# Does air resistance have a greater affect on longer pendulums than shorter ones due to the greater exposure it has to air? I'm thinking, because longer pendulums travel for a greater time period through the medium of air, air resistance will have a greater affect on the pendulum bob (and string) and so the angle the pendulum travels back at would be a lot less compared to that of a smaller length pendulum?

I have uploaded a picture to help explain my question.

In case my photograph is blurry - In the drawing a pendulum is released. Then the angle that it travels to on the opposite side is recorded, so is the distance from the centre of mass of the pendulum to the hypothetical trajectory (if pendulum were to swing in a complete vacuum) distance labelled "X". If length of pendulum were to be increased, would X remain constant? Or would the angle remain constant? Or perhaps, because of air resistance, would the angle decrease proportionally to the increasing of length of the pendulum?

Air drag typically increases approximately like $$v^2$$. The velocity of the pendulum scales like $$L^{1/2}$$. Therefore the force probably scales like $$L$$, and the work per oscillation like $$L^2$$. The energy in the pendulum is proportional to $$L$$, so the fraction of the energy dissipated per cycle should scale like $$L^2/L=L$$. The decrease in angle per cycle should therefore also increase in proportion to $$L$$.