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More turns with a short screwdriver?
Less turns with a long screwdriver?
The same amount of turns ?
I give up !
Three pumps with an 18” Yankee should do it.
Fewer turns with a long screwdriver?
If we’re talking about the cocktail, i’d suggest you put the bottle down..
can someone mansplain why a longer screwdriver appears to increase torque?
Shirly the twisting movement is dependant on muscles and tendons , but .- a longer one seems to give moar ooomph
Easier to get a long screwdriver set straight in the screwhead. Having the screwdriver slightly off straight gives the effect of a wider turning circle compared to a short one being way off straight to achieve a similar advantage.
Confirmation bias?
Imagine a cone with the point at the screwhead. For a given angle a longer screwdriver will have a bigger top to the cone which is the effective lever that you are using to undo the screw. There’s a limit to the angle before the screwdriver will slip so a longer handle is the most effective way to apply more torque.
parkesie has it - its a lever thing , stubby screwdrivers although needed for access sometimes are horrible to use.

Surely once the thread bites it will be drawn in to the hilt by exactly the same number of turns on the helix whether you use a long or a short screwdriver. A nut doesn't screw down onto a bolt faster with a long spanner compared to a short one. It makes the same number of turns regardless.
Perchy got it in one. Why would you use anything else?