How does 2nd gear create more thrust than 1st gear?

Question

Let’s analyze a vehicle parallel to velocity and forces applying on it.

The 1st gear has a maximum velocity value after which you can’t accelerate more. It means that thrust force on wheels generated by the first gear’s torque is cancelled out by external forces such as rolling resistance, air drag and other frictions. So net force on wheels is 0, this is why we can’t accelerate more after the maximum speed/rpm of the 1st gear.

When we shift to the 2nd gear, we start to accelerate again, which causes my question. We know that thrust force on wheels generated by the 1st gear is more than the 2nd, because the 1st gear produces more torque.

If so, how can we accelerate with the 2nd gear producing less thrust force than the 1st that we couldn’t accelerate by after some point?

For that maximum velocity value of the 1st gear,

F = m*a = 0 = Fthrust(1st gear) - Ffrictions

Then we will change Fthrust(1st gear) with Fthrust(2nd gear).

However, Fthrust(1st gear) > Fthrust(2nd gear)

So I can’t understand how can’t we accelerate with 1st gear after some point, but we can do it with 2nd gear that produces less thrust. How does 2nd gear beat external frictonal forces that 1st gear can’t beat?

Answer 1

I think that you've totally missed the limiting factor - maximum engine speed.

The 1st gear has a maximum velocity value after which you can’t accelerate more.

No, it's the engine RPM is limited.

Figure 1. Torque and power as a function of RPM. Image source: X-Engineer.

Boyond some point the engine power starts to fall off. Changing gear moves the system back into the "power band".

Thought experiment: why do you not cycle everywhere in first gear on your bike?

Answer 2

The torque an engine can produce depends on the RPM of the engine. The torque it can produce actually decreases after a certain point. See e.g. the graphs on the bottom of this page:

While accelerating, once in the region where the torque decreases, it can be beneficial to move up a gear. This will reduce the engine's RPM, resulting in more torque from the engine.

The ideal RPM to shift gears depends on your engine AND your gearbox. Moving up too early can result in a higher engine torque, but not necessarily more wheel torque, depending on your gearbox. The selection of the gearbox and engine are often adapted to one another.

P.S. to expand: Your assumption of "Fthrust(1st gear) > Fthrust(2nd gear)" is not correct for all RPM.