the physics behind how modern archery bows work

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I’ve spent about 2 hours watching videos on YouTube to understand how bows work but I’m getting more videos that are pitched at comparisons between different modern bows or how to shoot videos.

What I don’t understand is how a compound bow or springed bow is able to make a small person shoot at higher power. In my physics mind, I understand that cams and springs provide leverage. But the force applied to build potential energy is the same direction as the arrow being fired, so how does the arrow have more power?

if I’m using a seesaw analogy, I’m charging potential energy with the end of the seesaw, when I jump off, the far end of the seesaw still has the same distance to the fulcrum

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>if I’m using a seesaw analogy, I’m charging potential energy with the end of the seesaw, when I jump off, the far end of the seesaw still has the same distance to the fulcrum

The seesaw analogy doesn’t work because the whole point of the gears and cams in a compound bow is to turn the seesaw into not a seesaw

A standard bow has a linear draw weight. It’s lowest when you start to pull the string and highest at maximum pull, if it’s 40 pounds of force at 20 inches then it’s 20 at 10. This means it’s hard to hold a draw bow (you’re at max force) and most of the travel is at low force. Work=force x distance and since you plot of force vs distance is a triangle work=1/2 x max force x draw distance

A compound bow doesn’t have a linear draw, it looks more like an upside down U. They can tweak the shape of the cams so max draw force is in the middle of the range. If you’ve got a 20 inch draw you can rig it so it quickly ramps up in force, 5-15 inches are at max weight then it drops down. Now it’s easier to hold since you’re not at max force and you’ve got more energy stored in the bow because more is at the max force. The middle half of the draw being max force holds as much energy as the other bow at max draw plus you get additional energy from the 0-5 and 15-20 sections

The big thing here is weird shaped cams so you tension the bow aggressively at the beginning, slow that rate in the middle, and really drop off at the end

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