Wouldn’t the traction be the same in any gear, and the point at which you lose traction be the same regardless?
Edit: Thanks for all the explanations, I think I understand now. 🙂
In: 7
Picture three gears that you can swap out from one another, all with the same space between sprockets. One is large, the second is medium sized, and the third is small. To the left is a handle you can grab with your fingers and spin to cause the left most gear to spin. To the right is a smaller shaft the second gear helps drive perpendicular to how the gears touch. The faster this shaft turns, the more speed you get.
If you want the most speed in the quickest amount of time, you would stick the large gear first, and connect the smallest gear with the speed shaft. Why? Because for each fraction of a turn of the large gear, you would be able to make the smaller gear turn with a much greater speed due to being smaller with a less amount of sprockets on it to push. This is 1st gear.
Okay, so while it keeps that momentum going, you decide your arm is getting tired, so you swap out the large gear with a medium one so you don’t have to push as hard. The speed slightly declines when you do this, but with less turns overall you can maintain the same speed. 2nd gear.
3rd gear would be to swap the small and large. Suddenly, you have to push really fast to get that little gear to get the large one spinning, but it works if the handle you’re spinning with your hand already is spinning fast.
So, 2nd gear is the best compromise between harder startup speed, and controlling that speed safely when your hand might slip off the handle since it’s slick.
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