain minimum RPM to prevent stalling, and a certain maximum RPM to prevent damage.
It is possible to change the sprockets on motorcycles to increase the top speed while reducing the low-end power by changing the sprockets to having more (or fewer) teeth
That is assuming that the engine redlines at top speed with the current gear. Or at least is above its top horsepower speed. Having another gear will then put the engine speed back into a better range which will prodcue a bit more force to accelerate. However you get quite a bit of deminishing returns the higher gears you have. The problem is usually not that the engine speed is too high at the top gear and top speed but rather that the air resistance and the rolling resistance is too high at the top speed so that the engine is not able to overcome all this resistance and produce enough energy to accelerate. However if you were to upgrade the engine, either put in a 250cc engine or tune the existing engine a lot, you may get higher top speed with an extra gear.
The higher the gear the more power required to turn it. Drag increases with the square of the speed, so to go twice as fast you need four times the power to overcome that drag.
Put another way, at 75 mph your motorcycle experiences about 0.1 psi of drag pressure, times the frontal area and the coefficient of drag. At 100 mph your motorcycle experiences about 0.18 psi. [Chegg suggests](https://www.chegg.com/homework-help/frontal-area-small-motorcycle-060-m2-drag-coefficient-062-ma-chapter-8-problem-41p-solution-9780521192453-exc) we can use 0.60m^2 for frontal area and 0.62 for drag coefficient. Passing this through my [favorite physics calculator](http://qalculate.github.io/) shows we need to overcome 60 pounds of force to go 75 mph and 103 pounds of force to go 100 mph.
0.5 × 0.00238slug/ft^3 (100mph)^2 × 0.6m^2 × 0.62
Think about a bicycle. In a higher gear you can achieve a higher top speed given the same RPM of the pedals, but you have to push them harder. Make the gearing [too big](https://cyclingtips.com/wp-content/uploads/2020/12/bigRing.jpg) and you aren’t able to push hard enough to get up to speed. As your speed increases so does the amount of drag, if there were no drag you could push that really high gear up to ridiculous speeds given enough space. The record for the fastest bicycle was set at 184mph using a [special vehicle faring](https://images.wsj.net/im-26794?width=1280&size=1) to block the wind. Because of all this, the best gearing for typical bikes is one that keeps the pedals at an optimal RPM for efficient power to balance against drag. The same is true in a motor vehicle, it’s a balance of power and efficiency.
Edit: you said motorbike and I said car at the end, whoops.
Imagine you’re pedaling your bike, if you keep shifting to higher gears it gets harder to pedal, your legs don’t magically become stronger.
Eventually if you had a ton of gears you wouldn’t be able to push the pedals hard enough.
You’d just be pushing really hard and the pedals would be moving really slow, but your bike wouldn’t be going any faster, in fact you’d start to slow down.
When talking about gears, always remember this:
Transmission gears trade speed for torque (and vice versa).
Torque is force x distance, when applied in rotation. So you put a wrench on a bolt, the torque applied to the bolt is the force you apply to the end of the wrench multiplied by the length of the wrench.
Your engine has a fixed amount of power it can deliver across a range of engine RPM. The result of the power is high rotational speed, but low torque. Your wheels need a lot more torque to start turning to move the car, so your lower gears trade the rotational speed of the engine for more torque. As the car builds momentum and inertia, less torque is needed at the wheels, and more speed is required, so you shift up.
If wind resistance, and rotating friction were not concerns, you could just keep adding gears and get more speed, but they (& other losses) exist, so even at the top end, you have to have a minimum amount of torque at the wheels, so you can’t keep adding gears (& you start running out of room in the transmission case).
I actually had custom amps made this way. It always went from 0-10 on standard amps. Well I had some made that go from 0-11; one higher. So when I needed just a bit more volume I could go to 11. Some people have a hard time understanding it. I often get asked why I just didn’t just make 10 louder… I usually just stare at the fool and answer *These go to eleven*.
The same concept should be true for adding extra gears for more speed. Just add a bunch more gears and away you go. Top speed: to the moon.
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