Alan Pozner <AlanP@identicard.com> wrote:
> BLoring wrote:
>>...Put another way: to accelerate from 0-20 mph in 4 seconds takes less
>> energy in 1st gear than it does in 4th gear. Isn't this correct?...
> This is untrue. The reason for the difference in the time it takes is
that
> in first gear at that speed your engine can produce more power than in
4th
> at that speed (since in first gear we are at higher rpm). I think you are
> confusing work(or energy as you put it) and force. The 4th gear car
applies
> less force for a longer time then the 1st gear car but the amount of work
is
> the same.
There's an easier way to look at this.
First, consider this: a gear is a rotary lever.
Secondly, levers trade force for distance - so a long lever arm with a
short distance after the fulcrum will multiply force many times over at the
penalty of requiring a longer (proportional) swept distance.
In gear terms, the driving gear turns more often than the driven gear, and
gains a proportional force multiplier. You can see this easily on a
multi-speed bicycle - the lower gears are "easier" to pedal (they multiply
the force of your leg muscles more) but you have to pedal faster to
maintain a given speed. The higher gears will turn the rear wheel faster,
but it's "harder" to pedal because you get less force multiplication.
The total *energy* expended, all else being equal, is the same in both
cases. What changes is the amount of thrust delivered to the wheels.
In first gear, you get more torque multiplication (so more thrust) but
because the drive gear must cover proportionally more distance (rev higher)
you reach the max rpm limit of the motor fairly quickly. As you shift into
numerically higher gears, the drive wheels are turned faster and faster,
but the amount of thrust developed drops proportionately. As acceleration
depends on thrust and weight, each upshift (assuming a flat engine torque
curve) reduces the amount of acceleration produced. Most modern 5 speed
transmissions have an "overdrive" 5th gear, where the crank is actually
turning slower than the driveshaft, which produces a _negative_ torque
(thrust) multiplication - so in 5th, with a 0.80 overdrive gear, only 80%
of the engine torque is being delivered to the wheels.
DG
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